Subgroups — C₅×#34333 #11957053

Order 1280.

2288 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#554	C₂	1	1	yes	maximal, characteristic
2	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2368	C₂	1	2	yes	maximal, complemented
5	C₅×#2368	C₂	1	2	yes	maximal, complemented
6	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2360	C₂	1	2	yes	maximal, complemented
8	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2349	C₂	1	1	yes	maximal, characteristic
10	C₅×#2349	C₂	1	1	yes	maximal, characteristic
11	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2345	C₂	1	2	yes	maximal, complemented
13	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2329	C₂	1	2	yes	maximal, complemented
16	C₅×#2329	C₂	1	2	yes	maximal, complemented
17	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅×#387	C₂	1	2	yes	maximal, complemented
21	C₅×#2275	C₂	1	1	yes	maximal, characteristic
22	C₅×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
24	C₅×#554	C₄	1	16	yes	complemented
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#125	C₂²	1	1	yes	characteristic
27	C₂×C₅×#125	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₄²×C₅	C₂²	1	2	yes	—
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	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×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	2	yes	—
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#389	C₂²	1	2	yes	—
55	C₅×#389	C₂²	1	2	yes	—
56	C₅×#389	C₂²	1	2	yes	—
57	C₅×#389	C₂²	1	1	yes	characteristic
58	C₅×#389	C₂²	1	1	yes	characteristic
59	C₅×#389	C₂²	1	1	yes	characteristic
60	C₅×#389	C₂²	1	1	yes	characteristic
61	C₅×#387	C₂²	1	1	yes	characteristic
62	C₅×#387	C₂²	1	2	yes	—
63	C₅×#387	C₂²	1	2	yes	—
64	C₅×#387	C₂²	1	2	yes	—
65	C₅×#387	C₂²	1	2	yes	—
66	C₅×#387	C₂²	1	2	yes	—
67	C₅×#387	C₂²	1	2	yes	—
68	C₅×#387	C₂²	1	2	yes	—
69	C₅×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
79	C₅×#385	C₂²	1	2	yes	—
80	C₅×#385	C₂²	1	2	yes	—
81	C₅×#385	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	2	yes	—
84	C₅×#385	C₂²	1	2	yes	—
85	C₅×#384	C₂²	1	1	yes	characteristic
86	C₅×#382	C₂²	1	1	yes	characteristic
87	C₅×#382	C₂²	1	1	yes	characteristic
88	C₅×#380	C₂²	1	2	yes	—
89	C₅×#380	C₂²	1	2	yes	—
90	C₅×#380	C₂²	1	2	yes	—
91	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₅×#376	C₂²	1	1	yes	characteristic
118	C₅×#376	C₂²	1	1	yes	characteristic
119	C₂×C₅×#95	C₂²	1	2	yes	—
120	C₂×C₅×#95	C₂²	1	2	yes	—
121	C₂×C₅×#95	C₂²	1	2	yes	—
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34333	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂³	1	2	yes	—
127	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	2	yes	—
129	C₂³×C₄×C₅	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₂³×C₄×C₅	C₂³	1	2	yes	—
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	2	yes	—
134	C₂³×C₄×C₅	C₂³	1	2	yes	—
135	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
136	C₅×#125	C₂×C₄	1	8	yes	complemented
137	C₅×#125	C₂×C₄	1	8	yes	complemented
138	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
139	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
140	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
141	C₄×C₅×Q₈	—	4	4	no	—
142	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
143	C₄×C₅×D₄	—	2	4	no	—
144	C₄×C₅×D₄	—	2	4	no	—
145	C₄×C₅×D₄	—	2	4	no	—
146	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
148	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
149	C₄×C₅×D₄	Q₈	1	8	yes	complemented
150	C₂×C₅×C₄⋊C₄	—	4	4	no	—
151	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
188	C₂×C₄²×C₅	—	4	4	no	—
189	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	2	yes	—
