Subgroups — C₅×#34941 #11957661

Order 1280.

1900 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2574	C₂	1	4	yes	maximal, complemented
2	C₅×#2567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2563	C₂	1	1	yes	maximal, characteristic
4	C₅×#2552	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2538	C₂	1	1	yes	maximal, characteristic
6	C₅×#2508	C₂	1	2	yes	maximal, complemented
7	C₅×#2497	C₂	1	2	yes	maximal, complemented
8	C₅×#2454	C₂	1	2	yes	maximal
9	C₅×#2423	C₂	1	2	yes	maximal, complemented
10	C₅×#2396	C₂	1	4	yes	maximal, complemented
11	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#125	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₅×#2293	C₂	1	2	yes	maximal
15	C₅×#2285	C₂	1	2	yes	maximal, complemented
16	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#125	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×#117	C₂²	1	4	yes	—
29	C₂²×C₄²×C₅	C₂²	1	2	yes	—
30	C₅×#400	C₂²	1	4	yes	—
31	C₅×#399	C₂²	1	4	yes	—
32	C₅×#398	C₂²	1	4	yes	—
33	C₅×#398	C₂²	1	4	yes	—
34	C₅×#396	C₂²	1	4	yes	—
35	C₅×#396	C₂²	1	4	yes	—
36	C₅×#395	C₂²	1	4	yes	—
37	C₅×#393	C₂²	1	4	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#390	C₂²	1	2	yes	—
41	C₅×#390	C₂²	1	2	yes	—
42	C₅×#389	C₂²	1	2	yes	—
43	C₅×#389	C₂²	1	2	yes	—
44	C₅×#389	C₂²	1	2	yes	—
45	C₅×#389	C₂²	1	2	yes	—
46	C₅×#389	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#388	C₂²	1	4	yes	—
50	C₅×#388	C₂²	1	4	yes	—
51	C₅×#387	C₂²	1	4	yes	—
52	C₅×#387	C₂²	1	4	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#385	C₂²	1	4	yes	—
55	C₅×#384	C₂²	1	2	yes	—
56	C₅×#384	C₂²	1	1	yes	characteristic
57	C₅×#384	C₂²	1	2	yes	—
58	C₅×#382	C₂²	1	4	yes	—
59	C₅×#382	C₂²	1	2	yes	—
60	C₅×#380	C₂²	1	2	yes	—
61	C₅×#380	C₂²	1	2	yes	—
62	C₅×#380	C₂²	1	2	yes	—
63	C₅×#380	C₂²	1	4	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
75	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
77	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄³×C₅	C₂²	1	1	yes	characteristic
82	C₄³×C₅	C₂²	1	2	yes	—
83	#34941	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×Q₈	C₂³	1	2	yes	—
86	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂³	1	2	yes	—
88	C₂³×C₄×C₅	C₂³	1	2	yes	—
89	C₂³×C₄×C₅	C₂³	1	2	yes	—
90	C₅×C₄⋊Q₈	—	2	4	no	—
91	C₅×#125	—	2	8	no	—
92	C₅×C₂²⋊Q₈	—	2	8	no	—
93	C₄×C₅×Q₈	—	2	4	no	—
94	C₄×C₅×Q₈	—	2	4	no	—
95	C₄×C₅×Q₈	—	2	4	no	—
96	C₄×C₅×Q₈	—	4	4	no	—
97	C₄×C₅×D₄	—	2	4	no	—
98	C₄×C₅×D₄	—	2	4	no	—
99	C₄×C₅×D₄	Q₈	1	8	yes	complemented
100	C₅×#117	—	4	8	no	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₄²×C₅	—	2	8	no	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂³	1	2	yes	—
133	C₂×C₄²×C₅	C₂³	1	2	yes	—
134	C₂×C₄²×C₅	C₂³	1	2	yes	—
135	C₂×C₄²×C₅	C₂³	1	2	yes	—
136	C₂×C₄²×C₅	C₂³	1	2	yes	—
137	C₂×C₄²×C₅	C₂³	1	2	yes	—
138	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂³	1	2	yes	—
140	C₂×C₄²×C₅	C₂³	1	2	yes	—
141	C₂×C₄²×C₅	C₂³	1	4	yes	—
142	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂³	1	2	yes	—
