Subgroups — C₅×#34471 #11957191

Order 1280.

3112 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₅×#2377	C₂	1	2	yes	maximal, complemented
3	C₅×#2375	C₂	1	2	yes	maximal, complemented
4	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2358	C₂	1	2	yes	maximal, complemented
8	C₅×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₄×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2333	C₂	1	2	yes	maximal, complemented
14	C₅×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2321	C₂	1	2	yes	maximal, complemented
17	C₅×#2321	C₂	1	2	yes	maximal, complemented
18	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2309	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2308	C₂	1	2	yes	maximal, complemented
21	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂³×C₅×D₄	C₂²	1	2	yes	—
26	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₅×D₄²	C₄	1	16	yes	complemented
28	C₂×C₅×#127	C₂²	1	1	yes	characteristic
29	C₂×C₅×#121	C₂²	1	1	yes	characteristic
30	C₂×C₅×#121	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	2	yes	—
32	C₂×C₅×#120	C₂²	1	2	yes	—
33	C₂×C₅×#120	C₂²	1	2	yes	—
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
39	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
47	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
48	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
50	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	1	yes	characteristic
53	C₅×#390	C₂²	1	1	yes	characteristic
54	C₅×#390	C₂²	1	1	yes	characteristic
55	C₅×#390	C₂²	1	2	yes	complemented
56	C₅×#390	C₂²	1	1	yes	characteristic, complemented
57	C₅×#390	C₂²	1	1	yes	characteristic, complemented
58	C₅×#390	C₂²	1	2	yes	complemented
59	C₅×#390	C₂²	1	1	yes	characteristic, complemented
60	C₅×#390	C₂²	1	2	yes	complemented
61	C₅×#390	C₂²	1	2	yes	complemented
62	C₅×#390	C₂²	1	1	yes	characteristic, complemented
63	C₅×#390	C₂²	1	2	yes	complemented
64	C₅×#390	C₂²	1	2	yes	complemented
65	C₅×#390	C₂²	1	2	yes	complemented
66	C₅×#389	C₂²	1	1	yes	characteristic, complemented
67	C₅×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅×#388	C₂²	1	1	yes	characteristic, complemented
69	C₅×#388	C₂²	1	1	yes	characteristic, complemented
70	C₅×#388	C₂²	1	2	yes	complemented
71	C₅×#388	C₂²	1	2	yes	complemented
72	C₅×#388	C₂²	1	2	yes	complemented
73	C₅×#388	C₂²	1	2	yes	complemented
74	C₅×#388	C₂²	1	2	yes	complemented
75	C₅×#388	C₂²	1	2	yes	complemented
76	C₅×#388	C₂²	1	2	yes	complemented
77	C₅×#388	C₂²	1	2	yes	complemented
78	C₅×#388	C₂²	1	2	yes	complemented
79	C₅×#387	C₂²	1	1	yes	characteristic, complemented
80	C₅×#387	C₂²	1	1	yes	characteristic, complemented
81	C₅×#387	C₂²	1	2	yes	complemented
82	C₅×#386	C₂²	1	1	yes	characteristic
83	C₅×#386	C₂²	1	1	yes	characteristic
84	C₅×#386	C₂²	1	2	yes	—
85	C₅×#386	C₂²	1	2	yes	complemented
86	C₅×#386	C₂²	1	2	yes	complemented
87	C₅×#386	C₂²	1	2	yes	complemented
88	C₅×#386	C₂²	1	2	yes	complemented
89	C₅×#386	C₂²	1	2	yes	complemented
90	C₅×#386	C₂²	1	2	yes	complemented
91	C₅×#386	C₂²	1	2	yes	complemented
92	C₅×#386	C₂²	1	2	yes	complemented
93	C₅×#386	C₂²	1	2	yes	complemented
94	C₅×#386	C₂²	1	2	yes	complemented
95	C₅×#386	C₂²	1	2	yes	complemented
96	C₅×#386	C₂²	1	2	yes	complemented
97	C₅×#386	C₂²	1	2	yes	complemented
98	C₅×#386	C₂²	1	2	yes	complemented
99	C₅×#385	C₂²	1	1	yes	characteristic, complemented
100	C₅×#385	C₂²	1	1	yes	characteristic, complemented
101	C₅×#385	C₂²	1	2	yes	complemented
102	C₅×#385	C₂²	1	2	yes	complemented
103	C₅×#382	C₂²	1	1	yes	characteristic, complemented
104	C₅×#381	C₂²	1	2	yes	complemented
105	C₅×#381	C₂²	1	2	yes	complemented
106	C₅×#380	C₂²	1	1	yes	characteristic, complemented
107	C₅×#380	C₂²	1	2	yes	complemented
108	C₅×#380	C₂²	1	1	yes	characteristic, complemented
109	C₅×#379	C₂²	1	2	yes	complemented
110	C₅×#379	C₂²	1	2	yes	complemented
111	C₅×#379	C₂²	1	2	yes	complemented
112	C₅×#379	C₂²	1	2	yes	complemented
113	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₅×#376	C₂²	1	1	yes	characteristic, complemented
124	#34471	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₅	C₂³	1	2	yes	—
126	C₂⁵×C₅	C₂³	1	2	yes	—
127	C₂²×C₅×D₄	—	4	2	no	—
128	C₂²×C₅×D₄	—	4	2	no	—
129	C₂²×C₅×D₄	—	4	2	no	—
130	C₂²×C₅×D₄	—	4	2	no	—
131	C₂²×C₅×D₄	—	4	4	no	—
132	C₂²×C₅×D₄	—	4	4	no	—
133	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
134	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
135	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
136	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
137	C₂²×C₅×D₄	C₂³	1	2	yes	—
138	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
140	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
141	C₂²×C₅×D₄	C₂³	1	2	yes	—
142	C₂²×C₅×D₄	C₂³	1	2	yes	—
