Subgroups — C₂×C₃×#65979 #14480939

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4092	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65979	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4044	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4040	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4036	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4032	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4027	C₂	1	2	yes	maximal, complemented
11	C₂×#65979	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
15	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
19	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×#4092	C₂²	1	16	yes	complemented
24	C₃×#4076	C₂²	1	8	yes	—
25	C₂×C₃×#685	C₂²	1	2	yes	—
26	C₂×C₃×#685	C₂²	1	2	yes	—
27	C₂×C₃×#685	C₂²	1	2	yes	—
28	C₂×C₃×#685	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×C₄⋊Dic₅	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	8	yes	complemented
36	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
37	C₃×#4044	C₂²	1	16	yes	complemented
38	C₃×#4040	C₂²	1	16	yes	complemented
39	C₃×#4036	C₂²	1	16	yes	complemented
40	C₃×#4032	C₂²	1	16	yes	complemented
41	C₃×#4027	C₂²	1	16	yes	complemented
42	C₂×C₃×#539	—	5	1	no	maximal, Hall
43	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4092	C₂×C₃	1	2	yes	complemented
45	C₂×#4076	C₂×C₃	1	1	yes	characteristic
46	C₂²×#683	C₂×C₃	1	1	yes	characteristic, complemented
47	#65979	C₂×C₃	1	16	yes	direct product factor
48	C₂×#4044	C₂×C₃	1	2	yes	complemented
49	C₂×#4040	C₂×C₃	1	2	yes	complemented
50	C₂×#4036	C₂×C₃	1	2	yes	complemented
51	C₂×#4032	C₂×C₃	1	2	yes	complemented
52	C₂×#4027	C₂×C₃	1	2	yes	complemented
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂³×C₃×D₅	C₂³	1	2	yes	—
55	C₂×C₃×C₅×Q₈	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
57	C₂²×C₃×C₄×C₅	—	4	2	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
63	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
64	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
65	C₂²×C₃×Dic₅	—	2	4	no	—
66	C₂²×C₃×Dic₅	—	4	2	no	—
67	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
68	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
69	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
71	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
72	C₂×C₃×D₂₀	—	4	2	no	—
73	C₂×C₃×D₂₀	C₂³	1	4	yes	—
74	C₂×C₃×C₄×D₅	—	4	4	no	—
75	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
78	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₃×#685	C₂³	1	8	yes	—
80	C₃×#685	C₂³	1	8	yes	—
81	C₃×#685	C₂³	1	8	yes	—
82	C₃×#685	C₂³	1	8	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
84	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
85	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
86	C₃×#683	C₂³	1	8	yes	—
87	C₃×#683	C₂³	1	8	yes	—
88	C₃×#683	C₂³	1	8	yes	—
89	C₃×C₄×Dic₅	C₂³	1	8	yes	—
90	C₃×#539	—	5	16	no	—
91	C₂×C₃×#126	—	5	2	no	—
92	C₂×C₃×#125	—	5	2	no	—
93	C₂×C₃×#123	—	5	2	no	—
94	C₂×C₃×#123	—	5	2	no	—
95	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
96	C₂×C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, complemented
97	C₂×C₃×#121	—	5	1	no	—
98	C₂×C₃×C₄×D₄	—	5	2	no	—
99	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
100	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
103	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
104	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
105	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
107	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	#4092	C₂²×C₃	1	16	yes	complemented
112	#4076	C₂²×C₃	1	8	yes	—
