Subgroups — C₅×#34946 #11957666

Order 1280.

2834 conjugacy classes of subgroups.

The subgroup lattice has 500 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	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#2563	C₂	1	2	yes	maximal, complemented
4	C₅×#2562	C₂	1	4	yes	maximal, complemented
5	C₅×#2561	C₂	1	4	yes	maximal, complemented
6	C₅×#2547	C₂	1	2	yes	maximal, complemented
7	C₅×#2503	C₂	1	2	yes	maximal, complemented
8	C₅×#2435	C₂	1	2	yes	maximal
9	C₅×#2398	C₂	1	4	yes	maximal, complemented
10	C₄×C₅×#124	C₂	1	4	yes	maximal, complemented
11	C₅×#2280	C₂	1	4	yes	maximal, complemented
12	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
15	C₅×#533	—	2	8	no	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×#125	C₂²	1	2	yes	complemented
19	C₂×C₅×#124	C₂²	1	4	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
24	C₂×C₄×C₅×D₄	—	2	8	no	—
25	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₅×#117	C₂²	1	2	yes	—
30	C₂×C₅×#117	C₂²	1	2	yes	—
31	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₅×#400	C₂²	1	8	yes	complemented
35	C₅×#397	C₂²	1	8	yes	complemented
36	C₅×#394	C₂²	1	8	yes	—
37	C₅×#393	C₂²	1	8	yes	complemented
38	C₅×#391	C₂²	1	4	yes	complemented
39	C₅×#390	C₂²	1	4	yes	—
40	C₅×#388	C₂²	1	16	yes	complemented
41	C₅×#382	C₂²	1	4	yes	complemented
42	C₅×#381	C₂²	1	8	yes	—
43	C₅×#380	C₂²	1	8	yes	complemented
44	C₅×#380	C₂²	1	8	yes	complemented
45	C₅×#379	C₂²	1	8	yes	—
46	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
48	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₄×C₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
51	C₅×#376	C₂²	1	2	yes	complemented
52	C₄³×C₅	C₂²	1	2	yes	complemented
53	#34946	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁵×C₅	C₂³	1	2	yes	—
55	C₂²×C₅×Q₈	C₂³	1	2	yes	—
56	C₂²×C₅×Q₈	C₂³	1	2	yes	—
57	C₂²×C₅×D₄	—	2	8	no	—
58	C₂²×C₅×D₄	—	2	4	no	—
59	C₂²×C₅×D₄	C₂³	1	2	yes	—
60	C₂²×C₅×D₄	C₂³	1	2	yes	—
61	C₂³×C₄×C₅	—	2	8	no	—
62	C₂³×C₄×C₅	—	2	16	no	—
63	C₂³×C₄×C₅	C₂³	1	4	yes	—
64	C₂³×C₄×C₅	C₂³	1	2	yes	—
65	C₂³×C₄×C₅	C₂³	1	4	yes	—
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₅×C₄⋊Q₈	—	2	4	no	—
70	C₅×C₄⋊Q₈	—	2	4	no	—
71	C₅×#125	—	2	8	no	—
72	C₅×#124	—	2	16	no	—
73	C₅×C₂²⋊Q₈	—	2	8	no	—
74	C₅×C₂²⋊Q₈	—	2	8	no	—
75	C₄×C₅×Q₈	—	2	8	no	—
76	C₄×C₅×Q₈	—	2	8	no	—
77	C₄×C₅×D₄	—	2	8	no	—
78	C₄×C₅×D₄	—	2	8	no	—
79	C₄×C₅×D₄	—	2	8	no	—
80	C₄×C₅×D₄	—	2	8	no	—
81	C₅×#117	—	2	8	no	—
82	C₅×#117	—	2	8	no	—
83	C₂×C₅×C₄⋊C₄	—	2	4	no	—
84	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
100	C₂×C₄²×C₅	D₄	1	8	yes	—
101	C₂×C₄²×C₅	C₂³	1	4	yes	—
102	C₂×C₄²×C₅	C₂³	1	4	yes	—
103	C₂×C₄²×C₅	C₂³	1	4	yes	—
104	C₂×C₄²×C₅	C₂³	1	4	yes	—
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#95	C₂³	1	4	yes	—
110	C₅×#95	C₂³	1	4	yes	—
111	C₅×#95	C₂³	1	16	yes	—
112	C₅×#95	C₂³	1	16	yes	—
113	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic
115	#2563	C₂×C₅	1	2	yes	complemented
116	#2562	C₂×C₅	1	4	yes	complemented
117	#2561	C₂×C₅	1	4	yes	complemented
118	#2547	C₂×C₅	1	2	yes	complemented
119	#2503	C₂×C₅	1	2	yes	complemented
120	#2435	C₂×C₅	1	2	yes	—
121	#2398	C₂×C₅	1	4	yes	complemented
122	C₄×#124	C₂×C₅	1	4	yes	complemented
123	#2280	C₂×C₅	1	4	yes	complemented
124	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂⁴×C₅	—	2	4	no	—
126	C₂⁴×C₅	—	2	8	no	—
127	C₂⁴×C₅	—	2	8	no	—
128	C₂⁴×C₅	—	4	4	no	—
129	C₂⁴×C₅	C₂⁴	1	4	yes	—
130	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂×C₅×Q₈	—	2	4	no	—
