Subgroups — C₂×C₃×#65912 #14480118

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4092	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65912	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#4042	C₂	1	2	yes	maximal
7	C₂×C₃×#4035	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4018	C₂	1	2	yes	maximal
10	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₄×Dic₁₀	C₂	1	2	yes	maximal, complemented
13	C₂×#65912	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
20	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₃×#4092	C₂²	1	8	yes	—
26	C₃×#4090	C₂²	1	8	yes	complemented
27	C₂×C₃×#685	C₂²	1	2	yes	—
28	C₂×C₃×#685	C₂²	1	2	yes	—
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
30	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×#683	C₂²	1	2	yes	—
32	C₂×C₃×#683	C₂²	1	2	yes	—
33	C₂×C₃×#683	C₂²	1	2	yes	—
34	C₂×C₃×#683	C₂²	1	2	yes	—
35	C₂×C₃×#683	C₂²	1	2	yes	—
36	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×#4043	C₂²	1	8	yes	—
41	C₃×#4042	C₂²	1	16	yes	—
42	C₃×#4035	C₂²	1	16	yes	complemented
43	C₃×#4034	C₂²	1	8	yes	complemented
44	C₃×#4018	C₂²	1	16	yes	—
45	C₃×C₄²×D₅	C₂²	1	8	yes	—
46	C₃×C₄×Dic₁₀	C₂²	1	16	yes	complemented
47	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
48	C₂×C₃×#533	—	5	1	no	maximal, Hall
49	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4092	C₂×C₃	1	1	yes	characteristic
51	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
52	#65912	C₂×C₃	1	16	yes	direct product factor
53	C₂×#4043	C₂×C₃	1	1	yes	characteristic
54	C₂×#4042	C₂×C₃	1	2	yes	—
55	C₂×#4035	C₂×C₃	1	2	yes	complemented
56	C₂×#4034	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#4018	C₂×C₃	1	2	yes	—
58	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
59	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₁₀	C₂×C₃	1	2	yes	complemented
61	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	—	2	4	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
71	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	—	2	4	no	—
75	C₂×C₃×C₄×D₅	—	2	4	no	—
76	C₂×C₃×C₄×D₅	Q₈	1	8	yes	complemented
77	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
78	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
79	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
80	C₂×C₃×Dic₁₀	—	2	4	no	—
81	C₂×C₃×Dic₁₀	—	2	8	no	—
82	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
83	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
86	C₃×C₄²×C₅	C₂³	1	4	yes	—
87	C₃×C₄²×C₅	C₂³	1	8	yes	—
88	C₃×#685	C₂³	1	8	yes	—
89	C₃×#685	C₂³	1	8	yes	—
90	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
91	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
92	C₃×#683	C₂³	1	8	yes	—
93	C₃×#683	C₂³	1	8	yes	—
94	C₃×#683	C₂³	1	8	yes	—
95	C₃×#683	C₂³	1	8	yes	—
96	C₃×#683	C₂³	1	8	yes	—
97	C₃×C₄×Dic₅	C₂³	1	4	yes	—
98	C₃×C₄×Dic₅	C₂³	1	4	yes	—
99	C₃×C₄×Dic₅	C₂³	1	8	yes	—
100	C₃×C₄×Dic₅	C₂³	1	4	yes	—
101	C₃×#533	—	5	16	no	—
102	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
103	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
104	C₂×C₃×#125	—	5	2	no	—
105	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
106	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
107	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
108	C₂×C₃×C₄×Q₈	—	5	2	no	—
109	C₂×C₃×C₄×Q₈	—	5	1	no	—
110	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
