Subgroups — C₂×C₃×#65917 #14481194

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 544 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×#65917	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4044	C₂	1	2	yes	maximal
6	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4035	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4022	C₂	1	2	yes	maximal
10	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×#4016	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65917	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×Dic₁₀	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×#4092	C₂²	1	8	yes	—
23	C₃×#4090	C₂²	1	8	yes	complemented
24	C₂×C₃×#685	C₂²	1	2	yes	—
25	C₂×C₃×#685	C₂²	1	1	yes	characteristic
26	C₂×C₃×#685	C₂²	1	2	yes	—
27	C₂×C₃×#685	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Dic₅	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	1	yes	characteristic
36	C₂×C₃×#683	C₂²	1	1	yes	characteristic
37	C₂×C₃×#683	C₂²	1	2	yes	—
38	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×#4044	C₂²	1	16	yes	—
41	C₃×#4043	C₂²	1	8	yes	—
42	C₃×#4036	C₂²	1	8	yes	complemented
43	C₃×#4035	C₂²	1	16	yes	complemented
44	C₃×#4022	C₂²	1	16	yes	—
45	C₃×#4018	C₂²	1	8	yes	—
46	C₃×#4016	C₂²	1	16	yes	complemented
47	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
48	C₂×C₃×#541	—	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	#65917	C₂×C₃	1	16	yes	direct product factor
53	C₂×#4044	C₂×C₃	1	2	yes	—
54	C₂×#4043	C₂×C₃	1	1	yes	characteristic
55	C₂×#4036	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4035	C₂×C₃	1	2	yes	complemented
57	C₂×#4022	C₂×C₃	1	2	yes	—
58	C₂×#4018	C₂×C₃	1	1	yes	characteristic
59	C₂×#4016	C₂×C₃	1	2	yes	complemented
60	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, 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	1	yes	characteristic
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	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
73	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	—	2	4	no	—
75	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
76	C₂×C₃×Dic₁₀	—	2	4	no	—
77	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₃×C₄²×C₅	C₂³	1	4	yes	—
81	C₃×C₄²×C₅	C₂³	1	8	yes	—
82	C₃×#685	C₂³	1	8	yes	—
83	C₃×#685	C₂³	1	4	yes	—
84	C₃×#685	C₂³	1	4	yes	—
85	C₃×#685	C₂³	1	8	yes	—
86	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
87	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
88	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
89	C₃×#683	C₂³	1	8	yes	—
90	C₃×#683	C₂³	1	8	yes	—
91	C₃×#683	C₂³	1	8	yes	—
92	C₃×#683	C₂³	1	8	yes	—
93	C₃×#683	C₂³	1	4	yes	—
94	C₃×#683	C₂³	1	4	yes	—
95	C₃×#683	C₂³	1	8	yes	—
96	C₃×C₄×Dic₅	C₂³	1	4	yes	—
97	C₃×C₄×Dic₅	C₂³	1	8	yes	—
98	C₃×#541	—	5	16	no	—
99	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
100	C₂×C₃×#126	—	5	2	no	—
101	C₂×C₃×#126	—	5	2	no	—
102	C₂×C₃×#125	—	5	2	no	—
103	C₂×C₃×#125	—	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×C₄×Q₈	—	5	1	no	—
108	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
109	C₂×C₃×#117	—	5	1	no	—
110	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
111	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
112	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×Q₈	C₂²×C₃	1	8	yes	complemented
114	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
118	#4092	C₂²×C₃	1	8	yes	—
119	#4090	C₂²×C₃	1	8	yes	complemented
120	C₂×#685	C₂²×C₃	1	1	yes	characteristic
121	C₂×#685	C₂²×C₃	1	1	yes	characteristic
122	C₂×#685	C₂²×C₃	1	2	yes	—
123	C₂×#685	C₂²×C₃	1	2	yes	—
124	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
