Subgroups — C₅×#34953 #11957673

Order 1280.

2402 conjugacy classes of subgroups.

The subgroup lattice has 462 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
2	C₂²×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2584	C₂	1	4	yes	maximal, complemented
4	C₅×#2583	C₂	1	4	yes	maximal
5	C₅×#2567	C₂	1	2	yes	maximal, complemented
6	C₅×#2546	C₂	1	2	yes	maximal, complemented
7	C₅×#2502	C₂	1	2	yes	maximal
8	C₅×#2434	C₂	1	2	yes	maximal
9	C₅×#2399	C₂	1	4	yes	maximal, complemented
10	C₄×C₅×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
11	C₅×#2296	C₂	1	4	yes	maximal
12	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#533	—	2	8	no	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#125	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Q₈	—	2	8	no	—
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
28	C₂×C₅×#117	C₂²	1	2	yes	—
29	C₂×C₅×#117	C₂²	1	2	yes	—
30	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₅	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₅×#398	C₂²	1	8	yes	—
35	C₅×#398	C₂²	1	8	yes	—
36	C₅×#395	C₂²	1	8	yes	—
37	C₅×#395	C₂²	1	8	yes	—
38	C₅×#391	C₂²	1	4	yes	—
39	C₅×#391	C₂²	1	4	yes	—
40	C₅×#389	C₂²	1	8	yes	—
41	C₅×#389	C₂²	1	8	yes	—
42	C₅×#389	C₂²	1	16	yes	—
43	C₅×#385	C₂²	1	8	yes	—
44	C₅×#385	C₂²	1	8	yes	—
45	C₅×#384	C₂²	1	4	yes	—
46	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₅×C₄⋊C₄	C₂²	1	16	yes	—
49	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₅×#376	C₂²	1	2	yes	—
52	C₄³×C₅	C₂²	1	2	yes	—
53	#34953	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂²×C₅×Q₈	—	2	8	no	—
55	C₂²×C₅×Q₈	—	2	4	no	—
56	C₂²×C₅×Q₈	C₂³	1	2	yes	—
57	C₂²×C₅×Q₈	C₂³	1	2	yes	—
58	C₂²×C₅×Q₈	C₂³	1	2	yes	—
59	C₂²×C₅×Q₈	C₂³	1	2	yes	—
60	C₂³×C₄×C₅	C₂³	1	2	yes	—
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂³	1	2	yes	—
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	—	2	16	no	—
66	C₅×C₄⋊Q₈	—	2	4	no	—
67	C₅×C₄⋊Q₈	—	2	4	no	—
68	C₅×#125	—	2	8	no	—
69	C₅×C₂²⋊Q₈	—	2	8	no	—
70	C₅×C₂²⋊Q₈	—	2	8	no	—
71	C₄×C₅×Q₈	—	2	8	no	—
72	C₄×C₅×Q₈	—	2	8	no	—
73	C₄×C₅×Q₈	—	2	8	no	—
74	C₄×C₅×Q₈	—	2	8	no	—
75	C₄×C₅×Q₈	—	2	8	no	—
76	C₄×C₅×Q₈	—	2	8	no	—
77	C₅×#117	—	2	8	no	—
78	C₅×#117	Q₈	1	16	yes	complemented
79	C₂×C₅×C₄⋊C₄	—	2	8	no	—
80	C₂×C₅×C₄⋊C₄	—	2	4	no	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
93	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₄²×C₅	—	2	8	no	—
97	C₂×C₄²×C₅	D₄	1	8	yes	—
98	C₂×C₄²×C₅	C₂³	1	4	yes	—
99	C₂×C₄²×C₅	C₂³	1	4	yes	—
100	C₂×C₄²×C₅	C₂³	1	4	yes	—
101	C₂×C₄²×C₅	C₂³	1	4	yes	—
102	C₂×C₄²×C₅	C₂³	1	4	yes	—
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	4	yes	—
108	C₅×#95	C₂³	1	4	yes	—
109	C₅×#95	C₂³	1	4	yes	—
110	C₅×#95	C₂³	1	16	yes	—
111	C₅×#95	C₂³	1	16	yes	—
112	C₂×#533	C₂×C₅	1	1	yes	characteristic
113	C₂²×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
114	#2584	C₂×C₅	1	4	yes	complemented
115	#2583	C₂×C₅	1	4	yes	—
116	#2567	C₂×C₅	1	2	yes	complemented