111	C₂×C₃×#117	—	5	2	no	—
112	C₂²×C₃×C₄²	—	5	1	no	—
113	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
116	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
117	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
118	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×Q₈	C₂²×C₃	1	8	yes	complemented
120	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
122	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
124	#4092	C₂²×C₃	1	8	yes	—
125	#4090	C₂²×C₃	1	8	yes	complemented
126	C₂×#685	C₂²×C₃	1	2	yes	—
127	C₂×#685	C₂²×C₃	1	2	yes	—
128	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
130	C₂×#683	C₂²×C₃	1	2	yes	—
131	C₂×#683	C₂²×C₃	1	2	yes	—
132	C₂×#683	C₂²×C₃	1	2	yes	—
133	C₂×#683	C₂²×C₃	1	2	yes	—
134	C₂×#683	C₂²×C₃	1	2	yes	—
135	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
137	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
139	#4043	C₂²×C₃	1	8	yes	—
140	#4042	C₂²×C₃	1	16	yes	—
141	#4035	C₂²×C₃	1	16	yes	complemented
142	#4034	C₂²×C₃	1	8	yes	complemented
143	#4018	C₂²×C₃	1	16	yes	—
144	C₄²×D₅	C₂²×C₃	1	8	yes	—
145	C₄×Dic₁₀	C₂²×C₃	1	16	yes	complemented
146	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
147	C₂×#533	—	5	1	no	Sylow
148	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
149	C₂²×C₃×D₅	—	2	2	no	—
150	C₂²×C₃×D₅	—	2	2	no	—
151	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
152	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
153	C₃×C₅×Q₈	—	2	8	no	—
154	C₂×C₃×C₄×C₅	—	2	4	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	4	no	—
157	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
158	C₂×C₃×C₄×C₅	#41	1	4	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
164	C₂×C₃×Dic₅	—	2	4	no	—
165	C₂×C₃×Dic₅	—	2	4	no	—
166	C₂×C₃×Dic₅	—	2	2	no	—
167	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
168	C₂×C₃×Dic₅	#41	1	4	yes	—
169	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
170	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
171	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
172	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
173	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
174	C₃×C₄×D₅	—	2	8	no	—
175	C₃×C₄×D₅	—	2	8	no	—
176	C₃×C₄×D₅	C₂×Q₈	1	16	yes	complemented
177	C₃×Dic₁₀	—	2	8	no	—
178	C₃×Dic₁₀	—	2	16	no	—
179	C₂²×C₃×Q₈	—	5	2	no	—
180	C₂²×C₃×Q₈	—	5	1	no	—
181	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
182	C₂³×C₃×C₄	—	5	1	no	—
183	C₂³×C₃×C₄	—	5	1	no	—
184	C₂³×C₃×C₄	—	5	1	no	—
185	C₃×C₄⋊Q₈	—	5	8	no	—
186	C₃×C₄⋊Q₈	—	5	8	no	—
187	C₃×#125	—	5	16	no	—
188	C₃×C₂²⋊Q₈	—	5	8	no	—
189	C₃×C₂²⋊Q₈	—	5	16	no	—
190	C₃×C₂²⋊Q₈	—	5	8	no	—
191	C₃×C₄×Q₈	—	5	16	no	—
192	C₃×C₄×Q₈	—	5	8	no	—
193	C₃×C₄×Q₈	C₂×D₅	1	8	yes	complemented
194	C₃×#117	—	5	16	no	—
195	C₂×C₃×C₄⋊C₄	—	5	2	no	—
196	C₂×C₃×C₄⋊C₄	—	5	2	no	—
197	C₂×C₃×C₄⋊C₄	—	5	2	no	—
198	C₂×C₃×C₄⋊C₄	—	5	2	no	—
199	C₂×C₃×C₄⋊C₄	—	5	2	no	—
200	C₂×C₃×C₄⋊C₄	—	5	2	no	—
201	C₂×C₃×C₄⋊C₄	—	5	1	no	—
202	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
205	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
206	C₂×C₃×C₄²	—	5	1	no	—
207	C₂×C₃×C₄²	—	5	1	no	—
208	C₂×C₃×C₄²	—	5	1	no	—
209	C₂×C₃×C₄²	—	5	2	no	—
210	C₂×C₃×C₄²	—	5	8	no	—
211	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
213	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₅×Q₈	—	2	4	no	—
