Subgroups — C₂×C₃×#65919 #14484709

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 440 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×#4093	C₂	1	2	yes	maximal, complemented
3	C₃×#65919	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4040	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4021	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃×C₄×D₂₀	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65919	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
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×#4093	C₂²	1	16	yes	complemented
23	C₂×C₃×#685	C₂²	1	4	yes	—
24	C₂×C₃×#685	C₂²	1	4	yes	—
25	C₂×C₃×#685	C₂²	1	4	yes	—
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	2	yes	—
29	C₃×#4040	C₂²	1	32	yes	complemented
30	C₃×#4039	C₂²	1	16	yes	complemented
31	C₃×#4021	C₂²	1	16	yes	complemented
32	C₃×#4020	C₂²	1	8	yes	—
33	C₃×C₄×D₂₀	C₂²	1	16	yes	complemented
34	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
35	C₂×C₃×#559	—	5	1	no	maximal, Hall
36	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4093	C₂×C₃	1	2	yes	complemented
38	#65919	C₂×C₃	1	16	yes	direct product factor
39	C₂×#4040	C₂×C₃	1	4	yes	complemented
40	C₂×#4039	C₂×C₃	1	2	yes	complemented
41	C₂×#4021	C₂×C₃	1	2	yes	complemented
42	C₂×#4020	C₂×C₃	1	1	yes	characteristic
43	C₂×C₄×D₂₀	C₂×C₃	1	2	yes	complemented
44	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×D₅	C₂³	1	4	yes	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂×C₃×D₂₀	—	2	8	no	—
56	C₂×C₃×D₂₀	—	2	8	no	—
57	C₂×C₃×D₂₀	—	4	4	no	—
58	C₂×C₃×D₂₀	C₂³	1	8	yes	—
59	C₂×C₃×D₂₀	C₂³	1	8	yes	—
60	C₂×C₃×D₂₀	C₂³	1	8	yes	—
61	C₂×C₃×C₄×D₅	—	4	8	no	—
62	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
63	C₂×C₃×Dic₁₀	—	2	4	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
67	C₃×C₄²×C₅	C₂³	1	4	yes	—
68	C₃×C₄²×C₅	C₂³	1	8	yes	—
69	C₃×#685	C₂³	1	16	yes	—
70	C₃×#685	C₂³	1	16	yes	—
71	C₃×#685	C₂³	1	16	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
73	C₃×#683	C₂³	1	8	yes	—
74	C₃×C₄×Dic₅	C₂³	1	8	yes	—
75	C₃×#559	—	5	16	no	—
76	C₂×C₃×#127	—	5	1	no	—
77	C₂×C₃×#124	—	5	2	no	—
78	C₂×C₃×#124	—	5	2	no	—
79	C₂×C₃×#123	—	5	4	no	—
80	C₂×C₃×C₄×Q₈	—	5	1	no	—
81	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
82	C₂×C₃×C₄×D₄	—	5	2	no	—
83	C₂×C₃×C₄×D₄	—	5	2	no	—
84	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
86	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
87	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
88	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
89	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
90	C₄×C₅×Q₈	C₂²×C₃	1	8	yes	complemented
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
95	#4093	C₂²×C₃	1	16	yes	complemented
96	C₂×#685	C₂²×C₃	1	4	yes	—
97	C₂×#685	C₂²×C₃	1	4	yes	—
98	C₂×#685	C₂²×C₃	1	4	yes	—
99	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×#683	C₂²×C₃	1	2	yes	—
101	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
102	#4040	C₂²×C₃	1	32	yes	complemented
