Subgroups — C₅×#34604 #11957324

Order 1280.

1536 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2666	C₂	1	2	yes	maximal, complemented
2	C₅×#2664	C₂	1	2	yes	maximal
3	C₅×#2655	C₂	1	2	yes	maximal, complemented
4	C₅×#2655	C₂	1	2	yes	maximal, complemented
5	C₅×#2654	C₂	1	2	yes	maximal
6	C₅×#2650	C₂	1	2	yes	maximal
7	C₅×#2637	C₂	1	2	yes	maximal
8	C₅×#2634	C₂	1	2	yes	maximal, complemented
9	C₅×#2402	C₂	1	2	yes	maximal, complemented
10	C₅×#2402	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2401	C₂	1	2	yes	maximal
12	C₅×#2399	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2396	C₂	1	1	yes	maximal, characteristic
14	C₅×#2396	C₂	1	1	yes	maximal, characteristic
15	C₄×C₅×#125	C₂	1	2	yes	maximal, complemented
16	C₄×C₅×#126	C₂	1	2	yes	maximal
17	C₅×#2298	C₂	1	1	yes	maximal, characteristic
18	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅×#126	C₂²	1	2	yes	—
21	C₂×C₅×#125	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#117	C₂²	1	1	yes	characteristic
26	C₅×#401	C₂²	1	2	yes	—
27	C₅×#400	C₂²	1	2	yes	—
28	C₅×#400	C₂²	1	2	yes	—
29	C₅×#400	C₂²	1	2	yes	—
30	C₅×#400	C₂²	1	2	yes	—
31	C₅×#400	C₂²	1	2	yes	—
32	C₅×#400	C₂²	1	2	yes	—
33	C₅×#400	C₂²	1	1	yes	characteristic
34	C₅×#400	C₂²	1	1	yes	characteristic
35	C₅×#400	C₂²	1	2	yes	—
36	C₅×#400	C₂²	1	2	yes	—
37	C₅×#400	C₂²	1	2	yes	—
38	C₅×#399	C₂²	1	1	yes	characteristic
39	C₅×#399	C₂²	1	1	yes	characteristic
40	C₅×#398	C₂²	1	2	yes	—
41	C₅×#398	C₂²	1	2	yes	—
42	C₅×#398	C₂²	1	2	yes	—
43	C₅×#398	C₂²	1	2	yes	—
44	C₅×#398	C₂²	1	2	yes	—
45	C₅×#398	C₂²	1	2	yes	—
46	C₅×#398	C₂²	1	2	yes	—
47	C₅×#398	C₂²	1	2	yes	—
48	C₅×#398	C₂²	1	2	yes	—
49	C₅×#398	C₂²	1	2	yes	—
50	C₅×#397	C₂²	1	2	yes	—
51	C₅×#397	C₂²	1	2	yes	—
52	C₅×#397	C₂²	1	2	yes	—
53	C₅×#396	C₂²	1	2	yes	—
54	C₅×#396	C₂²	1	2	yes	—
55	C₅×#396	C₂²	1	2	yes	—
56	C₅×#395	C₂²	1	1	yes	characteristic
57	C₅×#395	C₂²	1	2	yes	—
58	C₅×#395	C₂²	1	2	yes	—
59	C₅×#395	C₂²	1	1	yes	characteristic
60	C₅×#393	C₂²	1	1	yes	characteristic
61	C₅×#393	C₂²	1	1	yes	characteristic
62	C₅×#391	C₂²	1	2	yes	—
63	C₅×#389	C₂²	1	2	yes	—
64	C₅×#389	C₂²	1	2	yes	—
65	C₅×#389	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×#388	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×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#383	C₂²	1	2	yes	—
83	C₅×#382	C₂²	1	2	yes	—
84	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
85	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
87	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
