Subgroups — C₅×#34298 #11957018

Order 1280.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₅×#2374	C₂	1	2	yes	maximal, complemented
3	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2368	C₂	1	2	yes	maximal, complemented
5	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2359	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×#2345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2339	C₂	1	2	yes	maximal, complemented
13	C₅×#2335	C₂	1	2	yes	maximal, complemented
14	C₅×#2332	C₂	1	2	yes	maximal, complemented
15	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2297	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	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	2	yes	—
25	C₅×#547	C₄	1	16	yes	complemented
26	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×#123	C₂²	1	2	yes	—
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₅×#121	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
36	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×D₄	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	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₅×C₄⋊C₄	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	C₂²×C₄²×C₅	C₂²	1	2	yes	—
46	C₅×#391	C₂²	1	2	yes	—
47	C₅×#391	C₂²	1	2	yes	—
48	C₅×#391	C₂²	1	2	yes	—
49	C₅×#391	C₂²	1	2	yes	—
50	C₅×#390	C₂²	1	2	yes	—
51	C₅×#390	C₂²	1	2	yes	—
52	C₅×#390	C₂²	1	1	yes	characteristic
53	C₅×#390	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	1	yes	characteristic
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#388	C₂²	1	1	yes	characteristic
60	C₅×#388	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	1	yes	characteristic
69	C₅×#387	C₂²	1	1	yes	characteristic
70	C₅×#387	C₂²	1	2	yes	—
71	C₅×#387	C₂²	1	2	yes	—
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×#386	C₂²	1	1	yes	characteristic
78	C₅×#386	C₂²	1	1	yes	characteristic
79	C₅×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	—
88	C₅×#382	C₂²	1	1	yes	characteristic
89	C₅×#381	C₂²	1	2	yes	—
90	C₅×#381	C₂²	1	2	yes	—
91	C₅×#380	C₂²	1	1	yes	characteristic
92	C₅×#380	C₂²	1	1	yes	characteristic
93	C₅×#380	C₂²	1	2	yes	—
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	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₅×C₄⋊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	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	1	yes	characteristic
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₂×C₅×#95	C₂²	1	2	yes	—
124	#34298	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₅×#41	—	4	4	no	—
126	C₂×C₅×#41	—	4	4	no	—
127	C₂×C₅×#41	C₂×C₄	1	16	yes	complemented
128	C₂²×C₅×Q₈	C₂³	1	2	yes	—
129	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₅×D₄	C₂³	1	2	yes	—
131	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₅×D₄	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂³	1	2	yes	—
140	C₂³×C₄×C₅	C₂³	1	2	yes	—
141	C₂³×C₄×C₅	C₂³	1	2	yes	—
142	C₂³×C₄×C₅	C₂³	1	2	yes	—
143	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
144	C₅×#123	C₂×C₄	1	16	yes	complemented
145	C₅×#123	C₂×C₄	1	16	yes	complemented
146	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
147	C₅×#121	C₂×C₄	1	8	yes	—
148	C₅×#121	C₂×C₄	1	8	yes	complemented
149	C₄×C₅×D₄	—	2	4	no	—
150	C₄×C₅×D₄	—	2	4	no	—
151	C₄×C₅×D₄	—	4	4	no	—
152	C₄×C₅×D₄	—	4	4	no	—
153	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
154	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