133	C₂×C₅×Q₈	—	2	8	no	—
134	C₂×C₅×Q₈	—	4	4	no	—
135	C₂×C₅×D₄	—	2	32	no	—
136	C₂×C₅×D₄	—	2	8	no	—
137	C₂×C₅×D₄	—	2	4	no	—
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	#41	1	8	yes	—
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	—	2	8	no	—
144	C₂²×C₄×C₅	—	2	8	no	—
145	C₂²×C₄×C₅	—	2	8	no	—
146	C₂²×C₄×C₅	—	2	16	no	—
147	C₂²×C₄×C₅	—	2	16	no	—
148	C₂²×C₄×C₅	—	4	2	no	—
149	C₂²×C₄×C₅	—	4	32	no	—
150	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₅	#41	1	8	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	8	no	—
169	C₅×C₄⋊C₄	—	2	8	no	—
170	C₅×C₄⋊C₄	—	2	4	no	—
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	—	2	8	no	—
173	C₅×C₂²⋊C₄	—	2	8	no	—
174	C₅×C₂²⋊C₄	—	2	8	no	—
175	C₅×C₂²⋊C₄	—	2	32	no	—
176	C₅×C₂²⋊C₄	—	2	8	no	—
177	C₅×C₂²⋊C₄	—	2	8	no	—
178	C₅×C₂²⋊C₄	—	4	16	no	—
179	C₄²×C₅	—	2	8	no	—
180	C₄²×C₅	—	2	8	no	—
181	C₄²×C₅	—	2	8	no	—
182	C₄²×C₅	—	4	4	no	—
183	C₄²×C₅	C₂×D₄	1	4	yes	—
184	C₄²×C₅	C₂×D₄	1	4	yes	—
185	C₄²×C₅	C₂×D₄	1	4	yes	—
186	C₄²×C₅	C₂×D₄	1	4	yes	—
187	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
189	#533	—	2	8	no	—
190	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₂×#125	C₂²×C₅	1	2	yes	complemented
193	C₂×#124	C₂²×C₅	1	4	yes	—
194	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
195	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
197	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
198	C₂×C₄×D₄	—	2	8	no	—
199	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
200	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
201	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
202	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
203	C₂×#117	C₂²×C₅	1	2	yes	—
204	C₂×#117	C₂²×C₅	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
207	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
208	#400	C₂²×C₅	1	8	yes	complemented
209	#397	C₂²×C₅	1	8	yes	complemented
210	#394	C₂²×C₅	1	8	yes	—
211	#393	C₂²×C₅	1	8	yes	complemented
212	#391	C₂²×C₅	1	4	yes	complemented
213	#390	C₂²×C₅	1	4	yes	—
214	#388	C₂²×C₅	1	16	yes	complemented
215	#382	C₂²×C₅	1	4	yes	complemented
216	#381	C₂²×C₅	1	8	yes	—
217	#380	C₂²×C₅	1	8	yes	complemented
218	#380	C₂²×C₅	1	8	yes	complemented
219	#379	C₂²×C₅	1	8	yes	—
220	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
221	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
222	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
223	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
224	C₄×C₂²⋊C₄	C₂²×C₅	1	16	yes	complemented
225	#376	C₂²×C₅	1	2	yes	complemented
226	C₄³	C₂²×C₅	1	2	yes	complemented
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	16	no	—
230	C₂³×C₅	—	2	4	no	—
231	C₂³×C₅	—	2	8	no	—
232	C₂³×C₅	—	2	4	no	—
233	C₂³×C₅	—	2	8	no	—
234	C₂³×C₅	—	4	32	no	—
235	C₂³×C₅	—	4	8	no	—
236	C₂³×C₅	—	4	8	no	—
237	C₂³×C₅	C₂²×D₄	1	2	yes	—
238	C₂³×C₅	C₂×#41	1	8	yes	—
239	C₂³×C₅	C₂×#41	1	4	yes	—
240	C₂³×C₅	C₂⁵	1	1	yes	characteristic
241	C₅×Q₈	—	4	8	no	—
242	C₅×Q₈	—	4	8	no	—
243	C₅×D₄	—	2	16	no	—
244	C₅×D₄	—	2	16	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	8	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	8	no	—
253	C₂×C₄×C₅	—	2	8	no	—
254	C₂×C₄×C₅	—	2	8	no	—
255	C₂×C₄×C₅	—	2	8	no	—
256	C₂×C₄×C₅	—	2	8	no	—
257	C₂×C₄×C₅	—	2	8	no	—
258	C₂×C₄×C₅	—	4	4	no	—
259	C₂×C₄×C₅	—	4	8	no	—
260	C₂×C₄×C₅	—	4	16	no	—
261	C₂×C₄×C₅	—	4	16	no	—
262	C₂×C₄×C₅	#124	1	16	yes	complemented