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₂×C₄²×C₅	C₂³	1	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	2	yes	—
200	C₂×C₄²×C₅	C₂³	1	2	yes	—
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	C₅×#95	C₂³	1	1	yes	characteristic
210	C₅×#95	C₂³	1	1	yes	characteristic
211	C₅×#95	C₂³	1	1	yes	characteristic
212	C₅×#95	C₂³	1	1	yes	characteristic
213	C₅×#95	C₂³	1	2	yes	—
214	C₅×#95	C₂³	1	2	yes	—
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	2	yes	—
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	1	yes	characteristic
226	C₅×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	1	yes	characteristic
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	1	yes	characteristic
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	C₂×#554	C₂×C₅	1	1	yes	characteristic
243	#2370	C₂×C₅	1	1	yes	characteristic, complemented
244	#2370	C₂×C₅	1	1	yes	characteristic, complemented
245	#2368	C₂×C₅	1	2	yes	complemented
246	#2368	C₂×C₅	1	2	yes	complemented
247	#2365	C₂×C₅	1	1	yes	characteristic, complemented
248	#2360	C₂×C₅	1	2	yes	complemented
249	#2355	C₂×C₅	1	1	yes	characteristic, complemented
250	#2349	C₂×C₅	1	1	yes	characteristic
251	#2349	C₂×C₅	1	1	yes	characteristic
252	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
253	#2345	C₂×C₅	1	2	yes	complemented
254	#2331	C₂×C₅	1	1	yes	characteristic, complemented
255	#2330	C₂×C₅	1	1	yes	characteristic, complemented
256	#2329	C₂×C₅	1	2	yes	complemented
257	#2329	C₂×C₅	1	2	yes	complemented
258	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
259	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
260	#2295	C₂×C₅	1	1	yes	characteristic, complemented
261	C₂×#387	C₂×C₅	1	2	yes	complemented
262	#2275	C₂×C₅	1	1	yes	characteristic
263	#2275	C₂×C₅	1	1	yes	characteristic
264	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
265	C₂⁴×C₅	C₂⁴	1	2	yes	—
266	C₂×C₅×Q₈	—	4	2	no	—
267	C₂×C₅×Q₈	—	4	1	no	—
268	C₂×C₅×Q₈	—	4	1	no	—
269	C₂×C₅×Q₈	—	4	2	no	—
270	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
271	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
272	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
273	C₂×C₅×D₄	C₂×Q₈	1	4	yes	—
274	C₂×C₅×D₄	#41	1	4	yes	—
275	C₂²×C₄×C₅	—	2	4	no	—
276	C₂²×C₄×C₅	—	2	4	no	—
277	C₂²×C₄×C₅	—	2	4	no	—
278	C₂²×C₄×C₅	—	2	4	no	—
279	C₂²×C₄×C₅	—	4	2	no	—
280	C₂²×C₄×C₅	—	4	2	no	—
281	C₂²×C₄×C₅	—	4	2	no	—
282	C₂²×C₄×C₅	—	4	2	no	—
283	C₂²×C₄×C₅	—	4	2	no	—
284	C₂²×C₄×C₅	—	4	2	no	—
285	C₂²×C₄×C₅	—	4	2	no	—
286	C₂²×C₄×C₅	—	4	2	no	—
287	C₂²×C₄×C₅	—	4	2	no	—
288	C₂²×C₄×C₅	—	4	2	no	—
289	C₂²×C₄×C₅	—	4	2	no	—
290	C₂²×C₄×C₅	—	4	2	no	—
291	C₂²×C₄×C₅	—	4	2	no	—
292	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
295	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
318	C₅×C₄⋊C₄	—	2	2	no	—
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	2	no	—
321	C₅×C₄⋊C₄	—	2	2	no	—
322	C₅×C₄⋊C₄	—	2	4	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	4	2	no	—
325	C₅×C₄⋊C₄	—	4	2	no	—
326	C₅×C₄⋊C₄	—	4	2	no	—
327	C₅×C₄⋊C₄	—	4	2	no	—
328	C₅×C₄⋊C₄	—	4	1	no	—
329	C₅×C₄⋊C₄	—	4	1	no	—
330	C₅×C₄⋊C₄	—	4	2	no	—
331	C₅×C₄⋊C₄	—	4	1	no	—
332	C₅×C₄⋊C₄	—	4	2	no	—
333	C₅×C₄⋊C₄	—	4	1	no	—
334	C₅×C₄⋊C₄	—	4	2	no	—
335	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
336	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
337	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
338	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
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	4	yes	—
342	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
343	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