155	C₅×#117	—	2	4	no	—
156	C₅×#117	—	2	4	no	—
157	C₅×#117	—	4	4	no	—
158	C₂×C₅×C₄⋊C₄	—	2	4	no	—
159	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
160	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
197	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₅	—	2	4	no	—
202	C₂×C₄²×C₅	—	4	4	no	—
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	1	yes	characteristic
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	2	yes	—
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
220	C₅×#95	C₂³	1	1	yes	characteristic
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
245	C₅×#95	C₂³	1	1	yes	characteristic
246	C₅×#95	C₂³	1	2	yes	—
247	C₂×#547	C₂×C₅	1	1	yes	characteristic
248	#2374	C₂×C₅	1	2	yes	complemented
249	#2369	C₂×C₅	1	1	yes	characteristic, complemented
250	#2368	C₂×C₅	1	2	yes	complemented
251	#2363	C₂×C₅	1	1	yes	characteristic, complemented
252	#2361	C₂×C₅	1	1	yes	characteristic, complemented
253	#2359	C₂×C₅	1	2	yes	complemented
254	#2357	C₂×C₅	1	1	yes	characteristic, complemented
255	#2352	C₂×C₅	1	1	yes	characteristic, complemented
256	#2345	C₂×C₅	1	1	yes	characteristic, complemented
257	#2344	C₂×C₅	1	1	yes	characteristic, complemented
258	#2339	C₂×C₅	1	2	yes	complemented
259	#2335	C₂×C₅	1	2	yes	complemented
260	#2332	C₂×C₅	1	2	yes	complemented
261	#2331	C₂×C₅	1	1	yes	characteristic, complemented
262	#2324	C₂×C₅	1	1	yes	characteristic, complemented
263	C₄×#123	C₂×C₅	1	2	yes	complemented
264	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
265	#2297	C₂×C₅	1	2	yes	complemented
266	#2290	C₂×C₅	1	1	yes	characteristic, complemented
267	#2275	C₂×C₅	1	1	yes	characteristic, complemented
268	#2274	C₂×C₅	1	1	yes	characteristic, complemented
269	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
270	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₅	C₂⁴	1	2	yes	—
272	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
273	C₅×#41	—	4	32	no	—
274	C₂×C₅×Q₈	—	4	2	no	—
275	C₂×C₅×Q₈	—	4	2	no	—
276	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
277	C₂×C₅×D₄	—	2	4	no	—
278	C₂×C₅×D₄	—	2	4	no	—
279	C₂×C₅×D₄	—	2	2	no	—
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	—	2	2	no	—
282	C₂×C₅×D₄	—	2	2	no	—
283	C₂×C₅×D₄	—	4	2	no	—
284	C₂×C₅×D₄	—	4	2	no	—
285	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
286	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
287	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
288	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	2	4	no	—
291	C₂²×C₄×C₅	—	2	4	no	—
292	C₂²×C₄×C₅	—	2	2	no	—
293	C₂²×C₄×C₅	—	2	2	no	—
294	C₂²×C₄×C₅	—	2	2	no	—
295	C₂²×C₄×C₅	—	2	2	no	—
296	C₂²×C₄×C₅	—	2	2	no	—
297	C₂²×C₄×C₅	—	2	2	no	—
298	C₂²×C₄×C₅	—	2	4	no	—
299	C₂²×C₄×C₅	—	2	2	no	—
300	C₂²×C₄×C₅	—	2	2	no	—
301	C₂²×C₄×C₅	—	2	4	no	—
302	C₂²×C₄×C₅	—	2	4	no	—
303	C₂²×C₄×C₅	—	2	4	no	—
304	C₂²×C₄×C₅	—	4	2	no	—
305	C₂²×C₄×C₅	—	4	1	no	—
306	C₂²×C₄×C₅	—	4	2	no	—
307	C₂²×C₄×C₅	—	4	2	no	—
308	C₂²×C₄×C₅	—	4	2	no	—
309	C₂²×C₄×C₅	—	4	2	no	—
310	C₂²×C₄×C₅	—	4	2	no	—
311	C₂²×C₄×C₅	—	4	2	no	—
312	C₂²×C₄×C₅	—	4	2	no	—
313	C₂²×C₄×C₅	—	4	2	no	—
314	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
315	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
316	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
317	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
318	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
339	C₅×C₄⋊C₄	—	2	4	no	—
