Subgroups — C₅×#34292 #11957012

Order 1280.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2361	C₂	1	2	yes	maximal, complemented
8	C₅×#2359	C₂	1	2	yes	maximal, complemented
9	C₅×#2358	C₂	1	2	yes	maximal, complemented
10	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2342	C₂	1	2	yes	maximal, complemented
13	C₅×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2325	C₂	1	2	yes	maximal, complemented
17	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#2321	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅×#388	C₂	1	2	yes	maximal, complemented
23	C₅×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#546	C₄	1	16	yes	complemented
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	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	C₅×#518	—	2	8	no	—
34	C₄×C₅×#41	—	2	8	no	—
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
41	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
43	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
48	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
49	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
50	C₂×C₅×#117	C₂²	1	1	yes	characteristic
51	C₂×C₅×#117	C₂²	1	1	yes	characteristic
52	C₂×C₅×#117	C₂²	1	2	yes	complemented
53	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
55	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
60	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
61	C₅×#391	C₂²	1	1	yes	characteristic, complemented
62	C₅×#391	C₂²	1	1	yes	characteristic, complemented
63	C₅×#390	C₂²	1	1	yes	characteristic
64	C₅×#390	C₂²	1	2	yes	—
65	C₅×#390	C₂²	1	1	yes	characteristic
66	C₅×#390	C₂²	1	2	yes	complemented
67	C₅×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅×#389	C₂²	1	1	yes	characteristic, complemented
69	C₅×#389	C₂²	1	2	yes	complemented
70	C₅×#388	C₂²	1	1	yes	characteristic
71	C₅×#388	C₂²	1	2	yes	—
72	C₅×#388	C₂²	1	2	yes	—
73	C₅×#388	C₂²	1	2	yes	—
74	C₅×#388	C₂²	1	1	yes	characteristic
75	C₅×#388	C₂²	1	2	yes	—
76	C₅×#388	C₂²	1	2	yes	—
77	C₅×#388	C₂²	1	2	yes	complemented
78	C₅×#388	C₂²	1	2	yes	complemented
79	C₅×#388	C₂²	1	2	yes	complemented
80	C₅×#388	C₂²	1	2	yes	complemented
81	C₅×#388	C₂²	1	2	yes	complemented
82	C₅×#388	C₂²	1	2	yes	complemented
83	C₅×#388	C₂²	1	2	yes	complemented
84	C₅×#387	C₂²	1	1	yes	characteristic, complemented
85	C₅×#387	C₂²	1	1	yes	characteristic, complemented
86	C₅×#387	C₂²	1	2	yes	complemented
87	C₅×#387	C₂²	1	2	yes	complemented
88	C₅×#386	C₂²	1	1	yes	characteristic
89	C₅×#386	C₂²	1	1	yes	characteristic
90	C₅×#386	C₂²	1	2	yes	—
91	C₅×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	1	yes	characteristic, complemented
97	C₅×#385	C₂²	1	1	yes	characteristic, complemented
98	C₅×#385	C₂²	1	2	yes	complemented
99	C₅×#385	C₂²	1	2	yes	complemented
100	C₅×#385	C₂²	1	2	yes	complemented
101	C₅×#385	C₂²	1	2	yes	complemented
102	C₅×#385	C₂²	1	2	yes	complemented
103	C₅×#384	C₂²	1	1	yes	characteristic, complemented
104	C₅×#381	C₂²	1	2	yes	complemented
105	C₅×#380	C₂²	1	1	yes	characteristic
106	C₅×#380	C₂²	1	1	yes	characteristic, complemented
107	C₅×#380	C₂²	1	2	yes	complemented
108	C₅×#379	C₂²	1	2	yes	—
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, 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	C₂×C₅×#95	C₂²	1	2	yes	complemented
125	C₂×C₅×#95	C₂²	1	2	yes	complemented
126	#34292	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁵×C₅	C₂³	1	2	yes	—
128	C₂×C₅×#41	—	2	4	no	—
129	C₂×C₅×#41	—	2	4	no	—
130	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
131	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₅×D₄	—	2	4	no	—
133	C₂²×C₅×D₄	—	2	4	no	—
134	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
135	C₂²×C₅×D₄	C₂³	1	2	yes	—
136	C₂²×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₅×D₄	C₂³	1	2	yes	—
140	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅	C₂³	1	2	yes	—
142	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅	C₂³	1	2	yes	—
144	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅	C₂³	1	2	yes	—
147	C₂³×C₄×C₅	C₂³	1	2	yes	—
148	C₂³×C₄×C₅	C₂³	1	2	yes	—
149	C₂³×C₄×C₅	C₂³	1	2	yes	—
150	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₅	C₂³	1	2	yes	—
152	C₂³×C₄×C₅	C₂³	1	2	yes	—
153	C₅×#124	C₂×C₄	1	8	yes	complemented
154	C₅×#123	C₂×C₄	1	16	yes	complemented
155	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
156	C₅×#121	C₂×C₄	1	8	yes	complemented