143	C₂²×C₅×D₄	C₂³	1	2	yes	—
144	C₂²×C₅×D₄	C₂³	1	2	yes	—
145	C₂²×C₅×D₄	C₂³	1	2	yes	—
146	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₅	C₂³	1	2	yes	—
150	C₂³×C₄×C₅	C₂³	1	2	yes	—
151	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₅	C₂³	1	2	yes	—
153	C₂³×C₄×C₅	C₂³	1	2	yes	—
154	C₂³×C₄×C₅	C₂³	1	2	yes	—
155	C₂³×C₄×C₅	C₂³	1	2	yes	—
156	C₅×#127	C₂×C₄	1	8	yes	complemented
157	C₅×#121	C₂×C₄	1	8	yes	complemented
158	C₅×#121	C₂×C₄	1	8	yes	complemented
159	C₅×#121	C₂×C₄	1	16	yes	complemented
160	C₅×#120	C₂×C₄	1	16	yes	complemented
161	C₅×#120	C₂×C₄	1	16	yes	complemented
162	C₄×C₅×D₄	—	4	2	no	—
163	C₄×C₅×D₄	—	4	2	no	—
164	C₄×C₅×D₄	—	4	2	no	—
165	C₄×C₅×D₄	—	4	2	no	—
166	C₄×C₅×D₄	—	4	4	no	—
167	C₄×C₅×D₄	—	4	4	no	—
168	C₄×C₅×D₄	—	4	4	no	—
169	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
170	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
171	C₅×#117	—	4	2	no	—
172	C₅×#117	—	4	2	no	—
173	C₂×C₅×C₄⋊C₄	—	4	2	no	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
188	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
189	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
190	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
191	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₄²×C₅	—	4	2	no	—
226	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅	C₂³	1	2	yes	—
231	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅	C₂³	1	2	yes	—
233	C₂×C₄²×C₅	C₂³	1	2	yes	—
234	C₂×C₄²×C₅	C₂³	1	2	yes	—
235	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	1	yes	characteristic
238	C₅×#95	C₂³	1	1	yes	characteristic
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	1	yes	characteristic
241	C₅×#95	C₂³	1	1	yes	characteristic
242	C₅×#95	C₂³	1	1	yes	characteristic
243	C₅×#95	C₂³	1	2	yes	—
244	C₅×#95	C₂³	1	2	yes	—
245	C₅×#95	C₂³	1	2	yes	—
246	C₅×#95	C₂³	1	2	yes	—
247	C₅×#95	C₂³	1	2	yes	—
248	C₅×#95	C₂³	1	2	yes	—
249	C₅×#95	C₂³	1	1	yes	characteristic
250	C₅×#95	C₂³	1	1	yes	characteristic
251	C₅×#95	C₂³	1	1	yes	characteristic
252	C₅×#95	C₂³	1	2	yes	—
253	C₅×#95	C₂³	1	1	yes	characteristic
254	C₅×#95	C₂³	1	2	yes	—
255	C₅×#95	C₂³	1	2	yes	—
256	C₂×D₄²	C₂×C₅	1	1	yes	characteristic
257	#2377	C₂×C₅	1	2	yes	complemented
258	#2375	C₂×C₅	1	2	yes	complemented
259	#2366	C₂×C₅	1	1	yes	characteristic, complemented
260	#2363	C₂×C₅	1	1	yes	characteristic, complemented
261	#2361	C₂×C₅	1	1	yes	characteristic, complemented
262	#2358	C₂×C₅	1	2	yes	complemented
263	#2357	C₂×C₅	1	1	yes	characteristic, complemented
264	#2352	C₂×C₅	1	1	yes	characteristic, complemented
265	D₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
266	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
267	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
268	#2333	C₂×C₅	1	2	yes	complemented
269	#2328	C₂×C₅	1	1	yes	characteristic, complemented
270	#2324	C₂×C₅	1	1	yes	characteristic, complemented
271	#2321	C₂×C₅	1	2	yes	complemented
272	#2321	C₂×C₅	1	2	yes	complemented
273	#2319	C₂×C₅	1	1	yes	characteristic, complemented
274	#2309	C₂×C₅	1	1	yes	characteristic, complemented
275	#2308	C₂×C₅	1	2	yes	complemented
276	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
277	C₂×#390	C₂×C₅	1	1	yes	characteristic, complemented
278	#2290	C₂×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	2	4	no	—
280	C₂⁴×C₅	—	2	4	no	—
281	C₂⁴×C₅	—	4	2	no	—
282	C₂⁴×C₅	—	4	2	no	—
283	C₂⁴×C₅	—	4	2	no	—
284	C₂⁴×C₅	—	4	2	no	—
285	C₂⁴×C₅	—	4	2	no	—
286	C₂⁴×C₅	—	4	2	no	—
287	C₂⁴×C₅	—	4	2	no	—
288	C₂⁴×C₅	—	4	2	no	—
289	C₂⁴×C₅	—	4	2	no	—
290	C₂⁴×C₅	—	4	2	no	—
291	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
292	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
293	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
294	C₂⁴×C₅	C₂⁴	1	2	yes	—
295	C₂⁴×C₅	C₂⁴	1	2	yes	—
296	C₂⁴×C₅	C₂⁴	1	2	yes	—
297	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
298	C₂×C₅×D₄	—	2	4	no	—
299	C₂×C₅×D₄	—	2	4	no	—
300	C₂×C₅×D₄	—	2	2	no	—
301	C₂×C₅×D₄	—	2	2	no	—
302	C₂×C₅×D₄	—	2	2	no	—
303	C₂×C₅×D₄	—	2	2	no	—
304	C₂×C₅×D₄	—	2	2	no	—
305	C₂×C₅×D₄	—	2	2	no	—
306	C₂×C₅×D₄	—	2	2	no	—
307	C₂×C₅×D₄	—	2	2	no	—
308	C₂×C₅×D₄	—	4	16	no	—
309	C₂×C₅×D₄	—	4	16	no	—
310	C₂×C₅×D₄	—	4	2	no	—
311	C₂×C₅×D₄	—	4	2	no	—
312	C₂×C₅×D₄	—	4	2	no	—
313	C₂×C₅×D₄	—	4	2	no	—
314	C₂×C₅×D₄	—	4	2	no	—
315	C₂×C₅×D₄	—	4	2	no	—
316	C₂×C₅×D₄	—	4	2	no	—
317	C₂×C₅×D₄	—	4	2	no	—
318	C₂×C₅×D₄	—	4	2	no	—
319	C₂×C₅×D₄	—	4	2	no	—
320	C₂×C₅×D₄	—	4	32	no	—
321	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
322	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
323	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
324	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
325	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
