Subgroups — C₅×#34631 #11957351

Order 1280.

2138 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic
3	C₅×#2664	C₂	1	4	yes	maximal, complemented
4	C₅×#2663	C₂	1	4	yes	maximal, complemented
5	C₅×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2658	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2621	C₂	1	2	yes	maximal, complemented
10	C₅×#2620	C₂	1	2	yes	maximal
11	C₅×#2396	C₂	1	4	yes	maximal, complemented
12	C₅×#2395	C₂	1	4	yes	maximal, complemented
13	C₄×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×#124	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#533	—	2	8	no	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₅×#529	—	2	8	no	—
21	C₂×C₅×#126	C₂²	1	2	yes	—
22	C₂×C₅×#125	C₂²	1	1	yes	characteristic
23	C₂×C₅×#125	C₂²	1	2	yes	—
24	C₂×C₅×#124	C₂²	1	1	yes	characteristic
25	C₂×C₅×#124	C₂²	1	2	yes	—
26	C₂×C₅×#123	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊Q₈	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×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
33	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
36	C₂×C₅×#117	C₂²	1	2	yes	—
37	C₂×C₅×#117	C₂²	1	2	yes	—
38	C₂×C₅×#117	C₂²	1	2	yes	—
39	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
40	C₅×#400	C₂²	1	4	yes	—
41	C₅×#400	C₂²	1	4	yes	—
42	C₅×#399	C₂²	1	4	yes	—
43	C₅×#399	C₂²	1	4	yes	—
44	C₅×#398	C₂²	1	8	yes	—
45	C₅×#398	C₂²	1	4	yes	—
46	C₅×#397	C₂²	1	8	yes	—
47	C₅×#397	C₂²	1	4	yes	—
48	C₅×#396	C₂²	1	8	yes	—
49	C₅×#395	C₂²	1	4	yes	—
50	C₅×#394	C₂²	1	8	yes	—
51	C₅×#393	C₂²	1	4	yes	—
52	C₅×#391	C₂²	1	2	yes	—
53	C₅×#391	C₂²	1	2	yes	—
54	C₅×#391	C₂²	1	2	yes	—
55	C₅×#390	C₂²	1	2	yes	—
56	C₅×#389	C₂²	1	8	yes	—
57	C₅×#388	C₂²	1	8	yes	—
58	C₅×#384	C₂²	1	2	yes	—
59	C₅×#382	C₂²	1	2	yes	—
60	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₅×C₄⋊C₄	C₂²	1	8	yes	—
63	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
66	C₅×#376	C₂²	1	1	yes	characteristic
67	C₅×#376	C₂²	1	1	yes	characteristic
68	C₄³×C₅	C₂²	1	2	yes	—
69	#34631	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×Q₈	C₂³	1	2	yes	—
72	C₂²×C₅×Q₈	C₂³	1	2	yes	—
73	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₂²×C₅×D₄	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	2	yes	—
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	—	2	4	no	—
80	C₅×C₄⋊Q₈	—	2	4	no	—
81	C₅×C₄⋊Q₈	—	2	8	no	—
82	C₅×#126	—	2	8	no	—
83	C₅×#125	—	2	4	no	—
84	C₅×#125	—	2	8	no	—
85	C₅×#124	—	2	4	no	—
86	C₅×#124	—	2	8	no	—
87	C₅×#123	—	2	8	no	—
88	C₅×C₂²⋊Q₈	—	2	4	no	—
89	C₅×C₂²⋊Q₈	—	2	8	no	—
90	C₅×C₂²⋊Q₈	—	2	8	no	—
91	C₅×#121	—	2	4	no	—
92	C₄×C₅×Q₈	—	2	4	no	—
93	C₄×C₅×Q₈	—	2	8	no	—
94	C₄×C₅×Q₈	—	2	8	no	—
95	C₄×C₅×D₄	—	2	8	no	—
96	C₄×C₅×D₄	—	2	4	no	—
97	C₅×#117	—	2	8	no	—
98	C₅×#117	—	2	8	no	—
99	C₅×#117	—	2	8	no	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	4	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	2	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	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
124	C₂×C₄²×C₅	D₄	1	8	yes	—
125	C₂×C₄²×C₅	C₂³	1	2	yes	—
126	C₂×C₄²×C₅	C₂³	1	4	yes	—
127	C₂×C₄²×C₅	C₂³	1	4	yes	—
128	C₂×C₄²×C₅	C₂³	1	2	yes	—
129	C₂×C₄²×C₅	C₂³	1	4	yes	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	2	yes	—
135	C₅×#95	C₂³	1	2	yes	—
136	C₅×#95	C₂³	1	2	yes	—