94	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₅×#376	C₂²	1	2	yes	—
104	C₅×#376	C₂²	1	1	yes	characteristic
105	C₄³×C₅	C₂²	1	1	yes	characteristic
106	C₄³×C₅	C₂²	1	2	yes	—
107	#34604	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₅×#126	—	2	8	no	—
112	C₅×#125	—	2	8	no	—
113	C₄×C₅×Q₈	—	2	4	no	—
114	C₄×C₅×Q₈	—	2	4	no	—
115	C₄×C₅×Q₈	—	2	8	no	—
116	C₅×#117	—	2	4	no	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₄²×C₅	C₂³	1	2	yes	—
152	C₂×C₄²×C₅	C₂³	1	2	yes	—
153	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅	C₂³	1	2	yes	—
156	C₂×C₄²×C₅	C₂³	1	2	yes	—
157	C₂×C₄²×C₅	C₂³	1	2	yes	—
158	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₅	C₂³	1	2	yes	—
161	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅	C₂³	1	2	yes	—
163	C₂×C₄²×C₅	C₂³	1	2	yes	—
164	C₂×C₄²×C₅	C₂³	1	2	yes	—
165	C₂×C₄²×C₅	C₂³	1	2	yes	—
166	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₅×#95	C₂³	1	2	yes	—
168	C₅×#95	C₂³	1	2	yes	—
169	C₅×#95	C₂³	1	2	yes	—
170	C₅×#95	C₂³	1	2	yes	—
171	C₅×#95	C₂³	1	2	yes	—
172	C₅×#95	C₂³	1	2	yes	—
173	C₅×#95	C₂³	1	2	yes	—
174	C₅×#95	C₂³	1	2	yes	—
175	C₅×#95	C₂³	1	2	yes	—
176	C₅×#95	C₂³	1	2	yes	—
177	C₅×#95	C₂³	1	2	yes	—
178	C₅×#95	C₂³	1	2	yes	—
179	C₅×#95	C₂³	1	1	yes	characteristic
180	C₅×#95	C₂³	1	1	yes	characteristic
181	C₅×#95	C₂³	1	2	yes	—
182	C₅×#95	C₂³	1	2	yes	—
183	C₅×#95	C₂³	1	2	yes	—
184	C₅×#95	C₂³	1	2	yes	—
185	C₅×#95	C₂³	1	2	yes	—
186	C₅×#95	C₂³	1	2	yes	—
187	C₅×#95	C₂³	1	2	yes	—
188	C₅×#95	C₂³	1	2	yes	—
189	C₅×#95	C₂³	1	2	yes	—
190	C₅×#95	C₂³	1	1	yes	characteristic
191	C₅×#95	C₂³	1	2	yes	—
192	C₅×#95	C₂³	1	1	yes	characteristic
193	C₅×#95	C₂³	1	2	yes	—
194	C₅×#95	C₂³	1	2	yes	—
195	C₅×#95	C₂³	1	2	yes	—
196	C₅×#95	C₂³	1	2	yes	—
197	C₅×#95	C₂³	1	2	yes	—
198	C₅×#95	C₂³	1	2	yes	—
199	C₅×#95	C₂³	1	2	yes	—
200	C₅×#95	C₂³	1	2	yes	—
201	#2666	C₂×C₅	1	2	yes	complemented
202	#2664	C₂×C₅	1	2	yes	—
203	#2655	C₂×C₅	1	2	yes	complemented
204	#2655	C₂×C₅	1	2	yes	complemented
205	#2654	C₂×C₅	1	2	yes	—
206	#2650	C₂×C₅	1	2	yes	—
207	#2637	C₂×C₅	1	2	yes	—
208	#2634	C₂×C₅	1	2	yes	complemented
209	#2402	C₂×C₅	1	1	yes	characteristic, complemented
210	#2402	C₂×C₅	1	2	yes	complemented
211	#2401	C₂×C₅	1	2	yes	—
212	#2399	C₂×C₅	1	1	yes	characteristic, complemented
213	#2396	C₂×C₅	1	1	yes	characteristic
214	#2396	C₂×C₅	1	1	yes	characteristic
215	C₄×#125	C₂×C₅	1	2	yes	complemented
216	C₄×#126	C₂×C₅	1	2	yes	—
217	#2298	C₂×C₅	1	1	yes	characteristic
218	#2295	C₂×C₅	1	1	yes	characteristic, complemented
