Subgroups — C₂×D₄×Q₈×D₅ #13006212

Order 1280.

11798 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	D₄×Q₈×D₅	C₂	1	32	yes	maximal, direct product factor
5	C₂×#66061	C₂	1	3	yes	maximal, complemented
6	C₂×D₅×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
7	C₂×D₅×C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
8	C₂×#65966	C₂	1	6	yes	maximal, complemented
9	C₂×Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×D₅	C₂	1	3	yes	maximal
12	C₂×D₄×Dic₁₀	C₂	1	3	yes	maximal, complemented
13	C₂³×C₅×Q₈	C₂²	1	2	yes	complemented
14	C₂²×Q₈×D₅	—	2	32	no	—
15	C₂²×Q₈×D₅	C₂²	1	6	yes	—
16	C₂²×Q₈×D₅	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×D₅	C₂²	1	6	yes	complemented
18	C₂²×Q₈×D₅	C₂²	1	2	yes	complemented
19	C₂²×Q₈×D₅	C₂²	1	32	yes	complemented
20	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₅	C₂²	1	6	yes	—
22	C₂³×Dic₁₀	C₂²	1	6	yes	complemented
23	C₅×D₄×Q₈	C₂²	1	16	yes	complemented
24	C₂×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	6	yes	complemented
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×C₅×D₄	C₂²	1	3	yes	—
28	Q₈×C₂²⋊D₅	C₂²	1	32	yes	complemented
29	C₂×#4092	C₂²	1	6	yes	complemented
30	C₂×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₂×#4090	C₂²	1	6	yes	complemented
32	C₂×D₄×Dic₅	C₂²	1	3	yes	—
33	C₂×C₄×C₂²⋊D₅	C₂²	1	6	yes	—
34	C₂×#4070	C₂²	1	6	yes	complemented
35	#66061	C₂²	1	48	yes	complemented
36	D₅×C₄⋊Q₈	C₂²	1	48	yes	complemented
37	#65966	C₂²	1	96	yes	complemented
38	D₅×C₂²⋊Q₈	C₂²	1	96	yes	complemented
39	Q₈×D₂₀	C₂²	1	16	yes	complemented
40	C₄×Q₈×D₅	C₂²	1	16	yes	complemented
41	C₄×D₄×D₅	C₂²	1	48	yes	—
42	D₄×Dic₁₀	C₂²	1	48	yes	complemented
43	C₂×#4043	C₂²	1	6	yes	complemented
44	C₂×#4042	C₂²	1	12	yes	complemented
45	C₂×#4039	C₂²	1	3	yes	—
46	C₂×D₅×C₄⋊C₄	C₂²	1	3	yes	—
47	C₂×D₅×C₄⋊C₄	C₂²	1	6	yes	—
48	C₂×D₅×C₄⋊C₄	C₂²	1	3	yes	—
49	C₂×#4034	C₂²	1	6	yes	complemented
50	C₂×#4034	C₂²	1	6	yes	complemented
51	C₂×#4033	C₂²	1	3	yes	complemented
52	C₂×#4027	C₂²	1	6	yes	—
53	C₂×D₅×C₂²⋊C₄	C₂²	1	6	yes	—
54	C₂×#4024	C₂²	1	12	yes	complemented
55	C₂×C₄×D₂₀	C₂²	1	3	yes	—
56	C₂×C₄²×D₅	C₂²	1	3	yes	—
57	C₂×#4015	C₂²	1	3	yes	complemented
58	C₂×C₄×Dic₁₀	C₂²	1	3	yes	complemented
59	C₂²×D₄×Q₈	—	5	1	no	maximal, Sylow
60	C₂⁴×D₅	C₂³	1	2	yes	—
61	C₂²×C₅×Q₈	—	2	16	no	—
62	C₂²×C₅×Q₈	C₂³	1	6	yes	—
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Q₈	C₂³	1	16	yes	complemented
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	6	yes	—
67	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
68	C₂³×Dic₅	C₂³	1	6	yes	—
69	C₂×Q₈×D₅	—	2	16	no	—
70	C₂×Q₈×D₅	—	2	256	no	—
71	C₂×Q₈×D₅	—	2	48	no	—
