Subgroups — C₅×#34301 #11957021

Order 1280.

2336 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#553	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	2	yes	maximal, complemented
3	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2359	C₂	1	2	yes	maximal, complemented
8	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2353	C₂	1	2	yes	maximal, complemented
11	C₅×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2335	C₂	1	2	yes	maximal, complemented
14	C₅×#2333	C₂	1	2	yes	maximal, complemented
15	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#126	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2293	C₂	1	2	yes	maximal, complemented
20	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2275	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#553	C₄	1	16	yes	complemented
25	C₂×C₅×#126	C₂²	1	2	yes	—
26	C₂×C₅×#125	C₂²	1	1	yes	characteristic
27	C₂×C₅×#123	C₂²	1	2	yes	—
28	C₂×C₅×#121	C₂²	1	1	yes	characteristic
29	C₂×C₅×#121	C₂²	1	1	yes	characteristic
30	C₂×C₅×#121	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	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	—
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₂×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₅×#117	C₂²	1	2	yes	—
41	C₂×C₅×#117	C₂²	1	2	yes	—
42	C₂×C₅×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
45	C₅×#390	C₂²	1	2	yes	—
46	C₅×#390	C₂²	1	2	yes	—
47	C₅×#390	C₂²	1	1	yes	characteristic
48	C₅×#390	C₂²	1	1	yes	characteristic
49	C₅×#390	C₂²	1	2	yes	—
50	C₅×#390	C₂²	1	2	yes	—
51	C₅×#389	C₂²	1	2	yes	—
52	C₅×#389	C₂²	1	2	yes	—
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#389	C₂²	1	1	yes	characteristic
55	C₅×#389	C₂²	1	1	yes	characteristic
56	C₅×#389	C₂²	1	1	yes	characteristic
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#388	C₂²	1	1	yes	characteristic
59	C₅×#388	C₂²	1	1	yes	characteristic
60	C₅×#388	C₂²	1	2	yes	—
61	C₅×#388	C₂²	1	2	yes	—
62	C₅×#388	C₂²	1	2	yes	—
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#388	C₂²	1	2	yes	—
65	C₅×#388	C₂²	1	2	yes	—
66	C₅×#388	C₂²	1	2	yes	—
67	C₅×#388	C₂²	1	2	yes	—
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#387	C₂²	1	1	yes	characteristic
71	C₅×#387	C₂²	1	1	yes	characteristic
72	C₅×#387	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#387	C₂²	1	2	yes	—
76	C₅×#387	C₂²	1	2	yes	—
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#386	C₂²	1	1	yes	characteristic
79	C₅×#386	C₂²	1	1	yes	characteristic
80	C₅×#386	C₂²	1	2	yes	—
81	C₅×#386	C₂²	1	2	yes	—
82	C₅×#386	C₂²	1	2	yes	—
83	C₅×#386	C₂²	1	2	yes	—
84	C₅×#385	C₂²	1	1	yes	characteristic
85	C₅×#385	C₂²	1	1	yes	characteristic
86	C₅×#385	C₂²	1	2	yes	—
87	C₅×#384	C₂²	1	1	yes	characteristic
88	C₅×#383	C₂²	1	2	yes	—
89	C₅×#381	C₂²	1	2	yes	—
90	C₅×#380	C₂²	1	1	yes	characteristic
91	C₅×#380	C₂²	1	1	yes	characteristic
92	C₅×#380	C₂²	1	2	yes	—
93	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₅×#376	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	1	yes	characteristic