326	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
327	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
328	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
329	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
330	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
331	C₂²×C₄×C₅	—	2	2	no	—
332	C₂²×C₄×C₅	—	2	2	no	—
333	C₂²×C₄×C₅	—	2	2	no	—
334	C₂²×C₄×C₅	—	2	2	no	—
335	C₂²×C₄×C₅	—	2	2	no	—
336	C₂²×C₄×C₅	—	2	2	no	—
337	C₂²×C₄×C₅	—	2	4	no	—
338	C₂²×C₄×C₅	—	2	2	no	—
339	C₂²×C₄×C₅	—	2	4	no	—
340	C₂²×C₄×C₅	—	4	1	no	—
341	C₂²×C₄×C₅	—	4	1	no	—
342	C₂²×C₄×C₅	—	4	1	no	—
343	C₂²×C₄×C₅	—	4	2	no	—
344	C₂²×C₄×C₅	—	4	2	no	—
345	C₂²×C₄×C₅	—	4	2	no	—
346	C₂²×C₄×C₅	—	4	2	no	—
347	C₂²×C₄×C₅	—	4	2	no	—
348	C₂²×C₄×C₅	—	4	2	no	—
349	C₂²×C₄×C₅	—	4	2	no	—
350	C₂²×C₄×C₅	—	4	2	no	—
351	C₂²×C₄×C₅	—	4	2	no	—
352	C₂²×C₄×C₅	—	4	2	no	—
353	C₂²×C₄×C₅	—	4	2	no	—
354	C₂²×C₄×C₅	—	4	2	no	—
355	C₂²×C₄×C₅	—	4	2	no	—
356	C₂²×C₄×C₅	—	4	2	no	—
357	C₂²×C₄×C₅	—	4	2	no	—
358	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
359	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
360	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
361	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
379	C₅×C₄⋊C₄	—	2	2	no	—
380	C₅×C₄⋊C₄	—	2	2	no	—
381	C₅×C₄⋊C₄	—	2	2	no	—
382	C₅×C₄⋊C₄	—	2	2	no	—
383	C₅×C₄⋊C₄	—	2	2	no	—
384	C₅×C₄⋊C₄	—	4	2	no	—
385	C₅×C₄⋊C₄	—	4	1	no	—
386	C₅×C₄⋊C₄	—	4	1	no	—
387	C₅×C₄⋊C₄	—	4	1	no	—
388	C₅×C₄⋊C₄	—	4	2	no	—
389	C₅×C₄⋊C₄	—	4	2	no	—
390	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
391	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
392	C₅×C₂²⋊C₄	—	2	2	no	—
393	C₅×C₂²⋊C₄	—	2	4	no	—
394	C₅×C₂²⋊C₄	—	2	2	no	—
395	C₅×C₂²⋊C₄	—	2	2	no	—
396	C₅×C₂²⋊C₄	—	2	4	no	—
397	C₅×C₂²⋊C₄	—	2	4	no	—
398	C₅×C₂²⋊C₄	—	4	2	no	—
399	C₅×C₂²⋊C₄	—	4	2	no	—
400	C₅×C₂²⋊C₄	—	4	2	no	—
401	C₅×C₂²⋊C₄	—	4	2	no	—
402	C₅×C₂²⋊C₄	—	4	2	no	—
403	C₅×C₂²⋊C₄	—	4	2	no	—
404	C₅×C₂²⋊C₄	—	4	2	no	—
405	C₅×C₂²⋊C₄	—	4	2	no	—
406	C₅×C₂²⋊C₄	—	4	2	no	—
407	C₅×C₂²⋊C₄	—	4	2	no	—
408	C₅×C₂²⋊C₄	—	4	2	no	—
409	C₅×C₂²⋊C₄	—	4	2	no	—
410	C₅×C₂²⋊C₄	—	4	1	no	—
411	C₅×C₂²⋊C₄	—	4	1	no	—
412	C₅×C₂²⋊C₄	—	4	1	no	—
413	C₅×C₂²⋊C₄	—	4	2	no	—
414	C₅×C₂²⋊C₄	—	4	2	no	—
415	C₅×C₂²⋊C₄	—	4	2	no	—
416	C₅×C₂²⋊C₄	—	4	2	no	—
417	C₅×C₂²⋊C₄	—	4	2	no	—
418	C₅×C₂²⋊C₄	—	4	2	no	—
419	C₅×C₂²⋊C₄	—	4	2	no	—
420	C₅×C₂²⋊C₄	—	4	2	no	—
421	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
422	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
423	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
424	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
425	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
426	C₄²×C₅	—	2	2	no	—
427	C₄²×C₅	—	2	2	no	—
428	C₄²×C₅	—	2	2	no	—
429	C₄²×C₅	—	2	2	no	—
430	C₄²×C₅	—	4	1	no	—
431	C₄²×C₅	—	4	1	no	—
432	C₄²×C₅	—	4	2	no	—
433	C₄²×C₅	—	4	2	no	—
434	C₄²×C₅	—	4	2	no	—
435	C₄²×C₅	—	4	2	no	—
436	C₄²×C₅	C₂²×C₄	1	4	yes	—
437	C₂³×D₄	C₂²×C₅	1	2	yes	—
438	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
439	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
440	D₄²	C₄×C₅	1	16	yes	complemented
441	C₂×#127	C₂²×C₅	1	1	yes	characteristic
442	C₂×#121	C₂²×C₅	1	1	yes	characteristic
443	C₂×#121	C₂²×C₅	1	2	yes	—
444	C₂×#121	C₂²×C₅	1	1	yes	characteristic
445	C₂×#120	C₂²×C₅	1	2	yes	—
446	C₂×#120	C₂²×C₅	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
450	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
451	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
452	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
453	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
454	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
455	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
456	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
457	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
458	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
459	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
460	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
461	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
462	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
463	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
464	#390	C₂²×C₅	1	1	yes	characteristic
465	#390	C₂²×C₅	1	1	yes	characteristic
466	#390	C₂²×C₅	1	1	yes	characteristic
467	#390	C₂²×C₅	1	1	yes	characteristic
468	#390	C₂²×C₅	1	2	yes	complemented
469	#390	C₂²×C₅	1	1	yes	characteristic, complemented
470	#390	C₂²×C₅	1	2	yes	complemented
471	#390	C₂²×C₅	1	1	yes	characteristic, complemented
472	#390	C₂²×C₅	1	2	yes	complemented
473	#390	C₂²×C₅	1	2	yes	complemented
474	#390	C₂²×C₅	1	2	yes	complemented
475	#390	C₂²×C₅	1	1	yes	characteristic, complemented