103	#4039	C₂²×C₃	1	16	yes	complemented
104	#4021	C₂²×C₃	1	16	yes	complemented
105	#4020	C₂²×C₃	1	8	yes	—
106	C₄×D₂₀	C₂²×C₃	1	16	yes	complemented
107	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
108	C₂×#559	—	5	1	no	Sylow
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₂²×C₃×D₅	—	2	8	no	—
111	C₂²×C₃×D₅	—	2	8	no	—
112	C₂²×C₃×D₅	—	2	8	no	—
113	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
114	C₃×C₅×Q₈	—	2	8	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	#41	1	4	yes	—
119	C₂×C₃×C₄×C₅	#41	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂×C₃×Dic₅	—	2	4	no	—
126	C₂×C₃×Dic₅	—	2	4	no	—
127	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
128	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
129	C₃×D₂₀	—	2	16	no	—
130	C₃×D₂₀	—	2	16	no	—
131	C₃×D₂₀	—	4	8	no	—
132	C₃×C₄×D₅	—	4	16	no	—
133	C₃×Dic₁₀	—	2	8	no	—
134	C₂²×C₃×Q₈	—	5	1	no	—
135	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
136	C₂²×C₃×D₄	—	5	2	no	—
137	C₂²×C₃×D₄	—	5	2	no	—
138	C₂²×C₃×D₄	—	5	2	no	—
139	C₂³×C₃×C₄	—	5	4	no	—
140	C₃×#127	—	5	8	no	—
141	C₃×#124	—	5	16	no	—
142	C₃×#124	—	5	16	no	—
143	C₃×#123	—	5	32	no	—
144	C₃×C₄×Q₈	—	5	8	no	—
145	C₃×C₄×Q₈	C₂×D₅	1	8	yes	complemented
146	C₃×C₄×D₄	—	5	16	no	—
147	C₃×C₄×D₄	—	5	16	no	—
148	C₂×C₃×C₄⋊C₄	—	5	1	no	—
149	C₂×C₃×C₄⋊C₄	—	5	2	no	—
150	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
153	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
154	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
155	C₂×C₃×C₄²	—	5	2	no	—
156	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
157	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
158	C₂³×D₅	C₂³×C₃	1	4	yes	—
159	C₂×C₅×Q₈	—	2	4	no	—
160	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
167	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
168	C₂×D₂₀	—	2	8	no	—
169	C₂×D₂₀	—	2	8	no	—
170	C₂×D₂₀	—	4	4	no	—
171	C₂×D₂₀	C₂³×C₃	1	8	yes	—
172	C₂×D₂₀	C₂³×C₃	1	8	yes	—
173	C₂×D₂₀	C₂³×C₃	1	8	yes	—
174	C₂×C₄×D₅	—	4	8	no	—
175	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
176	C₂×Dic₁₀	—	2	4	no	—
177	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
178	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
179	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
180	C₄²×C₅	C₂³×C₃	1	4	yes	—
181	C₄²×C₅	C₂³×C₃	1	8	yes	—
182	#685	C₂³×C₃	1	16	yes	—
183	#685	C₂³×C₃	1	16	yes	—
184	#685	C₂³×C₃	1	16	yes	—
185	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
186	#683	C₂³×C₃	1	8	yes	—
187	C₄×Dic₅	C₂³×C₃	1	8	yes	—
188	#559	—	5	16	no	—
189	C₂×#127	—	5	1	no	—
190	C₂×#124	—	5	2	no	—
191	C₂×#124	—	5	2	no	—
192	C₂×#123	—	5	4	no	—
193	C₂×C₄×Q₈	—	5	1	no	—
194	C₂×C₄×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
195	C₂×C₄×D₄	—	5	2	no	—
196	C₂×C₄×D₄	—	5	2	no	—
197	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
198	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
200	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
201	C₂×C₃×D₅	—	2	8	no	—
202	C₂×C₃×D₅	—	2	8	no	—
