Subgroups — C₂×C₃×#66062 #14480121

Order 1920.

2336 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4092	C₂	1	2	yes	maximal
3	C₂×C₃×Q₈×Dic₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66062	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4043	C₂	1	2	yes	maximal
6	C₂×C₃×#4038	C₂	1	2	yes	maximal
7	C₂×C₃×#4036	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4033	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×#4015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#66062	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×#4092	C₂²	1	16	yes	—
22	C₃×Q₈×Dic₅	C₂²	1	16	yes	complemented
23	C₂×C₃×#685	C₂²	1	4	yes	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
27	C₂×C₃×#683	C₂²	1	4	yes	—
28	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
30	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
32	C₃×#4043	C₂²	1	16	yes	—
33	C₃×#4038	C₂²	1	16	yes	—
34	C₃×#4036	C₂²	1	16	yes	complemented
35	C₃×#4033	C₂²	1	16	yes	complemented
36	C₃×C₄²×D₅	C₂²	1	8	yes	—
37	C₃×#4015	C₂²	1	8	yes	complemented
38	C₂×C₃×#533	—	5	1	no	maximal, Hall
39	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#4092	C₂×C₃	1	2	yes	—
41	C₂×Q₈×Dic₅	C₂×C₃	1	2	yes	complemented
42	#66062	C₂×C₃	1	16	yes	direct product factor
43	C₂×#4043	C₂×C₃	1	2	yes	—
44	C₂×#4038	C₂×C₃	1	2	yes	—
45	C₂×#4036	C₂×C₃	1	2	yes	complemented
46	C₂×#4033	C₂×C₃	1	2	yes	complemented
47	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
48	C₂×#4015	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×Q₈	—	2	8	no	—
51	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	—	2	4	no	—
61	C₂×C₃×C₄×D₅	—	2	4	no	—
62	C₂×C₃×C₄×D₅	Q₈	1	8	yes	complemented
63	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
64	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
65	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
66	C₂×C₃×Dic₁₀	—	2	8	no	—
67	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
70	C₃×C₄²×C₅	C₂³	1	4	yes	—
71	C₃×#685	C₂³	1	16	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
73	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
74	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
75	C₃×#683	C₂³	1	16	yes	—
76	C₃×C₄×Dic₅	C₂³	1	4	yes	—
77	C₃×C₄×Dic₅	C₂³	1	16	yes	—
78	C₃×C₄×Dic₅	C₂³	1	4	yes	—
79	C₃×C₄×Dic₅	C₂³	1	4	yes	—
80	C₃×#533	—	5	16	no	—
81	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
82	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
83	C₂×C₃×#125	—	5	2	no	—
84	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
85	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
86	C₂×C₃×C₄×Q₈	—	5	2	no	—
87	C₂×C₃×C₄×Q₈	—	5	2	no	—
88	C₂×C₃×#117	—	5	2	no	—
89	C₂²×C₃×C₄²	—	5	1	no	—
90	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
91	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
94	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
95	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	#4092	C₂²×C₃	1	16	yes	—
100	Q₈×Dic₅	C₂²×C₃	1	16	yes	complemented
101	C₂×#685	C₂²×C₃	1	4	yes	—
102	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
103	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
104	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
105	C₂×#683	C₂²×C₃	1	4	yes	—
106	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
110	#4043	C₂²×C₃	1	16	yes	—