476	#390	C₂²×C₅	1	2	yes	complemented
477	#390	C₂²×C₅	1	1	yes	characteristic, complemented
478	#390	C₂²×C₅	1	2	yes	complemented
479	#389	C₂²×C₅	1	1	yes	characteristic, complemented
480	#389	C₂²×C₅	1	1	yes	characteristic, complemented
481	#388	C₂²×C₅	1	2	yes	complemented
482	#388	C₂²×C₅	1	2	yes	complemented
483	#388	C₂²×C₅	1	1	yes	characteristic, complemented
484	#388	C₂²×C₅	1	2	yes	complemented
485	#388	C₂²×C₅	1	2	yes	complemented
486	#388	C₂²×C₅	1	2	yes	complemented
487	#388	C₂²×C₅	1	2	yes	complemented
488	#388	C₂²×C₅	1	2	yes	complemented
489	#388	C₂²×C₅	1	2	yes	complemented
490	#388	C₂²×C₅	1	1	yes	characteristic, complemented
491	#388	C₂²×C₅	1	2	yes	complemented
492	#387	C₂²×C₅	1	1	yes	characteristic, complemented
493	#387	C₂²×C₅	1	2	yes	complemented
494	#387	C₂²×C₅	1	1	yes	characteristic, complemented
495	#386	C₂²×C₅	1	1	yes	characteristic
496	#386	C₂²×C₅	1	2	yes	—
497	#386	C₂²×C₅	1	1	yes	characteristic
498	#386	C₂²×C₅	1	2	yes	complemented
499	#386	C₂²×C₅	1	2	yes	complemented
500	#386	C₂²×C₅	1	2	yes	complemented
501	#386	C₂²×C₅	1	2	yes	complemented
502	#386	C₂²×C₅	1	2	yes	complemented
503	#386	C₂²×C₅	1	2	yes	complemented
504	#386	C₂²×C₅	1	2	yes	complemented
505	#386	C₂²×C₅	1	2	yes	complemented
506	#386	C₂²×C₅	1	2	yes	complemented
507	#386	C₂²×C₅	1	2	yes	complemented
508	#386	C₂²×C₅	1	2	yes	complemented
509	#386	C₂²×C₅	1	2	yes	complemented
510	#386	C₂²×C₅	1	2	yes	complemented
511	#386	C₂²×C₅	1	2	yes	complemented
512	#385	C₂²×C₅	1	1	yes	characteristic, complemented
513	#385	C₂²×C₅	1	2	yes	complemented
514	#385	C₂²×C₅	1	2	yes	complemented
515	#385	C₂²×C₅	1	1	yes	characteristic, complemented
516	#382	C₂²×C₅	1	1	yes	characteristic, complemented
517	#381	C₂²×C₅	1	2	yes	complemented
518	#381	C₂²×C₅	1	2	yes	complemented
519	#380	C₂²×C₅	1	2	yes	complemented
520	#380	C₂²×C₅	1	1	yes	characteristic, complemented
521	#380	C₂²×C₅	1	1	yes	characteristic, complemented
522	#379	C₂²×C₅	1	2	yes	complemented
523	#379	C₂²×C₅	1	2	yes	complemented
524	#379	C₂²×C₅	1	2	yes	complemented
525	#379	C₂²×C₅	1	2	yes	complemented
526	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
527	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
528	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
529	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
531	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
532	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
533	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
534	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
535	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
536	#376	C₂²×C₅	1	1	yes	characteristic, complemented
537	C₂³×C₅	—	2	1	no	—
538	C₂³×C₅	—	2	1	no	—
539	C₂³×C₅	—	2	1	no	—
540	C₂³×C₅	—	2	1	no	—
541	C₂³×C₅	—	2	1	no	—
542	C₂³×C₅	—	2	2	no	—
543	C₂³×C₅	—	2	2	no	—
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	1	no	—
546	C₂³×C₅	—	2	2	no	—
547	C₂³×C₅	—	2	2	no	—
548	C₂³×C₅	—	2	2	no	—
549	C₂³×C₅	—	2	2	no	—
550	C₂³×C₅	—	2	2	no	—
551	C₂³×C₅	—	2	2	no	—
552	C₂³×C₅	—	2	2	no	—
553	C₂³×C₅	—	2	2	no	—
554	C₂³×C₅	—	2	2	no	—
555	C₂³×C₅	—	2	2	no	—
556	C₂³×C₅	—	2	2	no	—
557	C₂³×C₅	—	2	2	no	—
558	C₂³×C₅	—	2	1	no	—
559	C₂³×C₅	—	2	1	no	—
560	C₂³×C₅	—	2	2	no	—
561	C₂³×C₅	—	2	2	no	—
562	C₂³×C₅	—	2	1	no	—
563	C₂³×C₅	—	2	2	no	—
564	C₂³×C₅	—	2	2	no	—
565	C₂³×C₅	—	2	16	no	—
566	C₂³×C₅	—	4	8	no	—
567	C₂³×C₅	—	4	8	no	—
568	C₂³×C₅	—	4	8	no	—
569	C₂³×C₅	—	4	8	no	—
570	C₂³×C₅	—	4	8	no	—
571	C₂³×C₅	—	8	4	no	—
572	C₂³×C₅	—	8	4	no	—
573	C₂³×C₅	—	8	4	no	—
574	C₂³×C₅	—	8	4	no	—
575	C₂³×C₅	—	8	4	no	—
576	C₂³×C₅	—	8	4	no	—
577	C₂³×C₅	—	8	4	no	—
578	C₂³×C₅	—	8	4	no	—
579	C₂³×C₅	C₂³×C₄	1	2	yes	—
580	C₂³×C₅	C₂³×C₄	1	4	yes	—
581	C₂³×C₅	C₂³×C₄	1	4	yes	—
582	C₂³×C₅	C₂³×C₄	1	4	yes	—
583	C₂³×C₅	C₂³×C₄	1	2	yes	—
584	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
585	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
586	C₂³×C₅	C₂⁵	1	1	yes	characteristic
587	C₅×D₄	—	2	8	no	—
588	C₅×D₄	—	2	16	no	—
589	C₅×D₄	—	2	8	no	—
590	C₅×D₄	—	2	8	no	—
591	C₅×D₄	—	2	8	no	—
592	C₅×D₄	—	4	8	no	—
593	C₅×D₄	—	4	8	no	—
594	C₅×D₄	—	4	8	no	—
595	C₅×D₄	—	4	8	no	—
596	C₅×D₄	—	4	8	no	—
597	C₂×C₄×C₅	—	2	1	no	—
598	C₂×C₄×C₅	—	2	1	no	—
599	C₂×C₄×C₅	—	2	1	no	—
600	C₂×C₄×C₅	—	2	1	no	—
601	C₂×C₄×C₅	—	2	1	no	—
602	C₂×C₄×C₅	—	2	2	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	1	no	—
606	C₂×C₄×C₅	—	2	1	no	—
607	C₂×C₄×C₅	—	2	1	no	—
608	C₂×C₄×C₅	—	2	1	no	—
609	C₂×C₄×C₅	—	2	8	no	—
610	C₂×C₄×C₅	—	2	8	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	2	1	no	—
613	C₂×C₄×C₅	—	2	1	no	—
614	C₂×C₄×C₅	—	2	1	no	—
615	C₂×C₄×C₅	—	2	1	no	—
616	C₂×C₄×C₅	—	2	1	no	—
617	C₂×C₄×C₅	—	2	1	no	—
618	C₂×C₄×C₅	—	2	1	no	—
619	C₂×C₄×C₅	—	2	2	no	—