203	C₂×C₃×D₅	—	2	8	no	—
204	C₂×C₃×D₅	—	4	16	no	—
205	C₃×C₄×C₅	—	2	4	no	—
206	C₃×C₄×C₅	—	2	4	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	C₂×#41	1	4	yes	—
209	C₃×C₄×C₅	C₂×#41	1	4	yes	—
210	C₃×Dic₅	—	2	4	no	—
211	C₃×Dic₅	—	2	4	no	—
212	C₂⁴×C₃	—	5	4	no	—
213	C₂×C₃×Q₈	—	2	4	no	—
214	C₂×C₃×Q₈	—	5	4	no	—
215	C₂×C₃×Q₈	—	10	4	no	—
216	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
217	C₂×C₃×D₄	—	5	8	no	—
218	C₂×C₃×D₄	—	5	8	no	—
219	C₂×C₃×D₄	—	5	8	no	—
220	C₂×C₃×D₄	—	10	8	no	—
221	C₂×C₃×D₄	—	10	8	no	—
222	C₂×C₃×D₄	—	20	4	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	—	5	16	no	—
226	C₂²×C₃×C₄	—	20	8	no	—
227	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₃×C₄⋊C₄	—	5	8	no	—
233	C₃×C₄⋊C₄	—	5	4	no	—
234	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
235	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
236	C₃×C₂²⋊C₄	—	5	16	no	—
237	C₃×C₂²⋊C₄	—	5	16	no	—
238	C₃×C₂²⋊C₄	—	5	16	no	—
239	C₃×C₄²	—	5	8	no	—
240	C₃×C₄²	C₂²×D₅	1	8	yes	—
241	C₃×C₄²	C₂²×D₅	1	4	yes	—
242	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
243	C₂²×D₅	—	2	8	no	—
244	C₂²×D₅	—	2	8	no	—
245	C₂²×D₅	—	2	8	no	—
246	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
247	C₅×Q₈	—	2	8	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	4	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	C₃×#41	1	4	yes	—
252	C₂×C₄×C₅	C₃×#41	1	4	yes	—
253	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
254	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
255	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
256	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
257	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
258	C₂×Dic₅	—	2	4	no	—
259	C₂×Dic₅	—	2	4	no	—
260	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
261	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
262	D₂₀	—	2	16	no	—
263	D₂₀	—	2	16	no	—
264	D₂₀	—	4	8	no	—
265	C₄×D₅	—	4	16	no	—
266	Dic₁₀	—	2	8	no	—
267	C₂²×Q₈	—	5	1	no	—
268	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
269	C₂²×D₄	—	5	2	no	—
270	C₂²×D₄	—	5	2	no	—
271	C₂²×D₄	—	5	2	no	—
272	C₂³×C₄	—	5	4	no	—
273	#127	—	5	8	no	—
274	#124	—	5	16	no	—
275	#124	—	5	16	no	—
276	#123	—	5	32	no	—
277	C₄×Q₈	—	5	8	no	—
278	C₄×Q₈	C₂×C₃×D₅	1	8	yes	complemented
279	C₄×D₄	—	5	16	no	—
280	C₄×D₄	—	5	16	no	—
281	C₂×C₄⋊C₄	—	5	1	no	—
282	C₂×C₄⋊C₄	—	5	2	no	—
283	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
285	C₂×C₂²⋊C₄	—	5	4	no	—
286	C₂×C₂²⋊C₄	—	5	4	no	—
287	C₂×C₂²⋊C₄	—	5	4	no	—
288	C₂×C₄²	—	5	2	no	—
289	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
290	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
291	C₂×C₃×C₅	#559	1	4	yes	complemented
292	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
295	C₃×D₅	—	4	8	no	—
296	C₂³×C₃	—	5	8	no	—
297	C₂³×C₃	—	10	8	no	—
298	C₂³×C₃	—	10	8	no	—
299	C₂³×C₃	—	10	8	no	—
300	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
301	C₃×Q₈	—	2	8	no	—
302	C₃×Q₈	—	10	8	no	—
303	C₃×D₄	—	10	16	no	—