72	C₂×Q₈×D₅	—	2	48	no	—
73	C₂×Q₈×D₅	D₄	1	16	yes	direct product factor
74	C₂×Q₈×D₅	C₂³	1	48	yes	—
75	C₂×Q₈×D₅	C₂³	1	8	yes	—
76	C₂×Q₈×D₅	C₂³	1	48	yes	complemented
77	C₂×Q₈×D₅	C₂³	1	16	yes	complemented
78	C₂×D₄×D₅	Q₈	1	16	yes	direct product factor
79	C₂×D₄×D₅	C₂³	1	8	yes	—
80	C₂²×D₂₀	C₂³	1	1	yes	characteristic
81	C₂²×C₄×D₅	—	2	48	no	—
82	C₂²×C₄×D₅	C₂³	1	3	yes	—
83	C₂²×C₄×D₅	C₂³	1	6	yes	—
84	C₂²×C₄×D₅	C₂³	1	6	yes	—
85	C₂²×C₄×D₅	C₂³	1	6	yes	—
86	C₂²×C₄×D₅	C₂³	1	48	yes	—
87	C₂²×C₄×D₅	C₂³	1	3	yes	—
88	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₂²×Dic₁₀	—	2	48	no	—
90	C₂²×Dic₁₀	C₂³	1	6	yes	—
91	C₂²×Dic₁₀	C₂³	1	12	yes	—
92	C₂²×Dic₁₀	C₂³	1	3	yes	—
93	C₂²×Dic₁₀	C₂³	1	48	yes	complemented
94	C₅×C₄⋊Q₈	C₂³	1	24	yes	complemented
95	C₅×C₂²⋊Q₈	C₂³	1	48	yes	complemented
96	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
97	C₄×C₅×D₄	C₂³	1	24	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	3	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₄²×C₅	C₂³	1	3	yes	—
103	C₂×C₂²⋊Dic₅	C₂³	1	6	yes	—
104	#4092	C₂³	1	48	yes	complemented
105	Q₈×Dic₅	C₂³	1	8	yes	complemented
106	#4090	C₂³	1	48	yes	complemented
107	D₄×Dic₅	C₂³	1	24	yes	—
108	C₄×C₂²⋊D₅	C₂³	1	48	yes	—
109	C₂×#685	C₂³	1	6	yes	—
110	C₂×#685	C₂³	1	6	yes	—
111	C₂×C₄⋊Dic₅	C₂³	1	3	yes	—
112	C₂×C₄⋊Dic₅	C₂³	1	3	yes	—
113	C₂×C₄⋊Dic₅	C₂³	1	6	yes	—
114	#4070	C₂³	1	48	yes	complemented
115	C₂×#683	C₂³	1	6	yes	—
116	C₂×#683	C₂³	1	12	yes	—
117	C₂×#683	C₂³	1	6	yes	—
118	C₂×C₄×Dic₅	C₂³	1	3	yes	—
119	C₂×C₄×Dic₅	C₂³	1	3	yes	—
120	C₂×C₄×Dic₅	C₂³	1	3	yes	—
121	#4043	C₂³	1	48	yes	complemented
122	#4042	C₂³	1	96	yes	complemented
123	#4039	C₂³	1	24	yes	—
124	D₅×C₄⋊C₄	C₂³	1	24	yes	—
125	D₅×C₄⋊C₄	C₂³	1	48	yes	—
126	D₅×C₄⋊C₄	C₂³	1	24	yes	—
127	#4034	C₂³	1	48	yes	complemented
128	#4034	C₂³	1	48	yes	complemented
129	#4033	C₂³	1	24	yes	complemented
130	#4027	C₂³	1	48	yes	—
131	D₅×C₂²⋊C₄	C₂³	1	48	yes	—
132	#4024	C₂³	1	96	yes	complemented
133	C₄×D₂₀	C₂³	1	24	yes	—
134	C₄²×D₅	C₂³	1	24	yes	—
135	#4015	C₂³	1	24	yes	complemented
136	C₄×Dic₁₀	C₂³	1	24	yes	complemented
137	C₂⁴×Q₈	—	5	2	no	—
138	C₂×D₄×Q₈	—	5	2	no	—
139	C₂×D₄×Q₈	—	5	32	no	—
140	C₂×D₄×Q₈	—	5	3	no	—
141	C₂×D₄×Q₈	—	5	6	no	—
142	C₂×D₄×Q₈	—	5	1	no	—
143	C₂×D₄×Q₈	—	5	3	no	—
144	C₂×D₄×Q₈	D₅	1	1	yes	characteristic, direct product factor
145	C₂²×C₄⋊Q₈	—	5	3	no	—
146	C₂²×C₂²⋊Q₈	—	5	6	no	—
147	C₂²×C₄×Q₈	—	5	1	no	—
148	C₂²×C₄×D₄	—	5	3	no	—
149	C₂⁴×C₅	C₂⁴	1	2	yes	—
150	C₂³×D₅	—	2	8	no	—
151	C₂³×D₅	—	2	8	no	—
152	C₂³×D₅	C₂×Q₈	1	16	yes	complemented
153	C₂³×D₅	C₂⁴	1	2	yes	—
154	C₂³×D₅	C₂⁴	1	8	yes	—
155	C₂³×D₅	C₂⁴	1	1	yes	characteristic
156	C₂×C₅×Q₈	—	2	64	no	—