157	C₅×#121	C₂×C₄	1	16	yes	complemented
158	C₅×#120	C₂×C₄	1	16	yes	complemented
159	C₄×C₅×Q₈	—	2	4	no	—
160	C₄×C₅×Q₈	—	2	4	no	—
161	C₄×C₅×D₄	—	2	4	no	—
162	C₄×C₅×D₄	—	2	4	no	—
163	C₄×C₅×D₄	—	2	4	no	—
164	C₄×C₅×D₄	—	2	8	no	—
165	C₄×C₅×D₄	—	2	8	no	—
166	C₄×C₅×D₄	—	2	4	no	—
167	C₄×C₅×D₄	—	2	8	no	—
168	C₄×C₅×D₄	—	2	8	no	—
169	C₄×C₅×D₄	—	2	4	no	—
170	C₄×C₅×D₄	—	4	4	no	—
171	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
172	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
173	C₄×C₅×D₄	D₄	1	8	yes	complemented
174	C₅×#117	—	2	4	no	—
175	C₅×#117	—	2	4	no	—
176	C₅×#117	—	2	8	no	—
177	C₅×#117	—	2	4	no	—
178	C₂×C₅×C₄⋊C₄	—	4	4	no	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
184	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
197	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
198	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
199	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
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	2	yes	—
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	1	yes	characteristic
206	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
215	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
225	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₄²×C₅	—	2	8	no	—
228	C₂×C₄²×C₅	—	2	4	no	—
229	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	2	yes	—
236	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅	C₂³	1	2	yes	—
238	C₂×C₄²×C₅	C₂³	1	2	yes	—
239	C₂×C₄²×C₅	C₂³	1	2	yes	—
240	C₂×C₄²×C₅	C₂³	1	2	yes	—
241	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
243	C₅×#95	C₂³	1	1	yes	characteristic
244	C₅×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
250	C₅×#95	C₂³	1	2	yes	—
251	C₅×#95	C₂³	1	1	yes	characteristic
252	C₅×#95	C₂³	1	1	yes	characteristic
253	C₅×#95	C₂³	1	1	yes	characteristic
254	C₅×#95	C₂³	1	1	yes	characteristic
255	C₅×#95	C₂³	1	1	yes	characteristic
256	C₅×#95	C₂³	1	1	yes	characteristic
257	C₅×#95	C₂³	1	1	yes	characteristic
258	C₅×#95	C₂³	1	2	yes	—
259	C₅×#95	C₂³	1	2	yes	—
260	C₅×#95	C₂³	1	2	yes	—
261	C₅×#95	C₂³	1	2	yes	—
262	C₅×#95	C₂³	1	2	yes	—
263	C₅×#95	C₂³	1	1	yes	characteristic
264	C₂×#546	C₂×C₅	1	1	yes	characteristic
265	C₂×#518	C₂×C₅	1	1	yes	characteristic, complemented
266	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
267	#2367	C₂×C₅	1	1	yes	characteristic, complemented
268	#2363	C₂×C₅	1	1	yes	characteristic, complemented
269	#2362	C₂×C₅	1	1	yes	characteristic, complemented
270	#2361	C₂×C₅	1	2	yes	complemented
271	#2359	C₂×C₅	1	2	yes	complemented
272	#2358	C₂×C₅	1	2	yes	complemented
273	#2354	C₂×C₅	1	1	yes	characteristic, complemented
274	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
275	#2342	C₂×C₅	1	2	yes	complemented
276	#2339	C₂×C₅	1	1	yes	characteristic, complemented
277	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
278	#2326	C₂×C₅	1	1	yes	characteristic, complemented
279	#2325	C₂×C₅	1	2	yes	complemented
280	#2323	C₂×C₅	1	1	yes	characteristic, complemented
281	#2321	C₂×C₅	1	2	yes	complemented
282	C₄×#123	C₂×C₅	1	2	yes	complemented
283	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
284	#2290	C₂×C₅	1	1	yes	characteristic, complemented
285	C₂×#388	C₂×C₅	1	2	yes	complemented
286	#2275	C₂×C₅	1	1	yes	characteristic, complemented
287	C₂⁴×C₅	—	2	4	no	—
288	C₂⁴×C₅	—	2	4	no	—
289	C₂⁴×C₅	—	4	2	no	—
290	C₂⁴×C₅	—	4	2	no	—
291	C₂⁴×C₅	—	4	2	no	—
292	C₂⁴×C₅	—	4	2	no	—
293	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
294	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
295	C₂⁴×C₅	C₂⁴	1	2	yes	—
296	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
297	C₂⁴×C₅	C₂⁴	1	2	yes	—
298	C₅×#41	—	2	32	no	—
299	C₂×C₅×Q₈	—	2	2	no	—
300	C₂×C₅×Q₈	—	2	2	no	—
301	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
302	C₂×C₅×D₄	—	2	4	no	—
303	C₂×C₅×D₄	—	2	4	no	—
304	C₂×C₅×D₄	—	2	4	no	—
305	C₂×C₅×D₄	—	2	4	no	—
306	C₂×C₅×D₄	—	2	32	no	—
307	C₂×C₅×D₄	—	2	2	no	—
308	C₂×C₅×D₄	—	2	2	no	—
309	C₂×C₅×D₄	—	4	2	no	—
310	C₂×C₅×D₄	—	4	1	no	—
311	C₂×C₅×D₄	—	4	2	no	—
312	C₂×C₅×D₄	—	4	1	no	—
313	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
314	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
315	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
316	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
317	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
318	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