304	C₃×D₄	—	10	16	no	—
305	C₃×D₄	—	20	8	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	5	4	no	—
310	C₂×C₃×C₄	—	5	4	no	—
311	C₂×C₃×C₄	—	10	4	no	—
312	C₂×C₃×C₄	—	10	4	no	—
313	C₂×C₃×C₄	—	20	16	no	—
314	C₂×C₃×C₄	#709	1	4	yes	—
315	C₂×C₃×C₄	#713	1	4	yes	—
316	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
317	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
318	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
319	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
320	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
321	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
322	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
323	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
324	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
325	C₂×D₅	—	2	8	no	—
326	C₂×D₅	—	2	8	no	—
327	C₂×D₅	—	2	8	no	—
328	C₂×D₅	—	4	16	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	2	4	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	C₂×C₃×#41	1	4	yes	—
333	C₄×C₅	C₂×C₃×#41	1	4	yes	—
334	Dic₅	—	2	4	no	—
335	Dic₅	—	2	4	no	—
336	C₂⁴	—	5	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	5	4	no	—
339	C₂×Q₈	—	10	4	no	—
340	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
341	C₂×D₄	—	5	8	no	—
342	C₂×D₄	—	5	8	no	—
343	C₂×D₄	—	5	8	no	—
344	C₂×D₄	—	10	8	no	—
345	C₂×D₄	—	10	8	no	—
346	C₂×D₄	—	20	4	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	—	5	2	no	—
349	C₂²×C₄	—	5	16	no	—
350	C₂²×C₄	—	20	8	no	—
351	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
352	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
353	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
356	C₄⋊C₄	—	5	4	no	—
357	C₄⋊C₄	—	5	8	no	—
358	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
359	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
360	C₂²⋊C₄	—	5	16	no	—
361	C₂²⋊C₄	—	5	16	no	—
362	C₂²⋊C₄	—	5	16	no	—
363	C₄²	—	5	8	no	—
364	C₄²	C₂²×C₃×D₅	1	8	yes	—
365	C₄²	C₂²×C₃×D₅	1	4	yes	—
366	C₃×C₅	C₂×#559	1	1	yes	characteristic, complemented, Hall
367	C₂²×C₃	—	10	8	no	—
368	C₂²×C₃	—	10	8	no	—
369	C₂²×C₃	—	10	8	no	—
370	C₂²×C₃	—	20	16	no	—
371	C₂²×C₃	C₂×#709	1	2	yes	—
372	C₂²×C₃	C₂×#713	1	2	yes	—
373	C₂²×C₃	#4149	1	2	yes	—
374	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	10	4	no	—
379	C₃×C₄	—	10	4	no	—
380	C₃×C₄	C₂×#709	1	4	yes	—
381	C₃×C₄	C₂×#713	1	4	yes	—
382	C₂×C₅	C₃×#559	1	4	yes	complemented
383	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
384	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
385	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
386	D₅	—	4	8	no	—
387	C₂³	—	5	8	no	—
388	C₂³	—	10	8	no	—
389	C₂³	—	10	8	no	—
390	C₂³	—	10	8	no	—
391	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
392	Q₈	—	2	8	no	—
393	Q₈	—	10	8	no	—
394	D₄	—	10	16	no	—
395	D₄	—	10	16	no	—
396	D₄	—	20	8	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	5	4	no	—
401	C₂×C₄	—	5	4	no	—
402	C₂×C₄	—	10	4	no	—
403	C₂×C₄	—	10	4	no	—
404	C₂×C₄	—	20	16	no	—