111	#4038	C₂²×C₃	1	16	yes	—
112	#4036	C₂²×C₃	1	16	yes	complemented
113	#4033	C₂²×C₃	1	16	yes	complemented
114	C₄²×D₅	C₂²×C₃	1	8	yes	—
115	#4015	C₂²×C₃	1	8	yes	complemented
116	C₂×#533	—	5	1	no	Sylow
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×C₃×D₅	—	2	2	no	—
119	C₂²×C₃×D₅	—	2	2	no	—
120	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
121	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
122	C₃×C₅×Q₈	—	2	16	no	—
123	C₂×C₃×C₄×C₅	—	2	8	no	—
124	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
125	C₂×C₃×C₄×C₅	#41	1	4	yes	—
126	C₂×C₃×C₄×C₅	#41	1	4	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂×C₃×Dic₅	—	2	8	no	—
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	—	2	2	no	—
134	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
135	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
136	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
137	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
138	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
139	C₃×C₄×D₅	—	2	8	no	—
140	C₃×C₄×D₅	—	2	8	no	—
141	C₃×C₄×D₅	C₂×Q₈	1	16	yes	complemented
142	C₃×Dic₁₀	—	2	16	no	—
143	C₂²×C₃×Q₈	—	5	2	no	—
144	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
145	C₂³×C₃×C₄	—	5	1	no	—
146	C₂³×C₃×C₄	—	5	1	no	—
147	C₂³×C₃×C₄	—	5	1	no	—
148	C₃×C₄⋊Q₈	—	5	8	no	—
149	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
150	C₃×#125	—	5	16	no	—
151	C₃×C₂²⋊Q₈	—	5	16	no	—
152	C₃×C₂²⋊Q₈	—	5	16	no	—
153	C₃×C₄×Q₈	—	5	16	no	—
154	C₃×C₄×Q₈	—	5	16	no	—
155	C₃×#117	—	5	16	no	—
156	C₂×C₃×C₄⋊C₄	—	5	2	no	—
157	C₂×C₃×C₄⋊C₄	—	5	4	no	—
158	C₂×C₃×C₄⋊C₄	—	5	4	no	—
159	C₂×C₃×C₄⋊C₄	—	5	2	no	—
160	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
163	C₂×C₃×C₄²	—	5	1	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×C₃×C₄²	—	5	1	no	—
166	C₂×C₃×C₄²	—	5	4	no	—
167	C₂×C₃×C₄²	—	5	8	no	—
168	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
169	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₅×Q₈	—	2	8	no	—
171	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
177	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
178	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
179	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₄×D₅	—	2	4	no	—
181	C₂×C₄×D₅	—	2	4	no	—
182	C₂×C₄×D₅	C₃×Q₈	1	8	yes	complemented
183	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
184	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
185	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
186	C₂×Dic₁₀	—	2	8	no	—
187	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
188	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
190	C₄²×C₅	C₂³×C₃	1	4	yes	—
191	#685	C₂³×C₃	1	16	yes	—
192	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
193	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
194	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
195	#683	C₂³×C₃	1	16	yes	—
196	C₄×Dic₅	C₂³×C₃	1	4	yes	—
197	C₄×Dic₅	C₂³×C₃	1	4	yes	—
198	C₄×Dic₅	C₂³×C₃	1	4	yes	—
199	C₄×Dic₅	C₂³×C₃	1	16	yes	—
200	#533	—	5	16	no	—
201	C₂×C₄⋊Q₈	—	5	1	no	—
202	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
203	C₂×#125	—	5	2	no	—
204	C₂×C₂²⋊Q₈	—	5	2	no	—
205	C₂×C₂²⋊Q₈	—	5	2	no	—
206	C₂×C₄×Q₈	—	5	2	no	—
207	C₂×C₄×Q₈	—	5	2	no	—
208	C₂×#117	—	5	2	no	—
209	C₂²×C₄²	—	5	1	no	—