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	2	yes	—
124	#34301	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₅×D₄	C₂³	1	2	yes	—
128	C₂²×C₅×D₄	C₂³	1	2	yes	—
129	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	2	yes	—
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	2	yes	—
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₅×#126	C₂×C₄	1	16	yes	complemented
138	C₅×#125	C₂×C₄	1	8	yes	complemented
139	C₅×#123	C₂×C₄	1	16	yes	complemented
140	C₅×#121	C₂×C₄	1	8	yes	—
141	C₅×#121	C₂×C₄	1	16	yes	complemented
142	C₅×#121	C₂×C₄	1	8	yes	complemented
143	C₄×C₅×D₄	—	2	4	no	—
144	C₄×C₅×D₄	—	2	4	no	—
145	C₄×C₅×D₄	—	4	4	no	—
146	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
148	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
149	C₅×#117	—	2	4	no	—
150	C₅×#117	—	2	4	no	—
151	C₅×#117	—	2	4	no	—
152	C₅×#117	—	4	4	no	—
153	C₅×#117	—	4	4	no	—
154	C₅×#117	C₂×C₄	1	8	yes	complemented
155	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
156	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
199	C₂×C₄²×C₅	—	2	4	no	—
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅	C₂³	1	2	yes	—
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅	C₂³	1	2	yes	—
209	C₂×C₄²×C₅	C₂³	1	2	yes	—
210	C₂×C₄²×C₅	C₂³	1	2	yes	—
211	C₂×C₄²×C₅	C₂³	1	2	yes	—
212	C₂×C₄²×C₅	C₂³	1	2	yes	—
213	C₂×C₄²×C₅	C₂³	1	2	yes	—
214	C₂×C₄²×C₅	C₂³	1	2	yes	—
215	C₂×C₄²×C₅	C₂³	1	2	yes	—
216	C₂×C₄²×C₅	C₂³	1	2	yes	—
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₅×#95	C₂³	1	1	yes	characteristic
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	1	yes	characteristic
224	C₅×#95	C₂³	1	1	yes	characteristic
225	C₅×#95	C₂³	1	1	yes	characteristic
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	1	yes	characteristic
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	2	yes	—
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	1	yes	characteristic
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	1	yes	characteristic
244	C₂×#553	C₂×C₅	1	1	yes	characteristic
245	#2373	C₂×C₅	1	2	yes	complemented
246	#2370	C₂×C₅	1	1	yes	characteristic, complemented
247	#2363	C₂×C₅	1	1	yes	characteristic, complemented
248	#2363	C₂×C₅	1	1	yes	characteristic, complemented
249	#2363	C₂×C₅	1	2	yes	complemented
250	#2359	C₂×C₅	1	2	yes	complemented
251	#2354	C₂×C₅	1	1	yes	characteristic, complemented
252	#2354	C₂×C₅	1	1	yes	characteristic, complemented
253	#2353	C₂×C₅	1	2	yes	complemented
254	#2347	C₂×C₅	1	1	yes	characteristic, complemented
255	#2344	C₂×C₅	1	1	yes	characteristic, complemented
256	#2335	C₂×C₅	1	2	yes	complemented
257	#2333	C₂×C₅	1	2	yes	complemented
258	#2330	C₂×C₅	1	1	yes	characteristic, complemented
259	#2324	C₂×C₅	1	1	yes	characteristic, complemented
260	C₄×#126	C₂×C₅	1	2	yes	complemented
261	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
262	#2293	C₂×C₅	1	2	yes	complemented
263	#2290	C₂×C₅	1	1	yes	characteristic, complemented
264	#2275	C₂×C₅	1	1	yes	characteristic, complemented