137	C₅×#95	C₂³	1	2	yes	—
138	C₅×#95	C₂³	1	2	yes	—
139	C₅×#95	C₂³	1	8	yes	—
140	C₅×#95	C₂³	1	8	yes	—
141	C₅×#95	C₂³	1	8	yes	—
142	C₅×#95	C₂³	1	8	yes	—
143	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂×#529	C₂×C₅	1	1	yes	characteristic
145	#2664	C₂×C₅	1	4	yes	complemented
146	#2663	C₂×C₅	1	4	yes	complemented
147	#2660	C₂×C₅	1	1	yes	characteristic, complemented
148	#2658	C₂×C₅	1	1	yes	characteristic, complemented
149	#2642	C₂×C₅	1	1	yes	characteristic, complemented
150	#2640	C₂×C₅	1	1	yes	characteristic, complemented
151	#2621	C₂×C₅	1	2	yes	complemented
152	#2620	C₂×C₅	1	2	yes	—
153	#2396	C₂×C₅	1	4	yes	complemented
154	#2395	C₂×C₅	1	4	yes	complemented
155	C₄×C₄⋊Q₈	C₂×C₅	1	2	yes	complemented
156	C₄×#124	C₂×C₅	1	2	yes	complemented
157	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂⁴×C₅	C₂⁴	1	2	yes	—
159	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	2	4	no	—
162	C₂×C₅×Q₈	—	2	4	no	—
163	C₂×C₅×Q₈	—	2	4	no	—
164	C₂×C₅×Q₈	—	2	4	no	—
165	C₂×C₅×Q₈	—	2	4	no	—
166	C₂×C₅×Q₈	—	4	4	no	—
167	C₂×C₅×D₄	—	2	4	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	4	no	—
170	C₂×C₅×D₄	—	4	4	no	—
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	2	4	no	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	2	8	no	—
175	C₂²×C₄×C₅	—	4	2	no	—
176	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₅×C₄⋊C₄	—	2	4	no	—
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	2	4	no	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	4	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	8	no	—
200	C₅×C₄⋊C₄	—	2	8	no	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₄⋊C₄	—	2	4	no	—
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₅×C₄⋊C₄	—	2	8	no	—
205	C₅×C₄⋊C₄	—	2	16	no	—
206	C₅×C₄⋊C₄	—	4	8	no	—
207	C₅×C₂²⋊C₄	—	2	8	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	8	no	—
214	C₅×C₂²⋊C₄	—	2	16	no	—
215	C₅×C₂²⋊C₄	—	4	8	no	—
216	C₄²×C₅	—	2	4	no	—
217	C₄²×C₅	—	2	8	no	—
218	C₄²×C₅	—	2	4	no	—
219	C₄²×C₅	—	2	8	no	—
220	C₄²×C₅	—	4	4	no	—
221	C₄²×C₅	C₂×D₄	1	4	yes	—
222	C₄²×C₅	C₂×D₄	1	4	yes	—
223	C₄²×C₅	C₂×D₄	1	4	yes	—
224	C₄²×C₅	C₂×D₄	1	4	yes	—
225	C₄²×C₅	#41	1	8	yes	—
226	#533	—	2	8	no	—
227	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
230	#529	—	2	8	no	—
231	C₂×#126	C₂²×C₅	1	2	yes	—
232	C₂×#125	C₂²×C₅	1	1	yes	characteristic
233	C₂×#125	C₂²×C₅	1	2	yes	—
234	C₂×#124	C₂²×C₅	1	2	yes	—
235	C₂×#124	C₂²×C₅	1	1	yes	characteristic
236	C₂×#123	C₂²×C₅	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
238	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
240	C₂×#121	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×#117	C₂²×C₅	1	2	yes	—
247	C₂×#117	C₂²×C₅	1	2	yes	—
248	C₂×#117	C₂²×C₅	1	2	yes	—
249	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
250	#400	C₂²×C₅	1	4	yes	—
251	#400	C₂²×C₅	1	4	yes	—
252	#399	C₂²×C₅	1	4	yes	—
253	#399	C₂²×C₅	1	4	yes	—
254	#398	C₂²×C₅	1	8	yes	—
255	#398	C₂²×C₅	1	4	yes	—
256	#397	C₂²×C₅	1	8	yes	—
257	#397	C₂²×C₅	1	4	yes	—
258	#396	C₂²×C₅	1	8	yes	—
259	#395	C₂²×C₅	1	4	yes	—
260	#394	C₂²×C₅	1	8	yes	—
261	#393	C₂²×C₅	1	4	yes	—
262	#391	C₂²×C₅	1	2	yes	—
263	#391	C₂²×C₅	1	2	yes	—
264	#391	C₂²×C₅	1	2	yes	—
265	#390	C₂²×C₅	1	2	yes	—
266	#389	C₂²×C₅	1	8	yes	—
267	#388	C₂²×C₅	1	8	yes	—
268	#384	C₂²×C₅	1	2	yes	—