126	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
127	C₂×#683	C₂²×C₃	1	2	yes	—
128	C₂×#683	C₂²×C₃	1	1	yes	characteristic
129	C₂×#683	C₂²×C₃	1	2	yes	—
130	C₂×#683	C₂²×C₃	1	2	yes	—
131	C₂×#683	C₂²×C₃	1	1	yes	characteristic
132	C₂×#683	C₂²×C₃	1	2	yes	—
133	C₂×#683	C₂²×C₃	1	2	yes	—
134	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
135	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	#4044	C₂²×C₃	1	16	yes	—
137	#4043	C₂²×C₃	1	8	yes	—
138	#4036	C₂²×C₃	1	8	yes	complemented
139	#4035	C₂²×C₃	1	16	yes	complemented
140	#4022	C₂²×C₃	1	16	yes	—
141	#4018	C₂²×C₃	1	8	yes	—
142	#4016	C₂²×C₃	1	16	yes	complemented
143	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
144	C₂×#541	—	5	1	no	Sylow
145	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
146	C₂²×C₃×D₅	—	2	2	no	—
147	C₂²×C₃×D₅	—	2	2	no	—
148	C₂²×C₃×D₅	—	2	2	no	—
149	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
150	C₃×C₅×Q₈	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	4	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	4	no	—
155	C₂×C₃×C₄×C₅	#41	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
161	C₂×C₃×Dic₅	—	2	4	no	—
162	C₂×C₃×Dic₅	—	2	2	no	—
163	C₂×C₃×Dic₅	—	2	4	no	—
164	C₂×C₃×Dic₅	—	2	2	no	—
165	C₂×C₃×Dic₅	—	2	2	no	—
166	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
167	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
168	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
169	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
170	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
171	C₃×C₄×D₅	—	2	8	no	—
172	C₃×Dic₁₀	—	2	8	no	—
173	C₂²×C₃×Q₈	—	5	1	no	—
174	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
175	C₂³×C₃×C₄	—	5	1	no	—
176	C₃×C₄⋊Q₈	—	5	8	no	—
177	C₃×#126	—	5	16	no	—
178	C₃×#126	—	5	16	no	—
179	C₃×#125	—	5	16	no	—
180	C₃×#125	—	5	8	no	—
181	C₃×#125	—	5	16	no	—
182	C₃×C₂²⋊Q₈	—	5	8	no	—
183	C₃×C₂²⋊Q₈	—	5	8	no	—
184	C₃×C₄×Q₈	—	5	8	no	—
185	C₃×C₄×Q₈	C₂×D₅	1	8	yes	complemented
186	C₃×#117	—	5	8	no	—
187	C₂×C₃×C₄⋊C₄	—	5	1	no	—
188	C₂×C₃×C₄⋊C₄	—	5	1	no	—
189	C₂×C₃×C₄⋊C₄	—	5	1	no	—
190	C₂×C₃×C₄⋊C₄	—	5	2	no	—
191	C₂×C₃×C₄⋊C₄	—	5	2	no	—
192	C₂×C₃×C₄⋊C₄	—	5	2	no	—
193	C₂×C₃×C₄⋊C₄	—	5	2	no	—
194	C₂×C₃×C₄⋊C₄	—	5	2	no	—
195	C₂×C₃×C₄⋊C₄	—	5	2	no	—
196	C₂×C₃×C₄⋊C₄	—	5	2	no	—
197	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
200	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
201	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
202	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
203	C₂×C₃×C₄²	—	5	1	no	—
204	C₂×C₃×C₄²	—	5	2	no	—
205	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
206	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
207	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₅×Q₈	—	2	4	no	—
209	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
213	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
216	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
217	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
218	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
219	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₄×D₅	—	2	4	no	—
221	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
222	C₂×Dic₁₀	—	2	4	no	—
223	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
224	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
225	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
226	C₄²×C₅	C₂³×C₃	1	4	yes	—
227	C₄²×C₅	C₂³×C₃	1	8	yes	—
228	#685	C₂³×C₃	1	4	yes	—
229	#685	C₂³×C₃	1	4	yes	—
230	#685	C₂³×C₃	1	8	yes	—
231	#685	C₂³×C₃	1	8	yes	—
232	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