265	#2274	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₅	C₂⁴	1	2	yes	—
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	2	no	—
272	C₂×C₅×D₄	—	4	2	no	—
273	C₂×C₅×D₄	—	4	1	no	—
274	C₂×C₅×D₄	—	4	2	no	—
275	C₂×C₅×D₄	—	4	2	no	—
276	C₂×C₅×D₄	—	4	2	no	—
277	C₂×C₅×D₄	—	4	1	no	—
278	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
279	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
280	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
281	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₅	—	2	2	no	—
283	C₂²×C₄×C₅	—	2	2	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	2	2	no	—
286	C₂²×C₄×C₅	—	2	2	no	—
287	C₂²×C₄×C₅	—	2	2	no	—
288	C₂²×C₄×C₅	—	2	2	no	—
289	C₂²×C₄×C₅	—	2	4	no	—
290	C₂²×C₄×C₅	—	2	4	no	—
291	C₂²×C₄×C₅	—	4	2	no	—
292	C₂²×C₄×C₅	—	4	2	no	—
293	C₂²×C₄×C₅	—	4	1	no	—
294	C₂²×C₄×C₅	—	4	1	no	—
295	C₂²×C₄×C₅	—	4	1	no	—
296	C₂²×C₄×C₅	—	4	2	no	—
297	C₂²×C₄×C₅	—	4	2	no	—
298	C₂²×C₄×C₅	—	4	2	no	—
299	C₂²×C₄×C₅	—	4	2	no	—
300	C₂²×C₄×C₅	—	4	2	no	—
301	C₂²×C₄×C₅	—	4	2	no	—
302	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
303	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
304	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
305	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
326	C₅×C₄⋊C₄	—	2	2	no	—
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	2	2	no	—
331	C₅×C₄⋊C₄	—	2	2	no	—
332	C₅×C₄⋊C₄	—	2	4	no	—
333	C₅×C₄⋊C₄	—	4	2	no	—
334	C₅×C₄⋊C₄	—	4	2	no	—
335	C₅×C₄⋊C₄	—	4	2	no	—
336	C₅×C₄⋊C₄	—	4	1	no	—
337	C₅×C₄⋊C₄	—	4	2	no	—
338	C₅×C₄⋊C₄	—	4	2	no	—
339	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
340	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
341	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
342	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
343	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
344	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
345	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
346	C₅×C₄⋊C₄	#41	1	4	yes	—
347	C₅×C₂²⋊C₄	—	2	4	no	—
348	C₅×C₂²⋊C₄	—	2	4	no	—
349	C₅×C₂²⋊C₄	—	2	2	no	—
350	C₅×C₂²⋊C₄	—	2	2	no	—
351	C₅×C₂²⋊C₄	—	2	4	no	—
352	C₅×C₂²⋊C₄	—	2	4	no	—
353	C₅×C₂²⋊C₄	—	2	2	no	—
354	C₅×C₂²⋊C₄	—	2	4	no	—
355	C₅×C₂²⋊C₄	—	4	2	no	—
356	C₅×C₂²⋊C₄	—	4	1	no	—
357	C₅×C₂²⋊C₄	—	4	2	no	—
358	C₅×C₂²⋊C₄	—	4	1	no	—
359	C₅×C₂²⋊C₄	—	4	1	no	—
360	C₅×C₂²⋊C₄	—	4	2	no	—
361	C₅×C₂²⋊C₄	—	4	2	no	—
362	C₅×C₂²⋊C₄	—	4	2	no	—
363	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
364	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
365	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
366	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
367	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
368	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
369	C₄²×C₅	—	2	2	no	—
370	C₄²×C₅	—	2	2	no	—
371	C₄²×C₅	—	2	2	no	—
372	C₄²×C₅	—	2	4	no	—
373	C₄²×C₅	—	2	4	no	—
374	C₄²×C₅	—	2	2	no	—
375	C₄²×C₅	—	2	2	no	—
376	C₄²×C₅	—	2	4	no	—
377	C₄²×C₅	—	4	2	no	—
378	C₄²×C₅	—	4	2	no	—
379	C₄²×C₅	—	4	2	no	—
380	C₄²×C₅	—	4	2	no	—