157	C₂×C₅×Q₈	—	2	24	no	—
158	C₂×C₅×Q₈	C₂×D₄	1	8	yes	complemented
159	C₂×C₅×Q₈	C₂⁴	1	24	yes	—
160	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
161	C₂×C₅×D₄	C₂×Q₈	1	8	yes	complemented
162	C₂×C₅×D₄	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₅	—	2	24	no	—
164	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
165	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
166	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
167	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
168	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₂²⋊D₅	C₂×Q₈	1	16	yes	complemented
170	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
171	C₂²×Dic₅	—	2	24	no	—
172	C₂²×Dic₅	C₂⁴	1	3	yes	—
173	C₂²×Dic₅	C₂⁴	1	6	yes	—
174	C₂²×Dic₅	C₂⁴	1	24	yes	—
175	C₂²×Dic₅	C₂⁴	1	3	yes	—
176	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
177	Q₈×D₅	—	2	64	no	—
178	Q₈×D₅	—	2	192	no	—
179	Q₈×D₅	—	2	192	no	—
180	Q₈×D₅	C₂×D₄	1	64	yes	direct product factor
181	D₄×D₅	C₂×Q₈	1	64	yes	direct product factor
182	C₂×D₂₀	C₂×Q₈	1	8	yes	complemented
183	C₂×D₂₀	C₂⁴	1	4	yes	—
184	C₂×C₄×D₅	—	2	24	no	—
185	C₂×C₄×D₅	—	2	12	no	—
186	C₂×C₄×D₅	—	2	24	no	—
187	C₂×C₄×D₅	—	2	24	no	—
188	C₂×C₄×D₅	—	2	192	no	—
189	C₂×C₄×D₅	C₂×D₄	1	24	yes	—
190	C₂×C₄×D₅	C₂×Q₈	1	8	yes	complemented
191	C₂×C₄×D₅	C₂⁴	1	24	yes	—
192	C₂×C₄×D₅	C₂⁴	1	24	yes	—
193	C₂×C₄×D₅	C₂⁴	1	24	yes	—
194	C₂×C₄×D₅	C₂⁴	1	12	yes	—
195	C₂×C₄×D₅	C₂⁴	1	12	yes	—
196	C₂×C₄×D₅	C₂⁴	1	4	yes	—
197	C₂×Dic₁₀	—	2	24	no	—
198	C₂×Dic₁₀	—	2	48	no	—
199	C₂×Dic₁₀	—	2	192	no	—
200	C₂×Dic₁₀	C₂×D₄	1	24	yes	complemented
201	C₂×Dic₁₀	C₂⁴	1	24	yes	—
202	C₂×Dic₁₀	C₂⁴	1	48	yes	—
203	C₂×Dic₁₀	C₂⁴	1	12	yes	—
204	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
205	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
206	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
207	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
208	C₄²×C₅	C₂⁴	1	12	yes	—
209	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
210	#685	C₂⁴	1	24	yes	—
211	#685	C₂⁴	1	24	yes	—
212	C₄⋊Dic₅	C₂⁴	1	12	yes	—
213	C₄⋊Dic₅	C₂⁴	1	12	yes	—
214	C₄⋊Dic₅	C₂⁴	1	24	yes	—
215	#683	C₂⁴	1	24	yes	—
216	#683	C₂⁴	1	48	yes	—
217	#683	C₂⁴	1	24	yes	—
218	C₄×Dic₅	C₂⁴	1	12	yes	—
219	C₄×Dic₅	C₂⁴	1	12	yes	—
220	C₄×Dic₅	C₂⁴	1	12	yes	—
221	C₂³×Q₈	—	5	1	no	—
222	C₂³×Q₈	—	5	6	no	—
223	C₂³×Q₈	—	5	6	no	—
224	C₂³×Q₈	—	5	2	no	—
225	C₂³×Q₈	—	5	32	no	—
226	C₂³×Q₈	—	5	6	no	—
227	C₂³×Q₈	—	10	32	no	—
228	C₂³×Q₈	C₂×D₅	1	2	yes	complemented
229	C₂³×D₄	—	5	1	no	—
230	C₂⁴×C₄	—	5	6	no	—
231	D₄×Q₈	—	5	32	no	—
232	D₄×Q₈	—	5	48	no	—
233	D₄×Q₈	—	5	96	no	—
234	D₄×Q₈	—	5	16	no	—
