Subgroups — C₂×C₅×#2117 #11956059

Order 1280.

1154 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2117	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#350	C₂	1	4	yes	maximal, complemented
6	C₂²×C₅×#41	C₄	1	1	yes	characteristic
7	C₂×C₅×#131	—	2	1	no	—
8	C₂×C₅×#131	—	2	2	no	—
9	C₂×C₅×#131	—	2	2	no	—
10	C₂×C₅×#131	—	2	1	no	—
11	C₂×C₅×#131	C₄	1	2	yes	—
12	C₂×C₅×#131	C₄	1	4	yes	—
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₂×C₅×#131	C₂²	1	4	yes	—
15	C₂²×C₅×M₁₆	—	2	1	no	—
16	C₂²×C₅×M₁₆	C₄	1	1	yes	characteristic
17	C₂³×C₅×C₈	—	2	1	no	—
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×M₃₂	—	2	1	no	—
20	C₂×C₅×M₃₂	—	2	2	no	—
21	C₂×C₅×M₃₂	—	2	1	no	—
22	C₂×C₅×M₃₂	—	2	2	no	—
23	C₂×C₅×M₃₂	—	2	1	no	—
24	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
25	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
26	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
27	C₂²×C₅×C₁₆	—	2	1	no	—
28	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
29	C₅×#350	C₂²	1	16	yes	complemented
30	C₂×#2117	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₅×#41	—	2	2	no	—
32	C₂×C₅×#41	—	2	1	no	—
33	C₂×C₅×#41	—	2	1	no	—
34	C₂×C₅×#41	—	2	2	no	—
35	C₂×C₅×#41	C₈	1	2	yes	—
36	C₂×C₅×#41	C₈	1	4	yes	—
37	C₂×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₅×#41	C₂×C₄	1	4	yes	—
39	C₂²×C₅×Q₈	C₈	1	1	yes	characteristic
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
42	C₂³×C₄×C₅	—	2	1	no	—
43	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₅×#131	—	2	4	no	—
45	C₅×#131	—	2	4	no	—
46	C₅×#131	—	2	4	no	—
47	C₅×#131	—	2	2	no	—
48	C₅×#131	—	2	4	no	—
49	C₅×#131	—	2	4	no	—
50	C₅×#131	—	2	2	no	—
51	C₅×#131	C₂×C₄	1	4	yes	—
52	C₅×#131	C₂×C₄	1	8	yes	—
53	C₅×#131	C₂³	1	4	yes	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	4	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	4	no	—
60	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
61	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	—	2	4	no	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	—	2	4	no	—
66	C₂²×C₅×C₈	—	2	2	no	—
67	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
69	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
70	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	D₄	1	2	yes	—
72	C₂²×C₅×C₈	D₄	1	2	yes	—
73	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
74	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	2	yes	—
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×M₃₂	—	2	4	no	—
78	C₅×M₃₂	—	2	2	no	—
79	C₅×M₃₂	—	2	4	no	—
80	C₅×M₃₂	—	2	4	no	—
81	C₅×M₃₂	C₂³	1	4	yes	complemented
82	C₂×C₅×C₁₆	—	2	4	no	—
83	C₂×C₅×C₁₆	—	2	2	no	—
84	C₂×C₅×C₁₆	—	2	2	no	—
85	C₂×C₅×C₁₆	—	2	2	no	—
86	C₂×C₅×C₁₆	C₂³	1	4	yes	complemented
87	C₂²×#131	C₂×C₅	1	1	yes	characteristic
88	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
90	#2117	C₂×C₅	1	8	yes	direct product factor
91	C₂×#350	C₂×C₅	1	4	yes	complemented
92	C₂⁴×C₅	—	2	1	no	—
93	C₂⁴×C₅	M₁₆	1	1	yes	characteristic
94	C₅×#41	—	2	4	no	—
95	C₅×#41	—	2	4	no	—
96	C₅×#41	—	2	4	no	—
97	C₅×#41	—	2	2	no	—
98	C₅×#41	—	2	4	no	—
99	C₅×#41	—	2	2	no	—
100	C₅×#41	—	2	4	no	—
101	C₅×#41	C₂×C₈	1	4	yes	—
102	C₅×#41	C₂×C₈	1	8	yes	—
103	C₅×#41	C₂²×C₄	1	4	yes	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	C₂×C₈	1	4	yes	—
107	C₂×C₅×Q₈	C₂×C₈	1	2	yes	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	4	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	4	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	C₂×C₈	1	4	yes	—
115	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	4	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
127	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
128	C₂²×C₄×C₅	M₁₆	1	2	yes	—
129	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	4	no	—
133	C₅×M₁₆	—	2	4	no	—
134	C₅×M₁₆	—	2	8	no	—
135	C₅×M₁₆	—	2	4	no	—
136	C₅×M₁₆	C₂²×C₄	1	4	yes	—
137	C₂×C₅×C₈	—	2	4	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	8	no	—
140	C₂×C₅×C₈	—	2	4	no	—
141	C₂×C₅×C₈	—	2	4	no	—
142	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
144	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
149	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
156	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
160	C₅×C₁₆	—	2	4	no	—
161	C₅×C₁₆	—	2	4	no	—
162	C₂²×#41	C₄×C₅	1	1	yes	characteristic
163	C₂×#131	—	2	1	no	—
164	C₂×#131	—	2	2	no	—
165	C₂×#131	—	2	1	no	—
166	C₂×#131	—	2	2	no	—
167	C₂×#131	C₄×C₅	1	2	yes	—