381	C₄²×C₅	—	4	2	no	—
382	C₄²×C₅	—	4	2	no	—
383	C₄²×C₅	—	4	2	no	—
384	C₄²×C₅	—	4	2	no	—
385	C₄²×C₅	C₂²×C₄	1	8	yes	—
386	C₄²×C₅	C₂²×C₄	1	4	yes	—
387	C₄²×C₅	#41	1	4	yes	—
388	#553	C₄×C₅	1	16	yes	complemented
389	C₂×#126	C₂²×C₅	1	2	yes	—
390	C₂×#125	C₂²×C₅	1	1	yes	characteristic
391	C₂×#123	C₂²×C₅	1	2	yes	—
392	C₂×#121	C₂²×C₅	1	1	yes	characteristic
393	C₂×#121	C₂²×C₅	1	1	yes	characteristic
394	C₂×#121	C₂²×C₅	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
401	C₂×#117	C₂²×C₅	1	1	yes	characteristic
402	C₂×#117	C₂²×C₅	1	1	yes	characteristic
403	C₂×#117	C₂²×C₅	1	1	yes	characteristic
404	C₂×#117	C₂²×C₅	1	2	yes	—
405	C₂×#117	C₂²×C₅	1	2	yes	—
406	C₂×#117	C₂²×C₅	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
409	#390	C₂²×C₅	1	2	yes	—
410	#390	C₂²×C₅	1	1	yes	characteristic
411	#390	C₂²×C₅	1	2	yes	—
412	#390	C₂²×C₅	1	2	yes	—
413	#390	C₂²×C₅	1	1	yes	characteristic
414	#390	C₂²×C₅	1	2	yes	—
415	#389	C₂²×C₅	1	1	yes	characteristic
416	#389	C₂²×C₅	1	2	yes	—
417	#389	C₂²×C₅	1	1	yes	characteristic
418	#389	C₂²×C₅	1	1	yes	characteristic
419	#389	C₂²×C₅	1	2	yes	—
420	#389	C₂²×C₅	1	1	yes	characteristic
421	#389	C₂²×C₅	1	2	yes	—
422	#388	C₂²×C₅	1	2	yes	—
423	#388	C₂²×C₅	1	2	yes	—
424	#388	C₂²×C₅	1	2	yes	—
425	#388	C₂²×C₅	1	2	yes	—
426	#388	C₂²×C₅	1	2	yes	—
427	#388	C₂²×C₅	1	2	yes	—
428	#388	C₂²×C₅	1	2	yes	—
429	#388	C₂²×C₅	1	2	yes	—
430	#388	C₂²×C₅	1	1	yes	characteristic
431	#388	C₂²×C₅	1	2	yes	—
432	#388	C₂²×C₅	1	2	yes	—
433	#388	C₂²×C₅	1	1	yes	characteristic
434	#387	C₂²×C₅	1	1	yes	characteristic
435	#387	C₂²×C₅	1	2	yes	—
436	#387	C₂²×C₅	1	2	yes	—
437	#387	C₂²×C₅	1	2	yes	—
438	#387	C₂²×C₅	1	2	yes	—
439	#387	C₂²×C₅	1	2	yes	—
440	#387	C₂²×C₅	1	2	yes	—
441	#387	C₂²×C₅	1	1	yes	characteristic
442	#386	C₂²×C₅	1	2	yes	—
443	#386	C₂²×C₅	1	1	yes	characteristic
444	#386	C₂²×C₅	1	2	yes	—
445	#386	C₂²×C₅	1	2	yes	—
446	#386	C₂²×C₅	1	2	yes	—
447	#386	C₂²×C₅	1	1	yes	characteristic
448	#385	C₂²×C₅	1	2	yes	—
449	#385	C₂²×C₅	1	1	yes	characteristic
450	#385	C₂²×C₅	1	1	yes	characteristic
451	#384	C₂²×C₅	1	1	yes	characteristic
452	#383	C₂²×C₅	1	2	yes	—
453	#381	C₂²×C₅	1	2	yes	—
454	#380	C₂²×C₅	1	1	yes	characteristic
455	#380	C₂²×C₅	1	2	yes	—
456	#380	C₂²×C₅	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
480	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
484	#376	C₂²×C₅	1	1	yes	characteristic
485	#376	C₂²×C₅	1	2	yes	—
486	C₂×#95	C₂²×C₅	1	2	yes	—
487	C₄³	C₂²×C₅	1	2	yes	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	—	2	2	no	—
492	C₂³×C₅	—	2	2	no	—
493	C₂³×C₅	—	2	1	no	—
494	C₂³×C₅	—	2	1	no	—
495	C₂³×C₅	—	2	2	no	—
496	C₂³×C₅	—	2	1	no	—
497	C₂³×C₅	—	2	2	no	—
498	C₂³×C₅	—	2	1	no	—
499	C₂³×C₅	—	2	1	no	—
500	C₂³×C₅	—	2	1	no	—
501	C₂³×C₅	—	2	2	no	—
502	C₂³×C₅	—	2	2	no	—
503	C₂³×C₅	—	2	1	no	—
504	C₂³×C₅	—	2	1	no	—
505	C₂³×C₅	—	2	1	no	—
506	C₂³×C₅	C₂³×C₄	1	2	yes	—
507	C₂³×C₅	C₂³×C₄	1	4	yes	—
508	C₂³×C₅	C₂³×C₄	1	2	yes	—
509	C₂³×C₅	C₂⁵	1	1	yes	characteristic
510	C₅×D₄	—	2	8	no	—
511	C₅×D₄	—	4	4	no	—
512	C₅×D₄	—	4	8	no	—