620	C₂×C₄×C₅	—	2	2	no	—
621	C₂×C₄×C₅	—	2	2	no	—
622	C₂×C₄×C₅	—	2	2	no	—
623	C₂×C₄×C₅	—	2	2	no	—
624	C₂×C₄×C₅	—	2	2	no	—
625	C₂×C₄×C₅	—	2	1	no	—
626	C₂×C₄×C₅	—	2	1	no	—
627	C₂×C₄×C₅	—	2	2	no	—
628	C₂×C₄×C₅	—	2	1	no	—
629	C₂×C₄×C₅	—	2	2	no	—
630	C₂×C₄×C₅	—	2	1	no	—
631	C₂×C₄×C₅	—	2	1	no	—
632	C₂×C₄×C₅	—	2	1	no	—
633	C₂×C₄×C₅	—	2	1	no	—
634	C₂×C₄×C₅	—	2	2	no	—
635	C₂×C₄×C₅	—	2	2	no	—
636	C₂×C₄×C₅	—	2	1	no	—
637	C₂×C₄×C₅	—	2	1	no	—
638	C₂×C₄×C₅	—	2	2	no	—
639	C₂×C₄×C₅	—	2	1	no	—
640	C₂×C₄×C₅	—	2	1	no	—
641	C₂×C₄×C₅	—	2	2	no	—
642	C₂×C₄×C₅	—	2	1	no	—
643	C₂×C₄×C₅	—	2	1	no	—
644	C₂×C₄×C₅	—	4	8	no	—
645	C₂×C₄×C₅	—	4	4	no	—
646	C₂×C₄×C₅	—	4	4	no	—
647	C₂×C₄×C₅	—	8	4	no	—
648	C₂×C₄×C₅	—	8	4	no	—
649	C₂×C₄×C₅	—	8	4	no	—
650	C₂×C₄×C₅	—	8	4	no	—
651	C₂×C₄×C₅	—	8	4	no	—
652	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
654	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
655	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
656	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
657	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
658	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
659	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
660	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
661	C₂⁵	C₂³×C₅	1	2	yes	—
662	C₂⁵	C₂³×C₅	1	2	yes	—
663	C₂²×D₄	—	4	2	no	—
664	C₂²×D₄	—	4	2	no	—
665	C₂²×D₄	—	4	2	no	—
666	C₂²×D₄	—	4	2	no	—
667	C₂²×D₄	—	4	4	no	—
668	C₂²×D₄	—	4	4	no	—
669	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
670	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
671	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
672	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₅	1	2	yes	—
675	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₅	1	2	yes	—
678	C₂²×D₄	C₂³×C₅	1	2	yes	—
679	C₂²×D₄	C₂³×C₅	1	2	yes	—
680	C₂²×D₄	C₂³×C₅	1	2	yes	—
681	C₂²×D₄	C₂³×C₅	1	2	yes	—
682	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₅	1	2	yes	—
686	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₅	1	2	yes	—
688	C₂³×C₄	C₂³×C₅	1	2	yes	—
689	C₂³×C₄	C₂³×C₅	1	2	yes	—
690	C₂³×C₄	C₂³×C₅	1	2	yes	—
691	C₂³×C₄	C₂³×C₅	1	2	yes	—
692	#127	C₂×C₄×C₅	1	8	yes	complemented
693	#121	C₂×C₄×C₅	1	8	yes	complemented
694	#121	C₂×C₄×C₅	1	8	yes	complemented
695	#121	C₂×C₄×C₅	1	16	yes	complemented
696	#120	C₂×C₄×C₅	1	16	yes	complemented
697	#120	C₂×C₄×C₅	1	16	yes	complemented
698	C₄×D₄	—	4	2	no	—
699	C₄×D₄	—	4	2	no	—
700	C₄×D₄	—	4	2	no	—
701	C₄×D₄	—	4	2	no	—
702	C₄×D₄	—	4	4	no	—
703	C₄×D₄	—	4	4	no	—
704	C₄×D₄	—	4	4	no	—
705	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
706	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
707	#117	—	4	2	no	—
708	#117	—	4	2	no	—
709	C₂×C₄⋊C₄	—	4	2	no	—
710	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	—	4	4	no	—
724	C₂×C₂²⋊C₄	—	4	4	no	—
725	C₂×C₂²⋊C₄	—	4	4	no	—
726	C₂×C₂²⋊C₄	—	4	4	no	—
727	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
733	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
761	C₂×C₄²	—	4	2	no	—
762	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₅	1	2	yes	—
767	C₂×C₄²	C₂³×C₅	1	2	yes	—
768	C₂×C₄²	C₂³×C₅	1	2	yes	—
769	C₂×C₄²	C₂³×C₅	1	2	yes	—
770	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
773	#95	C₂³×C₅	1	1	yes	characteristic
774	#95	C₂³×C₅	1	1	yes	characteristic
775	#95	C₂³×C₅	1	1	yes	characteristic
776	#95	C₂³×C₅	1	1	yes	characteristic
777	#95	C₂³×C₅	1	1	yes	characteristic
778	#95	C₂³×C₅	1	1	yes	characteristic
779	#95	C₂³×C₅	1	2	yes	—
780	#95	C₂³×C₅	1	2	yes	—
781	#95	C₂³×C₅	1	2	yes	—
782	#95	C₂³×C₅	1	2	yes	—
783	#95	C₂³×C₅	1	2	yes	—
784	#95	C₂³×C₅	1	2	yes	—
785	#95	C₂³×C₅	1	1	yes	characteristic
786	#95	C₂³×C₅	1	1	yes	characteristic
787	#95	C₂³×C₅	1	1	yes	characteristic
788	#95	C₂³×C₅	1	2	yes	—
789	#95	C₂³×C₅	1	1	yes	characteristic
790	#95	C₂³×C₅	1	2	yes	—
791	#95	C₂³×C₅	1	2	yes	—
792	C₂²×C₅	—	2	2	no	—
793	C₂²×C₅	—	2	2	no	—
794	C₂²×C₅	—	2	2	no	—
795	C₂²×C₅	—	2	2	no	—
796	C₂²×C₅	—	2	2	no	—
797	C₂²×C₅	—	2	2	no	—
798	C₂²×C₅	—	2	2	no	—
799	C₂²×C₅	—	2	4	no	—
800	C₂²×C₅	—	2	2	no	—
801	C₂²×C₅	—	2	4	no	—
802	C₂²×C₅	—	2	4	no	—
803	C₂²×C₅	—	2	4	no	—
804	C₂²×C₅	—	2	4	no	—
805	C₂²×C₅	—	2	4	no	—
806	C₂²×C₅	—	2	4	no	—
807	C₂²×C₅	—	2	4	no	—
808	C₂²×C₅	—	2	2	no	—
809	C₂²×C₅	—	2	4	no	—
810	C₂²×C₅	—	4	2	no	—
811	C₂²×C₅	—	4	2	no	—
812	C₂²×C₅	—	4	1	no	—
813	C₂²×C₅	—	4	2	no	—
814	C₂²×C₅	—	4	2	no	—
815	C₂²×C₅	—	4	2	no	—
816	C₂²×C₅	—	4	1	no	—
817	C₂²×C₅	—	4	2	no	—
818	C₂²×C₅	—	4	2	no	—
819	C₂²×C₅	—	4	2	no	—
820	C₂²×C₅	—	4	1	no	—
821	C₂²×C₅	—	4	2	no	—
822	C₂²×C₅	—	4	2	no	—
823	C₂²×C₅	—	4	2	no	—
824	C₂²×C₅	—	4	1	no	—
825	C₂²×C₅	—	4	2	no	—
826	C₂²×C₅	—	8	16	no	—
827	C₂²×C₅	—	8	16	no	—
828	C₂²×C₅	#518	1	4	yes	—