235	D₄×Q₈	—	5	48	no	—
236	D₄×Q₈	C₂×D₅	1	16	yes	direct product factor
237	C₂×C₄⋊Q₈	—	5	6	no	—
238	C₂×C₄⋊Q₈	—	5	48	no	—
239	C₂×C₄⋊Q₈	—	5	6	no	—
240	C₂×C₄⋊Q₈	—	5	6	no	—
241	C₂×C₄⋊Q₈	—	5	3	no	—
242	C₂×C₄⋊Q₈	C₂×D₅	1	3	yes	complemented
243	C₂×C₂²⋊Q₈	—	5	6	no	—
244	C₂×C₂²⋊Q₈	—	5	6	no	—
245	C₂×C₂²⋊Q₈	—	5	96	no	—
246	C₂×C₂²⋊Q₈	—	5	12	no	—
247	C₂×C₂²⋊Q₈	—	5	6	no	—
248	C₂×C₂²⋊Q₈	—	5	12	no	—
249	C₂×C₂²⋊Q₈	C₂×D₅	1	6	yes	complemented
250	C₂×C₄×Q₈	—	5	1	no	—
251	C₂×C₄×Q₈	—	5	16	no	—
252	C₂×C₄×Q₈	—	5	3	no	—
253	C₂×C₄×Q₈	—	5	3	no	—
254	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
255	C₂×C₄×D₄	—	5	3	no	—
256	C₂×C₄×D₄	—	5	6	no	—
257	C₂×C₄×D₄	—	5	48	no	—
258	C₂×C₄×D₄	—	5	3	no	—
259	C₂×C₄×D₄	—	5	6	no	—
260	C₂×C₄×D₄	—	5	3	no	—
261	C₂×C₄×D₄	C₂×D₅	1	3	yes	—
262	C₂²×C₄⋊C₄	—	5	3	no	—
263	C₂²×C₄⋊C₄	—	5	3	no	—
264	C₂²×C₄⋊C₄	—	5	6	no	—
265	C₂²×C₂²⋊C₄	—	5	6	no	—
266	C₂²×C₄²	—	5	3	no	—
267	C₂³×C₅	—	2	4	no	—
268	C₂³×C₅	—	2	4	no	—
269	C₂³×C₅	C₂²×Q₈	1	8	yes	complemented
270	C₂³×C₅	C₂⁵	1	4	yes	—
271	C₂³×C₅	C₂⁵	1	1	yes	characteristic
272	C₂²×D₅	—	2	4	no	—
273	C₂²×D₅	—	2	4	no	—
274	C₂²×D₅	—	2	64	no	—
275	C₂²×D₅	—	2	16	no	—
276	C₂²×D₅	—	2	16	no	—
277	C₂²×D₅	C₂²×D₄	1	4	yes	—
278	C₂²×D₅	C₂²×Q₈	1	4	yes	—
279	C₂²×D₅	C₂²×Q₈	1	32	yes	complemented
280	C₂²×D₅	C₂²×Q₈	1	8	yes	complemented
281	C₂²×D₅	2₋¹⁺⁴	1	4	yes	—
282	C₂²×D₅	C₂⁵	1	4	yes	—
283	C₂²×D₅	C₂⁵	1	2	yes	—
284	C₅×Q₈	—	2	48	no	—
285	C₅×Q₈	C₂²×D₄	1	16	yes	complemented
286	C₅×D₄	C₂²×Q₈	1	16	yes	complemented
287	C₂×C₄×C₅	—	2	12	no	—
288	C₂×C₄×C₅	—	2	6	no	—
289	C₂×C₄×C₅	—	2	48	no	—
290	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
291	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	complemented
292	C₂×C₄×C₅	C₂⁵	1	6	yes	—
293	C₂×C₄×C₅	C₂⁵	1	12	yes	—
294	C₂×C₄×C₅	C₂⁵	1	6	yes	—
295	C₂×C₄×C₅	C₂⁵	1	2	yes	—
296	C₂²⋊D₅	C₂²×Q₈	1	32	yes	complemented
297	C₂×Dic₅	—	2	12	no	—
298	C₂×Dic₅	—	2	6	no	—
299	C₂×Dic₅	—	2	48	no	—
300	C₂×Dic₅	C₂²×D₄	1	12	yes	—
301	C₂×Dic₅	C₂²×Q₈	1	4	yes	complemented
302	C₂×Dic₅	C₂⁵	1	6	yes	—
303	C₂×Dic₅	C₂⁵	1	12	yes	—
304	C₂×Dic₅	C₂⁵	1	6	yes	—
305	C₂×Dic₅	C₂⁵	1	2	yes	—
306	D₂₀	C₂²×Q₈	1	16	yes	complemented
307	C₄×D₅	—	2	48	no	—
308	C₄×D₅	—	2	24	no	—
309	C₄×D₅	—	2	48	no	—
310	C₄×D₅	—	2	48	no	—
311	C₄×D₅	C₂²×D₄	1	48	yes	—
312	C₄×D₅	C₂²×Q₈	1	16	yes	complemented
313	Dic₁₀	—	2	48	no	—
314	Dic₁₀	—	2	96	no	—
315	Dic₁₀	C₂²×D₄	1	48	yes	complemented
316	C₂⁵	—	5	2	no	—
317	C₂²×Q₈	—	2	16	no	—
318	C₂²×Q₈	—	5	16	no	—
319	C₂²×Q₈	—	5	8	no	—
320	C₂²×Q₈	—	5	48	no	—
321	C₂²×Q₈	—	5	48	no	—
322	C₂²×Q₈	—	5	16	no	—
323	C₂²×Q₈	—	5	3	no	—
324	C₂²×Q₈	—	5	12	no	—
325	C₂²×Q₈	—	5	6	no	—