210	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
211	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
212	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
213	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
214	C₂×C₃×D₅	—	2	8	no	—
215	C₂×C₃×D₅	—	2	2	no	—
216	C₂×C₃×D₅	—	2	2	no	—
217	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
218	C₃×C₄×C₅	—	2	8	no	—
219	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	—
220	C₃×C₄×C₅	C₂×#41	1	4	yes	—
221	C₃×C₄×C₅	C₂×#41	1	4	yes	—
222	C₃×Dic₅	—	2	8	no	—
223	C₃×Dic₅	—	2	2	no	—
224	C₃×Dic₅	—	2	2	no	—
225	C₃×Dic₅	C₂²×Q₈	1	4	yes	—
226	C₂⁴×C₃	—	5	1	no	—
227	C₂×C₃×Q₈	—	2	8	no	—
228	C₂×C₃×Q₈	—	5	8	no	—
229	C₂×C₃×Q₈	—	10	8	no	—
230	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
231	C₂²×C₃×C₄	—	5	1	no	—
232	C₂²×C₃×C₄	—	5	8	no	—
233	C₂²×C₃×C₄	—	5	4	no	—
234	C₂²×C₃×C₄	—	5	1	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	4	no	—
237	C₂²×C₃×C₄	—	5	4	no	—
238	C₂²×C₃×C₄	—	5	4	no	—
239	C₂²×C₃×C₄	—	10	4	no	—
240	C₂²×C₃×C₄	—	10	4	no	—
241	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
245	C₃×C₄⋊C₄	—	5	16	no	—
246	C₃×C₄⋊C₄	—	5	8	no	—
247	C₃×C₄⋊C₄	—	5	16	no	—
248	C₃×C₄⋊C₄	—	5	8	no	—
249	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
250	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
251	C₃×C₂²⋊C₄	—	5	16	no	—
252	C₃×C₄²	—	5	4	no	—
253	C₃×C₄²	—	5	4	no	—
254	C₃×C₄²	—	5	4	no	—
255	C₃×C₄²	—	5	16	no	—
256	C₃×C₄²	C₂²×D₅	1	4	yes	—
257	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
258	C₂²×D₅	—	2	2	no	—
259	C₂²×D₅	—	2	2	no	—
260	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
261	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
262	C₅×Q₈	—	2	16	no	—
263	C₂×C₄×C₅	—	2	8	no	—
264	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
265	C₂×C₄×C₅	C₃×#41	1	4	yes	—
266	C₂×C₄×C₅	C₃×#41	1	4	yes	—
267	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
268	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
271	C₂×Dic₅	—	2	8	no	—
272	C₂×Dic₅	—	2	2	no	—
273	C₂×Dic₅	—	2	2	no	—
274	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
275	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
276	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
277	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
278	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
279	C₄×D₅	—	2	8	no	—
280	C₄×D₅	—	2	8	no	—
281	C₄×D₅	C₂×C₃×Q₈	1	16	yes	complemented
282	Dic₁₀	—	2	16	no	—
283	C₂²×Q₈	—	5	2	no	—
284	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
285	C₂³×C₄	—	5	1	no	—
286	C₂³×C₄	—	5	1	no	—
287	C₂³×C₄	—	5	1	no	—
288	C₄⋊Q₈	—	5	8	no	—
289	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
290	#125	—	5	16	no	—
291	C₂²⋊Q₈	—	5	16	no	—
292	C₂²⋊Q₈	—	5	16	no	—
293	C₄×Q₈	—	5	16	no	—
294	C₄×Q₈	—	5	16	no	—
295	#117	—	5	16	no	—
296	C₂×C₄⋊C₄	—	5	2	no	—
297	C₂×C₄⋊C₄	—	5	4	no	—
298	C₂×C₄⋊C₄	—	5	4	no	—
299	C₂×C₄⋊C₄	—	5	2	no	—
300	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
302	C₂×C₂²⋊C₄	—	5	4	no	—
303	C₂×C₄²	—	5	4	no	—
304	C₂×C₄²	—	5	1	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₂×C₄²	—	5	8	no	—
308	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
309	C₂×C₃×C₅	#533	1	4	yes	complemented
310	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
312	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