233	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
234	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
235	#683	C₂³×C₃	1	8	yes	—
236	#683	C₂³×C₃	1	4	yes	—
237	#683	C₂³×C₃	1	8	yes	—
238	#683	C₂³×C₃	1	8	yes	—
239	#683	C₂³×C₃	1	4	yes	—
240	#683	C₂³×C₃	1	8	yes	—
241	#683	C₂³×C₃	1	8	yes	—
242	C₄×Dic₅	C₂³×C₃	1	8	yes	—
243	C₄×Dic₅	C₂³×C₃	1	4	yes	—
244	#541	—	5	16	no	—
245	C₂×C₄⋊Q₈	—	5	1	no	—
246	C₂×#126	—	5	2	no	—
247	C₂×#126	—	5	2	no	—
248	C₂×#125	—	5	2	no	—
249	C₂×#125	—	5	1	no	—
250	C₂×#125	—	5	2	no	—
251	C₂×C₂²⋊Q₈	—	5	1	no	—
252	C₂×C₂²⋊Q₈	—	5	1	no	—
253	C₂×C₄×Q₈	—	5	1	no	—
254	C₂×C₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
255	C₂×#117	—	5	1	no	—
256	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
257	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
258	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
259	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
260	C₂×C₃×D₅	—	2	2	no	—
261	C₂×C₃×D₅	—	2	2	no	—
262	C₂×C₃×D₅	—	2	2	no	—
263	C₂×C₃×D₅	—	4	4	no	—
264	C₃×C₄×C₅	—	2	4	no	—
265	C₃×C₄×C₅	—	2	2	no	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	—	2	4	no	—
268	C₃×C₄×C₅	C₂×#41	1	4	yes	—
269	C₃×Dic₅	—	2	4	no	—
270	C₃×Dic₅	—	2	2	no	—
271	C₃×Dic₅	—	2	2	no	—
272	C₃×Dic₅	—	2	4	no	—
273	C₃×Dic₅	—	2	2	no	—
274	C₂⁴×C₃	—	5	1	no	—
275	C₂×C₃×Q₈	—	2	4	no	—
276	C₂×C₃×Q₈	—	5	4	no	—
277	C₂×C₃×Q₈	—	10	4	no	—
278	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
279	C₂²×C₃×C₄	—	5	1	no	—
280	C₂²×C₃×C₄	—	5	2	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	5	2	no	—
283	C₂²×C₃×C₄	—	5	1	no	—
284	C₂²×C₃×C₄	—	5	4	no	—
285	C₂²×C₃×C₄	—	10	4	no	—
286	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
289	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
290	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
291	C₃×C₄⋊C₄	—	5	4	no	—
292	C₃×C₄⋊C₄	—	5	4	no	—
293	C₃×C₄⋊C₄	—	5	8	no	—
294	C₃×C₄⋊C₄	—	5	8	no	—
295	C₃×C₄⋊C₄	—	5	8	no	—
296	C₃×C₄⋊C₄	—	5	8	no	—
297	C₃×C₄⋊C₄	—	5	8	no	—
298	C₃×C₄⋊C₄	—	5	4	no	—
299	C₃×C₄⋊C₄	—	5	8	no	—
300	C₃×C₄⋊C₄	—	5	8	no	—
301	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
302	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
303	C₃×C₂²⋊C₄	—	5	4	no	—
304	C₃×C₂²⋊C₄	—	5	4	no	—
305	C₃×C₂²⋊C₄	—	5	8	no	—
306	C₃×C₂²⋊C₄	—	5	8	no	—
307	C₃×C₄²	—	5	4	no	—
308	C₃×C₄²	—	5	8	no	—
309	C₃×C₄²	C₂²×D₅	1	4	yes	—
310	C₃×C₄²	C₂²×D₅	1	8	yes	—
311	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
312	C₂²×D₅	—	2	2	no	—
313	C₂²×D₅	—	2	2	no	—
314	C₂²×D₅	—	2	2	no	—
315	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
316	C₅×Q₈	—	2	8	no	—
317	C₂×C₄×C₅	—	2	4	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	4	no	—
321	C₂×C₄×C₅	C₃×#41	1	4	yes	—
322	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
323	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
324	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
325	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
326	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
327	C₂×Dic₅	—	2	4	no	—
328	C₂×Dic₅	—	2	2	no	—
329	C₂×Dic₅	—	2	4	no	—
330	C₂×Dic₅	—	2	2	no	—
331	C₂×Dic₅	—	2	2	no	—
332	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
333	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
334	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
335	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
336	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
337	C₄×D₅	—	2	8	no	—
338	Dic₁₀	—	2	8	no	—
339	C₂²×Q₈	—	5	1	no	—
340	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
341	C₂³×C₄	—	5	1	no	—
342	C₄⋊Q₈	—	5	8	no	—
343	#126	—	5	16	no	—
344	#126	—	5	16	no	—
345	#125	—	5	16	no	—
346	#125	—	5	8	no	—