344	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
345	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
346	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
347	C₅×C₂²⋊C₄	—	2	4	no	—
348	C₅×C₂²⋊C₄	—	2	4	no	—
349	C₅×C₂²⋊C₄	—	2	4	no	—
350	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
351	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
352	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
353	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	2	no	—
356	C₄²×C₅	—	2	2	no	—
357	C₄²×C₅	—	2	2	no	—
358	C₄²×C₅	—	2	4	no	—
359	C₄²×C₅	—	4	2	no	—
360	C₄²×C₅	—	4	2	no	—
361	C₄²×C₅	—	4	2	no	—
362	C₄²×C₅	—	4	1	no	—
363	C₄²×C₅	—	4	1	no	—
364	C₄²×C₅	—	4	2	no	—
365	C₄²×C₅	—	4	2	no	—
366	C₄²×C₅	—	4	2	no	—
367	C₄²×C₅	—	4	1	no	—
368	C₄²×C₅	—	4	2	no	—
369	C₄²×C₅	—	4	2	no	—
370	C₄²×C₅	C₂²×C₄	1	4	yes	—
371	C₄²×C₅	C₂²×C₄	1	4	yes	—
372	C₄²×C₅	C₂²×C₄	1	4	yes	—
373	C₄²×C₅	C₂×Q₈	1	4	yes	—
374	#554	C₄×C₅	1	16	yes	complemented
375	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
376	C₂×#125	C₂²×C₅	1	1	yes	characteristic
377	C₂×#125	C₂²×C₅	1	1	yes	characteristic
378	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
379	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
380	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
381	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
391	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
392	C₂²×C₄²	C₂²×C₅	1	2	yes	—
393	#391	C₂²×C₅	1	1	yes	characteristic
394	#391	C₂²×C₅	1	2	yes	—
395	#391	C₂²×C₅	1	2	yes	—
396	#391	C₂²×C₅	1	2	yes	—
397	#391	C₂²×C₅	1	2	yes	—
398	#391	C₂²×C₅	1	1	yes	characteristic
399	#389	C₂²×C₅	1	1	yes	characteristic
400	#389	C₂²×C₅	1	1	yes	characteristic
401	#389	C₂²×C₅	1	1	yes	characteristic
402	#389	C₂²×C₅	1	2	yes	—
403	#389	C₂²×C₅	1	2	yes	—
404	#389	C₂²×C₅	1	2	yes	—
405	#389	C₂²×C₅	1	2	yes	—
406	#389	C₂²×C₅	1	1	yes	characteristic
407	#389	C₂²×C₅	1	1	yes	characteristic
408	#389	C₂²×C₅	1	1	yes	characteristic
409	#389	C₂²×C₅	1	1	yes	characteristic
410	#389	C₂²×C₅	1	1	yes	characteristic
411	#387	C₂²×C₅	1	2	yes	—
412	#387	C₂²×C₅	1	2	yes	—
413	#387	C₂²×C₅	1	2	yes	—
414	#387	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	2	yes	—
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	1	yes	characteristic
422	#387	C₂²×C₅	1	2	yes	—
423	#387	C₂²×C₅	1	2	yes	—
424	#387	C₂²×C₅	1	2	yes	—
425	#387	C₂²×C₅	1	1	yes	characteristic
426	#387	C₂²×C₅	1	2	yes	—
427	#387	C₂²×C₅	1	1	yes	characteristic
428	#387	C₂²×C₅	1	1	yes	characteristic
429	#385	C₂²×C₅	1	2	yes	—
430	#385	C₂²×C₅	1	2	yes	—
431	#385	C₂²×C₅	1	2	yes	—
432	#385	C₂²×C₅	1	2	yes	—
433	#385	C₂²×C₅	1	2	yes	—
434	#385	C₂²×C₅	1	2	yes	—
435	#384	C₂²×C₅	1	1	yes	characteristic
436	#382	C₂²×C₅	1	1	yes	characteristic
437	#382	C₂²×C₅	1	1	yes	characteristic
438	#380	C₂²×C₅	1	2	yes	—
439	#380	C₂²×C₅	1	2	yes	—
440	#380	C₂²×C₅	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
467	#376	C₂²×C₅	1	1	yes	characteristic
468	#376	C₂²×C₅	1	1	yes	characteristic
469	C₂×#95	C₂²×C₅	1	2	yes	—
470	C₂×#95	C₂²×C₅	1	2	yes	—
471	C₂×#95	C₂²×C₅	1	2	yes	—
472	C₂×#95	C₂²×C₅	1	2	yes	—
473	C₄³	C₂²×C₅	1	1	yes	characteristic
474	C₂³×C₅	—	2	2	no	—
475	C₂³×C₅	—	2	2	no	—
476	C₂³×C₅	—	2	2	no	—
477	C₂³×C₅	—	2	2	no	—
478	C₂³×C₅	C₂³×C₄	1	4	yes	—
479	C₂³×C₅	C₂²×Q₈	1	4	yes	—
480	C₂³×C₅	C₂×#41	1	4	yes	—
481	C₂³×C₅	C₂⁵	1	1	yes	characteristic
482	C₅×Q₈	—	4	4	no	—
483	C₅×Q₈	—	4	8	no	—
484	C₅×D₄	C₄×Q₈	1	16	yes	complemented
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	2	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	2	no	—