215	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
216	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
217	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
219	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
222	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
223	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
224	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
225	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₄×D₅	—	2	4	no	—
227	C₂×C₄×D₅	—	2	4	no	—
228	C₂×C₄×D₅	C₃×Q₈	1	8	yes	complemented
229	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
230	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
231	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
232	C₂×Dic₁₀	—	2	4	no	—
233	C₂×Dic₁₀	—	2	8	no	—
234	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
235	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
236	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
237	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
238	C₄²×C₅	C₂³×C₃	1	4	yes	—
239	C₄²×C₅	C₂³×C₃	1	8	yes	—
240	#685	C₂³×C₃	1	8	yes	—
241	#685	C₂³×C₃	1	8	yes	—
242	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
243	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
244	#683	C₂³×C₃	1	8	yes	—
245	#683	C₂³×C₃	1	8	yes	—
246	#683	C₂³×C₃	1	8	yes	—
247	#683	C₂³×C₃	1	8	yes	—
248	#683	C₂³×C₃	1	8	yes	—
249	C₄×Dic₅	C₂³×C₃	1	4	yes	—
250	C₄×Dic₅	C₂³×C₃	1	8	yes	—
251	C₄×Dic₅	C₂³×C₃	1	4	yes	—
252	C₄×Dic₅	C₂³×C₃	1	4	yes	—
253	#533	—	5	16	no	—
254	C₂×C₄⋊Q₈	—	5	1	no	—
255	C₂×C₄⋊Q₈	—	5	1	no	—
256	C₂×#125	—	5	2	no	—
257	C₂×C₂²⋊Q₈	—	5	1	no	—
258	C₂×C₂²⋊Q₈	—	5	2	no	—
259	C₂×C₂²⋊Q₈	—	5	1	no	—
260	C₂×C₄×Q₈	—	5	1	no	—
261	C₂×C₄×Q₈	—	5	2	no	—
262	C₂×C₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
263	C₂×#117	—	5	2	no	—
264	C₂²×C₄²	—	5	1	no	—
265	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
266	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
267	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
268	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
269	C₂×C₃×D₅	—	2	8	no	—
270	C₂×C₃×D₅	—	2	2	no	—
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
273	C₃×C₄×C₅	—	2	4	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	—	2	4	no	—
276	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	—
277	C₃×C₄×C₅	C₂×#41	1	4	yes	—
278	C₃×Dic₅	—	2	4	no	—
279	C₃×Dic₅	—	2	4	no	—
280	C₃×Dic₅	—	2	2	no	—
281	C₃×Dic₅	C₂²×Q₈	1	4	yes	—
282	C₃×Dic₅	C₂×#41	1	4	yes	—
283	C₂⁴×C₃	—	5	1	no	—
284	C₂×C₃×Q₈	—	2	4	no	—
285	C₂×C₃×Q₈	—	5	8	no	—
286	C₂×C₃×Q₈	—	5	4	no	—
287	C₂×C₃×Q₈	—	10	8	no	—
288	C₂×C₃×Q₈	—	10	4	no	—
289	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	—	5	8	no	—
293	C₂²×C₃×C₄	—	5	4	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	5	2	no	—
296	C₂²×C₃×C₄	—	5	2	no	—
297	C₂²×C₃×C₄	—	5	4	no	—
298	C₂²×C₃×C₄	—	5	4	no	—
299	C₂²×C₃×C₄	—	10	4	no	—
300	C₂²×C₃×C₄	—	10	4	no	—
301	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
303	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
304	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
306	C₃×C₄⋊C₄	—	5	8	no	—
307	C₃×C₄⋊C₄	—	5	8	no	—
308	C₃×C₄⋊C₄	—	5	8	no	—
309	C₃×C₄⋊C₄	—	5	8	no	—
310	C₃×C₄⋊C₄	—	5	8	no	—
311	C₃×C₄⋊C₄	—	5	8	no	—
312	C₃×C₄⋊C₄	—	5	4	no	—
313	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