513	C₅×D₄	—	4	8	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	2	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	2	2	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	8	no	—
537	C₂×C₄×C₅	—	2	8	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	1	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	2	no	—
543	C₂×C₄×C₅	—	2	2	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	2	2	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	2	2	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	2	no	—
553	C₂×C₄×C₅	—	2	2	no	—
554	C₂×C₄×C₅	—	2	1	no	—
555	C₂×C₄×C₅	—	2	1	no	—
556	C₂×C₄×C₅	—	2	1	no	—
557	C₂×C₄×C₅	—	2	1	no	—
558	C₂×C₄×C₅	—	2	2	no	—
559	C₂×C₄×C₅	—	2	1	no	—
560	C₂×C₄×C₅	—	2	1	no	—
561	C₂×C₄×C₅	—	2	1	no	—
562	C₂×C₄×C₅	—	4	8	no	—
563	C₂×C₄×C₅	—	4	8	no	—
564	C₂×C₄×C₅	—	4	4	no	—
565	C₂×C₄×C₅	—	4	4	no	—
566	C₂×C₄×C₅	—	8	4	no	—
567	C₂×C₄×C₅	—	8	4	no	—
568	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
569	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
570	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
571	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
572	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
575	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₅	C₂×#41	1	4	yes	—
577	C₂×C₄×C₅	C₂×#41	1	2	yes	—
578	C₂×C₄×C₅	C₂×#41	1	2	yes	—
579	C₂×C₄×C₅	C₂×#41	1	2	yes	—
580	C₂×C₄×C₅	C₂×#41	1	2	yes	—
581	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
582	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₅	1	2	yes	—
584	C₂²×D₄	C₂³×C₅	1	2	yes	—
585	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₅	1	2	yes	—
590	C₂³×C₄	C₂³×C₅	1	2	yes	—
591	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₅	1	2	yes	—
593	C₂³×C₄	C₂³×C₅	1	2	yes	—
594	#126	C₂×C₄×C₅	1	16	yes	complemented
595	#125	C₂×C₄×C₅	1	8	yes	complemented
596	#123	C₂×C₄×C₅	1	16	yes	complemented
597	#121	C₂×C₄×C₅	1	8	yes	—
598	#121	C₂×C₄×C₅	1	16	yes	complemented
599	#121	C₂×C₄×C₅	1	8	yes	complemented
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	4	no	—
602	C₄×D₄	—	4	4	no	—
603	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
604	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
605	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
606	#117	—	2	4	no	—
607	#117	—	2	4	no	—
608	#117	—	2	4	no	—
609	#117	—	4	4	no	—
610	#117	—	4	4	no	—
611	#117	C₂×C₄×C₅	1	8	yes	complemented
612	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
613	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₄²	—	2	4	no	—
657	C₂×C₄²	C₂³×C₅	1	2	yes	—
658	C₂×C₄²	C₂³×C₅	1	2	yes	—
659	C₂×C₄²	C₂³×C₅	1	2	yes	—
660	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₅	1	2	yes	—
666	C₂×C₄²	C₂³×C₅	1	2	yes	—
667	C₂×C₄²	C₂³×C₅	1	2	yes	—
668	C₂×C₄²	C₂³×C₅	1	2	yes	—
669	C₂×C₄²	C₂³×C₅	1	2	yes	—
670	C₂×C₄²	C₂³×C₅	1	2	yes	—
671	C₂×C₄²	C₂³×C₅	1	2	yes	—
672	C₂×C₄²	C₂³×C₅	1	2	yes	—
673	C₂×C₄²	C₂³×C₅	1	2	yes	—
674	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
676	#95	C₂³×C₅	1	1	yes	characteristic