340	C₅×C₄⋊C₄	—	2	2	no	—
341	C₅×C₄⋊C₄	—	2	2	no	—
342	C₅×C₄⋊C₄	—	2	2	no	—
343	C₅×C₄⋊C₄	—	2	2	no	—
344	C₅×C₄⋊C₄	—	2	2	no	—
345	C₅×C₄⋊C₄	—	2	2	no	—
346	C₅×C₄⋊C₄	—	4	1	no	—
347	C₅×C₄⋊C₄	—	4	2	no	—
348	C₅×C₄⋊C₄	—	4	2	no	—
349	C₅×C₄⋊C₄	—	4	2	no	—
350	C₅×C₄⋊C₄	—	4	2	no	—
351	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
352	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
353	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
354	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
355	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
356	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
357	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
358	C₅×C₄⋊C₄	#41	1	4	yes	complemented
359	C₅×C₂²⋊C₄	—	2	2	no	—
360	C₅×C₂²⋊C₄	—	2	4	no	—
361	C₅×C₂²⋊C₄	—	2	2	no	—
362	C₅×C₂²⋊C₄	—	2	2	no	—
363	C₅×C₂²⋊C₄	—	2	2	no	—
364	C₅×C₂²⋊C₄	—	2	4	no	—
365	C₅×C₂²⋊C₄	—	2	4	no	—
366	C₅×C₂²⋊C₄	—	2	4	no	—
367	C₅×C₂²⋊C₄	—	2	2	no	—
368	C₅×C₂²⋊C₄	—	2	4	no	—
369	C₅×C₂²⋊C₄	—	4	2	no	—
370	C₅×C₂²⋊C₄	—	4	2	no	—
371	C₅×C₂²⋊C₄	—	4	1	no	—
372	C₅×C₂²⋊C₄	—	4	2	no	—
373	C₅×C₂²⋊C₄	—	4	2	no	—
374	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
375	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
376	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
377	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
378	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
379	C₄²×C₅	—	2	2	no	—
380	C₄²×C₅	—	2	2	no	—
381	C₄²×C₅	—	2	2	no	—
382	C₄²×C₅	—	2	4	no	—
383	C₄²×C₅	—	2	2	no	—
384	C₄²×C₅	—	2	2	no	—
385	C₄²×C₅	—	4	2	no	—
386	C₄²×C₅	—	4	2	no	—
387	C₄²×C₅	—	4	2	no	—
388	C₄²×C₅	—	4	2	no	—
389	C₄²×C₅	—	4	2	no	—
390	C₄²×C₅	—	4	2	no	—
391	C₄²×C₅	—	4	2	no	—
392	C₄²×C₅	—	4	2	no	—
393	C₄²×C₅	—	4	2	no	—
394	C₄²×C₅	C₂²×C₄	1	4	yes	—
395	C₄²×C₅	#41	1	4	yes	complemented
396	C₂²×#41	C₂²×C₅	1	2	yes	—
397	#547	C₄×C₅	1	16	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
399	C₂×#123	C₂²×C₅	1	2	yes	—
400	C₂×#123	C₂²×C₅	1	2	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
402	C₂×#121	C₂²×C₅	1	1	yes	characteristic
403	C₂×#121	C₂²×C₅	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
410	C₂×#117	C₂²×C₅	1	1	yes	characteristic
411	C₂×#117	C₂²×C₅	1	1	yes	characteristic
412	C₂×#117	C₂²×C₅	1	2	yes	—
413	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₅	1	2	yes	—
418	#391	C₂²×C₅	1	2	yes	—
419	#391	C₂²×C₅	1	2	yes	—
420	#391	C₂²×C₅	1	2	yes	—
421	#391	C₂²×C₅	1	2	yes	—
422	#390	C₂²×C₅	1	2	yes	—
423	#390	C₂²×C₅	1	1	yes	characteristic
424	#390	C₂²×C₅	1	1	yes	characteristic
425	#390	C₂²×C₅	1	2	yes	—
426	#389	C₂²×C₅	1	1	yes	characteristic
427	#389	C₂²×C₅	1	1	yes	characteristic
428	#389	C₂²×C₅	1	1	yes	characteristic
429	#389	C₂²×C₅	1	2	yes	—
430	#389	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	2	yes	—
434	#388	C₂²×C₅	1	2	yes	—
435	#388	C₂²×C₅	1	1	yes	characteristic
436	#388	C₂²×C₅	1	2	yes	—
437	#388	C₂²×C₅	1	2	yes	—
438	#388	C₂²×C₅	1	2	yes	—
439	#388	C₂²×C₅	1	1	yes	characteristic
440	#387	C₂²×C₅	1	2	yes	—
441	#387	C₂²×C₅	1	2	yes	—
442	#387	C₂²×C₅	1	1	yes	characteristic
443	#387	C₂²×C₅	1	2	yes	—
444	#387	C₂²×C₅	1	2	yes	—
445	#387	C₂²×C₅	1	2	yes	—
446	#387	C₂²×C₅	1	2	yes	—
447	#387	C₂²×C₅	1	2	yes	—
448	#387	C₂²×C₅	1	1	yes	characteristic
449	#386	C₂²×C₅	1	2	yes	—
450	#386	C₂²×C₅	1	2	yes	—
451	#386	C₂²×C₅	1	1	yes	characteristic
452	#386	C₂²×C₅	1	2	yes	—
453	#386	C₂²×C₅	1	2	yes	—
454	#386	C₂²×C₅	1	1	yes	characteristic
455	#386	C₂²×C₅	1	2	yes	—