219	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
220	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
221	C₂×C₅×Q₈	—	2	2	no	—
222	C₂×C₅×Q₈	—	2	4	no	—
223	C₂×C₅×Q₈	—	2	2	no	—
224	C₂×C₅×Q₈	—	4	2	no	—
225	C₂²×C₄×C₅	—	2	2	no	—
226	C₂²×C₄×C₅	—	2	2	no	—
227	C₂²×C₄×C₅	—	2	2	no	—
228	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	2	no	—
248	C₅×C₄⋊C₄	—	2	4	no	—
249	C₅×C₄⋊C₄	—	2	4	no	—
250	C₅×C₄⋊C₄	—	2	4	no	—
251	C₅×C₄⋊C₄	—	2	4	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	—	2	2	no	—
254	C₅×C₄⋊C₄	—	2	4	no	—
255	C₅×C₄⋊C₄	—	2	4	no	—
256	C₅×C₄⋊C₄	—	2	4	no	—
257	C₅×C₄⋊C₄	—	2	4	no	—
258	C₅×C₄⋊C₄	—	2	4	no	—
259	C₅×C₄⋊C₄	—	2	4	no	—
260	C₅×C₄⋊C₄	—	2	4	no	—
261	C₅×C₄⋊C₄	—	2	4	no	—
262	C₅×C₄⋊C₄	—	2	4	no	—
263	C₅×C₄⋊C₄	—	2	4	no	—
264	C₅×C₄⋊C₄	—	4	2	no	—
265	C₅×C₄⋊C₄	—	4	2	no	—
266	C₅×C₄⋊C₄	—	4	2	no	—
267	C₅×C₄⋊C₄	—	4	2	no	—
268	C₅×C₄⋊C₄	—	4	2	no	—
269	C₅×C₄⋊C₄	—	4	2	no	—
270	C₅×C₄⋊C₄	—	4	2	no	—
271	C₅×C₄⋊C₄	—	4	2	no	—
272	C₅×C₂²⋊C₄	—	2	2	no	—
273	C₅×C₂²⋊C₄	—	2	2	no	—
274	C₅×C₂²⋊C₄	—	2	4	no	—
275	C₅×C₂²⋊C₄	—	2	4	no	—
276	C₅×C₂²⋊C₄	—	2	4	no	—
277	C₅×C₂²⋊C₄	—	4	2	no	—
278	C₅×C₂²⋊C₄	—	4	2	no	—
279	C₅×C₂²⋊C₄	—	4	2	no	—
280	C₄²×C₅	—	2	2	no	—
281	C₄²×C₅	—	2	4	no	—
282	C₄²×C₅	—	2	4	no	—
283	C₄²×C₅	—	2	4	no	—
284	C₄²×C₅	—	2	4	no	—
285	C₄²×C₅	—	2	2	no	—
286	C₄²×C₅	—	2	4	no	—
287	C₄²×C₅	—	2	2	no	—
288	C₄²×C₅	—	2	4	no	—
289	C₄²×C₅	—	2	2	no	—
290	C₄²×C₅	—	2	2	no	—
291	C₄²×C₅	—	4	2	no	—
292	C₄²×C₅	—	4	2	no	—
293	C₄²×C₅	—	4	2	no	—
294	C₄²×C₅	#41	1	4	yes	—
295	C₄²×C₅	#41	1	8	yes	—
296	C₂×#126	C₂²×C₅	1	2	yes	—
297	C₂×#125	C₂²×C₅	1	2	yes	—
298	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
301	C₂×#117	C₂²×C₅	1	1	yes	characteristic
302	#401	C₂²×C₅	1	2	yes	—
303	#400	C₂²×C₅	1	2	yes	—
304	#400	C₂²×C₅	1	2	yes	—
305	#400	C₂²×C₅	1	2	yes	—
306	#400	C₂²×C₅	1	2	yes	—
307	#400	C₂²×C₅	1	2	yes	—
308	#400	C₂²×C₅	1	2	yes	—
309	#400	C₂²×C₅	1	1	yes	characteristic
310	#400	C₂²×C₅	1	1	yes	characteristic
311	#400	C₂²×C₅	1	2	yes	—
312	#400	C₂²×C₅	1	2	yes	—
313	#400	C₂²×C₅	1	2	yes	—
314	#399	C₂²×C₅	1	1	yes	characteristic
315	#399	C₂²×C₅	1	1	yes	characteristic
316	#398	C₂²×C₅	1	2	yes	—
317	#398	C₂²×C₅	1	2	yes	—
318	#398	C₂²×C₅	1	2	yes	—
319	#398	C₂²×C₅	1	2	yes	—
320	#398	C₂²×C₅	1	2	yes	—
321	#398	C₂²×C₅	1	2	yes	—
322	#398	C₂²×C₅	1	2	yes	—
323	#398	C₂²×C₅	1	2	yes	—
324	#398	C₂²×C₅	1	2	yes	—
325	#398	C₂²×C₅	1	2	yes	—
326	#397	C₂²×C₅	1	2	yes	—
327	#397	C₂²×C₅	1	2	yes	—
328	#397	C₂²×C₅	1	2	yes	—
329	#396	C₂²×C₅	1	2	yes	—
330	#396	C₂²×C₅	1	2	yes	—