117	#2546	C₂×C₅	1	2	yes	complemented
118	#2502	C₂×C₅	1	2	yes	—
119	#2434	C₂×C₅	1	2	yes	—
120	#2399	C₂×C₅	1	4	yes	complemented
121	C₄×C₄⋊Q₈	C₂×C₅	1	4	yes	complemented
122	#2296	C₂×C₅	1	4	yes	—
123	C₄×#117	C₂×C₅	1	1	yes	characteristic
124	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
125	C₂×C₅×Q₈	—	2	32	no	—
126	C₂×C₅×Q₈	—	2	4	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	—	2	4	no	—
129	C₂×C₅×Q₈	—	2	4	no	—
130	C₂×C₅×Q₈	—	2	8	no	—
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂×C₅×Q₈	—	2	8	no	—
133	C₂×C₅×Q₈	—	4	4	no	—
134	C₂×C₅×Q₈	#41	1	8	yes	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	8	no	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	2	4	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	—	4	4	no	—
141	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₅×C₄⋊C₄	—	2	8	no	—
157	C₅×C₄⋊C₄	—	2	8	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	2	8	no	—
163	C₅×C₄⋊C₄	—	2	8	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	32	no	—
167	C₅×C₄⋊C₄	—	4	16	no	—
168	C₅×C₄⋊C₄	C₂×Q₈	1	16	yes	complemented
169	C₅×C₂²⋊C₄	—	2	8	no	—
170	C₅×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
171	C₄²×C₅	—	2	8	no	—
172	C₄²×C₅	—	2	8	no	—
173	C₄²×C₅	—	2	8	no	—
174	C₄²×C₅	—	2	8	no	—
175	C₄²×C₅	—	4	4	no	—
176	C₄²×C₅	C₂×D₄	1	4	yes	—
177	C₄²×C₅	C₂×D₄	1	4	yes	—
178	C₄²×C₅	C₂×D₄	1	4	yes	—
179	C₄²×C₅	C₂×D₄	1	4	yes	—
180	C₄²×C₅	C₂×Q₈	1	16	yes	complemented
181	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
182	#533	—	2	8	no	—
183	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×#125	C₂²×C₅	1	2	yes	—
187	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
188	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
189	C₂×C₄×Q₈	—	2	8	no	—
190	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
193	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
195	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
196	C₂×#117	C₂²×C₅	1	2	yes	—
197	C₂×#117	C₂²×C₅	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	C₂²×C₄²	C₂²×C₅	1	2	yes	—
201	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
202	#398	C₂²×C₅	1	8	yes	—
203	#398	C₂²×C₅	1	8	yes	—
204	#395	C₂²×C₅	1	8	yes	—
205	#395	C₂²×C₅	1	8	yes	—
206	#391	C₂²×C₅	1	4	yes	—
207	#391	C₂²×C₅	1	4	yes	—
208	#389	C₂²×C₅	1	16	yes	—
209	#389	C₂²×C₅	1	8	yes	—
210	#389	C₂²×C₅	1	8	yes	—
211	#385	C₂²×C₅	1	8	yes	—
212	#385	C₂²×C₅	1	8	yes	—
213	#384	C₂²×C₅	1	4	yes	—
214	C₄×C₄⋊C₄	C₂²×C₅	1	16	yes	—
215	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
218	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
219	#376	C₂²×C₅	1	2	yes	—
220	C₄³	C₂²×C₅	1	2	yes	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	C₂²×D₄	1	2	yes	—
224	C₂³×C₅	C₂²×Q₈	1	4	yes	—
225	C₂³×C₅	C₂⁵	1	1	yes	characteristic
226	C₅×Q₈	—	2	16	no	—
227	C₅×Q₈	—	2	16	no	—
228	C₅×Q₈	—	4	8	no	—
229	C₅×Q₈	—	4	8	no	—