319	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
320	C₂×C₅×D₄	#41	1	4	yes	—
321	C₂²×C₄×C₅	—	2	4	no	—
322	C₂²×C₄×C₅	—	2	4	no	—
323	C₂²×C₄×C₅	—	2	2	no	—
324	C₂²×C₄×C₅	—	2	2	no	—
325	C₂²×C₄×C₅	—	2	2	no	—
326	C₂²×C₄×C₅	—	2	2	no	—
327	C₂²×C₄×C₅	—	2	4	no	—
328	C₂²×C₄×C₅	—	2	4	no	—
329	C₂²×C₄×C₅	—	2	4	no	—
330	C₂²×C₄×C₅	—	2	2	no	—
331	C₂²×C₄×C₅	—	2	2	no	—
332	C₂²×C₄×C₅	—	2	4	no	—
333	C₂²×C₄×C₅	—	2	2	no	—
334	C₂²×C₄×C₅	—	2	4	no	—
335	C₂²×C₄×C₅	—	2	4	no	—
336	C₂²×C₄×C₅	—	4	2	no	—
337	C₂²×C₄×C₅	—	4	2	no	—
338	C₂²×C₄×C₅	—	4	2	no	—
339	C₂²×C₄×C₅	—	4	2	no	—
340	C₂²×C₄×C₅	—	4	1	no	—
341	C₂²×C₄×C₅	—	4	1	no	—
342	C₂²×C₄×C₅	—	4	2	no	—
343	C₂²×C₄×C₅	—	4	1	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	C₂²×C₄	1	8	yes	—
353	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
354	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
355	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
356	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
357	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
376	C₅×C₄⋊C₄	—	2	2	no	—
377	C₅×C₄⋊C₄	—	2	2	no	—
378	C₅×C₄⋊C₄	—	2	2	no	—
379	C₅×C₄⋊C₄	—	2	4	no	—
380	C₅×C₄⋊C₄	—	2	4	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	—	2	4	no	—
385	C₅×C₄⋊C₄	—	4	2	no	—
386	C₅×C₄⋊C₄	—	4	2	no	—
387	C₅×C₄⋊C₄	—	4	2	no	—
388	C₅×C₄⋊C₄	—	4	1	no	—
389	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
390	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
391	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
392	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
393	C₅×C₂²⋊C₄	—	2	4	no	—
394	C₅×C₂²⋊C₄	—	2	4	no	—
395	C₅×C₂²⋊C₄	—	2	4	no	—
396	C₅×C₂²⋊C₄	—	2	2	no	—
397	C₅×C₂²⋊C₄	—	2	4	no	—
398	C₅×C₂²⋊C₄	—	2	2	no	—
399	C₅×C₂²⋊C₄	—	2	4	no	—
400	C₅×C₂²⋊C₄	—	2	4	no	—
401	C₅×C₂²⋊C₄	—	2	4	no	—
402	C₅×C₂²⋊C₄	—	2	2	no	—
403	C₅×C₂²⋊C₄	—	2	4	no	—
404	C₅×C₂²⋊C₄	—	4	2	no	—
405	C₅×C₂²⋊C₄	—	4	2	no	—
406	C₅×C₂²⋊C₄	—	4	1	no	—
407	C₅×C₂²⋊C₄	—	4	2	no	—
408	C₅×C₂²⋊C₄	—	4	2	no	—
409	C₅×C₂²⋊C₄	—	4	1	no	—
410	C₅×C₂²⋊C₄	—	4	1	no	—
411	C₅×C₂²⋊C₄	—	4	2	no	—
412	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
413	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
414	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
415	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
416	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
417	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
418	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
419	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
420	C₄²×C₅	—	2	2	no	—
421	C₄²×C₅	—	2	4	no	—
422	C₄²×C₅	—	2	2	no	—
423	C₄²×C₅	—	2	4	no	—
424	C₄²×C₅	—	2	2	no	—
425	C₄²×C₅	—	2	4	no	—
426	C₄²×C₅	—	2	4	no	—
427	C₄²×C₅	—	2	2	no	—
428	C₄²×C₅	—	2	2	no	—
429	C₄²×C₅	—	4	2	no	—
430	C₄²×C₅	—	4	2	no	—
431	C₄²×C₅	—	4	2	no	—
432	C₄²×C₅	C₂²×C₄	1	4	yes	—
433	C₄²×C₅	C₂×D₄	1	4	yes	—
434	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
435	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
436	#546	C₄×C₅	1	16	yes	complemented
437	C₂×#124	C₂²×C₅	1	1	yes	characteristic
438	C₂×#123	C₂²×C₅	1	2	yes	—
439	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
440	C₂×#121	C₂²×C₅	1	2	yes	—
441	C₂×#121	C₂²×C₅	1	1	yes	characteristic
442	C₂×#120	C₂²×C₅	1	2	yes	—
443	#518	—	2	8	no	—
444	C₄×#41	—	2	8	no	—
445	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
447	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
458	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
459	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
460	C₂×#117	C₂²×C₅	1	1	yes	characteristic
461	C₂×#117	C₂²×C₅	1	1	yes	characteristic
462	C₂×#117	C₂²×C₅	1	2	yes	complemented
463	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
464	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
465	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
466	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
467	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
468	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
469	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
470	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
471	#391	C₂²×C₅	1	1	yes	characteristic, complemented
472	#391	C₂²×C₅	1	1	yes	characteristic, complemented
473	#390	C₂²×C₅	1	2	yes	—
474	#390	C₂²×C₅	1	1	yes	characteristic
475	#390	C₂²×C₅	1	1	yes	characteristic
476	#390	C₂²×C₅	1	2	yes	complemented