144	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₅×#95	C₂³	1	2	yes	—
148	C₅×#95	C₂³	1	2	yes	—
149	C₅×#95	C₂³	1	2	yes	—
150	C₅×#95	C₂³	1	4	yes	—
151	C₅×#95	C₂³	1	4	yes	—
152	C₅×#95	C₂³	1	2	yes	—
153	C₅×#95	C₂³	1	2	yes	—
154	C₅×#95	C₂³	1	2	yes	—
155	C₅×#95	C₂³	1	4	yes	—
156	C₅×#95	C₂³	1	4	yes	—
157	C₅×#95	C₂³	1	4	yes	—
158	C₅×#95	C₂³	1	4	yes	—
159	C₅×#95	C₂³	1	4	yes	—
160	C₅×#95	C₂³	1	4	yes	—
161	#2574	C₂×C₅	1	4	yes	complemented
162	#2567	C₂×C₅	1	1	yes	characteristic, complemented
163	#2563	C₂×C₅	1	1	yes	characteristic
164	#2552	C₂×C₅	1	1	yes	characteristic, complemented
165	#2538	C₂×C₅	1	1	yes	characteristic
166	#2508	C₂×C₅	1	2	yes	complemented
167	#2497	C₂×C₅	1	2	yes	complemented
168	#2454	C₂×C₅	1	2	yes	—
169	#2423	C₂×C₅	1	2	yes	complemented
170	#2396	C₂×C₅	1	4	yes	complemented
171	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
172	C₄×#125	C₂×C₅	1	2	yes	complemented
173	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
174	#2293	C₂×C₅	1	2	yes	—
175	#2285	C₂×C₅	1	2	yes	complemented
176	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
177	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
178	C₂⁴×C₅	C₂⁴	1	2	yes	—
179	C₂×C₅×Q₈	—	2	2	no	—
180	C₂×C₅×Q₈	—	2	2	no	—
181	C₂×C₅×Q₈	—	2	4	no	—
182	C₂×C₅×Q₈	—	4	2	no	—
183	C₂×C₅×Q₈	—	4	2	no	—
184	C₂×C₅×Q₈	#41	1	4	yes	—
185	C₂×C₅×D₄	—	2	2	no	—
186	C₂×C₅×D₄	—	2	2	no	—
187	C₂×C₅×D₄	C₂×Q₈	1	4	yes	—
188	C₂²×C₄×C₅	—	2	4	no	—
189	C₂²×C₄×C₅	—	2	4	no	—
190	C₂²×C₄×C₅	—	2	4	no	—
191	C₂²×C₄×C₅	—	2	4	no	—
192	C₂²×C₄×C₅	—	2	4	no	—
193	C₂²×C₄×C₅	—	2	4	no	—
194	C₂²×C₄×C₅	—	2	4	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	—
197	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₅×C₄⋊C₄	—	2	2	no	—
214	C₅×C₄⋊C₄	—	2	4	no	—
215	C₅×C₄⋊C₄	—	2	4	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	—	2	2	no	—
220	C₅×C₄⋊C₄	—	2	4	no	—
221	C₅×C₄⋊C₄	—	2	8	no	—
222	C₅×C₄⋊C₄	—	2	8	no	—
223	C₅×C₄⋊C₄	—	2	8	no	—
224	C₅×C₄⋊C₄	—	2	4	no	—
225	C₅×C₄⋊C₄	—	2	4	no	—
226	C₅×C₄⋊C₄	—	2	4	no	—
227	C₅×C₄⋊C₄	—	4	4	no	—
228	C₅×C₄⋊C₄	—	4	4	no	—
229	C₅×C₄⋊C₄	—	4	4	no	—
230	C₅×C₄⋊C₄	—	4	2	no	—
231	C₅×C₄⋊C₄	—	4	4	no	—
232	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
233	C₅×C₄⋊C₄	#41	1	4	yes	—
234	C₅×C₂²⋊C₄	—	2	4	no	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	—	2	8	no	—
237	C₅×C₂²⋊C₄	—	4	4	no	—
238	C₅×C₂²⋊C₄	—	4	4	no	—
239	C₅×C₂²⋊C₄	—	4	4	no	—
240	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
241	C₄²×C₅	—	2	4	no	—
242	C₄²×C₅	—	2	4	no	—
243	C₄²×C₅	—	2	4	no	—
244	C₄²×C₅	—	2	2	no	—
245	C₄²×C₅	—	2	4	no	—
246	C₄²×C₅	—	2	2	no	—
247	C₄²×C₅	—	2	4	no	—
248	C₄²×C₅	—	2	4	no	—
249	C₄²×C₅	—	2	4	no	—
250	C₄²×C₅	—	2	4	no	—
251	C₄²×C₅	—	2	8	no	—
252	C₄²×C₅	—	2	2	no	—
253	C₄²×C₅	—	4	1	no	—
254	C₄²×C₅	—	4	2	no	—
255	C₄²×C₅	C₂×Q₈	1	4	yes	—
256	C₄²×C₅	#41	1	4	yes	—
257	C₄²×C₅	#41	1	4	yes	—
