Subgroups — C₂×C₃×#66150 #14480474

Order 1920.

3024 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	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
3	C₃×#66150	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4093	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4092	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4090	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4075	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66150	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	—	2	8	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	8	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂×C₃×#709	—	2	8	no	—
18	C₂×C₃×#709	C₂²	1	8	yes	—
19	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
21	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
23	C₃×#4093	C₂²	1	16	yes	complemented
24	C₃×#4092	C₂²	1	32	yes	complemented
25	C₃×#4090	C₂²	1	16	yes	complemented
26	C₃×#4075	C₂²	1	32	yes	complemented
27	C₂×C₃×#685	C₂²	1	8	yes	—
28	C₃×#4072	C₂²	1	8	yes	complemented
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
30	C₂×C₃×#683	C₂²	1	8	yes	—
31	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
32	C₂×C₃×#536	—	5	1	no	maximal, Hall
33	C₂³×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×#709	C₂×C₃	1	1	yes	characteristic
35	#66150	C₂×C₃	1	16	yes	direct product factor
36	C₂×#4093	C₂×C₃	1	2	yes	complemented
37	C₂×#4092	C₂×C₃	1	4	yes	complemented
38	C₂×#4090	C₂×C₃	1	2	yes	complemented
39	C₂×#4075	C₂×C₃	1	4	yes	complemented
40	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂³×C₃×D₅	C₂³	1	2	yes	—
43	C₂×C₃×C₅×Q₈	—	2	8	no	—
44	C₂×C₃×C₅×Q₈	—	2	8	no	—
45	C₂×C₃×C₅×Q₈	—	2	32	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
47	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
48	C₂²×C₃×C₄×C₅	—	2	8	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
55	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
56	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
58	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
59	C₃×#709	—	2	32	no	—
60	C₂×C₃×D₂₀	—	2	4	no	—
61	C₂×C₃×D₂₀	C₂³	1	4	yes	—
62	C₂×C₃×C₄×D₅	—	2	8	no	—
63	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
64	C₂×C₃×Dic₁₀	—	2	4	no	—
65	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
66	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
67	C₃×#685	C₂³	1	32	yes	—
68	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
69	C₃×#683	C₂³	1	32	yes	—
70	C₃×C₄×Dic₅	C₂³	1	8	yes	—
71	C₂²×C₃×#41	—	5	1	no	—
72	C₂³×C₃×Q₈	D₅	1	1	yes	characteristic, complemented
73	C₃×#536	—	5	16	no	—
74	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
75	C₂×C₃×#124	—	5	2	no	—
76	C₂×C₃×#123	—	5	4	no	—
77	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
78	C₂×C₃×#117	—	5	1	no	—
79	C₂²×C₅×Q₈	—	2	8	no	—
80	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
81	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
82	C₂²×C₅×Q₈	C₂²×C₃	1	8	yes	complemented
83	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
84	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
86	C₂×#709	—	2	8	no	—
87	C₂×#709	C₂²×C₃	1	8	yes	—
88	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
90	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
92	#4093	C₂²×C₃	1	16	yes	complemented
93	#4092	C₂²×C₃	1	32	yes	complemented
94	#4090	C₂²×C₃	1	16	yes	complemented
95	#4075	C₂²×C₃	1	32	yes	complemented
96	C₂×#685	C₂²×C₃	1	8	yes	—
97	#4072	C₂²×C₃	1	8	yes	complemented
98	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
99	C₂×#683	C₂²×C₃	1	8	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
101	C₂×#536	—	5	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₂²×C₃×D₅	—	2	4	no	—
107	C₂²×C₃×D₅	—	2	8	no	—
108	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
109	C₃×C₅×Q₈	—	2	16	no	—
110	C₃×C₅×Q₈	—	2	16	no	—
111	C₂×C₃×C₄×C₅	—	2	16	no	—