230	C₂×C₄×C₅	—	2	16	no	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	8	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	8	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	8	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	8	no	—
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	—	4	4	no	—
246	C₂×C₄×C₅	—	4	8	no	—
247	C₂×C₄×C₅	C₄⋊Q₈	1	16	yes	complemented
248	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₅	C₂²×Q₈	1	16	yes	—
255	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
256	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
257	C₂×C₄×C₅	C₂×#41	1	8	yes	—
258	C₂×C₄×C₅	C₂×#41	1	4	yes	—
259	C₂²×Q₈	—	2	8	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂³×C₅	1	2	yes	—
262	C₂²×Q₈	C₂³×C₅	1	2	yes	—
263	C₂²×Q₈	C₂³×C₅	1	2	yes	—
264	C₂²×Q₈	C₂³×C₅	1	2	yes	—
265	C₂³×C₄	C₂³×C₅	1	2	yes	—
266	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₅	1	2	yes	—
268	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	16	no	—
271	C₄⋊Q₈	—	2	4	no	—
272	C₄⋊Q₈	—	2	4	no	—
273	#125	—	2	8	no	—
274	C₂²⋊Q₈	—	2	8	no	—
275	C₂²⋊Q₈	—	2	8	no	—
276	C₄×Q₈	—	2	8	no	—
277	C₄×Q₈	—	2	8	no	—
278	C₄×Q₈	—	2	8	no	—
279	C₄×Q₈	—	2	8	no	—
280	C₄×Q₈	—	2	8	no	—
281	C₄×Q₈	—	2	8	no	—
282	#117	—	2	8	no	—
283	#117	C₅×Q₈	1	16	yes	complemented
284	C₂×C₄⋊C₄	—	2	8	no	—
285	C₂×C₄⋊C₄	—	2	4	no	—
286	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
298	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
301	C₂×C₄²	—	2	8	no	—
302	C₂×C₄²	C₅×D₄	1	8	yes	—
303	C₂×C₄²	C₂³×C₅	1	4	yes	—
304	C₂×C₄²	C₂³×C₅	1	4	yes	—
305	C₂×C₄²	C₂³×C₅	1	4	yes	—
306	C₂×C₄²	C₂³×C₅	1	4	yes	—
307	C₂×C₄²	C₂³×C₅	1	4	yes	—
308	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₅	1	4	yes	—
313	#95	C₂³×C₅	1	4	yes	—
314	#95	C₂³×C₅	1	4	yes	—
315	#95	C₂³×C₅	1	16	yes	—
316	#95	C₂³×C₅	1	16	yes	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	2	no	—
319	C₂²×C₅	—	2	8	no	—
320	C₂²×C₅	C₂×C₄⋊Q₈	1	4	yes	—
321	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
322	C₂²×C₅	C₂³×Q₈	1	2	yes	—
323	C₂²×C₅	C₂²×#41	1	2	yes	—
324	C₂²×C₅	#585	1	2	yes	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	8	no	—
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	16	no	—
330	C₄×C₅	—	4	4	no	—
331	C₄×C₅	—	4	4	no	—
332	C₄×C₅	—	4	4	no	—
333	C₄×C₅	#525	1	4	yes	—
334	C₄×C₅	C₂×C₄⋊Q₈	1	4	yes	—
335	C₄×C₅	C₂×C₄⋊Q₈	1	4	yes	—
336	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×Q₈	—	2	32	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	8	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	C₅×#41	1	8	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
354	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
355	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
356	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	—
357	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
364	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	32	no	—
379	C₄⋊C₄	—	4	16	no	—
380	C₄⋊C₄	C₂×C₅×Q₈	1	16	yes	complemented