258	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×#125	C₂²×C₅	1	2	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×#117	C₂²×C₅	1	4	yes	—
269	C₂²×C₄²	C₂²×C₅	1	2	yes	—
270	#400	C₂²×C₅	1	4	yes	—
271	#399	C₂²×C₅	1	4	yes	—
272	#398	C₂²×C₅	1	4	yes	—
273	#398	C₂²×C₅	1	4	yes	—
274	#396	C₂²×C₅	1	4	yes	—
275	#396	C₂²×C₅	1	4	yes	—
276	#395	C₂²×C₅	1	4	yes	—
277	#393	C₂²×C₅	1	4	yes	—
278	#391	C₂²×C₅	1	2	yes	—
279	#391	C₂²×C₅	1	2	yes	—
280	#390	C₂²×C₅	1	2	yes	—
281	#390	C₂²×C₅	1	2	yes	—
282	#389	C₂²×C₅	1	2	yes	—
283	#389	C₂²×C₅	1	2	yes	—
284	#389	C₂²×C₅	1	2	yes	—
285	#389	C₂²×C₅	1	2	yes	—
286	#389	C₂²×C₅	1	2	yes	—
287	#389	C₂²×C₅	1	2	yes	—
288	#389	C₂²×C₅	1	2	yes	—
289	#388	C₂²×C₅	1	4	yes	—
290	#388	C₂²×C₅	1	4	yes	—
291	#387	C₂²×C₅	1	4	yes	—
292	#387	C₂²×C₅	1	4	yes	—
293	#387	C₂²×C₅	1	4	yes	—
294	#385	C₂²×C₅	1	4	yes	—
295	#384	C₂²×C₅	1	1	yes	characteristic
296	#384	C₂²×C₅	1	2	yes	—
297	#384	C₂²×C₅	1	2	yes	—
298	#382	C₂²×C₅	1	2	yes	—
299	#382	C₂²×C₅	1	4	yes	—
300	#380	C₂²×C₅	1	2	yes	—
301	#380	C₂²×C₅	1	2	yes	—
302	#380	C₂²×C₅	1	4	yes	—
303	#380	C₂²×C₅	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
307	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
308	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
309	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
317	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
319	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
321	C₄³	C₂²×C₅	1	2	yes	—
322	C₄³	C₂²×C₅	1	1	yes	characteristic
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	2	2	no	—
325	C₂³×C₅	—	2	2	no	—
326	C₂³×C₅	—	2	2	no	—
327	C₂³×C₅	—	2	2	no	—
328	C₂³×C₅	—	2	2	no	—
329	C₂³×C₅	C₂²×Q₈	1	4	yes	—
330	C₂³×C₅	C₂⁵	1	1	yes	characteristic
331	C₅×Q₈	—	2	8	no	—
332	C₅×Q₈	—	4	8	no	—
333	C₅×D₄	—	2	8	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	16	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	4	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	4	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	4	no	—
363	C₂×C₄×C₅	—	2	4	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	4	no	—
368	C₂×C₄×C₅	—	4	8	no	—
369	C₂×C₄×C₅	—	4	8	no	—
370	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
371	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
372	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
373	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
374	C₂×C₄×C₅	C₂×#41	1	2	yes	—
375	C₂×C₄×C₅	C₂×#41	1	4	yes	—
376	C₂×C₄×C₅	C₂×#41	1	2	yes	—
377	C₂×C₄×C₅	C₂×#41	1	4	yes	—
378	C₂×C₄×C₅	C₂×#41	1	2	yes	—
379	C₂×C₄×C₅	C₂×#41	1	2	yes	—
380	C₂×C₄×C₅	C₂×#41	1	2	yes	—
381	C₂×C₄×C₅	C₂×#41	1	2	yes	—
382	C₂×C₄×C₅	C₂×#41	1	2	yes	—
383	C₂×C₄×C₅	C₂×#41	1	2	yes	—
384	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
385	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₅	1	2	yes	—
387	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₅	1	2	yes	—
389	C₂³×C₄	C₂³×C₅	1	2	yes	—
390	C₂³×C₄	C₂³×C₅	1	2	yes	—
391	C₄⋊Q₈	—	2	4	no	—
392	#125	—	2	8	no	—
393	C₂²⋊Q₈	—	2	8	no	—