456	#385	C₂²×C₅	1	2	yes	—
457	#385	C₂²×C₅	1	2	yes	—
458	#385	C₂²×C₅	1	1	yes	characteristic
459	#385	C₂²×C₅	1	1	yes	characteristic
460	#382	C₂²×C₅	1	1	yes	characteristic
461	#381	C₂²×C₅	1	2	yes	—
462	#381	C₂²×C₅	1	2	yes	—
463	#380	C₂²×C₅	1	1	yes	characteristic
464	#380	C₂²×C₅	1	2	yes	—
465	#380	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
472	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
493	#376	C₂²×C₅	1	1	yes	characteristic
494	C₂×#95	C₂²×C₅	1	2	yes	—
495	C₂×#95	C₂²×C₅	1	2	yes	—
496	C₂³×C₅	—	2	1	no	—
497	C₂³×C₅	—	2	1	no	—
498	C₂³×C₅	—	2	1	no	—
499	C₂³×C₅	—	2	1	no	—
500	C₂³×C₅	—	2	1	no	—
501	C₂³×C₅	—	2	1	no	—
502	C₂³×C₅	—	2	2	no	—
503	C₂³×C₅	—	2	2	no	—
504	C₂³×C₅	—	2	2	no	—
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	1	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	2	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	2	2	no	—
512	C₂³×C₅	C₂³×C₄	1	4	yes	—
513	C₂³×C₅	C₂³×C₄	1	2	yes	—
514	C₂³×C₅	C₂³×C₄	1	2	yes	—
515	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
516	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
517	C₂³×C₅	C₂⁵	1	1	yes	characteristic
518	C₅×Q₈	—	4	8	no	—
519	C₅×D₄	—	2	16	no	—
520	C₅×D₄	—	2	8	no	—
521	C₅×D₄	—	2	8	no	—
522	C₅×D₄	—	4	8	no	—
523	C₂×C₄×C₅	—	2	8	no	—
524	C₂×C₄×C₅	—	2	16	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	2	no	—
533	C₂×C₄×C₅	—	2	2	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	2	2	no	—
538	C₂×C₄×C₅	—	2	2	no	—
539	C₂×C₄×C₅	—	2	2	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	8	no	—
548	C₂×C₄×C₅	—	2	8	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	2	1	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	2	no	—
554	C₂×C₄×C₅	—	2	1	no	—
555	C₂×C₄×C₅	—	2	2	no	—
556	C₂×C₄×C₅	—	2	2	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	2	no	—
562	C₂×C₄×C₅	—	2	2	no	—
563	C₂×C₄×C₅	—	2	1	no	—
564	C₂×C₄×C₅	—	2	1	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	2	no	—
567	C₂×C₄×C₅	—	2	1	no	—
568	C₂×C₄×C₅	—	2	2	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	2	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	4	8	no	—
574	C₂×C₄×C₅	—	4	8	no	—
575	C₂×C₄×C₅	—	4	4	no	—
576	C₂×C₄×C₅	—	4	8	no	—
577	C₂×C₄×C₅	—	8	4	no	—
578	C₂×C₄×C₅	—	8	4	no	—
579	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
580	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
584	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
585	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
586	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
587	C₂×C₄×C₅	C₂×#41	1	2	yes	—
588	C₂×C₄×C₅	C₂×#41	1	2	yes	—
589	C₂×C₄×C₅	C₂×#41	1	4	yes	—
590	C₂×C₄×C₅	C₂×#41	1	2	yes	—
591	C₂×C₄×C₅	C₂×#41	1	2	yes	—
592	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
593	C₂×#41	—	4	4	no	—
594	C₂×#41	—	4	4	no	—
595	C₂×#41	C₂×C₄×C₅	1	16	yes	complemented
596	C₂²×Q₈	C₂³×C₅	1	2	yes	—
597	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₅	1	2	yes	—
599	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₅	1	2	yes	—
601	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₅	1	2	yes	—
603	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₅	1	2	yes	—
607	C₂³×C₄	C₂³×C₅	1	2	yes	—
608	C₂³×C₄	C₂³×C₅	1	2	yes	—
609	C₂³×C₄	C₂³×C₅	1	2	yes	—
610	C₂³×C₄	C₂³×C₅	1	2	yes	—
611	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
612	#123	C₂×C₄×C₅	1	16	yes	complemented
613	#123	C₂×C₄×C₅	1	16	yes	complemented