498	C₂×C₄×C₅	—	2	2	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	2	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	2	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	4	8	no	—
536	C₂×C₄×C₅	—	4	8	no	—
537	C₂×C₄×C₅	—	4	8	no	—
538	C₂×C₄×C₅	—	4	8	no	—
539	C₂×C₄×C₅	—	4	8	no	—
540	C₂×C₄×C₅	—	8	4	no	—
541	C₂×C₄×C₅	—	8	4	no	—
542	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
543	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
546	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
547	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
548	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
549	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
550	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
551	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
552	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
553	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
554	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
555	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
556	C₂×C₄×C₅	C₂×#41	1	2	yes	—
557	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
558	C₂²×Q₈	C₂³×C₅	1	2	yes	—
559	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₅	1	2	yes	—
562	C₂³×C₄	C₂³×C₅	1	2	yes	—
563	C₂³×C₄	C₂³×C₅	1	2	yes	—
564	C₂³×C₄	C₂³×C₅	1	2	yes	—
565	C₂³×C₄	C₂³×C₅	1	2	yes	—
566	C₂³×C₄	C₂³×C₅	1	2	yes	—
567	C₂³×C₄	C₂³×C₅	1	2	yes	—
568	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
569	#125	C₂×C₄×C₅	1	8	yes	complemented
570	#125	C₂×C₄×C₅	1	8	yes	complemented
571	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
572	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
573	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
574	C₄×Q₈	—	4	4	no	—
575	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
580	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
581	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
582	C₄×D₄	C₅×Q₈	1	8	yes	complemented
583	C₂×C₄⋊C₄	—	4	4	no	—
584	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
585	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
621	C₂×C₄²	—	4	4	no	—
622	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₅	1	2	yes	—
626	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅	1	2	yes	—
628	C₂×C₄²	C₂³×C₅	1	2	yes	—
629	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₅	1	2	yes	—
633	C₂×C₄²	C₂³×C₅	1	2	yes	—
634	C₂×C₄²	C₂³×C₅	1	2	yes	—
635	C₂×C₄²	C₂³×C₅	1	2	yes	—
636	C₂×C₄²	C₂³×C₅	1	2	yes	—
637	C₂×C₄²	C₂³×C₅	1	2	yes	—
638	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
642	#95	C₂³×C₅	1	1	yes	characteristic
643	#95	C₂³×C₅	1	1	yes	characteristic
644	#95	C₂³×C₅	1	1	yes	characteristic
645	#95	C₂³×C₅	1	1	yes	characteristic
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	#95	C₂³×C₅	1	2	yes	—
652	#95	C₂³×C₅	1	2	yes	—
653	#95	C₂³×C₅	1	2	yes	—
654	#95	C₂³×C₅	1	2	yes	—
655	#95	C₂³×C₅	1	2	yes	—
656	#95	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	2	yes	—
658	#95	C₂³×C₅	1	1	yes	characteristic
659	#95	C₂³×C₅	1	1	yes	characteristic
660	#95	C₂³×C₅	1	1	yes	characteristic
661	#95	C₂³×C₅	1	1	yes	characteristic
662	#95	C₂³×C₅	1	1	yes	characteristic
663	#95	C₂³×C₅	1	1	yes	characteristic
664	#95	C₂³×C₅	1	2	yes	—
665	#95	C₂³×C₅	1	2	yes	—
666	#95	C₂³×C₅	1	2	yes	—
667	#95	C₂³×C₅	1	1	yes	characteristic
668	#95	C₂³×C₅	1	1	yes	characteristic
669	#95	C₂³×C₅	1	1	yes	characteristic
670	#95	C₂³×C₅	1	2	yes	—
671	#95	C₂³×C₅	1	2	yes	—
672	#95	C₂³×C₅	1	2	yes	—
673	#95	C₂³×C₅	1	2	yes	—
674	#95	C₂³×C₅	1	1	yes	characteristic
675	C₂²×C₅	—	2	4	no	—
676	C₂²×C₅	—	2	4	no	—
677	C₂²×C₅	—	2	4	no	—
678	C₂²×C₅	—	2	4	no	—
679	C₂²×C₅	—	2	4	no	—
680	C₂²×C₅	—	2	4	no	—
681	C₂²×C₅	C₂×C₄×Q₈	1	8	yes	—