314	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
315	C₃×C₂²⋊C₄	—	5	8	no	—
316	C₃×C₂²⋊C₄	—	5	8	no	—
317	C₃×C₄²	—	5	4	no	—
318	C₃×C₄²	—	5	4	no	—
319	C₃×C₄²	—	5	4	no	—
320	C₃×C₄²	—	5	8	no	—
321	C₃×C₄²	C₂²×D₅	1	4	yes	—
322	C₃×C₄²	C₂²×D₅	1	8	yes	—
323	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
324	C₂²×D₅	—	2	2	no	—
325	C₂²×D₅	—	2	2	no	—
326	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
327	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
328	C₅×Q₈	—	2	8	no	—
329	C₂×C₄×C₅	—	2	4	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	4	no	—
332	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
333	C₂×C₄×C₅	C₃×#41	1	4	yes	—
334	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
335	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
336	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
337	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
338	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
339	C₂×Dic₅	—	2	4	no	—
340	C₂×Dic₅	—	2	4	no	—
341	C₂×Dic₅	—	2	2	no	—
342	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
343	C₂×Dic₅	C₃×#41	1	4	yes	—
344	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
345	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
346	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
347	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
348	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
349	C₄×D₅	—	2	8	no	—
350	C₄×D₅	—	2	8	no	—
351	C₄×D₅	C₂×C₃×Q₈	1	16	yes	complemented
352	Dic₁₀	—	2	8	no	—
353	Dic₁₀	—	2	16	no	—
354	C₂²×Q₈	—	5	2	no	—
355	C₂²×Q₈	—	5	1	no	—
356	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂³×C₄	—	5	1	no	—
358	C₂³×C₄	—	5	1	no	—
359	C₂³×C₄	—	5	1	no	—
360	C₄⋊Q₈	—	5	8	no	—
361	C₄⋊Q₈	—	5	8	no	—
362	#125	—	5	16	no	—
363	C₂²⋊Q₈	—	5	8	no	—
364	C₂²⋊Q₈	—	5	16	no	—
365	C₂²⋊Q₈	—	5	8	no	—
366	C₄×Q₈	—	5	16	no	—
367	C₄×Q₈	—	5	8	no	—
368	C₄×Q₈	C₂×C₃×D₅	1	8	yes	complemented
369	#117	—	5	16	no	—
370	C₂×C₄⋊C₄	—	5	2	no	—
371	C₂×C₄⋊C₄	—	5	2	no	—
372	C₂×C₄⋊C₄	—	5	2	no	—
373	C₂×C₄⋊C₄	—	5	2	no	—
374	C₂×C₄⋊C₄	—	5	2	no	—
375	C₂×C₄⋊C₄	—	5	2	no	—
376	C₂×C₄⋊C₄	—	5	1	no	—
377	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
378	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	5	2	no	—
380	C₂×C₂²⋊C₄	—	5	2	no	—
381	C₂×C₄²	—	5	2	no	—
382	C₂×C₄²	—	5	1	no	—
383	C₂×C₄²	—	5	1	no	—
384	C₂×C₄²	—	5	1	no	—
385	C₂×C₄²	—	5	8	no	—
386	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
387	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
388	C₂×C₃×C₅	#533	1	4	yes	complemented
389	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
391	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
392	C₃×D₅	—	2	4	no	—
393	C₂³×C₃	—	5	4	no	—
394	C₂³×C₃	—	5	2	no	—
395	C₂³×C₃	—	10	2	no	—
396	C₂³×C₃	—	10	2	no	—
397	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
398	C₃×Q₈	—	2	8	no	—
399	C₃×Q₈	—	10	16	no	—
400	C₃×Q₈	—	10	8	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	5	4	no	—
405	C₂×C₃×C₄	—	5	4	no	—
406	C₂×C₃×C₄	—	5	2	no	—
407	C₂×C₃×C₄	—	5	2	no	—
408	C₂×C₃×C₄	—	5	16	no	—
409	C₂×C₃×C₄	—	5	2	no	—
410	C₂×C₃×C₄	—	5	4	no	—
411	C₂×C₃×C₄	—	5	4	no	—
412	C₂×C₃×C₄	—	10	8	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	10	4	no	—
415	C₂×C₃×C₄	—	10	4	no	—
416	C₂×C₃×C₄	—	10	8	no	—
417	C₂×C₃×C₄	#709	1	4	yes	—
418	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