326	C₂²×Q₈	—	5	48	no	—
327	C₂²×Q₈	—	10	48	no	—
328	C₂²×Q₈	—	10	48	no	—
329	C₂²×Q₈	—	10	256	no	—
330	C₂²×Q₈	—	10	48	no	—
331	C₂²×Q₈	—	10	16	no	—
332	C₂²×Q₈	C₂²×D₅	1	6	yes	—
333	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
334	C₂²×Q₈	C₂²×D₅	1	16	yes	complemented
335	C₂²×D₄	—	5	2	no	—
336	C₂²×D₄	—	5	16	no	—
337	C₂²×D₄	—	5	8	no	—
338	C₂²×D₄	—	5	1	no	—
339	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
340	C₂³×C₄	—	5	1	no	—
341	C₂³×C₄	—	5	3	no	—
342	C₂³×C₄	—	5	6	no	—
343	C₂³×C₄	—	5	3	no	—
344	C₂³×C₄	—	5	6	no	—
345	C₂³×C₄	—	5	6	no	—
346	C₂³×C₄	—	5	48	no	—
347	C₂³×C₄	—	5	6	no	—
348	C₂³×C₄	—	10	48	no	—
349	C₂³×C₄	C₂²×D₅	1	6	yes	—
350	C₄⋊Q₈	—	5	48	no	—
351	C₄⋊Q₈	—	5	48	no	—
352	C₄⋊Q₈	—	5	48	no	—
353	C₄⋊Q₈	—	5	24	no	—
354	C₄⋊Q₈	C₂²×D₅	1	24	yes	complemented
355	C₂²⋊Q₈	—	5	48	no	—
356	C₂²⋊Q₈	—	5	48	no	—
357	C₂²⋊Q₈	—	5	96	no	—
358	C₂²⋊Q₈	—	5	48	no	—
359	C₂²⋊Q₈	—	5	96	no	—
360	C₂²⋊Q₈	C₂²×D₅	1	48	yes	complemented
361	C₄×Q₈	—	5	8	no	—
362	C₄×Q₈	—	5	24	no	—
363	C₄×Q₈	—	5	24	no	—
364	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
365	C₄×D₄	—	5	24	no	—
366	C₄×D₄	—	5	48	no	—
367	C₄×D₄	—	5	24	no	—
368	C₄×D₄	—	5	48	no	—
369	C₄×D₄	—	5	24	no	—
370	C₄×D₄	C₂²×D₅	1	24	yes	—
371	C₂×C₄⋊C₄	—	5	6	no	—
372	C₂×C₄⋊C₄	—	5	3	no	—
373	C₂×C₄⋊C₄	—	5	6	no	—
374	C₂×C₄⋊C₄	—	5	3	no	—
375	C₂×C₄⋊C₄	—	5	12	no	—
376	C₂×C₄⋊C₄	—	5	6	no	—
377	C₂×C₄⋊C₄	—	5	24	no	—
378	C₂×C₄⋊C₄	—	5	24	no	—
379	C₂×C₄⋊C₄	—	5	48	no	—
380	C₂×C₄⋊C₄	C₂²×D₅	1	3	yes	—
381	C₂×C₄⋊C₄	C₂²×D₅	1	3	yes	—
382	C₂×C₄⋊C₄	C₂²×D₅	1	6	yes	—
383	C₂×C₂²⋊C₄	—	5	6	no	—
384	C₂×C₂²⋊C₄	—	5	6	no	—
385	C₂×C₂²⋊C₄	—	5	6	no	—
386	C₂×C₂²⋊C₄	—	5	48	no	—
387	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
388	C₂×C₄²	—	5	3	no	—
389	C₂×C₄²	—	5	3	no	—
390	C₂×C₄²	—	5	3	no	—
391	C₂×C₄²	—	5	24	no	—
392	C₂×C₄²	C₂²×D₅	1	3	yes	—
393	C₂²×C₅	—	2	4	no	—
394	C₂²×C₅	—	2	4	no	—
395	C₂²×C₅	—	2	16	no	—
396	C₂²×C₅	C₂³×D₄	1	2	yes	—
397	C₂²×C₅	C₂³×Q₈	1	2	yes	—
398	C₂²×C₅	C₂³×Q₈	1	8	yes	complemented
399	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
400	C₂²×C₅	C₂⁶	1	1	yes	characteristic
401	C₂×D₅	—	2	4	no	—
402	C₂×D₅	—	2	4	no	—
403	C₂×D₅	—	2	16	no	—
404	C₂×D₅	—	2	64	no	—
405	C₂×D₅	D₄×Q₈	1	16	yes	direct product factor
406	C₂×D₅	C₂³×D₄	1	4	yes	—
407	C₂×D₅	C₂³×Q₈	1	4	yes	—
408	C₂×D₅	C₂³×Q₈	1	8	yes	complemented
409	C₂×D₅	C₂×2₋¹⁺⁴	1	4	yes	—
410	C₄×C₅	—	2	12	no	—
411	C₄×C₅	—	2	6	no	—
412	C₄×C₅	C₂³×D₄	1	12	yes	—
413	C₄×C₅	C₂³×Q₈	1	4	yes	complemented
414	Dic₅	—	2	12	no	—
415	Dic₅	—	2	6	no	—
416	Dic₅	C₂³×D₄	1	12	yes	—
417	Dic₅	C₂³×Q₈	1	4	yes	complemented
418	C₂⁴	—	5	1	no	—
419	C₂⁴	—	5	16	no	—
420	C₂⁴	—	5	8	no	—