269	#382	C₂²×C₅	1	2	yes	—
270	C₄×C₄⋊C₄	C₂²×C₅	1	8	yes	—
271	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
272	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
273	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
276	#376	C₂²×C₅	1	1	yes	characteristic
277	#376	C₂²×C₅	1	1	yes	characteristic
278	C₄³	C₂²×C₅	1	2	yes	—
279	C₂³×C₅	—	2	2	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	2	2	no	—
283	C₂³×C₅	—	2	4	no	—
284	C₂³×C₅	—	2	4	no	—
285	C₂³×C₅	—	2	4	no	—
286	C₂³×C₅	C₂²×D₄	1	2	yes	—
287	C₂³×C₅	C₂⁵	1	1	yes	characteristic
288	C₅×Q₈	—	4	8	no	—
289	C₅×Q₈	—	4	4	no	—
290	C₅×Q₈	—	4	8	no	—
291	C₅×D₄	—	4	8	no	—
292	C₅×D₄	—	4	4	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	4	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	8	no	—
300	C₂×C₄×C₅	—	2	8	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	4	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	4	no	—
309	C₂×C₄×C₅	—	2	4	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	—	2	4	no	—
312	C₂×C₄×C₅	—	2	4	no	—
313	C₂×C₄×C₅	—	2	8	no	—
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	—	4	4	no	—
316	C₂×C₄×C₅	—	4	8	no	—
317	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₅	C₂×#41	1	8	yes	—
324	C₂×C₄×C₅	C₂×#41	1	4	yes	—
325	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
326	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₅	1	2	yes	—
328	C₂²×Q₈	C₂³×C₅	1	2	yes	—
329	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₅	1	2	yes	—
331	C₂³×C₄	C₂³×C₅	1	2	yes	—
332	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₄⋊Q₈	—	2	4	no	—
336	C₄⋊Q₈	—	2	4	no	—
337	C₄⋊Q₈	—	2	8	no	—
338	#126	—	2	8	no	—
339	#125	—	2	4	no	—
340	#125	—	2	8	no	—
341	#124	—	2	4	no	—
342	#124	—	2	8	no	—
343	#123	—	2	8	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	#121	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	—	2	8	no	—
350	C₄×Q₈	—	2	8	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	#117	—	2	8	no	—
354	#117	—	2	8	no	—
355	#117	—	2	8	no	—
356	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
370	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
380	C₂×C₄²	C₅×D₄	1	8	yes	—
381	C₂×C₄²	C₂³×C₅	1	2	yes	—
382	C₂×C₄²	C₂³×C₅	1	4	yes	—
383	C₂×C₄²	C₂³×C₅	1	2	yes	—
384	C₂×C₄²	C₂³×C₅	1	4	yes	—
385	C₂×C₄²	C₂³×C₅	1	4	yes	—
386	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	2	yes	—
391	#95	C₂³×C₅	1	2	yes	—
392	#95	C₂³×C₅	1	2	yes	—
393	#95	C₂³×C₅	1	2	yes	—
394	#95	C₂³×C₅	1	2	yes	—
395	#95	C₂³×C₅	1	8	yes	—
396	#95	C₂³×C₅	1	8	yes	—
397	#95	C₂³×C₅	1	8	yes	—
398	#95	C₂³×C₅	1	8	yes	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	4	4	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	—	4	8	no	—
407	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
408	C₂²×C₅	C₂²×#41	1	2	yes	—
409	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
410	C₂²×C₅	#585	1	2	yes	—
411	C₄×C₅	—	2	2	no	—
412	C₄×C₅	—	2	2	no	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	2	8	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	—	4	4	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	—	4	2	no	—
420	C₄×C₅	—	4	4	no	—
421	C₄×C₅	—	4	4	no	—
422	C₄×C₅	#532	1	4	yes	—
423	C₄×C₅	#536	1	4	yes	—
424	C₂⁴	C₂⁴×C₅	1	2	yes	—
425	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