113	C₂×#685	C₂²×C₃	1	2	yes	—
114	C₂×#685	C₂²×C₃	1	2	yes	—
115	C₂×#685	C₂²×C₃	1	2	yes	—
116	C₂×#685	C₂²×C₃	1	2	yes	—
117	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
118	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
119	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×#683	C₂²×C₃	1	2	yes	—
121	C₂×#683	C₂²×C₃	1	2	yes	—
122	C₂×#683	C₂²×C₃	1	2	yes	—
123	C₂×#683	C₂²×C₃	1	8	yes	complemented
124	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
125	#4044	C₂²×C₃	1	16	yes	complemented
126	#4040	C₂²×C₃	1	16	yes	complemented
127	#4036	C₂²×C₃	1	16	yes	complemented
128	#4032	C₂²×C₃	1	16	yes	complemented
129	#4027	C₂²×C₃	1	16	yes	complemented
130	C₂×#539	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	#41	1	4	yes	—
134	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
135	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
136	C₂²×C₃×D₅	—	2	4	no	—
137	C₂²×C₃×D₅	—	2	4	no	—
138	C₂²×C₃×D₅	—	2	4	no	—
139	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
140	C₃×C₅×Q₈	—	4	4	no	—
141	C₂×C₃×C₄×C₅	—	2	4	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	4	no	—
145	C₂×C₃×C₄×C₅	—	4	4	no	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
150	C₃×C₂²⋊D₅	—	2	16	no	—
151	C₂×C₃×Dic₅	—	2	8	no	—
152	C₂×C₃×Dic₅	—	2	4	no	—
153	C₂×C₃×Dic₅	—	2	4	no	—
154	C₂×C₃×Dic₅	—	2	4	no	—
155	C₂×C₃×Dic₅	—	4	4	no	—
156	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
157	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
158	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
159	C₃×D₂₀	—	4	4	no	—
160	C₃×C₄×D₅	—	4	8	no	—
161	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
162	C₂²×C₃×D₄	—	5	2	no	—
163	C₂²×C₃×D₄	—	5	1	no	—
164	C₂³×C₃×C₄	—	5	1	no	—
165	C₂³×C₃×C₄	—	5	1	no	—
166	C₂³×C₃×C₄	—	5	2	no	—
167	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
168	C₃×#126	—	5	16	no	—
169	C₃×#125	—	5	16	no	—
170	C₃×#123	—	5	16	no	—
171	C₃×#123	—	5	16	no	—
172	C₃×C₂²⋊Q₈	—	5	16	no	—
173	C₃×C₂²⋊Q₈	C₂×D₅	1	8	yes	complemented
174	C₃×#121	—	5	8	no	—
175	C₃×C₄×D₄	—	5	16	no	—
176	C₂×C₃×C₄⋊C₄	—	5	2	no	—
177	C₂×C₃×C₄⋊C₄	—	5	2	no	—
178	C₂×C₃×C₄⋊C₄	—	5	8	no	—
179	C₂×C₃×C₄⋊C₄	—	5	2	no	—
180	C₂×C₃×C₄⋊C₄	—	5	1	no	—
181	C₂×C₃×C₄⋊C₄	—	5	2	no	—
182	C₂×C₃×C₄⋊C₄	—	5	2	no	—
183	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
186	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
189	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
190	C₂×C₃×C₄²	—	5	2	no	—
191	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂³×D₅	C₂³×C₃	1	2	yes	—
193	C₂×C₅×Q₈	—	4	2	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
198	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
201	C₂×C₂²⋊D₅	—	2	8	no	—
202	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
203	C₂²×Dic₅	—	2	4	no	—
204	C₂²×Dic₅	—	4	2	no	—
205	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
206	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
207	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
208	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
209	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
210	C₂×D₂₀	—	4	2	no	—
211	C₂×D₂₀	C₂³×C₃	1	4	yes	—
212	C₂×C₄×D₅	—	4	4	no	—
213	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
216	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
217	#685	C₂³×C₃	1	8	yes	—
218	#685	C₂³×C₃	1	8	yes	—
219	#685	C₂³×C₃	1	8	yes	—
220	#685	C₂³×C₃	1	8	yes	—
221	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
222	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
223	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
224	#683	C₂³×C₃	1	8	yes	—
225	#683	C₂³×C₃	1	8	yes	—