421	C₂⁴	—	5	2	no	—
422	C₂⁴	—	10	8	no	—
423	C₂⁴	—	10	8	no	—
424	C₂⁴	C₂³×D₅	1	2	yes	—
425	C₂×Q₈	—	2	64	no	—
426	C₂×Q₈	—	2	24	no	—
427	C₂×Q₈	—	5	64	no	—
428	C₂×Q₈	—	5	24	no	—
429	C₂×Q₈	—	5	12	no	—
430	C₂×Q₈	—	5	48	no	—
431	C₂×Q₈	—	5	24	no	—
432	C₂×Q₈	—	10	48	no	—
433	C₂×Q₈	—	10	192	no	—
434	C₂×Q₈	—	10	192	no	—
435	C₂×Q₈	—	10	192	no	—
436	C₂×Q₈	—	10	64	no	—
437	C₂×Q₈	—	10	24	no	—
438	C₂×Q₈	D₄×D₅	1	8	yes	direct product factor
439	C₂×Q₈	C₂³×D₅	1	24	yes	—
440	C₂×Q₈	C₂³×D₅	1	4	yes	—
441	C₂×D₄	—	5	16	no	—
442	C₂×D₄	—	5	8	no	—
443	C₂×D₄	—	5	64	no	—
444	C₂×D₄	—	5	8	no	—
445	C₂×D₄	—	5	4	no	—
446	C₂×D₄	Q₈×D₅	1	8	yes	direct product factor
447	C₂×D₄	C₂³×D₅	1	4	yes	—
448	C₂²×C₄	—	2	24	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	3	no	—
451	C₂²×C₄	—	5	24	no	—
452	C₂²×C₄	—	5	8	no	—
453	C₂²×C₄	—	5	4	no	—
454	C₂²×C₄	—	5	12	no	—
455	C₂²×C₄	—	5	24	no	—
456	C₂²×C₄	—	5	3	no	—
457	C₂²×C₄	—	5	6	no	—
458	C₂²×C₄	—	5	12	no	—
459	C₂²×C₄	—	5	24	no	—
460	C₂²×C₄	—	5	24	no	—
461	C₂²×C₄	—	5	24	no	—
462	C₂²×C₄	—	10	24	no	—
463	C₂²×C₄	—	10	192	no	—
464	C₂²×C₄	—	10	24	no	—
465	C₂²×C₄	—	10	12	no	—
466	C₂²×C₄	—	10	24	no	—
467	C₂²×C₄	—	10	24	no	—
468	C₂²×C₄	C₂³×D₅	1	24	yes	—
469	C₂²×C₄	C₂³×D₅	1	3	yes	—
470	C₂²×C₄	C₂³×D₅	1	6	yes	—
471	C₂²×C₄	C₂³×D₅	1	3	yes	—
472	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
473	C₄⋊C₄	—	5	24	no	—
474	C₄⋊C₄	—	5	12	no	—
475	C₄⋊C₄	—	5	24	no	—
476	C₄⋊C₄	—	5	12	no	—
477	C₄⋊C₄	—	5	48	no	—
478	C₄⋊C₄	—	5	24	no	—
479	C₄⋊C₄	C₂³×D₅	1	12	yes	—
480	C₄⋊C₄	C₂³×D₅	1	12	yes	—
481	C₄⋊C₄	C₂³×D₅	1	24	yes	—
482	C₂²⋊C₄	—	5	24	no	—
483	C₂²⋊C₄	—	5	24	no	—
484	C₂²⋊C₄	—	5	24	no	—
485	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
486	C₄²	—	5	12	no	—
487	C₄²	—	5	12	no	—
488	C₄²	—	5	12	no	—
489	C₄²	C₂³×D₅	1	12	yes	—
490	C₂×C₅	—	2	8	no	—
491	C₂×C₅	C₂×D₄×Q₈	1	4	yes	complemented
492	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
493	C₂×C₅	C₂⁴×Q₈	1	1	yes	characteristic
494	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
495	D₅	—	2	8	no	—
496	D₅	C₂×D₄×Q₈	1	8	yes	direct product factor
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	5	4	no	—
500	C₂³	—	5	4	no	—
501	C₂³	—	5	4	no	—
502	C₂³	—	5	2	no	—
503	C₂³	—	5	8	no	—
504	C₂³	—	5	32	no	—
505	C₂³	—	5	4	no	—
506	C₂³	—	10	16	no	—
507	C₂³	—	10	64	no	—
508	C₂³	—	10	16	no	—
509	C₂³	—	10	4	no	—
510	C₂³	—	10	4	no	—
511	C₂³	C₂×Q₈×D₅	1	8	yes	complemented
512	C₂³	C₂⁴×D₅	1	4	yes	—
513	C₂³	C₂⁴×D₅	1	1	yes	characteristic
514	Q₈	—	2	48	no	—
515	Q₈	—	5	48	no	—
516	Q₈	—	10	96	no	—
517	Q₈	—	10	48	no	—
518	Q₈	C₂×D₄×D₅	1	16	yes	direct product factor
519	D₄	—	5	32	no	—
520	D₄	—	5	16	no	—