263	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₅	C₂×#41	1	4	yes	—
270	C₂×C₄×C₅	C₂×#41	1	4	yes	—
271	C₂×C₄×C₅	C₂×#41	1	4	yes	—
272	C₂⁵	C₂³×C₅	1	2	yes	—
273	C₂²×Q₈	C₂³×C₅	1	2	yes	—
274	C₂²×Q₈	C₂³×C₅	1	2	yes	—
275	C₂²×D₄	—	2	8	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	C₂³×C₅	1	2	yes	—
278	C₂²×D₄	C₂³×C₅	1	2	yes	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	2	16	no	—
281	C₂³×C₄	C₂³×C₅	1	2	yes	—
282	C₂³×C₄	C₂³×C₅	1	4	yes	—
283	C₂³×C₄	C₂³×C₅	1	4	yes	—
284	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	4	no	—
288	C₄⋊Q₈	—	2	4	no	—
289	#125	—	2	8	no	—
290	#124	—	2	16	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₄×Q₈	—	2	8	no	—
294	C₄×Q₈	—	2	8	no	—
295	C₄×D₄	—	2	8	no	—
296	C₄×D₄	—	2	8	no	—
297	C₄×D₄	—	2	8	no	—
298	C₄×D₄	—	2	8	no	—
299	#117	—	2	8	no	—
300	#117	—	2	8	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	8	no	—
312	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
318	C₂×C₄²	C₅×D₄	1	8	yes	—
319	C₂×C₄²	C₂³×C₅	1	4	yes	—
320	C₂×C₄²	C₂³×C₅	1	4	yes	—
321	C₂×C₄²	C₂³×C₅	1	4	yes	—
322	C₂×C₄²	C₂³×C₅	1	4	yes	—
323	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
327	#95	C₂³×C₅	1	4	yes	—
328	#95	C₂³×C₅	1	4	yes	—
329	#95	C₂³×C₅	1	16	yes	—
330	#95	C₂³×C₅	1	16	yes	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	—	2	8	no	—
334	C₂²×C₅	—	2	8	no	—
335	C₂²×C₅	—	2	16	no	—
336	C₂²×C₅	—	4	32	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	—	4	4	no	—
339	C₂²×C₅	—	4	8	no	—
340	C₂²×C₅	C₂×#124	1	4	yes	—
341	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
342	C₂²×C₅	C₂²×#41	1	2	yes	—
343	C₂²×C₅	C₂²×#41	1	2	yes	—
344	C₂²×C₅	#585	1	2	yes	—
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	4	4	no	—
349	C₄×C₅	—	4	4	no	—
350	C₄×C₅	—	4	4	no	—
351	C₄×C₅	—	4	8	no	—
352	C₄×C₅	#525	1	4	yes	—
353	C₄×C₅	C₂×#124	1	4	yes	—
354	C₄×C₅	C₂×#124	1	4	yes	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	8	no	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	C₂⁴×C₅	1	4	yes	—
360	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	8	no	—
364	C₂×Q₈	—	4	4	no	—
365	C₂×D₄	—	2	32	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	C₅×#41	1	8	yes	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	16	no	—
377	C₂²×C₄	—	2	16	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	32	no	—
380	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
381	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
382	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
383	C₂²×C₄	C₅×#41	1	8	yes	—
384	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
386	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	32	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	4	16	no	—
409	C₄²	—	2	8	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	2	8	no	—
412	C₄²	—	4	4	no	—
413	C₄²	C₂×C₅×D₄	1	4	yes	—
414	C₄²	C₂×C₅×D₄	1	4	yes	—
415	C₄²	C₂×C₅×D₄	1	4	yes	—
416	C₄²	C₂×C₅×D₄	1	4	yes	—
417	C₂×C₅	—	2	4	no	—
418	C₂×C₅	—	4	8	no	—
419	C₂×C₅	C₂×#525	1	1	yes	characteristic
420	C₂×C₅	C₂²×#124	1	1	yes	characteristic
421	C₂×C₅	#3449	1	1	yes	characteristic
422	C₂×C₅	#3475	1	4	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	16	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	4	32	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	C₂²×C₅×D₄	1	2	yes	—
434	C₂³	C₂×C₅×#41	1	8	yes	—
435	C₂³	C₂×C₅×#41	1	4	yes	—
436	C₂³	C₂⁵×C₅	1	1	yes	characteristic
437	Q₈	—	4	8	no	—