112	C₂×C₃×C₄×C₅	—	2	8	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	—
116	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
119	C₃×C₂²⋊D₅	—	2	16	no	—
120	C₂×C₃×Dic₅	—	2	4	no	—
121	C₂×C₃×Dic₅	—	2	8	no	—
122	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
123	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
124	C₃×D₂₀	—	2	8	no	—
125	C₃×C₄×D₅	—	2	16	no	—
126	C₃×Dic₁₀	—	2	8	no	—
127	C₂×C₃×#41	—	5	8	no	—
128	C₂×C₃×#41	—	10	8	no	—
129	C₂²×C₃×Q₈	—	2	8	no	—
130	C₂²×C₃×Q₈	—	5	1	no	—
131	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
132	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
133	C₂²×C₃×Q₈	C₂×D₅	1	8	yes	complemented
134	C₂²×C₃×D₄	—	5	2	no	—
135	C₂²×C₃×D₄	—	5	1	no	—
136	C₂³×C₃×C₄	—	5	2	no	—
137	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
138	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄⋊Q₈	—	5	16	no	—
140	C₃×#124	—	5	16	no	—
141	C₃×#123	—	5	32	no	—
142	C₃×C₂²⋊Q₈	—	5	32	no	—
143	C₃×#117	—	5	8	no	—
144	C₂×C₃×C₄⋊C₄	—	5	2	no	—
145	C₂×C₃×C₄⋊C₄	—	5	8	no	—
146	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
147	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂³×D₅	C₂³×C₃	1	2	yes	—
151	C₂×C₅×Q₈	—	2	8	no	—
152	C₂×C₅×Q₈	—	2	8	no	—
153	C₂×C₅×Q₈	—	2	32	no	—
154	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
155	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
156	C₂²×C₄×C₅	—	2	8	no	—
157	C₂²×C₄×C₅	C₃×D₄	1	8	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
163	C₂×C₂²⋊D₅	—	2	8	no	—
164	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
165	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
166	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
167	#709	—	2	32	no	—
168	C₂×D₂₀	—	2	4	no	—
169	C₂×D₂₀	C₂³×C₃	1	4	yes	—
170	C₂×C₄×D₅	—	2	8	no	—
171	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
172	C₂×Dic₁₀	—	2	4	no	—
173	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
174	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
175	#685	C₂³×C₃	1	32	yes	—
176	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
177	#683	C₂³×C₃	1	32	yes	—
178	C₄×Dic₅	C₂³×C₃	1	8	yes	—
179	C₂²×#41	—	5	1	no	—
180	C₂³×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
181	#536	—	5	16	no	—
182	C₂×C₄⋊Q₈	—	5	2	no	—
183	C₂×#124	—	5	2	no	—
184	C₂×#123	—	5	4	no	—
185	C₂×C₂²⋊Q₈	—	5	4	no	—
186	C₂×#117	—	5	1	no	—
187	C₂²×C₃×C₅	—	2	8	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
190	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
191	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
192	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	4	no	—
194	C₂×C₃×D₅	—	2	8	no	—
195	C₂×C₃×D₅	—	4	8	no	—
196	C₃×C₄×C₅	—	2	8	no	—
197	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
198	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
199	C₃×Dic₅	—	2	4	no	—
200	C₃×Dic₅	—	2	8	no	—
201	C₂⁴×C₃	—	5	2	no	—
202	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
203	C₃×#41	—	10	32	no	—
204	C₂×C₃×Q₈	—	2	8	no	—
205	C₂×C₃×Q₈	—	2	8	no	—
206	C₂×C₃×Q₈	—	2	32	no	—
207	C₂×C₃×Q₈	—	5	4	no	—
208	C₂×C₃×Q₈	—	10	4	no	—
209	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
210	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
211	C₂×C₃×D₄	—	5	8	no	—
212	C₂×C₃×D₄	—	5	4	no	—
213	C₂×C₃×D₄	—	10	8	no	—
214	C₂×C₃×D₄	—	10	4	no	—
215	C₂²×C₃×C₄	—	2	8	no	—
216	C₂²×C₃×C₄	—	5	4	no	—
217	C₂²×C₃×C₄	—	5	2	no	—
218	C₂²×C₃×C₄	—	5	8	no	—
219	C₂²×C₃×C₄	—	10	8	no	—
220	C₂²×C₃×C₄	C₂²⋊D₅	1	8	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
222	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
223	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
224	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	5	32	no	—
227	C₃×C₄⋊C₄	—	5	8	no	—
228	C₃×C₂²⋊C₄	—	5	8	no	—
229	C₃×C₂²⋊C₄	—	5	32	no	—
230	C₃×C₄²	—	5	8	no	—
231	C₂³×C₅	—	2	4	no	—
232	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
233	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