477	#389	C₂²×C₅	1	1	yes	characteristic, complemented
478	#389	C₂²×C₅	1	2	yes	complemented
479	#389	C₂²×C₅	1	1	yes	characteristic, complemented
480	#388	C₂²×C₅	1	2	yes	—
481	#388	C₂²×C₅	1	2	yes	—
482	#388	C₂²×C₅	1	2	yes	—
483	#388	C₂²×C₅	1	1	yes	characteristic
484	#388	C₂²×C₅	1	2	yes	—
485	#388	C₂²×C₅	1	2	yes	—
486	#388	C₂²×C₅	1	1	yes	characteristic
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	2	yes	complemented
491	#388	C₂²×C₅	1	2	yes	complemented
492	#388	C₂²×C₅	1	2	yes	complemented
493	#388	C₂²×C₅	1	2	yes	complemented
494	#387	C₂²×C₅	1	2	yes	complemented
495	#387	C₂²×C₅	1	2	yes	complemented
496	#387	C₂²×C₅	1	1	yes	characteristic, complemented
497	#387	C₂²×C₅	1	1	yes	characteristic, complemented
498	#386	C₂²×C₅	1	1	yes	characteristic
499	#386	C₂²×C₅	1	2	yes	—
500	#386	C₂²×C₅	1	2	yes	—
501	#386	C₂²×C₅	1	1	yes	characteristic
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	#385	C₂²×C₅	1	2	yes	complemented
507	#385	C₂²×C₅	1	1	yes	characteristic, complemented
508	#385	C₂²×C₅	1	2	yes	complemented
509	#385	C₂²×C₅	1	2	yes	complemented
510	#385	C₂²×C₅	1	2	yes	complemented
511	#385	C₂²×C₅	1	2	yes	complemented
512	#385	C₂²×C₅	1	1	yes	characteristic, complemented
513	#384	C₂²×C₅	1	1	yes	characteristic, complemented
514	#381	C₂²×C₅	1	2	yes	complemented
515	#380	C₂²×C₅	1	1	yes	characteristic
516	#380	C₂²×C₅	1	2	yes	complemented
517	#380	C₂²×C₅	1	1	yes	characteristic, complemented
518	#379	C₂²×C₅	1	2	yes	—
519	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
520	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
521	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
522	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
523	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
524	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
525	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
526	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
527	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
528	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
529	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	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	#376	C₂²×C₅	1	1	yes	characteristic, complemented
534	C₂×#95	C₂²×C₅	1	2	yes	complemented
535	C₂×#95	C₂²×C₅	1	2	yes	complemented
536	C₂³×C₅	—	2	2	no	—
537	C₂³×C₅	—	2	2	no	—
538	C₂³×C₅	—	2	2	no	—
539	C₂³×C₅	—	2	2	no	—
540	C₂³×C₅	—	2	1	no	—
541	C₂³×C₅	—	2	1	no	—
542	C₂³×C₅	—	2	2	no	—
543	C₂³×C₅	—	2	1	no	—
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	2	no	—
546	C₂³×C₅	—	2	1	no	—
547	C₂³×C₅	—	2	2	no	—
548	C₂³×C₅	—	2	1	no	—
549	C₂³×C₅	—	2	1	no	—
550	C₂³×C₅	—	2	1	no	—
551	C₂³×C₅	—	2	2	no	—
552	C₂³×C₅	—	2	2	no	—
553	C₂³×C₅	—	2	1	no	—
554	C₂³×C₅	—	2	1	no	—
555	C₂³×C₅	—	2	2	no	—
556	C₂³×C₅	—	2	1	no	—
557	C₂³×C₅	—	2	1	no	—
558	C₂³×C₅	—	2	16	no	—
559	C₂³×C₅	—	4	8	no	—
560	C₂³×C₅	—	4	8	no	—
561	C₂³×C₅	—	8	4	no	—
562	C₂³×C₅	—	8	4	no	—
563	C₂³×C₅	—	8	4	no	—
564	C₂³×C₅	—	8	4	no	—
565	C₂³×C₅	C₂³×C₄	1	2	yes	—
566	C₂³×C₅	C₂³×C₄	1	4	yes	—
567	C₂³×C₅	C₂³×C₄	1	2	yes	—
568	C₂³×C₅	C₂³×C₄	1	4	yes	—
569	C₂³×C₅	C₂²×D₄	1	4	yes	—
570	C₂³×C₅	C₂×#41	1	4	yes	—
571	C₂³×C₅	C₂⁵	1	1	yes	characteristic
572	C₅×Q₈	—	2	8	no	—
573	C₅×D₄	—	2	16	no	—
574	C₅×D₄	—	2	16	no	—
575	C₅×D₄	—	2	8	no	—
576	C₅×D₄	—	4	4	no	—
577	C₅×D₄	—	4	8	no	—
578	C₅×D₄	C₄×D₄	1	16	yes	complemented
579	C₂×C₄×C₅	—	2	16	no	—
580	C₂×C₄×C₅	—	2	1	no	—
581	C₂×C₄×C₅	—	2	1	no	—
582	C₂×C₄×C₅	—	2	1	no	—
583	C₂×C₄×C₅	—	2	2	no	—
584	C₂×C₄×C₅	—	2	1	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	2	2	no	—
587	C₂×C₄×C₅	—	2	1	no	—
588	C₂×C₄×C₅	—	2	2	no	—
589	C₂×C₄×C₅	—	2	1	no	—
590	C₂×C₄×C₅	—	2	1	no	—
591	C₂×C₄×C₅	—	2	2	no	—
592	C₂×C₄×C₅	—	2	2	no	—
593	C₂×C₄×C₅	—	2	2	no	—
594	C₂×C₄×C₅	—	2	1	no	—
595	C₂×C₄×C₅	—	2	1	no	—
596	C₂×C₄×C₅	—	2	1	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	8	no	—
601	C₂×C₄×C₅	—	2	8	no	—
602	C₂×C₄×C₅	—	2	1	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	2	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	2	no	—
610	C₂×C₄×C₅	—	2	2	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	2	2	no	—
613	C₂×C₄×C₅	—	2	2	no	—
614	C₂×C₄×C₅	—	2	1	no	—
615	C₂×C₄×C₅	—	2	1	no	—
616	C₂×C₄×C₅	—	2	2	no	—
617	C₂×C₄×C₅	—	2	1	no	—
618	C₂×C₄×C₅	—	2	1	no	—
619	C₂×C₄×C₅	—	2	1	no	—
620	C₂×C₄×C₅	—	2	2	no	—
621	C₂×C₄×C₅	—	2	1	no	—
622	C₂×C₄×C₅	—	2	1	no	—
623	C₂×C₄×C₅	—	2	1	no	—
624	C₂×C₄×C₅	—	2	1	no	—
