Subgroups — C₂×C₃×#66066 #14484007

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 424 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×#4093	C₂	1	2	yes	maximal
3	C₂×C₃×Q₈×Dic₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66066	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4044	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4043	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4038	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66066	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×#4093	C₂²	1	16	yes	—
20	C₃×Q₈×Dic₅	C₂²	1	16	yes	complemented
21	C₂×C₃×#685	C₂²	1	4	yes	—
22	C₂×C₃×#685	C₂²	1	2	yes	—
23	C₂×C₃×#685	C₂²	1	4	yes	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
25	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×#683	C₂²	1	2	yes	—
28	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
29	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
30	C₃×#4044	C₂²	1	32	yes	complemented
31	C₃×#4043	C₂²	1	16	yes	complemented
32	C₃×#4038	C₂²	1	16	yes	complemented
33	C₃×C₄×D₂₀	C₂²	1	8	yes	—
34	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
35	C₂×C₃×#556	—	5	1	no	maximal, Hall
36	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4093	C₂×C₃	1	2	yes	—
38	C₂×Q₈×Dic₅	C₂×C₃	1	2	yes	complemented
39	#66066	C₂×C₃	1	16	yes	direct product factor
40	C₂×#4044	C₂×C₃	1	4	yes	complemented
41	C₂×#4043	C₂×C₃	1	2	yes	complemented
42	C₂×#4038	C₂×C₃	1	2	yes	complemented
43	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
44	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×D₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	—	2	8	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂×C₃×D₂₀	—	2	4	no	—
56	C₂×C₃×D₂₀	C₂³	1	4	yes	—
57	C₂×C₃×C₄×D₅	—	2	8	no	—
58	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
59	C₂×C₃×Dic₁₀	—	2	4	no	—
60	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
62	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
63	C₃×C₄²×C₅	C₂³	1	4	yes	—
64	C₃×#685	C₂³	1	16	yes	—
65	C₃×#685	C₂³	1	16	yes	—
66	C₃×#685	C₂³	1	8	yes	—
67	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
68	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
69	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
70	C₃×#683	C₂³	1	8	yes	—
71	C₃×C₄×Dic₅	C₂³	1	8	yes	—
72	C₃×C₄×Dic₅	C₂³	1	16	yes	—
73	C₃×#556	—	5	16	no	—
74	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
75	C₂×C₃×#126	—	5	4	no	—
76	C₂×C₃×#124	—	5	2	no	—
77	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
78	C₂×C₃×C₄×Q₈	—	5	2	no	—
79	C₂×C₃×C₄×Q₈	—	5	1	no	—
80	C₂×C₃×C₄×D₄	—	5	1	no	—
81	C₂×C₃×#117	—	5	2	no	—
82	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
83	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
85	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
90	#4093	C₂²×C₃	1	16	yes	—
91	Q₈×Dic₅	C₂²×C₃	1	16	yes	complemented
92	C₂×#685	C₂²×C₃	1	2	yes	—
93	C₂×#685	C₂²×C₃	1	4	yes	—
94	C₂×#685	C₂²×C₃	1	4	yes	—
95	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
98	C₂×#683	C₂²×C₃	1	2	yes	—
99	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
101	#4044	C₂²×C₃	1	32	yes	complemented
102	#4043	C₂²×C₃	1	16	yes	complemented
103	#4038	C₂²×C₃	1	16	yes	complemented
104	C₄×D₂₀	C₂²×C₃	1	8	yes	—
105	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
106	C₂×#556	—	5	1	no	Sylow
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₂²×C₃×D₅	—	2	4	no	—
109	C₂²×C₃×D₅	—	2	4	no	—
110	C₂²×C₃×D₅	—	2	4	no	—
111	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
112	C₃×C₅×Q₈	—	2	16	no	—
113	C₂×C₃×C₄×C₅	—	2	8	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	#41	1	4	yes	—
116	C₂×C₃×C₄×C₅	#41	1	4	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
121	C₂×C₃×Dic₅	—	2	4	no	—