313	C₃×D₅	—	2	4	no	—
314	C₂³×C₃	—	5	4	no	—
315	C₂³×C₃	—	5	2	no	—
316	C₂³×C₃	—	10	2	no	—
317	C₂³×C₃	—	10	2	no	—
318	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
319	C₃×Q₈	—	2	16	no	—
320	C₃×Q₈	—	10	16	no	—
321	C₂×C₃×C₄	—	2	8	no	—
322	C₂×C₃×C₄	—	5	4	no	—
323	C₂×C₃×C₄	—	5	2	no	—
324	C₂×C₃×C₄	—	5	16	no	—
325	C₂×C₃×C₄	—	5	2	no	—
326	C₂×C₃×C₄	—	5	2	no	—
327	C₂×C₃×C₄	—	5	8	no	—
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	10	2	no	—
330	C₂×C₃×C₄	—	10	8	no	—
331	C₂×C₃×C₄	—	10	8	no	—
332	C₂×C₃×C₄	—	10	8	no	—
333	C₂×C₃×C₄	#711	1	4	yes	—
334	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
335	C₂×C₃×C₄	#713	1	4	yes	—
336	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
337	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
338	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
339	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
340	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
341	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
342	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
343	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
344	C₂×D₅	—	2	2	no	—
345	C₂×D₅	—	2	2	no	—
346	C₂×D₅	—	2	8	no	—
347	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
348	C₄×C₅	—	2	8	no	—
349	C₄×C₅	C₂²×C₃×Q₈	1	4	yes	—
350	C₄×C₅	C₂×C₃×#41	1	4	yes	—
351	C₄×C₅	C₂×C₃×#41	1	4	yes	—
352	Dic₅	—	2	8	no	—
353	Dic₅	—	2	2	no	—
354	Dic₅	—	2	2	no	—
355	Dic₅	C₂²×C₃×Q₈	1	4	yes	—
356	C₂⁴	—	5	1	no	—
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	5	8	no	—
359	C₂×Q₈	—	10	8	no	—
360	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
361	C₂²×C₄	—	5	1	no	—
362	C₂²×C₄	—	5	8	no	—
363	C₂²×C₄	—	5	4	no	—
364	C₂²×C₄	—	5	1	no	—
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	5	4	no	—
367	C₂²×C₄	—	5	4	no	—
368	C₂²×C₄	—	5	4	no	—
369	C₂²×C₄	—	10	4	no	—
370	C₂²×C₄	—	10	4	no	—
371	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
375	C₄⋊C₄	—	5	8	no	—
376	C₄⋊C₄	—	5	16	no	—
377	C₄⋊C₄	—	5	16	no	—
378	C₄⋊C₄	—	5	8	no	—
379	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
380	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
381	C₂²⋊C₄	—	5	16	no	—
382	C₄²	—	5	4	no	—
383	C₄²	—	5	4	no	—
384	C₄²	—	5	4	no	—
385	C₄²	—	5	16	no	—
386	C₄²	C₂²×C₃×D₅	1	4	yes	—
387	C₃×C₅	C₂×#533	1	1	yes	characteristic, complemented, Hall
388	C₂²×C₃	—	5	4	no	—
389	C₂²×C₃	—	10	8	no	—
390	C₂²×C₃	—	10	2	no	—
391	C₂²×C₃	—	10	2	no	—
392	C₂²×C₃	C₂×#711	1	2	yes	—
393	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
394	C₂²×C₃	C₂×#713	1	2	yes	—
395	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
396	C₃×C₄	—	2	8	no	—
397	C₃×C₄	—	5	4	no	—
398	C₃×C₄	—	10	2	no	—
399	C₃×C₄	—	10	2	no	—
400	C₃×C₄	—	10	8	no	—
401	C₃×C₄	C₂×#711	1	4	yes	—
402	C₃×C₄	C₂×Q₈×D₅	1	4	yes	—
403	C₃×C₄	C₂×#713	1	4	yes	—
404	C₂×C₅	C₃×#533	1	4	yes	complemented
405	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
406	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
407	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
408	D₅	—	2	4	no	—
409	C₂³	—	5	4	no	—
410	C₂³	—	5	2	no	—
411	C₂³	—	10	2	no	—
412	C₂³	—	10	2	no	—
413	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
414	Q₈	—	2	16	no	—
415	Q₈	—	10	16	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	5	4	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	5	16	no	—