829	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
830	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
832	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
833	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
834	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
835	C₂²×C₅	#585	1	1	yes	characteristic
836	C₄×C₅	—	2	2	no	—
837	C₄×C₅	—	2	2	no	—
838	C₄×C₅	—	2	2	no	—
839	C₄×C₅	—	2	4	no	—
840	C₄×C₅	—	2	2	no	—
841	C₄×C₅	—	2	2	no	—
842	C₄×C₅	—	4	1	no	—
843	C₄×C₅	—	4	1	no	—
844	C₄×C₅	—	4	2	no	—
845	C₄×C₅	—	4	1	no	—
846	C₄×C₅	—	4	1	no	—
847	C₄×C₅	—	4	1	no	—
848	C₄×C₅	—	4	2	no	—
849	C₄×C₅	—	4	1	no	—
850	C₄×C₅	—	4	2	no	—
851	C₄×C₅	—	4	2	no	—
852	C₄×C₅	—	4	1	no	—
853	C₄×C₅	#518	1	4	yes	—
854	C₂⁴	—	2	4	no	—
855	C₂⁴	—	2	4	no	—
856	C₂⁴	—	4	2	no	—
857	C₂⁴	—	4	2	no	—
858	C₂⁴	—	4	2	no	—
859	C₂⁴	—	4	2	no	—
860	C₂⁴	—	4	2	no	—
861	C₂⁴	—	4	2	no	—
862	C₂⁴	—	4	2	no	—
863	C₂⁴	—	4	2	no	—
864	C₂⁴	—	4	2	no	—
865	C₂⁴	—	4	2	no	—
866	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
867	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
868	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
869	C₂⁴	C₂⁴×C₅	1	2	yes	—
870	C₂⁴	C₂⁴×C₅	1	2	yes	—
871	C₂⁴	C₂⁴×C₅	1	2	yes	—
872	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	4	16	no	—
884	C₂×D₄	—	4	16	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	2	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	4	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	2	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	4	2	no	—
895	C₂×D₄	—	4	32	no	—
896	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
897	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
898	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
899	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
900	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
901	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
902	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
903	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
904	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
905	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	4	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	4	1	no	—
916	C₂²×C₄	—	4	1	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	2	no	—
919	C₂²×C₄	—	4	1	no	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
934	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
935	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
936	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
940	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	1	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	1	no	—
965	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
966	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	4	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	1	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	1	no	—
996	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
997	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
998	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
999	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
1000	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	4	1	no	—
1006	C₄²	—	4	1	no	—
1007	C₄²	—	4	2	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	4	2	no	—
1011	C₄²	C₂²×C₄×C₅	1	4	yes	—
1012	C₂×C₅	—	2	4	no	—
1013	C₂×C₅	—	4	4	no	—
1014	C₂×C₅	—	4	4	no	—
1015	C₂×C₅	—	4	2	no	—
1016	C₂×C₅	—	4	4	no	—
1017	C₂×C₅	C₂×#518	1	1	yes	characteristic
1018	C₂×C₅	C₂×#518	1	1	yes	characteristic
1019	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1020	C₂×C₅	#3537	1	1	yes	characteristic
1021	C₂×C₅	#3542	1	1	yes	characteristic
1022	C₂×C₅	#3543	1	1	yes	characteristic
1023	C₂×C₅	#3558	1	1	yes	characteristic
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	16	no	—
1053	C₂³	—	4	8	no	—
1054	C₂³	—	4	8	no	—
1055	C₂³	—	4	8	no	—
1056	C₂³	—	4	8	no	—
1057	C₂³	—	4	8	no	—
1058	C₂³	—	8	4	no	—
1059	C₂³	—	8	4	no	—
1060	C₂³	—	8	4	no	—
1061	C₂³	—	8	4	no	—
1062	C₂³	—	8	4	no	—
1063	C₂³	—	8	4	no	—
1064	C₂³	—	8	4	no	—
1065	C₂³	—	8	4	no	—
1066	C₂³	C₂³×C₄×C₅	1	2	yes	—
1067	C₂³	C₂³×C₄×C₅	1	4	yes	—
1068	C₂³	C₂³×C₄×C₅	1	4	yes	—
1069	C₂³	C₂³×C₄×C₅	1	4	yes	—
1070	C₂³	C₂³×C₄×C₅	1	2	yes	—
1071	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
1072	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
1073	C₂³	C₂⁵×C₅	1	1	yes	characteristic
1074	D₄	—	2	8	no	—
1075	D₄	—	2	16	no	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	8	no	—
1079	D₄	—	4	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	8	no	—
1097	C₂×C₄	—	2	8	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	4	8	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	8	4	no	—