331	#396	C₂²×C₅	1	2	yes	—
332	#395	C₂²×C₅	1	1	yes	characteristic
333	#395	C₂²×C₅	1	2	yes	—
334	#395	C₂²×C₅	1	2	yes	—
335	#395	C₂²×C₅	1	1	yes	characteristic
336	#393	C₂²×C₅	1	1	yes	characteristic
337	#393	C₂²×C₅	1	1	yes	characteristic
338	#391	C₂²×C₅	1	2	yes	—
339	#389	C₂²×C₅	1	2	yes	—
340	#389	C₂²×C₅	1	2	yes	—
341	#389	C₂²×C₅	1	2	yes	—
342	#388	C₂²×C₅	1	2	yes	—
343	#388	C₂²×C₅	1	2	yes	—
344	#388	C₂²×C₅	1	2	yes	—
345	#388	C₂²×C₅	1	2	yes	—
346	#388	C₂²×C₅	1	2	yes	—
347	#387	C₂²×C₅	1	2	yes	—
348	#387	C₂²×C₅	1	2	yes	—
349	#387	C₂²×C₅	1	2	yes	—
350	#387	C₂²×C₅	1	2	yes	—
351	#387	C₂²×C₅	1	2	yes	—
352	#387	C₂²×C₅	1	2	yes	—
353	#387	C₂²×C₅	1	2	yes	—
354	#387	C₂²×C₅	1	2	yes	—
355	#387	C₂²×C₅	1	2	yes	—
356	#387	C₂²×C₅	1	2	yes	—
357	#387	C₂²×C₅	1	2	yes	—
358	#383	C₂²×C₅	1	2	yes	—
359	#382	C₂²×C₅	1	2	yes	—
360	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
361	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
362	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
363	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
364	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
365	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
367	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
376	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
379	#376	C₂²×C₅	1	1	yes	characteristic
380	#376	C₂²×C₅	1	2	yes	—
381	C₄³	C₂²×C₅	1	2	yes	—
382	C₄³	C₂²×C₅	1	1	yes	characteristic
383	C₂³×C₅	—	2	2	no	—
384	C₂³×C₅	—	2	1	no	—
385	C₂³×C₅	—	2	1	no	—
386	C₂³×C₅	—	2	1	no	—
387	C₂³×C₅	—	2	2	no	—
388	C₂³×C₅	C₂⁵	1	1	yes	characteristic
389	C₅×Q₈	—	2	8	no	—
390	C₅×Q₈	—	4	4	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	2	2	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	2	2	no	—
404	C₂×C₄×C₅	—	2	2	no	—
405	C₂×C₄×C₅	—	2	2	no	—
406	C₂×C₄×C₅	—	2	2	no	—
407	C₂×C₄×C₅	—	2	2	no	—
408	C₂×C₄×C₅	—	2	2	no	—
409	C₂×C₄×C₅	—	2	2	no	—
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	2	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	2	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	2	no	—
417	C₂×C₄×C₅	—	2	2	no	—
418	C₂×C₄×C₅	—	2	2	no	—
419	C₂×C₄×C₅	—	2	2	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	2	no	—
423	C₂×C₄×C₅	—	2	2	no	—
424	C₂×C₄×C₅	—	2	2	no	—
425	C₂×C₄×C₅	—	2	2	no	—
426	C₂×C₄×C₅	—	2	2	no	—
427	C₂×C₄×C₅	—	2	2	no	—
428	C₂×C₄×C₅	—	2	2	no	—
429	C₂×C₄×C₅	—	2	2	no	—
430	C₂×C₄×C₅	—	2	2	no	—
431	C₂×C₄×C₅	—	2	2	no	—
432	C₂×C₄×C₅	—	2	2	no	—
433	C₂×C₄×C₅	—	4	4	no	—
434	C₂×C₄×C₅	C₂×#41	1	4	yes	—