394	C₄×Q₈	—	2	4	no	—
395	C₄×Q₈	—	2	4	no	—
396	C₄×Q₈	—	2	4	no	—
397	C₄×Q₈	—	4	4	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	4	no	—
400	C₄×D₄	C₅×Q₈	1	8	yes	complemented
401	#117	—	4	8	no	—
402	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
430	C₂×C₄²	—	2	8	no	—
431	C₂×C₄²	C₂³×C₅	1	2	yes	—
432	C₂×C₄²	C₂³×C₅	1	4	yes	—
433	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₅	1	2	yes	—
436	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₅	1	2	yes	—
438	C₂×C₄²	C₂³×C₅	1	2	yes	—
439	C₂×C₄²	C₂³×C₅	1	2	yes	—
440	C₂×C₄²	C₂³×C₅	1	2	yes	—
441	C₂×C₄²	C₂³×C₅	1	2	yes	—
442	C₂×C₄²	C₂³×C₅	1	2	yes	—
443	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₅	1	2	yes	—
445	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
448	#95	C₂³×C₅	1	2	yes	—
449	#95	C₂³×C₅	1	2	yes	—
450	#95	C₂³×C₅	1	2	yes	—
451	#95	C₂³×C₅	1	4	yes	—
452	#95	C₂³×C₅	1	4	yes	—
453	#95	C₂³×C₅	1	2	yes	—
454	#95	C₂³×C₅	1	2	yes	—
455	#95	C₂³×C₅	1	2	yes	—
456	#95	C₂³×C₅	1	4	yes	—
457	#95	C₂³×C₅	1	4	yes	—
458	#95	C₂³×C₅	1	4	yes	—
459	#95	C₂³×C₅	1	4	yes	—
460	#95	C₂³×C₅	1	4	yes	—
461	#95	C₂³×C₅	1	4	yes	—
462	C₂²×C₅	—	2	4	no	—
463	C₂²×C₅	—	2	4	no	—
464	C₂²×C₅	—	2	4	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	4	2	no	—
469	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
470	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
473	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂²×C₅	#585	1	1	yes	characteristic
476	C₄×C₅	—	2	4	no	—
477	C₄×C₅	—	2	2	no	—
478	C₄×C₅	—	2	4	no	—
479	C₄×C₅	—	2	2	no	—
480	C₄×C₅	—	2	4	no	—
481	C₄×C₅	—	2	2	no	—
482	C₄×C₅	—	4	2	no	—
483	C₄×C₅	—	4	2	no	—
484	C₄×C₅	—	4	4	no	—
485	C₄×C₅	—	4	2	no	—
486	C₄×C₅	—	4	1	no	—
487	C₄×C₅	—	4	2	no	—
488	C₄×C₅	—	4	4	no	—
489	C₄×C₅	#529	1	4	yes	—
490	C₄×C₅	#533	1	4	yes	—
491	C₄×C₅	#554	1	4	yes	—
492	C₂⁴	C₂⁴×C₅	1	2	yes	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	4	2	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	C₅×#41	1	4	yes	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	C₂×C₅×Q₈	1	4	yes	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	—
511	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	8	no	—
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	4	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
547	C₄⋊C₄	C₅×#41	1	4	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
555	C₄²	—	2	4	no	—
556	C₄²	—	2	4	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	2	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	8	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	4	1	no	—
568	C₄²	—	4	2	no	—
569	C₄²	C₂×C₅×Q₈	1	4	yes	—
570	C₄²	C₅×#41	1	4	yes	—
571	C₄²	C₅×#41	1	4	yes	—
572	C₂×C₅	—	4	4	no	—
573	C₂×C₅	C₂×#529	1	1	yes	characteristic
574	C₂×C₅	C₂×#533	1	1	yes	characteristic
575	C₂×C₅	#3460	1	1	yes	characteristic
576	C₂×C₅	C₂×#554	1	1	yes	characteristic
577	C₂×C₅	#3475	1	1	yes	characteristic
578	C₂×C₅	Q₈×#41	1	1	yes	characteristic