677	#95	C₂³×C₅	1	2	yes	—
678	#95	C₂³×C₅	1	2	yes	—
679	#95	C₂³×C₅	1	2	yes	—
680	#95	C₂³×C₅	1	1	yes	characteristic
681	#95	C₂³×C₅	1	1	yes	characteristic
682	#95	C₂³×C₅	1	1	yes	characteristic
683	#95	C₂³×C₅	1	2	yes	—
684	#95	C₂³×C₅	1	2	yes	—
685	#95	C₂³×C₅	1	2	yes	—
686	#95	C₂³×C₅	1	1	yes	characteristic
687	#95	C₂³×C₅	1	1	yes	characteristic
688	#95	C₂³×C₅	1	2	yes	—
689	#95	C₂³×C₅	1	2	yes	—
690	#95	C₂³×C₅	1	2	yes	—
691	#95	C₂³×C₅	1	2	yes	—
692	#95	C₂³×C₅	1	1	yes	characteristic
693	#95	C₂³×C₅	1	2	yes	—
694	#95	C₂³×C₅	1	2	yes	—
695	#95	C₂³×C₅	1	2	yes	—
696	#95	C₂³×C₅	1	1	yes	characteristic
697	#95	C₂³×C₅	1	1	yes	characteristic
698	#95	C₂³×C₅	1	2	yes	—
699	#95	C₂³×C₅	1	2	yes	—
700	#95	C₂³×C₅	1	1	yes	characteristic
701	C₂²×C₅	—	2	2	no	—
702	C₂²×C₅	—	2	2	no	—
703	C₂²×C₅	—	2	4	no	—
704	C₂²×C₅	—	2	2	no	—
705	C₂²×C₅	—	2	4	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	2	no	—
708	C₂²×C₅	—	2	4	no	—
709	C₂²×C₅	—	2	2	no	—
710	C₂²×C₅	—	4	1	no	—
711	C₂²×C₅	—	4	1	no	—
712	C₂²×C₅	—	4	2	no	—
713	C₂²×C₅	—	4	1	no	—
714	C₂²×C₅	—	4	2	no	—
715	C₂²×C₅	—	4	1	no	—
716	C₂²×C₅	—	4	1	no	—
717	C₂²×C₅	—	4	1	no	—
718	C₂²×C₅	—	4	2	no	—
719	C₂²×C₅	—	4	2	no	—
720	C₂²×C₅	—	4	1	no	—
721	C₂²×C₅	—	4	1	no	—
722	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
723	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
724	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
725	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂²×C₅	#585	1	1	yes	characteristic
727	C₂²×C₅	#585	1	1	yes	characteristic
728	C₂²×C₅	#585	1	1	yes	characteristic
729	C₄×C₅	—	2	2	no	—
730	C₄×C₅	—	2	2	no	—
731	C₄×C₅	—	2	2	no	—
732	C₄×C₅	—	2	4	no	—
733	C₄×C₅	—	2	4	no	—
734	C₄×C₅	—	2	2	no	—
735	C₄×C₅	—	2	4	no	—
736	C₄×C₅	—	2	2	no	—
737	C₄×C₅	—	2	2	no	—
738	C₄×C₅	—	2	2	no	—
739	C₄×C₅	—	2	4	no	—
740	C₄×C₅	—	4	1	no	—
741	C₄×C₅	—	4	1	no	—
742	C₄×C₅	—	4	1	no	—
743	C₄×C₅	—	4	2	no	—
744	C₄×C₅	—	4	1	no	—
745	C₄×C₅	—	4	2	no	—
746	C₄×C₅	—	4	2	no	—
747	C₄×C₅	—	4	1	no	—
748	C₄×C₅	C₄×#41	1	4	yes	—
749	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
750	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
751	C₂⁴	C₂⁴×C₅	1	2	yes	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	1	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	1	no	—
760	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
761	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
762	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
763	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	4	no	—
772	C₂²×C₄	—	2	4	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
785	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
786	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
787	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
788	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	1	no	—
821	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
822	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
823	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