420	C₂×C₄	—	5	2	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	8	no	—
423	C₂×C₄	—	10	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	8	no	—
426	C₂×C₄	—	10	8	no	—
427	C₂×C₄	—	10	8	no	—
428	C₂×C₄	C₃×#711	1	4	yes	—
429	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
430	C₂×C₄	C₃×#713	1	4	yes	—
431	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
432	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
433	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
434	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
435	C₂×C₃	—	10	4	no	—
436	C₂×C₃	#66062	1	4	yes	direct product factor
437	C₂×C₃	C₂²×#711	1	1	yes	characteristic
438	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
439	C₂×C₃	C₂²×#713	1	1	yes	characteristic
440	C₅	C₂×C₃×#533	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	5	4	no	—
442	C₂²	—	10	2	no	—
443	C₂²	—	10	2	no	—
444	C₂²	—	10	8	no	—
445	C₂²	C₂×C₃×#711	1	2	yes	—
446	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
447	C₂²	C₂×C₃×#713	1	2	yes	—
448	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
449	C₄	—	2	8	no	—
450	C₄	—	5	4	no	—
451	C₄	—	10	2	no	—
452	C₄	—	10	2	no	—
453	C₄	—	10	8	no	—
454	C₄	C₂×C₃×#711	1	4	yes	—
455	C₄	C₂×C₃×Q₈×D₅	1	4	yes	—
456	C₄	C₂×C₃×#713	1	4	yes	—
457	C₃	C₂×#66062	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	10	4	no	—
459	C₂	C₃×#66062	1	4	yes	direct product factor
460	C₂	C₂²×C₃×#711	1	1	yes	characteristic
461	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
462	C₂	C₂²×C₃×#713	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×C₅×C₄⋊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 ◁ 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×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×Q₈×Dic₅	C₂	semidirect
4. C₃×#66062	C₂	direct (N × H)
7. C₂×C₃×#4036	C₂	semidirect
8. C₂×C₃×#4033	C₂	semidirect
10. C₂×C₃×#4015	C₂	semidirect
11. C₂×#66062	C₃	direct (N × H)
17. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×Q₈×Dic₅	C₂²	semidirect
34. C₃×#4036	C₂²	semidirect
35. C₃×#4033	C₂²	semidirect
37. C₃×#4015	C₂²	semidirect
39. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
41. C₂×Q₈×Dic₅	C₂×C₃	semidirect
42. #66062	C₂×C₃	direct (N × H)
45. C₂×#4036	C₂×C₃	semidirect
46. C₂×#4033	C₂×C₃	semidirect
48. C₂×#4015	C₂×C₃	semidirect
62. C₂×C₃×C₄×D₅	Q₈	semidirect
82. C₂×C₃×C₄⋊Q₈	D₅	semidirect
95. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
100. Q₈×Dic₅	C₂²×C₃	semidirect
112. #4036	C₂²×C₃	semidirect
113. #4033	C₂²×C₃	semidirect
115. #4015	C₂²×C₃	semidirect
141. C₃×C₄×D₅	C₂×Q₈	semidirect
149. C₃×C₄⋊Q₈	C₂×D₅	semidirect
182. C₂×C₄×D₅	C₃×Q₈	semidirect
202. C₂×C₄⋊Q₈	C₃×D₅	semidirect
281. C₄×D₅	C₂×C₃×Q₈	semidirect
289. C₄⋊Q₈	C₂×C₃×D₅	semidirect
309. C₂×C₃×C₅	#533	semidirect
387. C₃×C₅	C₂×#533	semidirect
404. C₂×C₅	C₃×#533	semidirect
436. C₂×C₃	#66062	direct (N × H)
440. C₅	C₂×C₃×#533	semidirect
457. C₃	C₂×#66062	direct (N × H)
459. C₂	C₃×#66062	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×C₅×C₄⋊Q₈	2
C₂×C₃×#4092	2
C₂×C₃×Q₈×Dic₅	2
C₃×#66062	2
C₂×C₃×#4043	2
C₂×C₃×#4038	2
C₂×C₃×#4036	2
C₂×C₃×#4033	2
C₂×C₃×C₄²×D₅	2
C₂×C₃×#4015	2
C₂×#66062	3
C₂×C₃×#533	5

Subgroups — C2×C3×#66062 #14480121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66062 #14480121