168	C₂×#131	C₄×C₅	1	4	yes	—
169	C₂×#131	C₂²×C₅	1	2	yes	—
170	C₂×#131	C₂²×C₅	1	4	yes	—
171	C₂²×M₁₆	—	2	1	no	—
172	C₂²×M₁₆	C₄×C₅	1	1	yes	characteristic
173	C₂³×C₈	—	2	1	no	—
174	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×M₃₂	—	2	1	no	—
176	C₂×M₃₂	—	2	2	no	—
177	C₂×M₃₂	—	2	1	no	—
178	C₂×M₃₂	—	2	1	no	—
179	C₂×M₃₂	—	2	2	no	—
180	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
181	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
182	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
183	C₂²×C₁₆	—	2	1	no	—
184	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
185	#350	C₂²×C₅	1	16	yes	complemented
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	4	4	no	—
190	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
191	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
192	C₂³×C₅	C₂²⋊C₈	1	2	yes	—
193	C₂³×C₅	C₂×M₁₆	1	1	yes	characteristic
194	C₂³×C₅	C₂×M₁₆	1	2	yes	—
195	C₅×Q₈	—	2	2	no	—
196	C₅×Q₈	—	2	4	no	—
197	C₅×Q₈	C₂²×C₈	1	4	yes	—
198	C₅×D₄	—	2	4	no	—
199	C₅×D₄	—	2	8	no	—
200	C₅×D₄	—	2	4	no	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	—	2	4	no	—
203	C₅×D₄	C₂²×C₈	1	4	yes	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	8	no	—
208	C₂×C₄×C₅	—	2	4	no	—
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	2	yes	—
212	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
214	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
215	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
221	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
223	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
225	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₅×C₈	—	2	4	no	—
228	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
229	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
232	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
233	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
234	C₂×#41	—	2	1	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	1	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	C₅×C₈	1	2	yes	—
239	C₂×#41	C₅×C₈	1	4	yes	—
240	C₂×#41	C₂×C₄×C₅	1	2	yes	—
241	C₂×#41	C₂×C₄×C₅	1	4	yes	—
242	C₂²×Q₈	C₅×C₈	1	1	yes	characteristic
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₅×C₈	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
247	#131	—	2	4	no	—
248	#131	—	2	4	no	—
249	#131	—	2	4	no	—
250	#131	—	2	2	no	—
251	#131	—	2	4	no	—
252	#131	—	2	4	no	—
253	#131	—	2	2	no	—
254	#131	C₂×C₄×C₅	1	4	yes	—
255	#131	C₂×C₄×C₅	1	8	yes	—
256	#131	C₂³×C₅	1	4	yes	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
264	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
272	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
273	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
274	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
275	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
276	C₂²×C₈	C₅×D₄	1	2	yes	—
277	C₂²×C₈	C₅×D₄	1	2	yes	—
278	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₅	1	2	yes	—
280	M₃₂	—	2	4	no	—
281	M₃₂	—	2	2	no	—
282	M₃₂	—	2	4	no	—
283	M₃₂	—	2	4	no	—
284	M₃₂	C₂³×C₅	1	4	yes	complemented
285	C₂×C₁₆	—	2	2	no	—
286	C₂×C₁₆	—	2	4	no	—
287	C₂×C₁₆	—	2	2	no	—
288	C₂×C₁₆	—	2	2	no	—
289	C₂×C₁₆	C₂³×C₅	1	4	yes	complemented
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	4	no	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	4	8	no	—
297	C₂²×C₅	—	4	4	no	—
298	C₂²×C₅	C₂×C₂²⋊C₈	1	2	yes	—
299	C₂²×C₅	C₂×C₂²⋊C₈	1	2	yes	—
300	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
301	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
302	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
303	C₄×C₅	—	2	4	no	—
304	C₄×C₅	C₂×C₂²⋊C₈	1	2	yes	—
305	C₄×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
306	C₄×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
307	C₄×C₅	C₂×C₂²⋊C₈	1	2	yes	—
308	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
309	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
310	C₂⁴	—	2	1	no	—
311	C₂⁴	C₅×M₁₆	1	1	yes	characteristic
312	#41	—	2	2	no	—
313	#41	—	2	4	no	—
314	#41	—	2	2	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	2	4	no	—
318	#41	—	2	4	no	—
319	#41	C₂×C₅×C₈	1	4	yes	—
320	#41	C₂×C₅×C₈	1	8	yes	—
321	#41	C₂²×C₄×C₅	1	4	yes	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	C₂×C₅×C₈	1	4	yes	—
325	C₂×Q₈	C₂×C₅×C₈	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×C₅×C₈	1	4	yes	—
333	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