122	C₂×C₃×Dic₅	—	2	4	no	—
123	C₂×C₃×Dic₅	—	2	4	no	—
124	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
125	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
126	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
127	C₃×D₂₀	—	2	8	no	—
128	C₃×C₄×D₅	—	2	16	no	—
129	C₃×Dic₁₀	—	2	8	no	—
130	C₂²×C₃×Q₈	—	5	1	no	—
131	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
132	C₂²×C₃×D₄	—	5	1	no	—
133	C₂³×C₃×C₄	—	5	2	no	—
134	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
135	C₃×#126	—	5	32	no	—
136	C₃×#124	—	5	16	no	—
137	C₃×C₂²⋊Q₈	—	5	16	no	—
138	C₃×C₄×Q₈	—	5	16	no	—
139	C₃×C₄×Q₈	—	5	8	no	—
140	C₃×C₄×D₄	—	5	8	no	—
141	C₃×#117	—	5	16	no	—
142	C₂×C₃×C₄⋊C₄	—	5	1	no	—
143	C₂×C₃×C₄⋊C₄	—	5	1	no	—
144	C₂×C₃×C₄⋊C₄	—	5	4	no	—
145	C₂×C₃×C₄⋊C₄	—	5	2	no	—
146	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
149	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
150	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
151	C₂×C₃×C₄²	—	5	4	no	—
152	C₂×C₃×C₄²	—	5	2	no	—
153	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
154	C₂³×D₅	C₂³×C₃	1	2	yes	—
155	C₂×C₅×Q₈	—	2	8	no	—
156	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
162	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
163	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
164	C₂×D₂₀	—	2	4	no	—
165	C₂×D₂₀	C₂³×C₃	1	4	yes	—
166	C₂×C₄×D₅	—	2	8	no	—
167	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
168	C₂×Dic₁₀	—	2	4	no	—
169	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
170	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
171	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
172	C₄²×C₅	C₂³×C₃	1	4	yes	—
173	#685	C₂³×C₃	1	8	yes	—
174	#685	C₂³×C₃	1	16	yes	—
175	#685	C₂³×C₃	1	16	yes	—
176	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
177	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
178	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
179	#683	C₂³×C₃	1	8	yes	—
180	C₄×Dic₅	C₂³×C₃	1	8	yes	—
181	C₄×Dic₅	C₂³×C₃	1	16	yes	—
182	#556	—	5	16	no	—
183	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
184	C₂×#126	—	5	4	no	—
185	C₂×#124	—	5	2	no	—
186	C₂×C₂²⋊Q₈	—	5	2	no	—
187	C₂×C₄×Q₈	—	5	2	no	—
188	C₂×C₄×Q₈	—	5	1	no	—
189	C₂×C₄×D₄	—	5	1	no	—
190	C₂×#117	—	5	2	no	—
191	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
192	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
193	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
194	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
195	C₂×C₃×D₅	—	2	4	no	—
196	C₂×C₃×D₅	—	2	4	no	—
197	C₂×C₃×D₅	—	2	4	no	—
198	C₂×C₃×D₅	—	4	8	no	—
199	C₃×C₄×C₅	—	2	8	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	C₂×#41	1	4	yes	—
202	C₃×C₄×C₅	C₂×#41	1	4	yes	—
203	C₃×Dic₅	—	2	4	no	—
204	C₃×Dic₅	—	2	4	no	—
205	C₃×Dic₅	—	2	4	no	—
206	C₂⁴×C₃	—	5	2	no	—
207	C₂×C₃×Q₈	—	2	8	no	—
208	C₂×C₃×Q₈	—	5	4	no	—
209	C₂×C₃×Q₈	—	10	4	no	—
210	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
211	C₂×C₃×D₄	—	5	4	no	—
212	C₂×C₃×D₄	—	10	4	no	—
213	C₂²×C₃×C₄	—	5	2	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	—	5	2	no	—
216	C₂²×C₃×C₄	—	5	8	no	—
217	C₂²×C₃×C₄	—	10	8	no	—
218	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
219	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	5	8	no	—
223	C₃×C₄⋊C₄	—	5	4	no	—
224	C₃×C₄⋊C₄	—	5	4	no	—
225	C₃×C₄⋊C₄	—	5	16	no	—
226	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
227	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
228	C₃×C₂²⋊C₄	—	5	16	no	—
229	C₃×C₂²⋊C₄	—	5	8	no	—
230	C₃×C₂²⋊C₄	—	5	16	no	—
231	C₃×C₄²	—	5	16	no	—
232	C₃×C₄²	—	5	8	no	—
233	C₃×C₄²	C₂²×D₅	1	4	yes	—
234	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
235	C₂²×D₅	—	2	4	no	—
236	C₂²×D₅	—	2	4	no	—
237	C₂²×D₅	—	2	4	no	—