614	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
615	#121	C₂×C₄×C₅	1	8	yes	—
616	#121	C₂×C₄×C₅	1	8	yes	complemented
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	4	4	no	—
620	C₄×D₄	—	4	4	no	—
621	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
622	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
623	#117	—	2	4	no	—
624	#117	—	2	4	no	—
625	#117	—	4	4	no	—
626	C₂×C₄⋊C₄	—	2	4	no	—
627	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
628	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
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	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
648	C₂×C₄⋊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	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
669	C₂×C₄²	—	2	4	no	—
670	C₂×C₄²	—	4	4	no	—
671	C₂×C₄²	C₂³×C₅	1	2	yes	—
672	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₅	1	2	yes	—
678	C₂×C₄²	C₂³×C₅	1	2	yes	—
679	C₂×C₄²	C₂³×C₅	1	2	yes	—
680	C₂×C₄²	C₂³×C₅	1	2	yes	—
681	C₂×C₄²	C₂³×C₅	1	2	yes	—
682	C₂×C₄²	C₂³×C₅	1	2	yes	—
683	C₂×C₄²	C₂³×C₅	1	2	yes	—
684	C₂×C₄²	C₂³×C₅	1	2	yes	—
685	C₂×C₄²	C₂³×C₅	1	2	yes	—
686	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
688	#95	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
693	#95	C₂³×C₅	1	2	yes	—
694	#95	C₂³×C₅	1	2	yes	—
695	#95	C₂³×C₅	1	1	yes	characteristic
696	#95	C₂³×C₅	1	1	yes	characteristic
697	#95	C₂³×C₅	1	1	yes	characteristic
698	#95	C₂³×C₅	1	1	yes	characteristic
699	#95	C₂³×C₅	1	2	yes	—
700	#95	C₂³×C₅	1	1	yes	characteristic
701	#95	C₂³×C₅	1	2	yes	—
702	#95	C₂³×C₅	1	2	yes	—
703	#95	C₂³×C₅	1	2	yes	—
704	#95	C₂³×C₅	1	2	yes	—
705	#95	C₂³×C₅	1	2	yes	—
706	#95	C₂³×C₅	1	2	yes	—
707	#95	C₂³×C₅	1	2	yes	—
708	#95	C₂³×C₅	1	2	yes	—
709	#95	C₂³×C₅	1	1	yes	characteristic
710	#95	C₂³×C₅	1	1	yes	characteristic
711	#95	C₂³×C₅	1	2	yes	—
712	#95	C₂³×C₅	1	1	yes	characteristic
713	#95	C₂³×C₅	1	1	yes	characteristic
714	#95	C₂³×C₅	1	2	yes	—
715	C₂²×C₅	—	2	2	no	—
716	C₂²×C₅	—	2	2	no	—
717	C₂²×C₅	—	2	2	no	—
718	C₂²×C₅	—	2	2	no	—
719	C₂²×C₅	—	2	2	no	—
720	C₂²×C₅	—	2	2	no	—
721	C₂²×C₅	—	2	2	no	—
722	C₂²×C₅	—	2	4	no	—
723	C₂²×C₅	—	2	2	no	—
724	C₂²×C₅	—	2	4	no	—
725	C₂²×C₅	—	2	2	no	—
726	C₂²×C₅	—	2	4	no	—
727	C₂²×C₅	—	4	1	no	—
728	C₂²×C₅	—	4	2	no	—
729	C₂²×C₅	—	4	2	no	—
730	C₂²×C₅	—	4	1	no	—
731	C₂²×C₅	—	4	2	no	—
732	C₂²×C₅	—	4	1	no	—
733	C₂²×C₅	—	4	1	no	—
734	C₂²×C₅	—	4	2	no	—
735	C₂²×C₅	#518	1	4	yes	—
736	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
737	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
738	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
739	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
741	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂²×C₅	#585	1	1	yes	characteristic
743	C₄×C₅	—	2	2	no	—
744	C₄×C₅	—	2	2	no	—
745	C₄×C₅	—	2	4	no	—
746	C₄×C₅	—	2	4	no	—
747	C₄×C₅	—	2	2	no	—
748	C₄×C₅	—	2	4	no	—
749	C₄×C₅	—	2	2	no	—
750	C₄×C₅	—	2	2	no	—
751	C₄×C₅	—	2	2	no	—
752	C₄×C₅	—	2	2	no	—
753	C₄×C₅	—	2	4	no	—
754	C₄×C₅	—	4	1	no	—
755	C₄×C₅	—	4	1	no	—
756	C₄×C₅	—	4	1	no	—
757	C₄×C₅	—	4	2	no	—
758	C₄×C₅	—	4	2	no	—
759	C₄×C₅	—	4	1	no	—
760	C₄×C₅	—	4	1	no	—
761	C₄×C₅	—	4	2	no	—
762	C₄×C₅	C₄×#41	1	4	yes	—
763	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
764	C₂⁴	C₂⁴×C₅	1	2	yes	—
765	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
766	#41	—	4	32	no	—
767	C₂×Q₈	—	4	2	no	—
768	C₂×Q₈	—	4	2	no	—