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	C₂×C₅×Q₈	1	16	yes	—
383	C₄²	—	2	8	no	—
384	C₄²	—	2	8	no	—
385	C₄²	—	2	8	no	—
386	C₄²	—	2	8	no	—
387	C₄²	—	4	4	no	—
388	C₄²	C₂×C₅×D₄	1	4	yes	—
389	C₄²	C₂×C₅×D₄	1	4	yes	—
390	C₄²	C₂×C₅×D₄	1	4	yes	—
391	C₄²	C₂×C₅×D₄	1	4	yes	—
392	C₄²	C₂×C₅×Q₈	1	16	yes	complemented
393	C₂×C₅	—	2	4	no	—
394	C₂×C₅	C₂×#525	1	1	yes	characteristic
395	C₂×C₅	C₂²×C₄⋊Q₈	1	1	yes	characteristic
396	C₂×C₅	#3449	1	1	yes	characteristic
397	C₂×C₅	Q₈×#41	1	4	yes	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	C₂²×C₅×D₄	1	2	yes	—
401	C₂³	C₂²×C₅×Q₈	1	4	yes	—
402	C₂³	C₂⁵×C₅	1	1	yes	characteristic
403	Q₈	—	2	16	no	—
404	Q₈	—	2	16	no	—
405	Q₈	—	4	8	no	—
406	Q₈	—	4	8	no	—
407	C₂×C₄	—	2	16	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	C₅×C₄⋊Q₈	1	16	yes	complemented
425	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
426	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
427	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
428	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
429	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
430	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
431	C₂×C₄	C₂²×C₅×Q₈	1	16	yes	—
432	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
433	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
434	C₂×C₄	C₂×C₅×#41	1	8	yes	—
435	C₂×C₄	C₂×C₅×#41	1	4	yes	—
436	C₅	#34953	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	C₂×C₅×C₄⋊Q₈	1	4	yes	—
441	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
442	C₂²	C₂³×C₅×Q₈	1	2	yes	—
443	C₂²	C₂²×C₅×#41	1	2	yes	—
444	C₂²	C₅×#585	1	2	yes	—
445	C₄	—	2	2	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	16	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	4	no	—
453	C₄	C₅×#525	1	4	yes	—
454	C₄	C₂×C₅×C₄⋊Q₈	1	4	yes	—
455	C₄	C₂×C₅×C₄⋊Q₈	1	4	yes	—
456	C₂	—	2	4	no	—
457	C₂	C₂×C₅×#525	1	1	yes	characteristic
458	C₂	C₂²×C₅×C₄⋊Q₈	1	1	yes	characteristic
459	C₂	C₅×#3449	1	1	yes	characteristic
460	C₂	C₅×Q₈×#41	1	4	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
3. C₅×#2584	C₂	semidirect
5. C₅×#2567	C₂	semidirect
6. C₅×#2546	C₂	semidirect
9. C₅×#2399	C₂	semidirect
10. C₄×C₅×C₄⋊Q₈	C₂	semidirect
53. #34953	C₅	direct (N × H)
78. C₅×#117	Q₈	semidirect
114. #2584	C₂×C₅	semidirect
116. #2567	C₂×C₅	semidirect
117. #2546	C₂×C₅	semidirect
120. #2399	C₂×C₅	semidirect
121. C₄×C₄⋊Q₈	C₂×C₅	semidirect
168. C₅×C₄⋊C₄	C₂×Q₈	semidirect
180. C₄²×C₅	C₂×Q₈	semidirect
247. C₂×C₄×C₅	C₄⋊Q₈	semidirect
283. #117	C₅×Q₈	semidirect
380. C₄⋊C₄	C₂×C₅×Q₈	semidirect
392. C₄²	C₂×C₅×Q₈	semidirect
424. C₂×C₄	C₅×C₄⋊Q₈	semidirect
436. C₅	#34953	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×Q₈	2
C₅×#2584	2
C₅×#2583	2
C₅×#2567	2
C₅×#2546	2
C₅×#2502	2
C₅×#2434	2
C₅×#2399	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2296	2
C₄×C₅×#117	2
#34953	5

Subgroups — C5×#34953 #11957673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34953 #11957673