438	Q₈	—	4	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	16	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	16	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	C₅×#124	1	16	yes	complemented
459	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
460	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
461	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
462	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
463	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
465	C₂×C₄	C₂×C₅×#41	1	4	yes	—
466	C₂×C₄	C₂×C₅×#41	1	4	yes	—
467	C₂×C₄	C₂×C₅×#41	1	4	yes	—
468	C₅	#34946	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	16	no	—
474	C₂²	—	4	32	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	C₂×C₅×#124	1	4	yes	—
479	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
480	C₂²	C₂²×C₅×#41	1	2	yes	—
481	C₂²	C₂²×C₅×#41	1	2	yes	—
482	C₂²	C₅×#585	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	8	no	—
490	C₄	C₅×#525	1	4	yes	—
491	C₄	C₂×C₅×#124	1	4	yes	—
492	C₄	C₂×C₅×#124	1	4	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	4	8	no	—
495	C₂	C₂×C₅×#525	1	1	yes	characteristic
496	C₂	C₂²×C₅×#124	1	1	yes	characteristic
497	C₂	C₅×#3449	1	1	yes	characteristic
498	C₂	C₅×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂³×C₅×D₄	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×#2563	C₂	semidirect
4. C₅×#2562	C₂	semidirect
5. C₅×#2561	C₂	semidirect
6. C₅×#2547	C₂	semidirect
7. C₅×#2503	C₂	semidirect
9. C₅×#2398	C₂	semidirect
10. C₄×C₅×#124	C₂	semidirect
11. C₅×#2280	C₂	semidirect
12. C₄×C₅×#117	C₂	semidirect
16. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₅×#125	C₂²	semidirect
22. C₂×C₄×C₅×Q₈	C₂²	semidirect
23. C₂×C₄×C₅×Q₈	C₂²	semidirect
34. C₅×#400	C₂²	semidirect
35. C₅×#397	C₂²	semidirect
37. C₅×#393	C₂²	semidirect
38. C₅×#391	C₂²	semidirect
40. C₅×#388	C₂²	semidirect
41. C₅×#382	C₂²	semidirect
43. C₅×#380	C₂²	semidirect
44. C₅×#380	C₂²	semidirect
46. C₄×C₅×C₄⋊C₄	C₂²	semidirect
47. C₄×C₅×C₄⋊C₄	C₂²	semidirect
50. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
51. C₅×#376	C₂²	semidirect
52. C₄³×C₅	C₂²	semidirect
53. #34946	C₅	direct (N × H)
113. C₂×#533	C₂×C₅	semidirect
115. #2563	C₂×C₅	semidirect
116. #2562	C₂×C₅	semidirect
117. #2561	C₂×C₅	semidirect
118. #2547	C₂×C₅	semidirect
119. #2503	C₂×C₅	semidirect
121. #2398	C₂×C₅	semidirect
122. C₄×#124	C₂×C₅	semidirect
123. #2280	C₂×C₅	semidirect
124. C₄×#117	C₂×C₅	semidirect
190. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
191. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
192. C₂×#125	C₂²×C₅	semidirect
196. C₂×C₄×Q₈	C₂²×C₅	semidirect
197. C₂×C₄×Q₈	C₂²×C₅	semidirect
208. #400	C₂²×C₅	semidirect
209. #397	C₂²×C₅	semidirect
211. #393	C₂²×C₅	semidirect
212. #391	C₂²×C₅	semidirect
214. #388	C₂²×C₅	semidirect
215. #382	C₂²×C₅	semidirect
217. #380	C₂²×C₅	semidirect
218. #380	C₂²×C₅	semidirect
220. C₄×C₄⋊C₄	C₂²×C₅	semidirect
221. C₄×C₄⋊C₄	C₂²×C₅	semidirect
224. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
225. #376	C₂²×C₅	semidirect
226. C₄³	C₂²×C₅	semidirect
262. C₂×C₄×C₅	#124	semidirect
458. C₂×C₄	C₅×#124	semidirect
468. C₅	#34946	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
C₂²×C₄×C₅×D₄	2
C₅×#2563	2
C₅×#2562	2
C₅×#2561	2
C₅×#2547	2
C₅×#2503	2
C₅×#2435	2
C₅×#2398	2
C₄×C₅×#124	2
C₅×#2280	2
C₄×C₅×#117	2
#34946	5

Subgroups — C5×#34946 #11957666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34946 #11957666