625	C₂×C₄×C₅	—	2	2	no	—
626	C₂×C₄×C₅	—	4	8	no	—
627	C₂×C₄×C₅	—	4	8	no	—
628	C₂×C₄×C₅	—	4	4	no	—
629	C₂×C₄×C₅	—	4	8	no	—
630	C₂×C₄×C₅	—	4	4	no	—
631	C₂×C₄×C₅	—	8	4	no	—
632	C₂×C₄×C₅	—	8	4	no	—
633	C₂×C₄×C₅	—	8	4	no	—
634	C₂×C₄×C₅	—	8	4	no	—
635	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
637	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
638	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
639	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
640	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
641	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
642	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
643	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
644	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
645	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₅	C₂×#41	1	2	yes	—
647	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
648	C₂⁵	C₂³×C₅	1	2	yes	—
649	C₂×#41	—	2	4	no	—
650	C₂×#41	—	2	4	no	—
651	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
652	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
653	C₂²×D₄	—	2	4	no	—
654	C₂²×D₄	—	2	4	no	—
655	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
656	C₂²×D₄	C₂³×C₅	1	2	yes	—
657	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₅	1	2	yes	—
659	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₅	1	2	yes	—
661	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
662	C₂³×C₄	C₂³×C₅	1	2	yes	—
663	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₅	1	2	yes	—
665	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
666	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₅	1	2	yes	—
668	C₂³×C₄	C₂³×C₅	1	2	yes	—
669	C₂³×C₄	C₂³×C₅	1	2	yes	—
670	C₂³×C₄	C₂³×C₅	1	2	yes	—
671	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₅	1	2	yes	—
673	C₂³×C₄	C₂³×C₅	1	2	yes	—
674	#124	C₂×C₄×C₅	1	8	yes	complemented
675	#123	C₂×C₄×C₅	1	16	yes	complemented
676	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
677	#121	C₂×C₄×C₅	1	8	yes	complemented
678	#121	C₂×C₄×C₅	1	16	yes	complemented
679	#120	C₂×C₄×C₅	1	16	yes	complemented
680	C₄×Q₈	—	2	4	no	—
681	C₄×Q₈	—	2	4	no	—
682	C₄×D₄	—	2	4	no	—
683	C₄×D₄	—	2	4	no	—
684	C₄×D₄	—	2	4	no	—
685	C₄×D₄	—	2	8	no	—
686	C₄×D₄	—	2	8	no	—
687	C₄×D₄	—	2	4	no	—
688	C₄×D₄	—	2	8	no	—
689	C₄×D₄	—	2	8	no	—
690	C₄×D₄	—	2	4	no	—
691	C₄×D₄	—	4	4	no	—
692	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
693	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
694	C₄×D₄	C₅×D₄	1	8	yes	complemented
695	#117	—	2	4	no	—
696	#117	—	2	4	no	—
697	#117	—	2	8	no	—
698	#117	—	2	4	no	—
699	C₂×C₄⋊C₄	—	4	4	no	—
700	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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×C₂²⋊C₄	—	2	8	no	—
718	C₂×C₂²⋊C₄	—	2	8	no	—
719	C₂×C₂²⋊C₄	—	4	4	no	—
720	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
721	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
725	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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×C₄²	—	2	8	no	—
749	C₂×C₄²	—	2	4	no	—
750	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₅	1	2	yes	—
752	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₅	1	2	yes	—
754	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₅	1	2	yes	—
757	C₂×C₄²	C₂³×C₅	1	2	yes	—
758	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₅	1	2	yes	—
760	C₂×C₄²	C₂³×C₅	1	2	yes	—
761	C₂×C₄²	C₂³×C₅	1	2	yes	—
762	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
764	#95	C₂³×C₅	1	1	yes	characteristic
765	#95	C₂³×C₅	1	1	yes	characteristic
766	#95	C₂³×C₅	1	2	yes	—
767	#95	C₂³×C₅	1	2	yes	—
768	#95	C₂³×C₅	1	2	yes	—
769	#95	C₂³×C₅	1	2	yes	—
770	#95	C₂³×C₅	1	2	yes	—
771	#95	C₂³×C₅	1	2	yes	—
772	#95	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	1	yes	characteristic
785	C₂²×C₅	—	2	4	no	—
786	C₂²×C₅	—	2	4	no	—
787	C₂²×C₅	—	2	4	no	—
788	C₂²×C₅	—	2	4	no	—
789	C₂²×C₅	—	2	4	no	—
790	C₂²×C₅	—	2	4	no	—
791	C₂²×C₅	—	2	2	no	—
792	C₂²×C₅	—	2	2	no	—
793	C₂²×C₅	—	2	4	no	—
794	C₂²×C₅	—	2	2	no	—
795	C₂²×C₅	—	2	2	no	—
796	C₂²×C₅	—	2	4	no	—
797	C₂²×C₅	—	2	2	no	—
798	C₂²×C₅	—	2	4	no	—
799	C₂²×C₅	—	2	2	no	—
800	C₂²×C₅	—	4	1	no	—
801	C₂²×C₅	—	4	2	no	—
802	C₂²×C₅	—	4	1	no	—
803	C₂²×C₅	—	4	1	no	—
804	C₂²×C₅	—	4	2	no	—
805	C₂²×C₅	—	4	1	no	—
806	C₂²×C₅	—	4	1	no	—
807	C₂²×C₅	—	4	2	no	—
808	C₂²×C₅	—	4	1	no	—
809	C₂²×C₅	—	4	1	no	—
810	C₂²×C₅	—	4	2	no	—