769	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	2	4	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
779	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
780	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
781	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
808	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
809	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
810	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
811	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
812	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	—	4	2	no	—
843	C₄⋊C₄	—	4	1	no	—
844	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
845	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
846	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
847	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
848	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
849	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
850	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
851	C₄⋊C₄	C₅×#41	1	4	yes	complemented
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	1	no	—
867	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
868	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
869	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
870	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
871	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	4	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	4	2	no	—
879	C₄²	—	4	2	no	—
880	C₄²	—	4	2	no	—
881	C₄²	—	4	2	no	—
882	C₄²	—	4	2	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	C₂²×C₄×C₅	1	4	yes	—
888	C₄²	C₅×#41	1	4	yes	complemented
889	C₂×C₅	—	2	4	no	—
890	C₂×C₅	—	4	2	no	—
891	C₂×C₅	—	4	4	no	—
892	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
893	C₂×C₅	C₂×#518	1	1	yes	characteristic
894	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
895	C₂×C₅	#3492	1	1	yes	characteristic
896	C₂×C₅	#3494	1	1	yes	characteristic
897	C₂×C₅	#3513	1	1	yes	characteristic
898	C₂×C₅	#3522	1	1	yes	characteristic
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	C₂³×C₄×C₅	1	4	yes	—
916	C₂³	C₂³×C₄×C₅	1	2	yes	—
917	C₂³	C₂³×C₄×C₅	1	2	yes	—
918	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
919	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
920	C₂³	C₂⁵×C₅	1	1	yes	characteristic
921	Q₈	—	4	8	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	16	no	—
924	D₄	—	2	8	no	—
925	D₄	—	4	8	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	16	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	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	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	8	no	—
951	C₂×C₄	—	2	8	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
987	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
990	C₂×C₄	C₂×C₅×#41	1	2	yes	—
991	C₂×C₄	C₂×C₅×#41	1	2	yes	—
992	C₂×C₄	C₂×C₅×#41	1	4	yes	—
993	C₂×C₄	C₂×C₅×#41	1	2	yes	—
994	C₂×C₄	C₂×C₅×#41	1	2	yes	—
995	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
996	C₅	#34298	1	1	yes	characteristic, direct product factor, Sylow
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	1	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	C₅×#518	1	4	yes	—
1018	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1019	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1020	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1021	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1022	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1023	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1024	C₂²	C₅×#585	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	2	no	—