419	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
420	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
421	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
422	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
423	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
424	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
425	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
426	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
427	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
428	C₂×D₅	—	2	2	no	—
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	2	8	no	—
431	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
432	C₄×C₅	—	2	4	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	4	no	—
435	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	—
436	C₄×C₅	C₂×C₃×#41	1	4	yes	—
437	Dic₅	—	2	4	no	—
438	Dic₅	—	2	4	no	—
439	Dic₅	—	2	2	no	—
440	Dic₅	C₂²×C₃×Q₈	1	4	yes	—
441	Dic₅	C₂×C₃×#41	1	4	yes	—
442	C₂⁴	—	5	1	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	5	8	no	—
445	C₂×Q₈	—	5	4	no	—
446	C₂×Q₈	—	10	8	no	—
447	C₂×Q₈	—	10	4	no	—
448	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	8	no	—
452	C₂²×C₄	—	5	4	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	2	no	—
455	C₂²×C₄	—	5	2	no	—
456	C₂²×C₄	—	5	4	no	—
457	C₂²×C₄	—	5	4	no	—
458	C₂²×C₄	—	10	4	no	—
459	C₂²×C₄	—	10	4	no	—
460	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
462	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
463	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
465	C₄⋊C₄	—	5	8	no	—
466	C₄⋊C₄	—	5	8	no	—
467	C₄⋊C₄	—	5	8	no	—
468	C₄⋊C₄	—	5	8	no	—
469	C₄⋊C₄	—	5	8	no	—
470	C₄⋊C₄	—	5	8	no	—
471	C₄⋊C₄	—	5	4	no	—
472	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
473	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
474	C₂²⋊C₄	—	5	8	no	—
475	C₂²⋊C₄	—	5	8	no	—
476	C₄²	—	5	4	no	—
477	C₄²	—	5	4	no	—
478	C₄²	—	5	4	no	—
479	C₄²	—	5	8	no	—
480	C₄²	C₂²×C₃×D₅	1	4	yes	—
481	C₄²	C₂²×C₃×D₅	1	8	yes	—
482	C₃×C₅	C₂×#533	1	1	yes	characteristic, complemented, Hall
483	C₂²×C₃	—	5	4	no	—
484	C₂²×C₃	—	10	8	no	—
485	C₂²×C₃	—	10	2	no	—
486	C₂²×C₃	—	10	2	no	—
487	C₂²×C₃	C₂×#709	1	2	yes	—
488	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
489	C₂²×C₃	D₅×#41	1	2	yes	—
490	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
491	C₃×C₄	—	2	4	no	—
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	2	4	no	—
494	C₃×C₄	—	5	4	no	—
495	C₃×C₄	—	5	4	no	—
496	C₃×C₄	—	10	2	no	—
497	C₃×C₄	—	10	4	no	—
498	C₃×C₄	—	10	4	no	—
499	C₃×C₄	C₂×#709	1	4	yes	—
500	C₃×C₄	C₂×Q₈×D₅	1	4	yes	—
501	C₂×C₅	C₃×#533	1	4	yes	complemented
502	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
503	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
504	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
505	D₅	—	2	4	no	—
506	C₂³	—	5	4	no	—
507	C₂³	—	5	2	no	—
508	C₂³	—	10	2	no	—
509	C₂³	—	10	2	no	—
510	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
511	Q₈	—	2	8	no	—
512	Q₈	—	10	16	no	—
513	Q₈	—	10	8	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	5	4	no	—
518	C₂×C₄	—	5	4	no	—
519	C₂×C₄	—	5	2	no	—
520	C₂×C₄	—	5	2	no	—
521	C₂×C₄	—	5	16	no	—
522	C₂×C₄	—	5	2	no	—
523	C₂×C₄	—	5	4	no	—
524	C₂×C₄	—	5	4	no	—
525	C₂×C₄	—	10	8	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	10	4	no	—