238	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
239	C₅×Q₈	—	2	16	no	—
240	C₂×C₄×C₅	—	2	8	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	C₃×#41	1	4	yes	—
243	C₂×C₄×C₅	C₃×#41	1	4	yes	—
244	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
245	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
246	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
247	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
248	C₂×Dic₅	—	2	4	no	—
249	C₂×Dic₅	—	2	4	no	—
250	C₂×Dic₅	—	2	4	no	—
251	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
252	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
253	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
254	D₂₀	—	2	8	no	—
255	C₄×D₅	—	2	16	no	—
256	Dic₁₀	—	2	8	no	—
257	C₂²×Q₈	—	5	1	no	—
258	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
259	C₂²×D₄	—	5	1	no	—
260	C₂³×C₄	—	5	2	no	—
261	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
262	#126	—	5	32	no	—
263	#124	—	5	16	no	—
264	C₂²⋊Q₈	—	5	16	no	—
265	C₄×Q₈	—	5	16	no	—
266	C₄×Q₈	—	5	8	no	—
267	C₄×D₄	—	5	8	no	—
268	#117	—	5	16	no	—
269	C₂×C₄⋊C₄	—	5	1	no	—
270	C₂×C₄⋊C₄	—	5	1	no	—
271	C₂×C₄⋊C₄	—	5	4	no	—
272	C₂×C₄⋊C₄	—	5	2	no	—
273	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
275	C₂×C₂²⋊C₄	—	5	4	no	—
276	C₂×C₂²⋊C₄	—	5	2	no	—
277	C₂×C₂²⋊C₄	—	5	4	no	—
278	C₂×C₄²	—	5	4	no	—
279	C₂×C₄²	—	5	2	no	—
280	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
281	C₂×C₃×C₅	#556	1	4	yes	complemented
282	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
285	C₃×D₅	—	4	4	no	—
286	C₂³×C₃	—	5	4	no	—
287	C₂³×C₃	—	10	4	no	—
288	C₂³×C₃	—	10	4	no	—
289	C₂³×C₃	—	10	4	no	—
290	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
291	C₃×Q₈	—	2	16	no	—
292	C₃×Q₈	—	10	8	no	—
293	C₃×D₄	—	10	8	no	—
294	C₂×C₃×C₄	—	2	8	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	5	4	no	—
297	C₂×C₃×C₄	—	5	4	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	—	10	4	no	—
300	C₂×C₃×C₄	—	10	4	no	—
301	C₂×C₃×C₄	—	10	4	no	—
302	C₂×C₃×C₄	—	10	16	no	—
303	C₂×C₃×C₄	#711	1	4	yes	—
304	C₂×C₃×C₄	#713	1	4	yes	—
305	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
306	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
308	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
309	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
310	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
311	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
312	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
313	C₂×D₅	—	2	4	no	—
314	C₂×D₅	—	2	4	no	—
315	C₂×D₅	—	2	4	no	—
316	C₂×D₅	—	4	8	no	—
317	C₄×C₅	—	2	8	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	C₂×C₃×#41	1	4	yes	—
320	C₄×C₅	C₂×C₃×#41	1	4	yes	—
321	Dic₅	—	2	4	no	—
322	Dic₅	—	2	4	no	—
323	Dic₅	—	2	4	no	—
324	C₂⁴	—	5	2	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	5	4	no	—
327	C₂×Q₈	—	10	4	no	—
328	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
329	C₂×D₄	—	5	4	no	—
330	C₂×D₄	—	10	4	no	—
331	C₂²×C₄	—	5	2	no	—
332	C₂²×C₄	—	5	2	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	5	8	no	—
335	C₂²×C₄	—	10	8	no	—
336	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
337	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
340	C₄⋊C₄	—	5	4	no	—
341	C₄⋊C₄	—	5	4	no	—
342	C₄⋊C₄	—	5	16	no	—
343	C₄⋊C₄	—	5	8	no	—
344	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
345	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
346	C₂²⋊C₄	—	5	16	no	—
347	C₂²⋊C₄	—	5	8	no	—
348	C₂²⋊C₄	—	5	16	no	—
349	C₄²	—	5	16	no	—
350	C₄²	—	5	8	no	—
351	C₄²	C₂²×C₃×D₅	1	4	yes	—
352	C₃×C₅	C₂×#556	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	10	4	no	—
354	C₂²×C₃	—	10	4	no	—
355	C₂²×C₃	—	10	4	no	—
356	C₂²×C₃	—	20	8	no	—
357	C₂²×C₃	C₂×#711	1	2	yes	—
358	C₂²×C₃	C₂×#713	1	2	yes	—