824	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
825	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
826	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
827	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
828	C₄⋊C₄	C₅×#41	1	4	yes	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	1	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	1	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
846	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
847	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
848	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
849	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
850	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	4	no	—
855	C₄²	—	2	4	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	4	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	2	no	—
861	C₄²	—	4	2	no	—
862	C₄²	—	4	2	no	—
863	C₄²	—	4	2	no	—
864	C₄²	—	4	2	no	—
865	C₄²	—	4	2	no	—
866	C₄²	—	4	2	no	—
867	C₄²	C₂²×C₄×C₅	1	8	yes	—
868	C₄²	C₂²×C₄×C₅	1	4	yes	—
869	C₄²	C₅×#41	1	4	yes	—
870	C₂×C₅	—	4	2	no	—
871	C₂×C₅	—	4	2	no	—
872	C₂×C₅	—	4	4	no	—
873	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
874	C₂×C₅	#3428	1	1	yes	characteristic
875	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂×C₅	#3493	1	1	yes	characteristic
877	C₂×C₅	#3494	1	1	yes	characteristic
878	C₂×C₅	#3517	1	1	yes	characteristic
879	C₂×C₅	#3521	1	1	yes	characteristic
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	C₂³×C₄×C₅	1	2	yes	—
899	C₂³	C₂³×C₄×C₅	1	4	yes	—
900	C₂³	C₂³×C₄×C₅	1	2	yes	—
901	C₂³	C₂⁵×C₅	1	1	yes	characteristic
902	D₄	—	2	8	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	8	no	—
905	D₄	—	4	8	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	8	no	—
929	C₂×C₄	—	2	8	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	—	4	4	no	—
958	C₂×C₄	—	8	4	no	—
959	C₂×C₄	—	8	4	no	—
960	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
961	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
962	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
963	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
964	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
965	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
966	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
967	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
968	C₂×C₄	C₂×C₅×#41	1	4	yes	—
969	C₂×C₄	C₂×C₅×#41	1	2	yes	—
970	C₂×C₄	C₂×C₅×#41	1	2	yes	—
971	C₂×C₄	C₂×C₅×#41	1	2	yes	—
972	C₂×C₄	C₂×C₅×#41	1	2	yes	—
973	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
974	C₅	#34301	1	1	yes	characteristic, direct product factor, Sylow
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
997	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
998	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
999	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1000	C₂²	C₅×#585	1	1	yes	characteristic
1001	C₂²	C₅×#585	1	1	yes	characteristic
1002	C₂²	C₅×#585	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	4	no	—