528	C₂×C₄	—	10	4	no	—
529	C₂×C₄	—	10	8	no	—
530	C₂×C₄	C₃×#709	1	4	yes	—
531	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
532	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
533	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
534	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
535	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
536	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
537	C₂×C₃	—	10	4	no	—
538	C₂×C₃	#65912	1	4	yes	direct product factor
539	C₂×C₃	C₂²×#709	1	1	yes	characteristic
540	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
541	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
542	C₅	C₂×C₃×#533	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	5	4	no	—
544	C₂²	—	10	2	no	—
545	C₂²	—	10	2	no	—
546	C₂²	—	10	8	no	—
547	C₂²	C₂×C₃×#709	1	2	yes	—
548	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
549	C₂²	C₃×D₅×#41	1	2	yes	—
550	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
551	C₄	—	2	4	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	4	no	—
554	C₄	—	5	4	no	—
555	C₄	—	5	4	no	—
556	C₄	—	10	2	no	—
557	C₄	—	10	4	no	—
558	C₄	—	10	4	no	—
559	C₄	C₂×C₃×#709	1	4	yes	—
560	C₄	C₂×C₃×Q₈×D₅	1	4	yes	—
561	C₃	C₂×#65912	1	1	yes	characteristic, direct product factor, Sylow
562	C₂	—	10	4	no	—
563	C₂	C₃×#65912	1	4	yes	direct product factor
564	C₂	C₂²×C₃×#709	1	1	yes	characteristic
565	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
566	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₂×C₃×C₄×Q₈	D₅
hypocenter	C₅	C₂×C₃×#533
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₂×C₃×#4090	C₂	semidirect
4. C₃×#65912	C₂	direct (N × H)
7. C₂×C₃×#4035	C₂	semidirect
8. C₂×C₃×#4034	C₂	semidirect
11. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
12. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
13. C₂×#65912	C₃	direct (N × H)
20. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×#4090	C₂²	semidirect
42. C₃×#4035	C₂²	semidirect
43. C₃×#4034	C₂²	semidirect
46. C₃×C₄×Dic₁₀	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
51. C₂×#4090	C₂×C₃	semidirect
52. #65912	C₂×C₃	direct (N × H)
55. C₂×#4035	C₂×C₃	semidirect
56. C₂×#4034	C₂×C₃	semidirect
59. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
60. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
76. C₂×C₃×C₄×D₅	Q₈	semidirect
110. C₂×C₃×C₄×Q₈	D₅	semidirect
119. C₄×C₅×Q₈	C₂²×C₃	semidirect
125. #4090	C₂²×C₃	semidirect
141. #4035	C₂²×C₃	semidirect
142. #4034	C₂²×C₃	semidirect
145. C₄×Dic₁₀	C₂²×C₃	semidirect
146. C₄×Dic₁₀	C₂²×C₃	semidirect
176. C₃×C₄×D₅	C₂×Q₈	semidirect
193. C₃×C₄×Q₈	C₂×D₅	semidirect
228. C₂×C₄×D₅	C₃×Q₈	semidirect
262. C₂×C₄×Q₈	C₃×D₅	semidirect
351. C₄×D₅	C₂×C₃×Q₈	semidirect
368. C₄×Q₈	C₂×C₃×D₅	semidirect
388. C₂×C₃×C₅	#533	semidirect
482. C₃×C₅	C₂×#533	semidirect
501. C₂×C₅	C₃×#533	semidirect
538. C₂×C₃	#65912	direct (N × H)
542. C₅	C₂×C₃×#533	semidirect
561. C₃	C₂×#65912	direct (N × H)
563. C₂	C₃×#65912	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×C₃×C₄×C₅×Q₈	2
C₂×C₃×#4092	2
C₂×C₃×#4090	2
C₃×#65912	2
C₂×C₃×#4043	2
C₂×C₃×#4042	2
C₂×C₃×#4035	2
C₂×C₃×#4034	2
C₂×C₃×#4018	2
C₂×C₃×C₄²×D₅	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#65912	3
C₂×C₃×#533	5

Subgroups — C2×C3×#65912 #14480118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65912 #14480118