347	#125	—	5	16	no	—
348	C₂²⋊Q₈	—	5	8	no	—
349	C₂²⋊Q₈	—	5	8	no	—
350	C₄×Q₈	—	5	8	no	—
351	C₄×Q₈	C₂×C₃×D₅	1	8	yes	complemented
352	#117	—	5	8	no	—
353	C₂×C₄⋊C₄	—	5	1	no	—
354	C₂×C₄⋊C₄	—	5	1	no	—
355	C₂×C₄⋊C₄	—	5	1	no	—
356	C₂×C₄⋊C₄	—	5	2	no	—
357	C₂×C₄⋊C₄	—	5	2	no	—
358	C₂×C₄⋊C₄	—	5	2	no	—
359	C₂×C₄⋊C₄	—	5	2	no	—
360	C₂×C₄⋊C₄	—	5	2	no	—
361	C₂×C₄⋊C₄	—	5	2	no	—
362	C₂×C₄⋊C₄	—	5	2	no	—
363	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
365	C₂×C₂²⋊C₄	—	5	1	no	—
366	C₂×C₂²⋊C₄	—	5	1	no	—
367	C₂×C₂²⋊C₄	—	5	2	no	—
368	C₂×C₂²⋊C₄	—	5	2	no	—
369	C₂×C₄²	—	5	1	no	—
370	C₂×C₄²	—	5	2	no	—
371	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
372	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
373	C₂×C₃×C₅	#541	1	4	yes	complemented
374	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₃×D₅	—	4	2	no	—
378	C₂³×C₃	—	5	2	no	—
379	C₂³×C₃	—	10	2	no	—
380	C₂³×C₃	—	10	2	no	—
381	C₂³×C₃	—	10	2	no	—
382	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
383	C₃×Q₈	—	2	8	no	—
384	C₃×Q₈	—	10	8	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	4	no	—
389	C₂×C₃×C₄	—	5	2	no	—
390	C₂×C₃×C₄	—	5	4	no	—
391	C₂×C₃×C₄	—	5	2	no	—
392	C₂×C₃×C₄	—	5	4	no	—
393	C₂×C₃×C₄	—	5	2	no	—
394	C₂×C₃×C₄	—	10	2	no	—
395	C₂×C₃×C₄	—	10	4	no	—
396	C₂×C₃×C₄	—	10	2	no	—
397	C₂×C₃×C₄	—	10	4	no	—
398	C₂×C₃×C₄	—	10	2	no	—
399	C₂×C₃×C₄	—	10	8	no	—
400	C₂×C₃×C₄	#709	1	4	yes	—
401	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
402	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
403	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
404	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
405	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
406	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
407	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
408	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
409	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	—	2	2	no	—
413	C₂×D₅	—	4	4	no	—
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	4	no	—
418	C₄×C₅	C₂×C₃×#41	1	4	yes	—
419	Dic₅	—	2	4	no	—
420	Dic₅	—	2	2	no	—
421	Dic₅	—	2	4	no	—
422	Dic₅	—	2	2	no	—
423	Dic₅	—	2	2	no	—
424	C₂⁴	—	5	1	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	5	4	no	—
427	C₂×Q₈	—	10	4	no	—
428	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	2	no	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	2	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	4	no	—
435	C₂²×C₄	—	10	4	no	—
436	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
439	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
440	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
441	C₄⋊C₄	—	5	4	no	—
442	C₄⋊C₄	—	5	4	no	—
443	C₄⋊C₄	—	5	4	no	—
444	C₄⋊C₄	—	5	8	no	—
445	C₄⋊C₄	—	5	8	no	—
446	C₄⋊C₄	—	5	8	no	—
447	C₄⋊C₄	—	5	8	no	—
448	C₄⋊C₄	—	5	8	no	—
449	C₄⋊C₄	—	5	8	no	—
450	C₄⋊C₄	—	5	8	no	—
451	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
452	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
453	C₂²⋊C₄	—	5	4	no	—
454	C₂²⋊C₄	—	5	4	no	—
455	C₂²⋊C₄	—	5	8	no	—
456	C₂²⋊C₄	—	5	8	no	—
457	C₄²	—	5	4	no	—
458	C₄²	—	5	8	no	—
459	C₄²	C₂²×C₃×D₅	1	4	yes	—
460	C₄²	C₂²×C₃×D₅	1	8	yes	—
461	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
462	C₂²×C₃	—	10	2	no	—
463	C₂²×C₃	—	10	2	no	—
464	C₂²×C₃	—	10	2	no	—
465	C₂²×C₃	—	20	4	no	—
466	C₂²×C₃	C₂×#709	1	2	yes	—
467	C₂²×C₃	#4147	1	2	yes	—
468	C₂²×C₃	#4150	1	2	yes	—
469	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
470	C₃×C₄	—	2	4	no	—
471	C₃×C₄	—	2	2	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	10	2	no	—
475	C₃×C₄	—	10	4	no	—
476	C₃×C₄	—	10	2	no	—
477	C₃×C₄	—	10	4	no	—