579	C₂×C₅	#3483	1	1	yes	characteristic
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	C₂²×C₅×Q₈	1	4	yes	—
587	C₂³	C₂⁵×C₅	1	1	yes	characteristic
588	Q₈	—	2	8	no	—
589	Q₈	—	4	8	no	—
590	D₄	—	2	8	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	16	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
628	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
629	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
630	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
631	C₂×C₄	C₂×C₅×#41	1	2	yes	—
632	C₂×C₄	C₂×C₅×#41	1	4	yes	—
633	C₂×C₄	C₂×C₅×#41	1	2	yes	—
634	C₂×C₄	C₂×C₅×#41	1	4	yes	—
635	C₂×C₄	C₂×C₅×#41	1	2	yes	—
636	C₂×C₄	C₂×C₅×#41	1	2	yes	—
637	C₂×C₄	C₂×C₅×#41	1	2	yes	—
638	C₂×C₄	C₂×C₅×#41	1	2	yes	—
639	C₂×C₄	C₂×C₅×#41	1	2	yes	—
640	C₂×C₄	C₂×C₅×#41	1	2	yes	—
641	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
642	C₅	#34941	1	1	yes	characteristic, direct product factor, Sylow
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
651	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
652	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
653	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
654	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
655	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₅×#585	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	4	no	—
670	C₄	C₅×#529	1	4	yes	—
671	C₄	C₅×#533	1	4	yes	—
672	C₄	C₅×#554	1	4	yes	—
673	C₂	—	4	4	no	—
674	C₂	C₂×C₅×#529	1	1	yes	characteristic
675	C₂	C₂×C₅×#533	1	1	yes	characteristic
676	C₂	C₅×#3460	1	1	yes	characteristic
677	C₂	C₂×C₅×#554	1	1	yes	characteristic
678	C₂	C₅×#3475	1	1	yes	characteristic
679	C₂	C₅×Q₈×#41	1	1	yes	characteristic
680	C₂	C₅×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2574	C₂	semidirect
2. C₅×#2567	C₂	semidirect
4. C₅×#2552	C₂	semidirect
6. C₅×#2508	C₂	semidirect
7. C₅×#2497	C₂	semidirect
9. C₅×#2423	C₂	semidirect
10. C₅×#2396	C₂	semidirect
11. C₄×C₅×C₄⋊Q₈	C₂	semidirect
12. C₄×C₅×#125	C₂	semidirect
13. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
15. C₅×#2285	C₂	semidirect
16. C₄²×C₅×Q₈	C₂	semidirect
83. #34941	C₅	direct (N × H)
99. C₄×C₅×D₄	Q₈	semidirect
161. #2574	C₂×C₅	semidirect
162. #2567	C₂×C₅	semidirect
164. #2552	C₂×C₅	semidirect
166. #2508	C₂×C₅	semidirect
167. #2497	C₂×C₅	semidirect
169. #2423	C₂×C₅	semidirect
170. #2396	C₂×C₅	semidirect
171. C₄×C₄⋊Q₈	C₂×C₅	semidirect
172. C₄×#125	C₂×C₅	semidirect
173. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
175. #2285	C₂×C₅	semidirect
176. C₄²×Q₈	C₂×C₅	semidirect
400. C₄×D₄	C₅×Q₈	semidirect
642. C₅	#34941	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2574	2
C₅×#2567	2
C₅×#2563	2
C₅×#2552	2
C₅×#2538	2
C₅×#2508	2
C₅×#2497	2
C₅×#2454	2
C₅×#2423	2
C₅×#2396	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2293	2
C₅×#2285	2
C₄²×C₅×Q₈	2
C₄²×C₅×D₄	2
#34941	5

Subgroups — C5×#34941 #11957661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34941 #11957661