1135	C₂×C₄	—	8	4	no	—
1136	C₂×C₄	—	8	4	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1140	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1141	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1142	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1143	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1144	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1145	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1146	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1147	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1148	C₅	#34471	1	1	yes	characteristic, direct product factor, Sylow
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	4	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	2	4	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	4	no	—
1164	C₂²	—	2	4	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	4	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	8	16	no	—
1184	C₂²	—	8	16	no	—
1185	C₂²	C₅×#518	1	4	yes	—
1186	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1187	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₂²	C₅×#585	1	1	yes	characteristic
1193	C₄	—	2	2	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	4	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	C₅×#518	1	4	yes	—
1211	C₂	—	2	4	no	—
1212	C₂	—	4	2	no	—
1213	C₂	—	4	4	no	—
1214	C₂	—	4	4	no	—
1215	C₂	—	4	4	no	—
1216	C₂	C₂×C₅×#518	1	1	yes	characteristic
1217	C₂	C₂×C₅×#518	1	1	yes	characteristic
1218	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1219	C₂	C₅×#3537	1	1	yes	characteristic
1220	C₂	C₅×#3542	1	1	yes	characteristic
1221	C₂	C₅×#3543	1	1	yes	characteristic
1222	C₂	C₅×#3558	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×D₄²	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#2377	C₂	semidirect
3. C₅×#2375	C₂	semidirect
4. C₅×#2366	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2361	C₂	semidirect
7. C₅×#2358	C₂	semidirect
8. C₅×#2357	C₂	semidirect
9. C₅×#2352	C₂	semidirect
10. C₅×D₄×C₂²⋊C₄	C₂	semidirect
11. C₅×D₄×C₂²⋊C₄	C₂	semidirect
12. C₅×D₄×C₂²⋊C₄	C₂	semidirect
13. C₅×#2333	C₂	semidirect
14. C₅×#2328	C₂	semidirect
15. C₅×#2324	C₂	semidirect
16. C₅×#2321	C₂	semidirect
17. C₅×#2321	C₂	semidirect
18. C₅×#2319	C₂	semidirect
19. C₅×#2309	C₂	semidirect
20. C₅×#2308	C₂	semidirect
21. C₄×C₅×#121	C₂	semidirect
22. C₂×C₅×#390	C₂	semidirect
23. C₅×#2290	C₂	semidirect
27. C₅×D₄²	C₄	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
37. C₂×C₄×C₅×D₄	C₂²	semidirect
38. C₂×C₄×C₅×D₄	C₂²	semidirect
39. C₂×C₄×C₅×D₄	C₂²	semidirect
40. C₂×C₄×C₅×D₄	C₂²	semidirect
41. C₂×C₄×C₅×D₄	C₂²	semidirect
42. C₂×C₄×C₅×D₄	C₂²	semidirect
43. C₂×C₅×#117	C₂²	semidirect
44. C₂×C₅×#117	C₂²	semidirect
45. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
46. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
47. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
48. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
49. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
50. C₂²×C₄²×C₅	C₂²	semidirect
55. C₅×#390	C₂²	semidirect
56. C₅×#390	C₂²	semidirect
57. C₅×#390	C₂²	semidirect
58. C₅×#390	C₂²	semidirect
59. C₅×#390	C₂²	semidirect
60. C₅×#390	C₂²	semidirect
61. C₅×#390	C₂²	semidirect
62. C₅×#390	C₂²	semidirect
63. C₅×#390	C₂²	semidirect
64. C₅×#390	C₂²	semidirect
65. C₅×#390	C₂²	semidirect
66. C₅×#389	C₂²	semidirect
67. C₅×#389	C₂²	semidirect
68. C₅×#388	C₂²	semidirect
69. C₅×#388	C₂²	semidirect
70. C₅×#388	C₂²	semidirect
71. C₅×#388	C₂²	semidirect
72. C₅×#388	C₂²	semidirect
73. C₅×#388	C₂²	semidirect
74. C₅×#388	C₂²	semidirect
75. C₅×#388	C₂²	semidirect
76. C₅×#388	C₂²	semidirect
77. C₅×#388	C₂²	semidirect
78. C₅×#388	C₂²	semidirect
79. C₅×#387	C₂²	semidirect
80. C₅×#387	C₂²	semidirect
81. C₅×#387	C₂²	semidirect
85. C₅×#386	C₂²	semidirect
86. C₅×#386	C₂²	semidirect
87. C₅×#386	C₂²	semidirect
88. C₅×#386	C₂²	semidirect
89. C₅×#386	C₂²	semidirect
90. C₅×#386	C₂²	semidirect
91. C₅×#386	C₂²	semidirect
92. C₅×#386	C₂²	semidirect
93. C₅×#386	C₂²	semidirect
94. C₅×#386	C₂²	semidirect
95. C₅×#386	C₂²	semidirect
96. C₅×#386	C₂²	semidirect
97. C₅×#386	C₂²	semidirect
98. C₅×#386	C₂²	semidirect
99. C₅×#385	C₂²	semidirect
100. C₅×#385	C₂²	semidirect
101. C₅×#385	C₂²	semidirect
102. C₅×#385	C₂²	semidirect
103. C₅×#382	C₂²	semidirect
104. C₅×#381	C₂²	semidirect
105. C₅×#381	C₂²	semidirect
106. C₅×#380	C₂²	semidirect
107. C₅×#380	C₂²	semidirect
108. C₅×#380	C₂²	semidirect
109. C₅×#379	C₂²	semidirect
110. C₅×#379	C₂²	semidirect
111. C₅×#379	C₂²	semidirect
112. C₅×#379	C₂²	semidirect
113. C₄×C₅×C₄⋊C₄	C₂²	semidirect
114. C₄×C₅×C₄⋊C₄	C₂²	semidirect
115. C₄×C₅×C₄⋊C₄	C₂²	semidirect
116. C₄×C₅×C₄⋊C₄	C₂²	semidirect
117. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
119. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
123. C₅×#376	C₂²	semidirect
124. #34471	C₅	direct (N × H)
133. C₂²×C₅×D₄	C₂×C₄	semidirect
134. C₂²×C₅×D₄	C₂×C₄	semidirect
135. C₂²×C₅×D₄	C₂×C₄	semidirect
156. C₅×#127	C₂×C₄	semidirect
157. C₅×#121	C₂×C₄	semidirect
158. C₅×#121	C₂×C₄	semidirect
159. C₅×#121	C₂×C₄	semidirect
160. C₅×#120	C₂×C₄	semidirect
161. C₅×#120	C₂×C₄	semidirect
169. C₄×C₅×D₄	C₂×C₄	semidirect
170. C₄×C₅×D₄	C₂×C₄	semidirect
257. #2377	C₂×C₅	semidirect
258. #2375	C₂×C₅	semidirect
259. #2366	C₂×C₅	semidirect
260. #2363	C₂×C₅	semidirect
261. #2361	C₂×C₅	semidirect
262. #2358	C₂×C₅	semidirect
263. #2357	C₂×C₅	semidirect
264. #2352	C₂×C₅	semidirect
265. D₄×C₂²⋊C₄	C₂×C₅	semidirect
266. D₄×C₂²⋊C₄	C₂×C₅	semidirect
267. D₄×C₂²⋊C₄	C₂×C₅	semidirect
268. #2333	C₂×C₅	semidirect
269. #2328	C₂×C₅	semidirect
270. #2324	C₂×C₅	semidirect
271. #2321	C₂×C₅	semidirect
272. #2321	C₂×C₅	semidirect
273. #2319	C₂×C₅	semidirect
274. #2309	C₂×C₅	semidirect
275. #2308	C₂×C₅	semidirect
276. C₄×#121	C₂×C₅	semidirect
277. C₂×#390	C₂×C₅	semidirect
278. #2290	C₂×C₅	semidirect
440. D₄²	C₄×C₅	semidirect
449. C₂×C₄×D₄	C₂²×C₅	semidirect
450. C₂×C₄×D₄	C₂²×C₅	semidirect
451. C₂×C₄×D₄	C₂²×C₅	semidirect
452. C₂×C₄×D₄	C₂²×C₅	semidirect
453. C₂×C₄×D₄	C₂²×C₅	semidirect
454. C₂×C₄×D₄	C₂²×C₅	semidirect
455. C₂×C₄×D₄	C₂²×C₅	semidirect
456. C₂×#117	C₂²×C₅	semidirect
457. C₂×#117	C₂²×C₅	semidirect
458. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
459. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
460. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
461. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
462. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
463. C₂²×C₄²	C₂²×C₅	semidirect
468. #390	C₂²×C₅	semidirect
469. #390	C₂²×C₅	semidirect
470. #390	C₂²×C₅	semidirect
471. #390	C₂²×C₅	semidirect
472. #390	C₂²×C₅	semidirect
473. #390	C₂²×C₅	semidirect
474. #390	C₂²×C₅	semidirect
475. #390	C₂²×C₅	semidirect
476. #390	C₂²×C₅	semidirect
477. #390	C₂²×C₅	semidirect
478. #390	C₂²×C₅	semidirect
479. #389	C₂²×C₅	semidirect
480. #389	C₂²×C₅	semidirect
481. #388	C₂²×C₅	semidirect
482. #388	C₂²×C₅	semidirect
483. #388	C₂²×C₅	semidirect
484. #388	C₂²×C₅	semidirect
485. #388	C₂²×C₅	semidirect
486. #388	C₂²×C₅	semidirect
487. #388	C₂²×C₅	semidirect
488. #388	C₂²×C₅	semidirect
489. #388	C₂²×C₅	semidirect
490. #388	C₂²×C₅	semidirect
491. #388	C₂²×C₅	semidirect
492. #387	C₂²×C₅	semidirect
493. #387	C₂²×C₅	semidirect
494. #387	C₂²×C₅	semidirect
498. #386	C₂²×C₅	semidirect
499. #386	C₂²×C₅	semidirect
500. #386	C₂²×C₅	semidirect
501. #386	C₂²×C₅	semidirect
502. #386	C₂²×C₅	semidirect
503. #386	C₂²×C₅	semidirect
504. #386	C₂²×C₅	semidirect
505. #386	C₂²×C₅	semidirect
506. #386	C₂²×C₅	semidirect
507. #386	C₂²×C₅	semidirect
508. #386	C₂²×C₅	semidirect
509. #386	C₂²×C₅	semidirect
510. #386	C₂²×C₅	semidirect
511. #386	C₂²×C₅	semidirect
512. #385	C₂²×C₅	semidirect
513. #385	C₂²×C₅	semidirect
514. #385	C₂²×C₅	semidirect
515. #385	C₂²×C₅	semidirect
516. #382	C₂²×C₅	semidirect
517. #381	C₂²×C₅	semidirect
518. #381	C₂²×C₅	semidirect
519. #380	C₂²×C₅	semidirect
520. #380	C₂²×C₅	semidirect
521. #380	C₂²×C₅	semidirect
522. #379	C₂²×C₅	semidirect
523. #379	C₂²×C₅	semidirect
524. #379	C₂²×C₅	semidirect
525. #379	C₂²×C₅	semidirect
526. C₄×C₄⋊C₄	C₂²×C₅	semidirect
527. C₄×C₄⋊C₄	C₂²×C₅	semidirect
528. C₄×C₄⋊C₄	C₂²×C₅	semidirect
529. C₄×C₄⋊C₄	C₂²×C₅	semidirect
530. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
531. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
532. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
533. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
534. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
535. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
536. #376	C₂²×C₅	semidirect
669. C₂²×D₄	C₂×C₄×C₅	semidirect
670. C₂²×D₄	C₂×C₄×C₅	semidirect
671. C₂²×D₄	C₂×C₄×C₅	semidirect
692. #127	C₂×C₄×C₅	semidirect
693. #121	C₂×C₄×C₅	semidirect
694. #121	C₂×C₄×C₅	semidirect
695. #121	C₂×C₄×C₅	semidirect
696. #120	C₂×C₄×C₅	semidirect
697. #120	C₂×C₄×C₅	semidirect
705. C₄×D₄	C₂×C₄×C₅	semidirect
706. C₄×D₄	C₂×C₄×C₅	semidirect
1148. C₅	#34471	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×D₄²	2
C₅×#2377	2
C₅×#2375	2
C₅×#2366	2
C₅×#2363	2
C₅×#2361	2
C₅×#2358	2
C₅×#2357	2
C₅×#2352	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2333	2
C₅×#2328	2
C₅×#2324	2
C₅×#2321	2
C₅×#2319	2
C₅×#2309	2
C₅×#2308	2
C₄×C₅×#121	2
C₂×C₅×#390	2
C₅×#2290	2
#34471	5

Subgroups — C5×#34471 #11957191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34471 #11957191