234	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
235	C₂²×D₅	—	2	4	no	—
236	C₂²×D₅	—	2	8	no	—
237	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
238	C₅×Q₈	—	2	16	no	—
239	C₅×Q₈	—	2	16	no	—
240	C₂×C₄×C₅	—	2	16	no	—
241	C₂×C₄×C₅	—	2	8	no	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
243	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	16	yes	—
245	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
246	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
247	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
248	C₂²⋊D₅	—	2	16	no	—
249	C₂×Dic₅	—	2	4	no	—
250	C₂×Dic₅	—	2	8	no	—
251	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
252	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
253	D₂₀	—	2	8	no	—
254	C₄×D₅	—	2	16	no	—
255	Dic₁₀	—	2	8	no	—
256	C₂×#41	—	5	8	no	—
257	C₂×#41	—	10	8	no	—
258	C₂²×Q₈	—	2	8	no	—
259	C₂²×Q₈	—	5	1	no	—
260	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
261	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
262	C₂²×Q₈	C₂×C₃×D₅	1	8	yes	complemented
263	C₂²×D₄	—	5	2	no	—
264	C₂²×D₄	—	5	1	no	—
265	C₂³×C₄	—	5	2	no	—
266	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
267	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
268	C₄⋊Q₈	—	5	16	no	—
269	#124	—	5	16	no	—
270	#123	—	5	32	no	—
271	C₂²⋊Q₈	—	5	32	no	—
272	#117	—	5	8	no	—
273	C₂×C₄⋊C₄	—	5	2	no	—
274	C₂×C₄⋊C₄	—	5	8	no	—
275	C₂×C₂²⋊C₄	—	5	2	no	—
276	C₂×C₂²⋊C₄	—	5	8	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	#536	1	4	yes	complemented
280	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
282	C₃×D₅	—	4	4	no	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	—	5	4	no	—
285	C₂³×C₃	—	10	8	no	—
286	C₂³×C₃	—	10	4	no	—
287	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
288	C₂³×C₃	C₂³×D₅	1	2	yes	—
289	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
290	C₃×Q₈	—	2	16	no	—
291	C₃×Q₈	—	2	16	no	—
292	C₃×Q₈	—	10	8	no	—
293	C₃×D₄	—	10	16	no	—
294	C₃×D₄	—	10	8	no	—
295	C₂×C₃×C₄	—	2	16	no	—
296	C₂×C₃×C₄	—	2	8	no	—
297	C₂×C₃×C₄	—	5	8	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	—	10	8	no	—
300	C₂×C₃×C₄	—	10	4	no	—
301	C₂×C₃×C₄	—	10	16	no	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
304	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	16	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	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
311	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
312	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
313	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
314	C₂×D₅	—	2	4	no	—
315	C₂×D₅	—	2	8	no	—
316	C₂×D₅	—	4	8	no	—
317	C₄×C₅	—	2	8	no	—
318	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
319	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
320	Dic₅	—	2	4	no	—
321	Dic₅	—	2	8	no	—
322	C₂⁴	—	5	2	no	—
323	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
324	#41	—	10	32	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	8	no	—
327	C₂×Q₈	—	2	32	no	—
328	C₂×Q₈	—	5	4	no	—
329	C₂×Q₈	—	10	4	no	—
330	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
331	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
332	C₂×D₄	—	5	8	no	—
333	C₂×D₄	—	5	4	no	—
334	C₂×D₄	—	10	8	no	—
335	C₂×D₄	—	10	4	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	5	4	no	—
338	C₂²×C₄	—	5	2	no	—
339	C₂²×C₄	—	5	8	no	—
340	C₂²×C₄	—	10	8	no	—
341	C₂²×C₄	C₃×C₂²⋊D₅	1	8	yes	—
342	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
343	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
344	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
347	C₄⋊C₄	—	5	8	no	—
348	C₄⋊C₄	—	5	32	no	—
349	C₂²⋊C₄	—	5	8	no	—
350	C₂²⋊C₄	—	5	32	no	—
351	C₄²	—	5	8	no	—
352	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	10	8	no	—
356	C₂²×C₃	—	10	4	no	—
357	C₂²×C₃	—	20	8	no	—
358	C₂²×C₃	#4147	1	4	yes	—
359	C₂²×C₃	C₂²×C₂²⋊D₅	1	4	yes	—