359	C₂²×C₃	#4147	1	2	yes	—
360	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
361	C₃×C₄	—	2	8	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	10	4	no	—
364	C₃×C₄	—	10	4	no	—
365	C₃×C₄	—	10	4	no	—
366	C₃×C₄	C₂×#711	1	4	yes	—
367	C₃×C₄	C₂×#713	1	4	yes	—
368	C₂×C₅	C₃×#556	1	4	yes	complemented
369	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
370	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
371	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
372	D₅	—	4	4	no	—
373	C₂³	—	5	4	no	—
374	C₂³	—	10	4	no	—
375	C₂³	—	10	4	no	—
376	C₂³	—	10	4	no	—
377	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
378	Q₈	—	2	16	no	—
379	Q₈	—	10	8	no	—
380	D₄	—	10	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	5	4	no	—
384	C₂×C₄	—	5	4	no	—
385	C₂×C₄	—	5	4	no	—
386	C₂×C₄	—	10	4	no	—
387	C₂×C₄	—	10	4	no	—
388	C₂×C₄	—	10	4	no	—
389	C₂×C₄	—	10	16	no	—
390	C₂×C₄	C₃×#711	1	4	yes	—
391	C₂×C₄	C₃×#713	1	4	yes	—
392	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
393	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
394	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
395	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
396	C₂×C₃	—	20	4	no	—
397	C₂×C₃	#66066	1	4	yes	direct product factor
398	C₂×C₃	C₂²×#711	1	1	yes	characteristic
399	C₂×C₃	C₂²×#713	1	1	yes	characteristic
400	C₂×C₃	C₂×#4147	1	1	yes	characteristic
401	C₅	C₂×C₃×#556	1	1	yes	characteristic, complemented, Sylow
402	C₂²	—	10	4	no	—
403	C₂²	—	10	4	no	—
404	C₂²	—	10	4	no	—
405	C₂²	—	20	8	no	—
406	C₂²	C₂×C₃×#711	1	2	yes	—
407	C₂²	C₂×C₃×#713	1	2	yes	—
408	C₂²	C₃×#4147	1	2	yes	—
409	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
410	C₄	—	2	8	no	—
411	C₄	—	2	2	no	—
412	C₄	—	10	4	no	—
413	C₄	—	10	4	no	—
414	C₄	—	10	4	no	—
415	C₄	C₂×C₃×#711	1	4	yes	—
416	C₄	C₂×C₃×#713	1	4	yes	—
417	C₃	C₂×#66066	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	20	4	no	—
419	C₂	C₃×#66066	1	4	yes	direct product factor
420	C₂	C₂²×C₃×#711	1	1	yes	characteristic
421	C₂	C₂²×C₃×#713	1	1	yes	characteristic
422	C₂	C₂×C₃×#4147	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	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#556
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×#66066	C₂	direct (N × H)
5. C₂×C₃×#4044	C₂	semidirect
6. C₂×C₃×#4043	C₂	semidirect
7. C₂×C₃×#4038	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×#66066	C₃	direct (N × H)
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×Q₈×Dic₅	C₂²	semidirect
30. C₃×#4044	C₂²	semidirect
31. C₃×#4043	C₂²	semidirect
32. C₃×#4038	C₂²	semidirect
34. C₃×C₄×Dic₁₀	C₂²	semidirect
36. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
38. C₂×Q₈×Dic₅	C₂×C₃	semidirect
39. #66066	C₂×C₃	direct (N × H)
40. C₂×#4044	C₂×C₃	semidirect
41. C₂×#4043	C₂×C₃	semidirect
42. C₂×#4038	C₂×C₃	semidirect
44. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
74. C₂×C₃×C₄⋊Q₈	D₅	semidirect
86. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
91. Q₈×Dic₅	C₂²×C₃	semidirect
101. #4044	C₂²×C₃	semidirect
102. #4043	C₂²×C₃	semidirect
103. #4038	C₂²×C₃	semidirect
105. C₄×Dic₁₀	C₂²×C₃	semidirect
134. C₃×C₄⋊Q₈	C₂×D₅	semidirect
183. C₂×C₄⋊Q₈	C₃×D₅	semidirect
261. C₄⋊Q₈	C₂×C₃×D₅	semidirect
281. C₂×C₃×C₅	#556	semidirect
352. C₃×C₅	C₂×#556	semidirect
368. C₂×C₅	C₃×#556	semidirect
397. C₂×C₃	#66066	direct (N × H)
401. C₅	C₂×C₃×#556	semidirect
417. C₃	C₂×#66066	direct (N × H)
419. C₂	C₃×#66066	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×#4093	2
C₂×C₃×Q₈×Dic₅	2
C₃×#66066	2
C₂×C₃×#4044	2
C₂×C₃×#4043	2
C₂×C₃×#4038	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#66066	3
C₂×C₃×#556	5

Subgroups — C2×C3×#66066 #14484007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66066 #14484007