521	D₄	C₂×Q₈×D₅	1	16	yes	direct product factor
522	C₂×C₄	—	2	12	no	—
523	C₂×C₄	—	2	6	no	—
524	C₂×C₄	—	2	48	no	—
525	C₂×C₄	—	5	12	no	—
526	C₂×C₄	—	5	4	no	—
527	C₂×C₄	—	5	2	no	—
528	C₂×C₄	—	5	6	no	—
529	C₂×C₄	—	5	48	no	—
530	C₂×C₄	—	5	16	no	—
531	C₂×C₄	—	5	6	no	—
532	C₂×C₄	—	5	12	no	—
533	C₂×C₄	—	10	48	no	—
534	C₂×C₄	—	10	48	no	—
535	C₂×C₄	—	10	24	no	—
536	C₂×C₄	—	10	48	no	—
537	C₂×C₄	—	10	12	no	—
538	C₂×C₄	—	10	6	no	—
539	C₂×C₄	—	10	48	no	—
540	C₂×C₄	C₂×D₄×D₅	1	12	yes	—
541	C₂×C₄	C₂×Q₈×D₅	1	4	yes	complemented
542	C₂×C₄	C₂⁴×D₅	1	6	yes	—
543	C₂×C₄	C₂⁴×D₅	1	12	yes	—
544	C₂×C₄	C₂⁴×D₅	1	6	yes	—
545	C₂×C₄	C₂⁴×D₅	1	2	yes	—
546	C₅	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
547	C₂²	—	2	4	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	5	4	no	—
551	C₂²	—	5	16	no	—
552	C₂²	—	5	4	no	—
553	C₂²	—	5	4	no	—
554	C₂²	—	5	8	no	—
555	C₂²	—	10	64	no	—
556	C₂²	—	10	4	no	—
557	C₂²	—	10	16	no	—
558	C₂²	—	10	4	no	—
559	C₂²	C₂²×D₄×D₅	1	2	yes	—
560	C₂²	C₂²×Q₈×D₅	1	2	yes	—
561	C₂²	C₂²×Q₈×D₅	1	8	yes	complemented
562	C₂²	D₅×2₋¹⁺⁴	1	2	yes	—
563	C₂²	C₂⁵×D₅	1	1	yes	characteristic
564	C₄	—	2	12	no	—
565	C₄	—	2	6	no	—
566	C₄	—	5	12	no	—
567	C₄	—	5	4	no	—
568	C₄	—	10	12	no	—
569	C₄	—	10	6	no	—
570	C₄	C₂²×D₄×D₅	1	12	yes	—
571	C₄	C₂²×Q₈×D₅	1	4	yes	complemented
572	C₂	—	2	8	no	—
573	C₂	—	5	8	no	—
574	C₂	—	10	8	no	—
575	C₂	D₄×Q₈×D₅	1	4	yes	direct product factor
576	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
577	C₂	C₂³×Q₈×D₅	1	1	yes	characteristic
578	C₂	C₂×D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×D₄×Q₈	C₂
socle	C₂³×C₅	C₂⁵
prime radical	C₂²×D₄×D₅	C₂²
hypercenter	C₂×D₄×Q₈	D₅
hypocenter	C₅	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₅	C₂	semidirect
2. C₂×C₅×D₄×Q₈	C₂	semidirect
3. C₂×Q₈×C₂²⋊D₅	C₂	semidirect
4. D₄×Q₈×D₅	C₂	direct (N × H)
5. C₂×#66061	C₂	semidirect
6. C₂×D₅×C₄⋊Q₈	C₂	semidirect
7. C₂×D₅×C₂²⋊Q₈	C₂	semidirect
8. C₂×#65966	C₂	semidirect
9. C₂×Q₈×D₂₀	C₂	semidirect
10. C₂×C₄×Q₈×D₅	C₂	semidirect
12. C₂×D₄×Dic₁₀	C₂	semidirect
13. C₂³×C₅×Q₈	C₂²	semidirect
17. C₂²×Q₈×D₅	C₂²	semidirect
18. C₂²×Q₈×D₅	C₂²	semidirect
19. C₂²×Q₈×D₅	C₂²	semidirect
22. C₂³×Dic₁₀	C₂²	semidirect
23. C₅×D₄×Q₈	C₂²	semidirect
24. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×C₅×Q₈	C₂²	semidirect
28. Q₈×C₂²⋊D₅	C₂²	semidirect
29. C₂×#4092	C₂²	semidirect
30. C₂×Q₈×Dic₅	C₂²	semidirect
31. C₂×#4090	C₂²	semidirect
34. C₂×#4070	C₂²	semidirect
35. #66061	C₂²	semidirect
36. D₅×C₄⋊Q₈	C₂²	semidirect
37. #65966	C₂²	semidirect
38. D₅×C₂²⋊Q₈	C₂²	semidirect
39. Q₈×D₂₀	C₂²	semidirect
40. C₄×Q₈×D₅	C₂²	semidirect
42. D₄×Dic₁₀	C₂²	semidirect
