Subgroups — C₅×#33436 #11956156

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2929	C₂	1	1	yes	maximal, characteristic
4	C₅×#2169	C₂	1	2	yes	maximal, complemented
5	C₅×#2168	C₂	1	2	yes	maximal, complemented
6	C₅×#2168	C₂	1	2	yes	maximal, complemented
7	C₅×D₄×C₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#2151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#525	C₄	1	1	yes	characteristic
15	C₅×#504	—	2	4	no	—
16	C₂×C₅×M₃₂	—	2	4	no	—
17	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₅×M₃₂	C₂²	1	2	yes	—
19	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
21	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
24	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
25	C₅×#435	C₄	1	2	yes	—
26	C₅×#435	C₄	1	2	yes	—
27	C₅×C₈×D₄	C₂²	1	2	yes	—
28	C₅×C₈×D₄	C₂²	1	2	yes	—
29	C₅×#424	C₄	1	1	yes	characteristic
30	C₅×#408	C₄	1	1	yes	characteristic
31	C₅×#407	C₄	1	1	yes	characteristic
32	C₅×#405	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
34	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
35	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₅×#346	C₂²	1	2	yes	complemented
42	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
43	#33436	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₅×#131	—	2	2	no	—
47	C₅×#131	—	2	2	no	—
48	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×#123	C₈	1	2	yes	—
61	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
62	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
63	C₅×#121	C₈	1	1	yes	characteristic
64	C₅×#121	C₈	1	1	yes	characteristic
65	C₅×#120	C₈	1	2	yes	—
66	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
67	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
68	C₅×#117	C₂×C₄	1	1	yes	characteristic
69	C₅×M₃₂	—	2	2	no	—
70	C₅×M₃₂	—	2	4	no	—
71	C₅×M₃₂	—	2	4	no	—
72	C₅×M₃₂	D₄	1	4	yes	complemented
73	C₂×C₅×C₁₆	—	2	2	no	—
74	C₂×C₅×C₁₆	—	2	2	no	—
75	C₂×C₅×C₁₆	—	2	4	no	—
76	C₂×C₅×C₁₆	—	2	4	no	—
77	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
84	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
89	C₅×#97	C₂×C₄	1	2	yes	—
90	C₄×C₅×C₈	C₂³	1	2	yes	—
91	C₂×#504	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
93	#2929	C₂×C₅	1	1	yes	characteristic
94	#2169	C₂×C₅	1	2	yes	complemented
95	#2168	C₂×C₅	1	2	yes	complemented
96	#2168	C₂×C₅	1	2	yes	complemented
97	D₄×C₁₆	C₂×C₅	1	2	yes	complemented
98	#2151	C₂×C₅	1	1	yes	characteristic, complemented
99	#2113	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
101	#2108	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
103	C₅×#41	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
106	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
107	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
108	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
109	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₅×M₁₆	—	2	2	no	—
120	C₅×M₁₆	—	2	2	no	—
121	C₅×M₁₆	—	2	4	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	#41	1	2	yes	—
138	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
139	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
140	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
141	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
142	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
143	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
144	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
145	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
146	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
147	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
148	C₄²×C₅	C₂²×C₄	1	2	yes	—
149	C₅×C₁₆	—	2	1	no	—
150	C₅×C₁₆	—	2	1	no	—
151	C₅×C₁₆	—	2	2	no	—
152	C₅×C₁₆	—	2	1	no	—
153	C₅×C₁₆	—	2	1	no	—
154	C₅×C₁₆	C₂×D₄	1	4	yes	—
155	C₂×#131	C₂²×C₅	1	1	yes	characteristic
156	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
157	#525	C₄×C₅	1	1	yes	characteristic
158	#504	—	2	4	no	—
159	C₂×M₃₂	—	2	4	no	—
160	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
161	C₂×M₃₂	C₂²×C₅	1	2	yes	—
162	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
163	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
164	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
167	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
168	#435	C₄×C₅	1	2	yes	—
169	#435	C₄×C₅	1	2	yes	—
170	C₈×D₄	C₂²×C₅	1	2	yes	—
171	C₈×D₄	C₂²×C₅	1	2	yes	—
172	#424	C₄×C₅	1	1	yes	characteristic
173	#408	C₄×C₅	1	1	yes	characteristic
174	#407	C₄×C₅	1	1	yes	characteristic
175	#405	C₂²×C₅	1	1	yes	characteristic
176	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
177	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
178	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
180	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
181	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
182	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
183	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
184	#346	C₂²×C₅	1	2	yes	complemented
185	C₄×C₁₆	C₂²×C₅	1	2	yes	complemented
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
190	C₂³×C₅	C₂²×C₈	1	2	yes	—
191	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
192	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
193	C₅×Q₈	—	2	2	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
209	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
210	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
213	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₅	#131	1	2	yes	—
215	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	—	2	1	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	C₄×D₄	1	2	yes	—
221	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
222	C₅×C₈	C₂×#41	1	1	yes	characteristic
223	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	#131	—	2	2	no	—
226	#131	—	2	2	no	—
227	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
228	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