443	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
444	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
446	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	16	no	—
472	C₄⋊C₄	—	4	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	16	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	8	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	8	no	—
486	C₄²	—	4	4	no	—
487	C₄²	C₂×C₅×D₄	1	4	yes	—
488	C₄²	C₂×C₅×D₄	1	4	yes	—
489	C₄²	C₂×C₅×D₄	1	4	yes	—
490	C₄²	C₂×C₅×D₄	1	4	yes	—
491	C₄²	C₅×#41	1	8	yes	—
492	C₂×C₅	—	4	2	no	—
493	C₂×C₅	—	8	2	no	—
494	C₂×C₅	C₂×#532	1	1	yes	characteristic
495	C₂×C₅	C₂×#536	1	1	yes	characteristic
496	C₂×C₅	#3449	1	1	yes	characteristic
497	C₂×C₅	#3461	1	4	yes	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	C₂²×C₅×D₄	1	2	yes	—
506	C₂³	C₂⁵×C₅	1	1	yes	characteristic
507	Q₈	—	4	8	no	—
508	Q₈	—	4	4	no	—
509	Q₈	—	4	8	no	—
510	D₄	—	4	8	no	—
511	D₄	—	4	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
537	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
538	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
539	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
540	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
541	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
542	C₂×C₄	C₂×C₅×#41	1	8	yes	—
543	C₂×C₄	C₂×C₅×#41	1	4	yes	—
544	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
545	C₅	#34631	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	8	no	—
554	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
555	C₂²	C₂²×C₅×#41	1	2	yes	—
556	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
557	C₂²	C₅×#585	1	2	yes	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	8	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	C₅×#532	1	4	yes	—
570	C₄	C₅×#536	1	4	yes	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	C₂×C₅×#532	1	1	yes	characteristic
574	C₂	C₂×C₅×#536	1	1	yes	characteristic
575	C₂	C₅×#3449	1	1	yes	characteristic
576	C₂	C₅×#3461	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂×C₅×#121	C₂²
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. C₂×C₅×#533	C₂	semidirect
3. C₅×#2664	C₂	semidirect
4. C₅×#2663	C₂	semidirect
5. C₅×#2660	C₂	semidirect
6. C₅×#2658	C₂	semidirect
7. C₅×#2642	C₂	semidirect
8. C₅×#2640	C₂	semidirect
9. C₅×#2621	C₂	semidirect
11. C₅×#2396	C₂	semidirect
12. C₅×#2395	C₂	semidirect
13. C₄×C₅×C₄⋊Q₈	C₂	semidirect
14. C₄×C₅×#124	C₂	semidirect
15. C₄×C₅×#117	C₂	semidirect
69. #34631	C₅	direct (N × H)
143. C₂×#533	C₂×C₅	semidirect
145. #2664	C₂×C₅	semidirect
146. #2663	C₂×C₅	semidirect
147. #2660	C₂×C₅	semidirect
148. #2658	C₂×C₅	semidirect
149. #2642	C₂×C₅	semidirect
150. #2640	C₂×C₅	semidirect
151. #2621	C₂×C₅	semidirect
153. #2396	C₂×C₅	semidirect
154. #2395	C₂×C₅	semidirect
155. C₄×C₄⋊Q₈	C₂×C₅	semidirect
156. C₄×#124	C₂×C₅	semidirect
157. C₄×#117	C₂×C₅	semidirect
545. C₅	#34631	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×#533	2
C₂×C₅×#529	2
C₅×#2664	2
C₅×#2663	2
C₅×#2660	2
C₅×#2658	2
C₅×#2642	2
C₅×#2640	2
C₅×#2621	2
C₅×#2620	2
C₅×#2396	2
C₅×#2395	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#124	2
C₄×C₅×#117	2
#34631	5

Subgroups — C5×#34631 #11957351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34631 #11957351