435	C₂×C₄×C₅	C₂×#41	1	4	yes	—
436	C₂×C₄×C₅	C₂×#41	1	2	yes	—
437	C₂×C₄×C₅	C₂×#41	1	4	yes	—
438	C₂×C₄×C₅	C₂×#41	1	2	yes	—
439	C₂×C₄×C₅	C₂×#41	1	2	yes	—
440	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
441	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
442	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
445	#126	—	2	8	no	—
446	#125	—	2	8	no	—
447	C₄×Q₈	—	2	4	no	—
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	8	no	—
450	#117	—	2	4	no	—
451	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
485	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₅	1	2	yes	—
487	C₂×C₄²	C₂³×C₅	1	2	yes	—
488	C₂×C₄²	C₂³×C₅	1	2	yes	—
489	C₂×C₄²	C₂³×C₅	1	2	yes	—
490	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₅	1	2	yes	—
493	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₅	1	2	yes	—
496	C₂×C₄²	C₂³×C₅	1	2	yes	—
497	C₂×C₄²	C₂³×C₅	1	2	yes	—
498	C₂×C₄²	C₂³×C₅	1	2	yes	—
499	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₅	1	2	yes	—
501	#95	C₂³×C₅	1	2	yes	—
502	#95	C₂³×C₅	1	2	yes	—
503	#95	C₂³×C₅	1	2	yes	—
504	#95	C₂³×C₅	1	2	yes	—
505	#95	C₂³×C₅	1	2	yes	—
506	#95	C₂³×C₅	1	2	yes	—
507	#95	C₂³×C₅	1	2	yes	—
508	#95	C₂³×C₅	1	2	yes	—
509	#95	C₂³×C₅	1	2	yes	—
510	#95	C₂³×C₅	1	2	yes	—
511	#95	C₂³×C₅	1	2	yes	—
512	#95	C₂³×C₅	1	2	yes	—
513	#95	C₂³×C₅	1	1	yes	characteristic
514	#95	C₂³×C₅	1	1	yes	characteristic
515	#95	C₂³×C₅	1	2	yes	—
516	#95	C₂³×C₅	1	2	yes	—
517	#95	C₂³×C₅	1	2	yes	—
518	#95	C₂³×C₅	1	2	yes	—
519	#95	C₂³×C₅	1	2	yes	—
520	#95	C₂³×C₅	1	2	yes	—
521	#95	C₂³×C₅	1	2	yes	—
522	#95	C₂³×C₅	1	2	yes	—
523	#95	C₂³×C₅	1	2	yes	—
524	#95	C₂³×C₅	1	1	yes	characteristic
525	#95	C₂³×C₅	1	2	yes	—
526	#95	C₂³×C₅	1	1	yes	characteristic
527	#95	C₂³×C₅	1	2	yes	—
528	#95	C₂³×C₅	1	2	yes	—
529	#95	C₂³×C₅	1	2	yes	—
530	#95	C₂³×C₅	1	2	yes	—
531	#95	C₂³×C₅	1	2	yes	—
532	#95	C₂³×C₅	1	2	yes	—
533	#95	C₂³×C₅	1	2	yes	—
534	#95	C₂³×C₅	1	2	yes	—
535	C₂²×C₅	—	4	1	no	—
536	C₂²×C₅	—	4	1	no	—
537	C₂²×C₅	—	4	1	no	—
538	C₂²×C₅	—	4	2	no	—
539	C₂²×C₅	—	4	2	no	—
540	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
541	C₂²×C₅	C₂²×#41	1	2	yes	—
542	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	C₂²×C₅	#585	1	2	yes	—
545	C₄×C₅	—	2	4	no	—
546	C₄×C₅	—	2	2	no	—
547	C₄×C₅	—	2	2	no	—
548	C₄×C₅	—	2	4	no	—
549	C₄×C₅	—	2	4	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	2	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	—	4	2	no	—
555	C₄×C₅	—	4	2	no	—
556	C₄×C₅	—	4	2	no	—
557	C₄×C₅	—	4	2	no	—
558	C₄×C₅	—	4	2	no	—
559	C₄×C₅	—	4	2	no	—