682	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
683	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
684	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
685	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²×C₅	#585	1	1	yes	characteristic
687	C₂²×C₅	#585	1	1	yes	characteristic
688	C₂²×C₅	#585	1	1	yes	characteristic
689	C₄×C₅	—	2	2	no	—
690	C₄×C₅	—	2	4	no	—
691	C₄×C₅	—	2	2	no	—
692	C₄×C₅	—	2	2	no	—
693	C₄×C₅	—	2	2	no	—
694	C₄×C₅	—	2	2	no	—
695	C₄×C₅	—	2	4	no	—
696	C₄×C₅	—	2	4	no	—
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	4	no	—
700	C₄×C₅	—	2	2	no	—
701	C₄×C₅	—	2	2	no	—
702	C₄×C₅	—	4	1	no	—
703	C₄×C₅	—	4	2	no	—
704	C₄×C₅	—	4	2	no	—
705	C₄×C₅	—	4	1	no	—
706	C₄×C₅	—	4	1	no	—
707	C₄×C₅	—	4	1	no	—
708	C₄×C₅	—	4	2	no	—
709	C₄×C₅	—	4	1	no	—
710	C₄×C₅	C₂×C₄×Q₈	1	4	yes	—
711	C₂⁴	C₂⁴×C₅	1	2	yes	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	1	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	2	no	—
716	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
717	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
719	C₂×D₄	C₂×C₅×Q₈	1	4	yes	—
720	C₂×D₄	C₅×#41	1	4	yes	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
739	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
740	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
741	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	—
742	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
782	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
783	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
784	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
785	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
786	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
787	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
788	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
789	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
790	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
791	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
792	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
797	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
798	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
799	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	4	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	1	no	—
811	C₄²	—	4	1	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	1	no	—
816	C₄²	C₂²×C₄×C₅	1	4	yes	—
817	C₄²	C₂²×C₄×C₅	1	4	yes	—
818	C₄²	C₂²×C₄×C₅	1	4	yes	—
819	C₄²	C₂×C₅×Q₈	1	4	yes	—
820	C₂×C₅	—	2	8	no	—
821	C₂×C₅	C₂²×C₄×Q₈	1	1	yes	characteristic
822	C₂×C₅	#3428	1	1	yes	characteristic
823	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂×C₅	#3501	1	1	yes	characteristic
825	C₂×C₅	#3504	1	1	yes	characteristic
826	C₂×C₅	#3513	1	1	yes	characteristic
827	C₂×C₅	#3521	1	1	yes	characteristic
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	C₂³×C₄×C₅	1	4	yes	—
833	C₂³	C₂²×C₅×Q₈	1	4	yes	—
834	C₂³	C₂×C₅×#41	1	4	yes	—
835	C₂³	C₂⁵×C₅	1	1	yes	characteristic
836	Q₈	—	4	4	no	—
837	Q₈	—	4	8	no	—
838	D₄	C₄×C₅×Q₈	1	16	yes	complemented
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	4	8	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	8	4	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
897	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
898	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
900	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
901	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
902	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
903	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
905	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