43. C₂×#4043	C₂²	semidirect
44. C₂×#4042	C₂²	semidirect
49. C₂×#4034	C₂²	semidirect
50. C₂×#4034	C₂²	semidirect
51. C₂×#4033	C₂²	semidirect
54. C₂×#4024	C₂²	semidirect
57. C₂×#4015	C₂²	semidirect
58. C₂×C₄×Dic₁₀	C₂²	semidirect
64. C₂²×C₅×Q₈	C₂³	semidirect
73. C₂×Q₈×D₅	D₄	direct (N × H)
76. C₂×Q₈×D₅	C₂³	semidirect
77. C₂×Q₈×D₅	C₂³	semidirect
78. C₂×D₄×D₅	Q₈	direct (N × H)
93. C₂²×Dic₁₀	C₂³	semidirect
94. C₅×C₄⋊Q₈	C₂³	semidirect
95. C₅×C₂²⋊Q₈	C₂³	semidirect
96. C₄×C₅×Q₈	C₂³	semidirect
104. #4092	C₂³	semidirect
105. Q₈×Dic₅	C₂³	semidirect
106. #4090	C₂³	semidirect
114. #4070	C₂³	semidirect
121. #4043	C₂³	semidirect
122. #4042	C₂³	semidirect
127. #4034	C₂³	semidirect
128. #4034	C₂³	semidirect
129. #4033	C₂³	semidirect
132. #4024	C₂³	semidirect
135. #4015	C₂³	semidirect
136. C₄×Dic₁₀	C₂³	semidirect
144. C₂×D₄×Q₈	D₅	direct (N × H)
152. C₂³×D₅	C₂×Q₈	semidirect
158. C₂×C₅×Q₈	C₂×D₄	semidirect
161. C₂×C₅×D₄	C₂×Q₈	semidirect
169. C₂×C₂²⋊D₅	C₂×Q₈	semidirect
180. Q₈×D₅	C₂×D₄	direct (N × H)
181. D₄×D₅	C₂×Q₈	direct (N × H)
182. C₂×D₂₀	C₂×Q₈	semidirect
190. C₂×C₄×D₅	C₂×Q₈	semidirect
200. C₂×Dic₁₀	C₂×D₄	semidirect
228. C₂³×Q₈	C₂×D₅	semidirect
236. D₄×Q₈	C₂×D₅	direct (N × H)
242. C₂×C₄⋊Q₈	C₂×D₅	semidirect
249. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
254. C₂×C₄×Q₈	C₂×D₅	semidirect
269. C₂³×C₅	C₂²×Q₈	semidirect
279. C₂²×D₅	C₂²×Q₈	semidirect
280. C₂²×D₅	C₂²×Q₈	semidirect
285. C₅×Q₈	C₂²×D₄	semidirect
286. C₅×D₄	C₂²×Q₈	semidirect
291. C₂×C₄×C₅	C₂²×Q₈	semidirect
296. C₂²⋊D₅	C₂²×Q₈	semidirect
301. C₂×Dic₅	C₂²×Q₈	semidirect
306. D₂₀	C₂²×Q₈	semidirect
312. C₄×D₅	C₂²×Q₈	semidirect
315. Dic₁₀	C₂²×D₄	semidirect
334. C₂²×Q₈	C₂²×D₅	semidirect
354. C₄⋊Q₈	C₂²×D₅	semidirect
360. C₂²⋊Q₈	C₂²×D₅	semidirect
364. C₄×Q₈	C₂²×D₅	semidirect
398. C₂²×C₅	C₂³×Q₈	semidirect
405. C₂×D₅	D₄×Q₈	direct (N × H)
408. C₂×D₅	C₂³×Q₈	semidirect
413. C₄×C₅	C₂³×Q₈	semidirect
417. Dic₅	C₂³×Q₈	semidirect
438. C₂×Q₈	D₄×D₅	direct (N × H)
446. C₂×D₄	Q₈×D₅	direct (N × H)
491. C₂×C₅	C₂×D₄×Q₈	semidirect
496. D₅	C₂×D₄×Q₈	direct (N × H)
511. C₂³	C₂×Q₈×D₅	semidirect
518. Q₈	C₂×D₄×D₅	direct (N × H)
521. D₄	C₂×Q₈×D₅	direct (N × H)
541. C₂×C₄	C₂×Q₈×D₅	semidirect
546. C₅	C₂²×D₄×Q₈	semidirect
561. C₂²	C₂²×Q₈×D₅	semidirect
571. C₄	C₂²×Q₈×D₅	semidirect
575. C₂	D₄×Q₈×D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₅	2
C₂×C₅×D₄×Q₈	2
C₂×Q₈×C₂²⋊D₅	2
D₄×Q₈×D₅	2
C₂×#66061	2
C₂×D₅×C₄⋊Q₈	2
C₂×D₅×C₂²⋊Q₈	2
C₂×#65966	2
C₂×Q₈×D₂₀	2
C₂×C₄×Q₈×D₅	2
C₂×C₄×D₄×D₅	2
C₂×D₄×Dic₁₀	2
C₂²×D₄×Q₈	5

Subgroups — C2×D4×Q8×D5 #13006212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×Q₈×D₅ #13006212