811	C₂²×C₅	—	4	1	no	—
812	C₂²×C₅	—	8	16	no	—
813	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
814	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
815	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
816	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
817	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
818	C₂²×C₅	#585	1	1	yes	characteristic
819	C₂²×C₅	#585	1	1	yes	characteristic
820	C₂²×C₅	#585	1	1	yes	characteristic
821	C₄×C₅	—	2	2	no	—
822	C₄×C₅	—	2	2	no	—
823	C₄×C₅	—	2	4	no	—
824	C₄×C₅	—	2	2	no	—
825	C₄×C₅	—	2	2	no	—
826	C₄×C₅	—	2	4	no	—
827	C₄×C₅	—	2	2	no	—
828	C₄×C₅	—	2	4	no	—
829	C₄×C₅	—	2	2	no	—
830	C₄×C₅	—	2	2	no	—
831	C₄×C₅	—	4	1	no	—
832	C₄×C₅	—	4	1	no	—
833	C₄×C₅	—	4	2	no	—
834	C₄×C₅	—	4	2	no	—
835	C₄×C₅	—	4	1	no	—
836	C₄×C₅	—	4	2	no	—
837	C₄×C₅	—	4	1	no	—
838	C₄×C₅	—	4	1	no	—
839	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
840	C₂⁴	—	2	4	no	—
841	C₂⁴	—	2	4	no	—
842	C₂⁴	—	4	2	no	—
843	C₂⁴	—	4	2	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	—	4	2	no	—
846	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
847	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
848	C₂⁴	C₂⁴×C₅	1	2	yes	—
849	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
850	C₂⁴	C₂⁴×C₅	1	2	yes	—
851	#41	—	2	32	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	32	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	1	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	1	no	—
866	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
867	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
868	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
869	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
870	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
871	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
872	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
873	C₂×D₄	C₅×#41	1	4	yes	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	4	no	—
881	C₂²×C₄	—	2	4	no	—
882	C₂²×C₄	—	2	4	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	—	4	1	no	—
894	C₂²×C₄	—	4	1	no	—
895	C₂²×C₄	—	4	2	no	—
896	C₂²×C₄	—	4	1	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	—	4	2	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
906	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
907	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
908	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
909	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
910	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	4	no	—
933	C₄⋊C₄	—	2	4	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	4	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
943	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
944	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
945	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	1	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	1	no	—
964	C₂²⋊C₄	—	4	1	no	—
965	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
969	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
970	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
971	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
972	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	4	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	4	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	4	no	—
979	C₄²	—	2	4	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	4	2	no	—
983	C₄²	—	4	2	no	—
984	C₄²	—	4	2	no	—
985	C₄²	C₂²×C₄×C₅	1	4	yes	—
986	C₄²	C₂×C₅×D₄	1	4	yes	—
987	C₂×C₅	—	2	8	no	—
988	C₂×C₅	—	4	2	no	—
989	C₂×C₅	—	4	4	no	—
990	C₂×C₅	—	4	2	no	—
991	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
992	C₂×C₅	#3428	1	1	yes	characteristic
993	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
994	C₂×C₅	#3485	1	1	yes	characteristic
995	C₂×C₅	#3488	1	1	yes	characteristic
996	C₂×C₅	#3514	1	1	yes	characteristic
997	C₂×C₅	#3521	1	1	yes	characteristic
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	16	no	—
1021	C₂³	—	4	8	no	—
1022	C₂³	—	4	8	no	—
1023	C₂³	—	8	4	no	—
1024	C₂³	—	8	4	no	—
1025	C₂³	—	8	4	no	—
1026	C₂³	—	8	4	no	—
1027	C₂³	C₂³×C₄×C₅	1	2	yes	—
1028	C₂³	C₂³×C₄×C₅	1	4	yes	—
1029	C₂³	C₂³×C₄×C₅	1	2	yes	—
1030	C₂³	C₂³×C₄×C₅	1	4	yes	—
1031	C₂³	C₂²×C₅×D₄	1	4	yes	—
1032	C₂³	C₂×C₅×#41	1	4	yes	—
1033	C₂³	C₂⁵×C₅	1	1	yes	characteristic
1034	Q₈	—	2	8	no	—
1035	D₄	—	2	16	no	—