360	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
361	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
362	C₃×C₄	—	2	8	no	—
363	C₃×C₄	—	10	8	no	—
364	C₃×C₄	—	10	4	no	—
365	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
366	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
367	C₂×C₅	—	2	4	no	—
368	C₂×C₅	C₃×#536	1	4	yes	complemented
369	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
370	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
371	D₅	—	4	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	5	4	no	—
374	C₂³	—	10	8	no	—
375	C₂³	—	10	4	no	—
376	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
377	C₂³	C₂³×C₃×D₅	1	2	yes	—
378	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
379	Q₈	—	2	16	no	—
380	Q₈	—	2	16	no	—
381	Q₈	—	10	8	no	—
382	D₄	—	10	16	no	—
383	D₄	—	10	8	no	—
384	C₂×C₄	—	2	16	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	5	8	no	—
387	C₂×C₄	—	5	4	no	—
388	C₂×C₄	—	10	8	no	—
389	C₂×C₄	—	10	4	no	—
390	C₂×C₄	—	10	16	no	—
391	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
392	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
393	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	16	yes	—
394	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
395	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
396	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	—	20	4	no	—
399	C₂×C₃	#66150	1	4	yes	direct product factor
400	C₂×C₃	C₂×#4147	1	2	yes	—
401	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
402	C₅	C₂×C₃×#536	1	1	yes	characteristic, complemented, Sylow
403	C₂²	—	2	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	10	8	no	—
406	C₂²	—	10	4	no	—
407	C₂²	—	20	8	no	—
408	C₂²	C₃×#4147	1	4	yes	—
409	C₂²	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
410	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
411	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
412	C₄	—	2	8	no	—
413	C₄	—	10	8	no	—
414	C₄	—	10	4	no	—
415	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
416	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
417	C₃	C₂×#66150	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	2	4	no	—
419	C₂	—	20	4	no	—
420	C₂	C₃×#66150	1	4	yes	direct product factor
421	C₂	C₂×C₃×#4147	1	2	yes	—
422	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×#709	C₂
hypercenter	C₂³×C₃×Q₈	D₅
hypocenter	C₅	C₂×C₃×#536
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×Q₈	C₂	semidirect
3. C₃×#66150	C₂	direct (N × H)
4. C₂×C₃×#4093	C₂	semidirect
5. C₂×C₃×#4092	C₂	semidirect
6. C₂×C₃×#4090	C₂	semidirect
7. C₂×C₃×#4075	C₂	semidirect
8. C₂×C₃×#4072	C₂	semidirect
9. C₂×#66150	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
23. C₃×#4093	C₂²	semidirect
24. C₃×#4092	C₂²	semidirect
25. C₃×#4090	C₂²	semidirect
26. C₃×#4075	C₂²	semidirect
28. C₃×#4072	C₂²	semidirect
33. C₂³×C₅×Q₈	C₂×C₃	semidirect
35. #66150	C₂×C₃	direct (N × H)
36. C₂×#4093	C₂×C₃	semidirect
37. C₂×#4092	C₂×C₃	semidirect
38. C₂×#4090	C₂×C₃	semidirect
39. C₂×#4075	C₂×C₃	semidirect
40. C₂×#4072	C₂×C₃	semidirect
72. C₂³×C₃×Q₈	D₅	semidirect
82. C₂²×C₅×Q₈	C₂²×C₃	semidirect
92. #4093	C₂²×C₃	semidirect
93. #4092	C₂²×C₃	semidirect
94. #4090	C₂²×C₃	semidirect
95. #4075	C₂²×C₃	semidirect
97. #4072	C₂²×C₃	semidirect
133. C₂²×C₃×Q₈	C₂×D₅	semidirect
180. C₂³×Q₈	C₃×D₅	semidirect
262. C₂²×Q₈	C₂×C₃×D₅	semidirect
279. C₂×C₃×C₅	#536	semidirect
352. C₃×C₅	C₂×#536	semidirect
368. C₂×C₅	C₃×#536	semidirect
399. C₂×C₃	#66150	direct (N × H)
402. C₅	C₂×C₃×#536	semidirect
417. C₃	C₂×#66150	direct (N × H)
420. C₂	C₃×#66150	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×C₃×C₅×Q₈	2
C₂²×C₃×#709	2
C₃×#66150	2
C₂×C₃×#4093	2
C₂×C₃×#4092	2
C₂×C₃×#4090	2
C₂×C₃×#4075	2
C₂×C₃×#4072	2
C₂×#66150	3
C₂×C₃×#536	5

Subgroups — C2×C3×#66150 #14480474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66150 #14480474