906	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
907	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
908	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
909	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
910	C₂×C₄	C₂×C₅×#41	1	2	yes	—
911	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
912	C₅	#34333	1	1	yes	characteristic, direct product factor, Sylow
913	C₂²	—	2	4	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	C₂×C₄×C₅×Q₈	1	8	yes	—
920	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
921	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
922	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
923	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂²	C₅×#585	1	1	yes	characteristic
925	C₂²	C₅×#585	1	1	yes	characteristic
926	C₂²	C₅×#585	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	4	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	4	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	C₂×C₄×C₅×Q₈	1	4	yes	—
949	C₂	—	2	8	no	—
950	C₂	C₂²×C₄×C₅×Q₈	1	1	yes	characteristic
951	C₂	C₅×#3428	1	1	yes	characteristic
952	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂	C₅×#3501	1	1	yes	characteristic
954	C₂	C₅×#3504	1	1	yes	characteristic
955	C₂	C₅×#3513	1	1	yes	characteristic
956	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	C₂²×C₅×D₄	C₂³
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×#2370	C₂	semidirect
3. C₅×#2370	C₂	semidirect
4. C₅×#2368	C₂	semidirect
5. C₅×#2368	C₂	semidirect
6. C₅×#2365	C₂	semidirect
7. C₅×#2360	C₂	semidirect
8. C₅×#2355	C₂	semidirect
12. C₅×#2345	C₂	semidirect
13. C₅×#2331	C₂	semidirect
14. C₅×#2330	C₂	semidirect
15. C₅×#2329	C₂	semidirect
16. C₅×#2329	C₂	semidirect
17. C₄×C₅×#125	C₂	semidirect
18. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
19. C₅×#2295	C₂	semidirect
20. C₂×C₅×#387	C₂	semidirect
24. C₅×#554	C₄	semidirect
124. #34333	C₅	direct (N × H)
135. C₅×C₄⋊Q₈	C₂×C₄	semidirect
136. C₅×#125	C₂×C₄	semidirect
137. C₅×#125	C₂×C₄	semidirect
138. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
140. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
149. C₄×C₅×D₄	Q₈	semidirect
151. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
243. #2370	C₂×C₅	semidirect
244. #2370	C₂×C₅	semidirect
245. #2368	C₂×C₅	semidirect
246. #2368	C₂×C₅	semidirect
247. #2365	C₂×C₅	semidirect
248. #2360	C₂×C₅	semidirect
249. #2355	C₂×C₅	semidirect
253. #2345	C₂×C₅	semidirect
254. #2331	C₂×C₅	semidirect
255. #2330	C₂×C₅	semidirect
256. #2329	C₂×C₅	semidirect
257. #2329	C₂×C₅	semidirect
258. C₄×#125	C₂×C₅	semidirect
259. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
260. #2295	C₂×C₅	semidirect
261. C₂×#387	C₂×C₅	semidirect
374. #554	C₄×C₅	semidirect
484. C₅×D₄	C₄×Q₈	semidirect
568. C₄⋊Q₈	C₂×C₄×C₅	semidirect
569. #125	C₂×C₄×C₅	semidirect
570. #125	C₂×C₄×C₅	semidirect
571. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
572. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
573. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
575. C₄×Q₈	C₂×C₄×C₅	semidirect
582. C₄×D₄	C₅×Q₈	semidirect
584. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
838. D₄	C₄×C₅×Q₈	semidirect
912. C₅	#34333	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×#554	2
C₅×#2370	2
C₅×#2368	2
C₅×#2365	2
C₅×#2360	2
C₅×#2355	2
C₅×#2349	2
C₅×D₄×C₄⋊C₄	2
C₅×#2345	2
C₅×#2331	2
C₅×#2330	2
C₅×#2329	2
C₄×C₅×#125	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₂×C₅×#387	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34333	5

Subgroups — C5×#34333 #11957053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34333 #11957053