1044	C₄	C₄×C₅×#41	1	4	yes	—
1045	C₂	—	2	4	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	4	4	no	—
1048	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
1049	C₂	C₂×C₅×#518	1	1	yes	characteristic
1050	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1051	C₂	C₅×#3492	1	1	yes	characteristic
1052	C₂	C₅×#3494	1	1	yes	characteristic
1053	C₂	C₅×#3513	1	1	yes	characteristic
1054	C₂	C₅×#3522	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×#547	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×#2374	C₂	semidirect
3. C₅×#2369	C₂	semidirect
4. C₅×#2368	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2361	C₂	semidirect
7. C₅×#2359	C₂	semidirect
8. C₅×#2357	C₂	semidirect
9. C₅×#2352	C₂	semidirect
10. C₅×#2345	C₂	semidirect
11. C₅×#2344	C₂	semidirect
12. C₅×#2339	C₂	semidirect
13. C₅×#2335	C₂	semidirect
14. C₅×#2332	C₂	semidirect
15. C₅×#2331	C₂	semidirect
16. C₅×#2324	C₂	semidirect
17. C₄×C₅×#123	C₂	semidirect
18. C₄×C₅×#121	C₂	semidirect
19. C₅×#2297	C₂	semidirect
20. C₅×#2290	C₂	semidirect
21. C₅×#2275	C₂	semidirect
22. C₅×#2274	C₂	semidirect
23. C₂×C₄×C₅×C₄⋊C₄	C₂	semidirect
25. C₅×#547	C₄	semidirect
124. #34298	C₅	direct (N × H)
127. C₂×C₅×#41	C₂×C₄	semidirect
143. C₅×C₄⋊Q₈	C₂×C₄	semidirect
144. C₅×#123	C₂×C₄	semidirect
145. C₅×#123	C₂×C₄	semidirect
146. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
148. C₅×#121	C₂×C₄	semidirect
153. C₄×C₅×D₄	C₂×C₄	semidirect
154. C₄×C₅×D₄	C₂×C₄	semidirect
159. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
160. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
248. #2374	C₂×C₅	semidirect
249. #2369	C₂×C₅	semidirect
250. #2368	C₂×C₅	semidirect
251. #2363	C₂×C₅	semidirect
252. #2361	C₂×C₅	semidirect
253. #2359	C₂×C₅	semidirect
254. #2357	C₂×C₅	semidirect
255. #2352	C₂×C₅	semidirect
256. #2345	C₂×C₅	semidirect
257. #2344	C₂×C₅	semidirect
258. #2339	C₂×C₅	semidirect
259. #2335	C₂×C₅	semidirect
260. #2332	C₂×C₅	semidirect
261. #2331	C₂×C₅	semidirect
262. #2324	C₂×C₅	semidirect
263. C₄×#123	C₂×C₅	semidirect
264. C₄×#121	C₂×C₅	semidirect
265. #2297	C₂×C₅	semidirect
266. #2290	C₂×C₅	semidirect
267. #2275	C₂×C₅	semidirect
268. #2274	C₂×C₅	semidirect
269. C₂×C₄×C₄⋊C₄	C₂×C₅	semidirect
358. C₅×C₄⋊C₄	#41	semidirect
395. C₄²×C₅	#41	semidirect
397. #547	C₄×C₅	semidirect
595. C₂×#41	C₂×C₄×C₅	semidirect
611. C₄⋊Q₈	C₂×C₄×C₅	semidirect
612. #123	C₂×C₄×C₅	semidirect
613. #123	C₂×C₄×C₅	semidirect
614. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
616. #121	C₂×C₄×C₅	semidirect
621. C₄×D₄	C₂×C₄×C₅	semidirect
622. C₄×D₄	C₂×C₄×C₅	semidirect
627. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
628. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
851. C₄⋊C₄	C₅×#41	semidirect
888. C₄²	C₅×#41	semidirect
996. C₅	#34298	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×#547	2
C₅×#2374	2
C₅×#2369	2
C₅×#2368	2
C₅×#2363	2
C₅×#2361	2
C₅×#2359	2
C₅×#2357	2
C₅×#2352	2
C₅×#2345	2
C₅×#2344	2
C₅×#2339	2
C₅×#2335	2
C₅×#2332	2
C₅×#2331	2
C₅×#2324	2
C₄×C₅×#123	2
C₄×C₅×#121	2
C₅×#2297	2
C₅×#2290	2
C₅×#2275	2
C₅×#2274	2
C₂×C₄×C₅×C₄⋊C₄	2
#34298	5

Subgroups — C5×#34298 #11957018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34298 #11957018