1036	D₄	—	2	16	no	—
1037	D₄	—	2	8	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	8	no	—
1040	D₄	C₄×C₅×D₄	1	16	yes	complemented
1041	C₂×C₄	—	2	16	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	8	no	—
1063	C₂×C₄	—	2	8	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	4	8	no	—
1089	C₂×C₄	—	4	8	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	4	8	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	8	4	no	—
1094	C₂×C₄	—	8	4	no	—
1095	C₂×C₄	—	8	4	no	—
1096	C₂×C₄	—	8	4	no	—
1097	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1098	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1100	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1101	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1102	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1103	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1104	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1105	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
1106	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1107	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1108	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1109	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1110	C₅	#34292	1	1	yes	characteristic, direct product factor, Sylow
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	4	no	—
1113	C₂²	—	2	4	no	—
1114	C₂²	—	2	4	no	—
1115	C₂²	—	2	4	no	—
1116	C₂²	—	2	4	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	4	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	4	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	16	no	—
1139	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
1140	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1141	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1142	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1143	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1144	C₂²	C₅×#585	1	1	yes	characteristic
1145	C₂²	C₅×#585	1	1	yes	characteristic
1146	C₂²	C₅×#585	1	1	yes	characteristic
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	4	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	4	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	4	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
1166	C₂	—	2	8	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	4	no	—
1169	C₂	—	4	2	no	—
1170	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
1171	C₂	C₅×#3428	1	1	yes	characteristic
1172	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂	C₅×#3485	1	1	yes	characteristic
1174	C₂	C₅×#3488	1	1	yes	characteristic
1175	C₂	C₅×#3514	1	1	yes	characteristic
1176	C₂	C₅×#3521	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×#546	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. C₂×C₅×#518	C₂	semidirect
3. C₂×C₄×C₅×#41	C₂	semidirect
4. C₅×#2367	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2362	C₂	semidirect
7. C₅×#2361	C₂	semidirect
8. C₅×#2359	C₂	semidirect
9. C₅×#2358	C₂	semidirect
10. C₅×#2354	C₂	semidirect
11. C₅×D₄×C₄⋊C₄	C₂	semidirect
12. C₅×#2342	C₂	semidirect
13. C₅×#2339	C₂	semidirect
14. C₅×D₄×C₂²⋊C₄	C₂	semidirect
15. C₅×#2326	C₂	semidirect
16. C₅×#2325	C₂	semidirect
17. C₅×#2323	C₂	semidirect
18. C₅×#2321	C₂	semidirect
19. C₄×C₅×#123	C₂	semidirect
20. C₄×C₅×#121	C₂	semidirect
21. C₅×#2290	C₂	semidirect
22. C₂×C₅×#388	C₂	semidirect
23. C₅×#2275	C₂	semidirect
26. C₅×#546	C₄	semidirect
35. C₂×C₄×C₅×Q₈	C₂²	semidirect
36. C₂×C₄×C₅×Q₈	C₂²	semidirect
47. C₂×C₄×C₅×D₄	C₂²	semidirect
48. C₂×C₄×C₅×D₄	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂²	semidirect
52. C₂×C₅×#117	C₂²	semidirect
53. C₂×C₅×#117	C₂²	semidirect
54. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
59. C₂²×C₄²×C₅	C₂²	semidirect
60. C₂²×C₄²×C₅	C₂²	semidirect
61. C₅×#391	C₂²	semidirect
62. C₅×#391	C₂²	semidirect
66. C₅×#390	C₂²	semidirect
67. C₅×#389	C₂²	semidirect
68. C₅×#389	C₂²	semidirect
69. C₅×#389	C₂²	semidirect
77. C₅×#388	C₂²	semidirect
78. C₅×#388	C₂²	semidirect
79. C₅×#388	C₂²	semidirect
80. C₅×#388	C₂²	semidirect
81. C₅×#388	C₂²	semidirect
82. C₅×#388	C₂²	semidirect
83. C₅×#388	C₂²	semidirect
84. C₅×#387	C₂²	semidirect
85. C₅×#387	C₂²	semidirect
86. C₅×#387	C₂²	semidirect
87. C₅×#387	C₂²	semidirect
92. C₅×#386	C₂²	semidirect
93. C₅×#386	C₂²	semidirect
94. C₅×#386	C₂²	semidirect
95. C₅×#386	C₂²	semidirect
96. C₅×#385	C₂²	semidirect