478	C₃×C₄	—	10	2	no	—
479	C₃×C₄	C₂×#709	1	4	yes	—
480	C₂×C₅	C₃×#541	1	4	yes	complemented
481	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
482	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
484	D₅	—	4	2	no	—
485	C₂³	—	5	2	no	—
486	C₂³	—	10	2	no	—
487	C₂³	—	10	2	no	—
488	C₂³	—	10	2	no	—
489	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
490	Q₈	—	2	8	no	—
491	Q₈	—	10	8	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	5	2	no	—
497	C₂×C₄	—	5	4	no	—
498	C₂×C₄	—	5	2	no	—
499	C₂×C₄	—	5	4	no	—
500	C₂×C₄	—	5	2	no	—
501	C₂×C₄	—	10	2	no	—
502	C₂×C₄	—	10	4	no	—
503	C₂×C₄	—	10	2	no	—
504	C₂×C₄	—	10	4	no	—
505	C₂×C₄	—	10	2	no	—
506	C₂×C₄	—	10	8	no	—
507	C₂×C₄	C₃×#709	1	4	yes	—
508	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
509	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
510	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
511	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
512	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
513	C₂×C₃	—	20	2	no	—
514	C₂×C₃	#65917	1	4	yes	direct product factor
515	C₂×C₃	C₂²×#709	1	1	yes	characteristic
516	C₂×C₃	C₂×#4147	1	1	yes	characteristic
517	C₂×C₃	C₂×#4150	1	1	yes	characteristic
518	C₅	C₂×C₃×#541	1	1	yes	characteristic, complemented, Sylow
519	C₂²	—	10	2	no	—
520	C₂²	—	10	2	no	—
521	C₂²	—	10	2	no	—
522	C₂²	—	20	4	no	—
523	C₂²	C₂×C₃×#709	1	2	yes	—
524	C₂²	C₃×#4147	1	2	yes	—
525	C₂²	C₃×#4150	1	2	yes	—
526	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
527	C₄	—	2	4	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	10	2	no	—
532	C₄	—	10	4	no	—
533	C₄	—	10	2	no	—
534	C₄	—	10	4	no	—
535	C₄	—	10	2	no	—
536	C₄	C₂×C₃×#709	1	4	yes	—
537	C₃	C₂×#65917	1	1	yes	characteristic, direct product factor, Sylow
538	C₂	—	20	2	no	—
539	C₂	C₃×#65917	1	4	yes	direct product factor
540	C₂	C₂²×C₃×#709	1	1	yes	characteristic
541	C₂	C₂×C₃×#4147	1	1	yes	characteristic
542	C₂	C₂×C₃×#4150	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×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×#541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ 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×#65917	C₂	direct (N × H)
7. C₂×C₃×#4036	C₂	semidirect
8. C₂×C₃×#4035	C₂	semidirect
11. C₂×C₃×#4016	C₂	semidirect
12. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
13. C₂×#65917	C₃	direct (N × H)
17. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₃×#4090	C₂²	semidirect
42. C₃×#4036	C₂²	semidirect
43. C₃×#4035	C₂²	semidirect
46. C₃×#4016	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
51. C₂×#4090	C₂×C₃	semidirect
52. #65917	C₂×C₃	direct (N × H)
55. C₂×#4036	C₂×C₃	semidirect
56. C₂×#4035	C₂×C₃	semidirect
59. C₂×#4016	C₂×C₃	semidirect
60. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
108. C₂×C₃×C₄×Q₈	D₅	semidirect
113. C₄×C₅×Q₈	C₂²×C₃	semidirect
119. #4090	C₂²×C₃	semidirect
138. #4036	C₂²×C₃	semidirect
139. #4035	C₂²×C₃	semidirect
142. #4016	C₂²×C₃	semidirect
143. C₄×Dic₁₀	C₂²×C₃	semidirect
185. C₃×C₄×Q₈	C₂×D₅	semidirect
254. C₂×C₄×Q₈	C₃×D₅	semidirect
351. C₄×Q₈	C₂×C₃×D₅	semidirect
373. C₂×C₃×C₅	#541	semidirect
461. C₃×C₅	C₂×#541	semidirect
480. C₂×C₅	C₃×#541	semidirect
514. C₂×C₃	#65917	direct (N × H)
518. C₅	C₂×C₃×#541	semidirect
537. C₃	C₂×#65917	direct (N × H)
539. C₂	C₃×#65917	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×#65917	2
C₂×C₃×#4044	2
C₂×C₃×#4043	2
C₂×C₃×#4036	2
C₂×C₃×#4035	2
C₂×C₃×#4022	2
C₂×C₃×#4018	2
C₂×C₃×#4016	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#65917	3
C₂×C₃×#541	5

Subgroups — C2×C3×#65917 #14481194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65917 #14481194