560	C₄×C₅	—	4	2	no	—
561	C₄×C₅	—	4	2	no	—
562	C₄×C₅	#541	1	4	yes	—
563	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	2	no	—
636	C₄²	—	4	2	no	—
637	C₄²	C₅×#41	1	4	yes	—
638	C₄²	C₅×#41	1	8	yes	—
639	C₂×C₅	—	8	1	no	—
640	C₂×C₅	#3444	1	1	yes	characteristic
641	C₂×C₅	C₂×#541	1	1	yes	characteristic
642	C₂×C₅	#3455	1	1	yes	characteristic
643	C₂×C₅	#3461	1	2	yes	—
644	C₂×C₅	#3461	1	2	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	2	no	—
650	C₂³	C₂⁵×C₅	1	1	yes	characteristic
651	Q₈	—	2	8	no	—
652	Q₈	—	4	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	C₂×C₅×#41	1	4	yes	—
697	C₂×C₄	C₂×C₅×#41	1	4	yes	—
698	C₂×C₄	C₂×C₅×#41	1	2	yes	—
699	C₂×C₄	C₂×C₅×#41	1	4	yes	—
700	C₂×C₄	C₂×C₅×#41	1	2	yes	—
701	C₂×C₄	C₂×C₅×#41	1	2	yes	—
702	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
703	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
704	C₅	#34604	1	1	yes	characteristic, direct product factor, Sylow
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
711	C₂²	C₂²×C₅×#41	1	2	yes	—
712	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
713	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
714	C₂²	C₅×#585	1	2	yes	—
715	C₄	—	2	4	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	C₅×#541	1	4	yes	—
733	C₂	—	8	1	no	—
734	C₂	C₅×#3444	1	1	yes	characteristic
735	C₂	C₂×C₅×#541	1	1	yes	characteristic
736	C₂	C₅×#3455	1	1	yes	characteristic
737	C₂	C₅×#3461	1	2	yes	—
738	C₂	C₅×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂⁴×C₅	C₂⁴
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×#2666	C₂	semidirect
3. C₅×#2655	C₂	semidirect
4. C₅×#2655	C₂	semidirect
8. C₅×#2634	C₂	semidirect
9. C₅×#2402	C₂	semidirect
10. C₅×#2402	C₂	semidirect
12. C₅×#2399	C₂	semidirect
15. C₄×C₅×#125	C₂	semidirect
18. C₅×#2295	C₂	semidirect
19. C₄²×C₅×Q₈	C₂	semidirect
107. #34604	C₅	direct (N × H)
201. #2666	C₂×C₅	semidirect
203. #2655	C₂×C₅	semidirect
204. #2655	C₂×C₅	semidirect
208. #2634	C₂×C₅	semidirect
209. #2402	C₂×C₅	semidirect
210. #2402	C₂×C₅	semidirect
212. #2399	C₂×C₅	semidirect
215. C₄×#125	C₂×C₅	semidirect
218. #2295	C₂×C₅	semidirect
219. C₄²×Q₈	C₂×C₅	semidirect
704. C₅	#34604	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×#2666	2
C₅×#2664	2
C₅×#2655	2
C₅×#2654	2
C₅×#2650	2
C₅×#2637	2
C₅×#2634	2
C₅×#2402	2
C₅×#2401	2
C₅×#2399	2
C₅×#2396	2
C₄×C₅×#125	2
C₄×C₅×#126	2
C₅×#2298	2
C₅×#2295	2
C₄²×C₅×Q₈	2
#34604	5

Subgroups — C5×#34604 #11957324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34604 #11957324