97. C₅×#385	C₂²	semidirect
98. C₅×#385	C₂²	semidirect
99. C₅×#385	C₂²	semidirect
100. C₅×#385	C₂²	semidirect
101. C₅×#385	C₂²	semidirect
102. C₅×#385	C₂²	semidirect
103. C₅×#384	C₂²	semidirect
104. C₅×#381	C₂²	semidirect
106. C₅×#380	C₂²	semidirect
107. C₅×#380	C₂²	semidirect
109. C₄×C₅×C₄⋊C₄	C₂²	semidirect
110. C₄×C₅×C₄⋊C₄	C₂²	semidirect
111. C₄×C₅×C₄⋊C₄	C₂²	semidirect
112. C₄×C₅×C₄⋊C₄	C₂²	semidirect
113. C₄×C₅×C₄⋊C₄	C₂²	semidirect
114. C₄×C₅×C₄⋊C₄	C₂²	semidirect
116. C₄×C₅×C₂²⋊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. C₂×C₅×#95	C₂²	semidirect
125. C₂×C₅×#95	C₂²	semidirect
126. #34292	C₅	direct (N × H)
130. C₂×C₅×#41	C₂×C₄	semidirect
134. C₂²×C₅×D₄	C₂×C₄	semidirect
153. C₅×#124	C₂×C₄	semidirect
154. C₅×#123	C₂×C₄	semidirect
155. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
156. C₅×#121	C₂×C₄	semidirect
157. C₅×#121	C₂×C₄	semidirect
158. C₅×#120	C₂×C₄	semidirect
171. C₄×C₅×D₄	C₂×C₄	semidirect
172. C₄×C₅×D₄	C₂×C₄	semidirect
173. C₄×C₅×D₄	D₄	semidirect
199. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
265. C₂×#518	C₂×C₅	semidirect
266. C₂×C₄×#41	C₂×C₅	semidirect
267. #2367	C₂×C₅	semidirect
268. #2363	C₂×C₅	semidirect
269. #2362	C₂×C₅	semidirect
270. #2361	C₂×C₅	semidirect
271. #2359	C₂×C₅	semidirect
272. #2358	C₂×C₅	semidirect
273. #2354	C₂×C₅	semidirect
274. D₄×C₄⋊C₄	C₂×C₅	semidirect
275. #2342	C₂×C₅	semidirect
276. #2339	C₂×C₅	semidirect
277. D₄×C₂²⋊C₄	C₂×C₅	semidirect
278. #2326	C₂×C₅	semidirect
279. #2325	C₂×C₅	semidirect
280. #2323	C₂×C₅	semidirect
281. #2321	C₂×C₅	semidirect
282. C₄×#123	C₂×C₅	semidirect
283. C₄×#121	C₂×C₅	semidirect
284. #2290	C₂×C₅	semidirect
285. C₂×#388	C₂×C₅	semidirect
286. #2275	C₂×C₅	semidirect
436. #546	C₄×C₅	semidirect
445. C₂×C₄×Q₈	C₂²×C₅	semidirect
446. C₂×C₄×Q₈	C₂²×C₅	semidirect
457. C₂×C₄×D₄	C₂²×C₅	semidirect
458. C₂×C₄×D₄	C₂²×C₅	semidirect
459. C₂×C₄×D₄	C₂²×C₅	semidirect
462. C₂×#117	C₂²×C₅	semidirect
463. C₂×#117	C₂²×C₅	semidirect
464. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
469. C₂²×C₄²	C₂²×C₅	semidirect
470. C₂²×C₄²	C₂²×C₅	semidirect
471. #391	C₂²×C₅	semidirect
472. #391	C₂²×C₅	semidirect
476. #390	C₂²×C₅	semidirect
477. #389	C₂²×C₅	semidirect
478. #389	C₂²×C₅	semidirect
479. #389	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. #388	C₂²×C₅	semidirect
493. #388	C₂²×C₅	semidirect
494. #387	C₂²×C₅	semidirect
495. #387	C₂²×C₅	semidirect
496. #387	C₂²×C₅	semidirect
497. #387	C₂²×C₅	semidirect
502. #386	C₂²×C₅	semidirect
503. #386	C₂²×C₅	semidirect
504. #386	C₂²×C₅	semidirect
505. #386	C₂²×C₅	semidirect
506. #385	C₂²×C₅	semidirect
507. #385	C₂²×C₅	semidirect
508. #385	C₂²×C₅	semidirect
509. #385	C₂²×C₅	semidirect
510. #385	C₂²×C₅	semidirect
511. #385	C₂²×C₅	semidirect
512. #385	C₂²×C₅	semidirect
513. #384	C₂²×C₅	semidirect
514. #381	C₂²×C₅	semidirect
516. #380	C₂²×C₅	semidirect
517. #380	C₂²×C₅	semidirect
519. C₄×C₄⋊C₄	C₂²×C₅	semidirect
520. C₄×C₄⋊C₄	C₂²×C₅	semidirect
521. C₄×C₄⋊C₄	C₂²×C₅	semidirect
522. C₄×C₄⋊C₄	C₂²×C₅	semidirect
523. C₄×C₄⋊C₄	C₂²×C₅	semidirect
524. C₄×C₄⋊C₄	C₂²×C₅	semidirect
526. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
527. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
528. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
529. C₄×C₂²⋊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. #376	C₂²×C₅	semidirect
534. C₂×#95	C₂²×C₅	semidirect
535. C₂×#95	C₂²×C₅	semidirect
578. C₅×D₄	C₄×D₄	semidirect
651. C₂×#41	C₂×C₄×C₅	semidirect
655. C₂²×D₄	C₂×C₄×C₅	semidirect
674. #124	C₂×C₄×C₅	semidirect
675. #123	C₂×C₄×C₅	semidirect
676. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
677. #121	C₂×C₄×C₅	semidirect
678. #121	C₂×C₄×C₅	semidirect
679. #120	C₂×C₄×C₅	semidirect
692. C₄×D₄	C₂×C₄×C₅	semidirect
693. C₄×D₄	C₂×C₄×C₅	semidirect
694. C₄×D₄	C₅×D₄	semidirect
720. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
1040. D₄	C₄×C₅×D₄	semidirect
1110. C₅	#34292	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×#546	2
C₂×C₅×#518	2
C₂×C₄×C₅×#41	2
C₅×#2367	2
C₅×#2363	2
C₅×#2362	2
C₅×#2361	2
C₅×#2359	2
C₅×#2358	2
C₅×#2354	2
C₅×D₄×C₄⋊C₄	2
C₅×#2342	2
C₅×#2339	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2326	2
C₅×#2325	2
C₅×#2323	2
C₅×#2321	2
C₄×C₅×#123	2
C₄×C₅×#121	2
C₅×#2290	2
C₂×C₅×#388	2
C₅×#2275	2
#34292	5

Subgroups — C5×#34292 #11957012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34292 #11957012