342	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
345	C₂²×C₄	C₅×M₁₆	1	1	yes	characteristic
346	C₂²×C₄	C₅×M₁₆	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	8	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	C₂²×C₄×C₅	1	4	yes	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	8	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
361	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
364	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
365	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
366	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
367	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
368	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
369	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
376	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
378	C₁₆	—	2	4	no	—
379	C₁₆	—	2	4	no	—
380	C₂×C₅	—	2	2	no	—
381	C₂×C₅	—	2	1	no	—
382	C₂×C₅	—	2	2	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	4	4	no	—
385	C₂×C₅	#2117	1	2	yes	direct product factor
386	C₂×C₅	C₂²×C₂²⋊C₈	1	1	yes	characteristic
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	C₅×C₂²⋊C₈	1	1	yes	characteristic
392	C₂³	C₅×C₂²⋊C₈	1	1	yes	characteristic
393	C₂³	C₅×C₂²⋊C₈	1	2	yes	—
394	C₂³	C₂×C₅×M₁₆	1	1	yes	characteristic
395	C₂³	C₂×C₅×M₁₆	1	2	yes	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	2	no	—
398	Q₈	C₂²×C₅×C₈	1	4	yes	—
399	D₄	—	2	4	no	—
400	D₄	—	2	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	C₂²×C₅×C₈	1	4	yes	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
411	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
412	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
413	C₂×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
414	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
415	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
416	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
417	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
418	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
420	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
421	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
422	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
425	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
426	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
427	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
431	C₈	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
433	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
435	C₅	C₂×#2117	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	4	no	—
444	C₂²	C₂×C₅×C₂²⋊C₈	1	2	yes	—
445	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
446	C₂²	C₂×C₅×C₂²⋊C₈	1	2	yes	—
447	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
448	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	C₂×C₅×C₂²⋊C₈	1	2	yes	—
451	C₄	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
452	C₄	C₂×C₅×C₂²⋊C₈	1	2	yes	—
453	C₄	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
454	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
455	C₄	C₂³×C₅×C₈	1	1	yes	characteristic
456	C₂	—	2	2	no	—
457	C₂	—	2	1	no	—
458	C₂	—	2	2	no	—
459	C₂	—	2	1	no	—
460	C₂	—	4	4	no	—
461	C₂	C₅×#2117	1	2	yes	direct product factor
462	C₂	C₂²×C₅×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₄	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₂²⋊C₈
prime radical	C₂²×C₅×#41	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×M₃₂	C₂	semidirect
3. C₂²×C₅×M₃₂	C₂	semidirect
4. C₅×#2117	C₂	direct (N × H)
5. C₂×C₅×#350	C₂	semidirect
24. C₂×C₅×M₃₂	C₂²	semidirect
25. C₂×C₅×M₃₂	C₂²	semidirect
26. C₂×C₅×M₃₂	C₂²	semidirect
28. C₂²×C₅×C₁₆	C₂²	semidirect
29. C₅×#350	C₂²	semidirect
30. C₂×#2117	C₅	direct (N × H)
81. C₅×M₃₂	C₂³	semidirect
86. C₂×C₅×C₁₆	C₂³	semidirect
88. C₂²×M₃₂	C₂×C₅	semidirect
89. C₂²×M₃₂	C₂×C₅	semidirect
90. #2117	C₂×C₅	direct (N × H)
91. C₂×#350	C₂×C₅	semidirect
180. C₂×M₃₂	C₂²×C₅	semidirect
181. C₂×M₃₂	C₂²×C₅	semidirect
182. C₂×M₃₂	C₂²×C₅	semidirect
184. C₂²×C₁₆	C₂²×C₅	semidirect
185. #350	C₂²×C₅	semidirect
284. M₃₂	C₂³×C₅	semidirect
289. C₂×C₁₆	C₂³×C₅	semidirect
385. C₂×C₅	#2117	direct (N × H)
435. C₅	C₂×#2117	direct (N × H)
461. C₂	C₅×#2117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#131	2
C₂²×C₅×M₃₂	2
C₅×#2117	2
C₂×C₅×#350	2
C₂×#2117	5

Subgroups — C2×C5×#2117 #11956059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2117 #11956059