1007	C₄	—	2	4	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	4	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	C₄×C₅×#41	1	4	yes	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	4	no	—
1026	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
1027	C₂	C₅×#3428	1	1	yes	characteristic
1028	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1029	C₂	C₅×#3493	1	1	yes	characteristic
1030	C₂	C₅×#3494	1	1	yes	characteristic
1031	C₂	C₅×#3517	1	1	yes	characteristic
1032	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×#553	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×#2373	C₂	semidirect
3. C₅×#2370	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2363	C₂	semidirect
7. C₅×#2359	C₂	semidirect
8. C₅×#2354	C₂	semidirect
9. C₅×#2354	C₂	semidirect
10. C₅×#2353	C₂	semidirect
11. C₅×#2347	C₂	semidirect
12. C₅×#2344	C₂	semidirect
13. C₅×#2335	C₂	semidirect
14. C₅×#2333	C₂	semidirect
15. C₅×#2330	C₂	semidirect
16. C₅×#2324	C₂	semidirect
17. C₄×C₅×#126	C₂	semidirect
18. C₄×C₅×#121	C₂	semidirect
19. C₅×#2293	C₂	semidirect
20. C₅×#2290	C₂	semidirect
21. C₅×#2275	C₂	semidirect
22. C₅×#2274	C₂	semidirect
23. C₄×C₅×#117	C₂	semidirect
24. C₅×#553	C₄	semidirect
124. #34301	C₅	direct (N × H)
137. C₅×#126	C₂×C₄	semidirect
138. C₅×#125	C₂×C₄	semidirect
139. C₅×#123	C₂×C₄	semidirect
141. C₅×#121	C₂×C₄	semidirect
142. C₅×#121	C₂×C₄	semidirect
146. C₄×C₅×D₄	C₂×C₄	semidirect
147. C₄×C₅×D₄	C₂×C₄	semidirect
148. C₄×C₅×D₄	C₂×C₄	semidirect
154. C₅×#117	C₂×C₄	semidirect
155. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
245. #2373	C₂×C₅	semidirect
246. #2370	C₂×C₅	semidirect
247. #2363	C₂×C₅	semidirect
248. #2363	C₂×C₅	semidirect
249. #2363	C₂×C₅	semidirect
250. #2359	C₂×C₅	semidirect
251. #2354	C₂×C₅	semidirect
252. #2354	C₂×C₅	semidirect
253. #2353	C₂×C₅	semidirect
254. #2347	C₂×C₅	semidirect
255. #2344	C₂×C₅	semidirect
256. #2335	C₂×C₅	semidirect
257. #2333	C₂×C₅	semidirect
258. #2330	C₂×C₅	semidirect
259. #2324	C₂×C₅	semidirect
260. C₄×#126	C₂×C₅	semidirect
261. C₄×#121	C₂×C₅	semidirect
262. #2293	C₂×C₅	semidirect
263. #2290	C₂×C₅	semidirect
264. #2275	C₂×C₅	semidirect
265. #2274	C₂×C₅	semidirect
266. C₄×#117	C₂×C₅	semidirect
388. #553	C₄×C₅	semidirect
594. #126	C₂×C₄×C₅	semidirect
595. #125	C₂×C₄×C₅	semidirect
596. #123	C₂×C₄×C₅	semidirect
598. #121	C₂×C₄×C₅	semidirect
599. #121	C₂×C₄×C₅	semidirect
603. C₄×D₄	C₂×C₄×C₅	semidirect
604. C₄×D₄	C₂×C₄×C₅	semidirect
605. C₄×D₄	C₂×C₄×C₅	semidirect
611. #117	C₂×C₄×C₅	semidirect
612. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
974. C₅	#34301	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×#553	2
C₅×#2373	2
C₅×#2370	2
C₅×#2363	2
C₅×#2359	2
C₅×#2354	2
C₅×#2353	2
C₅×#2347	2
C₅×#2344	2
C₅×#2335	2
C₅×#2333	2
C₅×#2330	2
C₅×#2324	2
C₄×C₅×#126	2
C₄×C₅×#121	2
C₅×#2293	2
C₅×#2290	2
C₅×#2275	2
C₅×#2274	2
C₄×C₅×#117	2
#34301	5

Subgroups — C5×#34301 #11957021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34301 #11957021