229	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₅	1	2	yes	—
238	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
239	#123	C₅×C₈	1	2	yes	—
240	C₂²⋊Q₈	C₅×C₈	1	1	yes	characteristic
241	C₂²⋊Q₈	C₅×C₈	1	1	yes	characteristic
242	#121	C₅×C₈	1	1	yes	characteristic
243	#121	C₅×C₈	1	1	yes	characteristic
244	#120	C₅×C₈	1	2	yes	—
245	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
246	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
247	#117	C₂×C₄×C₅	1	1	yes	characteristic
248	M₃₂	—	2	2	no	—
249	M₃₂	—	2	4	no	—
250	M₃₂	—	2	4	no	—
251	M₃₂	C₅×D₄	1	4	yes	complemented
252	C₂×C₁₆	—	2	2	no	—
253	C₂×C₁₆	—	2	2	no	—
254	C₂×C₁₆	—	2	4	no	—
255	C₂×C₁₆	—	2	4	no	—
256	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₅	1	2	yes	—
261	C₂×C₁₆	C₂³×C₅	1	2	yes	—
262	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
263	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
264	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
265	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
266	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
267	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
268	#97	C₂×C₄×C₅	1	2	yes	—
269	C₄×C₈	C₂³×C₅	1	2	yes	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	4	4	no	—
281	C₂²×C₅	C₈×D₄	1	2	yes	—
282	C₂²×C₅	#504	1	2	yes	complemented
283	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	C₈×D₄	1	2	yes	—
290	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₅	C₂×#131	1	1	yes	characteristic
292	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
296	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
297	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
298	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
299	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	—	2	4	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
323	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
325	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
326	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₈	C₅×#41	1	2	yes	—
328	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
329	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
330	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
331	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
332	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
333	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
334	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
335	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
336	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
337	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
338	C₄²	C₂²×C₄×C₅	1	2	yes	—
339	C₁₆	—	2	1	no	—
340	C₁₆	—	2	1	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	1	no	—
343	C₁₆	—	2	1	no	—
344	C₁₆	C₂×C₅×D₄	1	4	yes	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	4	2	no	—
348	C₂×C₅	—	4	1	no	—
349	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
350	C₂×C₅	C₂×#504	1	1	yes	characteristic
351	C₂×C₅	#3407	1	1	yes	characteristic
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
356	C₂³	C₂²×C₅×C₈	1	2	yes	—
357	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
358	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	D₄	—	2	4	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
374	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
375	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
376	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
379	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
380	C₂×C₄	C₅×#131	1	2	yes	—
381	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	2	no	—
385	C₈	—	2	2	no	—
386	C₈	C₄×C₅×D₄	1	2	yes	—
387	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
388	C₈	C₂×C₅×#41	1	1	yes	characteristic
389	C₅	#33436	1	1	yes	characteristic, direct product factor, Sylow
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	C₅×C₈×D₄	1	2	yes	—
402	C₂²	C₅×#504	1	2	yes	complemented
403	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	C₅×C₈×D₄	1	2	yes	—
410	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
411	C₄	C₂×C₅×#131	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×C₅×C₈×D₄	1	1	yes	characteristic
417	C₂	C₂×C₅×#504	1	1	yes	characteristic
418	C₂	C₅×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₅×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#504	C₂	semidirect
2. C₂²×C₅×M₃₂	C₂	semidirect
4. C₅×#2169	C₂	semidirect
5. C₅×#2168	C₂	semidirect
6. C₅×#2168	C₂	semidirect
7. C₅×D₄×C₁₆	C₂	semidirect
8. C₅×#2151	C₂	semidirect
9. C₅×#2113	C₂	semidirect
10. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
11. C₅×#2108	C₂	semidirect
20. C₂×C₅×M₃₂	C₂²	semidirect
24. C₂²×C₅×C₁₆	C₂²	semidirect
33. C₅×C₄⋊C₁₆	C₂²	semidirect
34. C₅×C₄⋊C₁₆	C₂²	semidirect
39. C₅×C₂²⋊C₁₆	C₂²	semidirect
40. C₅×C₂²⋊C₁₆	C₂²	semidirect
41. C₅×#346	C₂²	semidirect
42. C₄×C₅×C₁₆	C₂²	semidirect
43. #33436	C₅	direct (N × H)
72. C₅×M₃₂	D₄	semidirect
91. C₂×#504	C₂×C₅	semidirect
92. C₂²×M₃₂	C₂×C₅	semidirect
94. #2169	C₂×C₅	semidirect
95. #2168	C₂×C₅	semidirect
96. #2168	C₂×C₅	semidirect
97. D₄×C₁₆	C₂×C₅	semidirect
98. #2151	C₂×C₅	semidirect
99. #2113	C₂×C₅	semidirect
100. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
101. #2108	C₂×C₅	semidirect
163. C₂×M₃₂	C₂²×C₅	semidirect
167. C₂²×C₁₆	C₂²×C₅	semidirect
176. C₄⋊C₁₆	C₂²×C₅	semidirect
177. C₄⋊C₁₆	C₂²×C₅	semidirect
182. C₂²⋊C₁₆	C₂²×C₅	semidirect
183. C₂²⋊C₁₆	C₂²×C₅	semidirect
184. #346	C₂²×C₅	semidirect
185. C₄×C₁₆	C₂²×C₅	semidirect
251. M₃₂	C₅×D₄	semidirect
282. C₂²×C₅	#504	semidirect
389. C₅	#33436	direct (N × H)
402. C₂²	C₅×#504	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#504	2
C₂²×C₅×M₃₂	2
C₅×#2929	2
C₅×#2169	2
C₅×#2168	2
C₅×D₄×C₁₆	2
C₅×#2151	2
C₅×#2113	2
C₂×C₅×C₂²⋊C₁₆	2
C₅×#2108	2
#33436	5

Subgroups — C5×#33436 #11956156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33436 #11956156