405	C₂×C₄	C₃×#709	1	4	yes	—
406	C₂×C₄	C₃×#713	1	4	yes	—
407	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
408	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
409	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
410	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
411	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
412	C₂×C₃	—	20	8	no	—
413	C₂×C₃	#65919	1	4	yes	direct product factor
414	C₂×C₃	C₂²×#709	1	1	yes	characteristic
415	C₂×C₃	C₂²×#713	1	1	yes	characteristic
416	C₂×C₃	C₂×#4149	1	1	yes	characteristic
417	C₅	C₂×C₃×#559	1	1	yes	characteristic, complemented, Sylow
418	C₂²	—	10	8	no	—
419	C₂²	—	10	8	no	—
420	C₂²	—	10	8	no	—
421	C₂²	—	20	16	no	—
422	C₂²	C₂×C₃×#709	1	2	yes	—
423	C₂²	C₂×C₃×#713	1	2	yes	—
424	C₂²	C₃×#4149	1	2	yes	—
425	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	2	no	—
429	C₄	—	10	4	no	—
430	C₄	—	10	4	no	—
431	C₄	C₂×C₃×#709	1	4	yes	—
432	C₄	C₂×C₃×#713	1	4	yes	—
433	C₃	C₂×#65919	1	1	yes	characteristic, direct product factor, Sylow
434	C₂	—	20	8	no	—
435	C₂	C₃×#65919	1	4	yes	direct product factor
436	C₂	C₂²×C₃×#709	1	1	yes	characteristic
437	C₂	C₂²×C₃×#713	1	1	yes	characteristic
438	C₂	C₂×C₃×#4149	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	C₂×C₃×#4020	C₂
hypercenter	C₂×C₃×C₄×Q₈	D₅
hypocenter	C₅	C₂×C₃×#559
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
2. C₂×C₃×#4093	C₂	semidirect
3. C₃×#65919	C₂	direct (N × H)
4. C₂×C₃×#4040	C₂	semidirect
5. C₂×C₃×#4039	C₂	semidirect
6. C₂×C₃×#4021	C₂	semidirect
8. C₂×C₃×C₄×D₂₀	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×#65919	C₃	direct (N × H)
17. C₃×C₄×C₅×Q₈	C₂²	semidirect
22. C₃×#4093	C₂²	semidirect
29. C₃×#4040	C₂²	semidirect
30. C₃×#4039	C₂²	semidirect
31. C₃×#4021	C₂²	semidirect
33. C₃×C₄×D₂₀	C₂²	semidirect
34. C₃×C₄×Dic₁₀	C₂²	semidirect
36. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
37. C₂×#4093	C₂×C₃	semidirect
38. #65919	C₂×C₃	direct (N × H)
39. C₂×#4040	C₂×C₃	semidirect
40. C₂×#4039	C₂×C₃	semidirect
41. C₂×#4021	C₂×C₃	semidirect
43. C₂×C₄×D₂₀	C₂×C₃	semidirect
44. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
81. C₂×C₃×C₄×Q₈	D₅	semidirect
90. C₄×C₅×Q₈	C₂²×C₃	semidirect
95. #4093	C₂²×C₃	semidirect
102. #4040	C₂²×C₃	semidirect
103. #4039	C₂²×C₃	semidirect
104. #4021	C₂²×C₃	semidirect
106. C₄×D₂₀	C₂²×C₃	semidirect
107. C₄×Dic₁₀	C₂²×C₃	semidirect
145. C₃×C₄×Q₈	C₂×D₅	semidirect
194. C₂×C₄×Q₈	C₃×D₅	semidirect
278. C₄×Q₈	C₂×C₃×D₅	semidirect
291. C₂×C₃×C₅	#559	semidirect
366. C₃×C₅	C₂×#559	semidirect
382. C₂×C₅	C₃×#559	semidirect
413. C₂×C₃	#65919	direct (N × H)
417. C₅	C₂×C₃×#559	semidirect
433. C₃	C₂×#65919	direct (N × H)
435. C₂	C₃×#65919	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×#4093	2
C₃×#65919	2
C₂×C₃×#4040	2
C₂×C₃×#4039	2
C₂×C₃×#4021	2
C₂×C₃×#4020	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#65919	3
C₂×C₃×#559	5

Subgroups — C2×C3×#65919 #14484709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65919 #14484709