226	#683	C₂³×C₃	1	8	yes	—
227	C₄×Dic₅	C₂³×C₃	1	8	yes	—
228	#539	—	5	16	no	—
229	C₂×#126	—	5	2	no	—
230	C₂×#125	—	5	2	no	—
231	C₂×#123	—	5	2	no	—
232	C₂×#123	—	5	2	no	—
233	C₂×C₂²⋊Q₈	—	5	2	no	—
234	C₂×C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
235	C₂×#121	—	5	1	no	—
236	C₂×C₄×D₄	—	5	2	no	—
237	C₂²×C₄⋊C₄	—	5	1	no	—
238	C₂²×C₃×C₅	—	2	8	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
242	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
243	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
244	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	4	no	—
247	C₂×C₃×D₅	—	2	4	no	—
248	C₂×C₃×D₅	—	2	4	no	—
249	C₂×C₃×D₅	—	4	8	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	2	no	—
253	C₃×C₄×C₅	—	2	4	no	—
254	C₃×Dic₅	—	2	4	no	—
255	C₃×Dic₅	—	2	4	no	—
256	C₃×Dic₅	—	2	4	no	—
257	C₂⁴×C₃	—	5	2	no	—
258	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
259	C₂×C₃×Q₈	—	4	2	no	—
260	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
261	C₂×C₃×D₄	—	5	8	no	—
262	C₂×C₃×D₄	—	5	4	no	—
263	C₂×C₃×D₄	—	10	8	no	—
264	C₂×C₃×D₄	—	20	2	no	—
265	C₂²×C₃×C₄	—	4	2	no	—
266	C₂²×C₃×C₄	—	5	4	no	—
267	C₂²×C₃×C₄	—	5	2	no	—
268	C₂²×C₃×C₄	—	5	2	no	—
269	C₂²×C₃×C₄	—	5	2	no	—
270	C₂²×C₃×C₄	—	5	4	no	—
271	C₂²×C₃×C₄	—	5	8	no	—
272	C₂²×C₃×C₄	—	10	4	no	—
273	C₂²×C₃×C₄	—	20	4	no	—
274	C₂²×C₃×C₄	—	20	2	no	—
275	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
276	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
278	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
280	C₃×C₄⋊C₄	—	5	8	no	—
281	C₃×C₄⋊C₄	—	5	8	no	—
282	C₃×C₄⋊C₄	—	5	8	no	—
283	C₃×C₄⋊C₄	—	5	4	no	—
284	C₃×C₄⋊C₄	—	5	8	no	—
285	C₃×C₄⋊C₄	—	5	8	no	—
286	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
287	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
288	C₃×C₂²⋊C₄	—	5	8	no	—
289	C₃×C₂²⋊C₄	—	5	8	no	—
290	C₃×C₂²⋊C₄	—	5	8	no	—
291	C₃×C₂²⋊C₄	—	5	8	no	—
292	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
293	C₃×C₄²	—	5	8	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	C₃×#41	1	4	yes	—
297	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
298	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
299	C₂²×D₅	—	2	4	no	—
300	C₂²×D₅	—	2	4	no	—
301	C₂²×D₅	—	2	4	no	—
302	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
303	C₅×Q₈	—	4	4	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	4	4	no	—
309	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
311	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
312	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
313	C₂²⋊D₅	—	2	16	no	—
314	C₂×Dic₅	—	2	8	no	—
315	C₂×Dic₅	—	2	4	no	—
316	C₂×Dic₅	—	2	4	no	—
317	C₂×Dic₅	—	2	4	no	—
318	C₂×Dic₅	—	4	4	no	—
319	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
320	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
321	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
322	D₂₀	—	4	4	no	—
323	C₄×D₅	—	4	8	no	—
324	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
325	C₂²×D₄	—	5	2	no	—
326	C₂²×D₄	—	5	1	no	—
327	C₂³×C₄	—	5	1	no	—
328	C₂³×C₄	—	5	1	no	—
329	C₂³×C₄	—	5	2	no	—
330	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
331	#126	—	5	16	no	—
332	#125	—	5	16	no	—
333	#123	—	5	16	no	—
334	#123	—	5	16	no	—
335	C₂²⋊Q₈	—	5	16	no	—
336	C₂²⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
337	#121	—	5	8	no	—
338	C₄×D₄	—	5	16	no	—
339	C₂×C₄⋊C₄	—	5	2	no	—
340	C₂×C₄⋊C₄	—	5	2	no	—
341	C₂×C₄⋊C₄	—	5	8	no	—
342	C₂×C₄⋊C₄	—	5	2	no	—
343	C₂×C₄⋊C₄	—	5	1	no	—
344	C₂×C₄⋊C₄	—	5	2	no	—
345	C₂×C₄⋊C₄	—	5	2	no	—
346	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	—	5	2	no	—
349	C₂×C₂²⋊C₄	—	5	2	no	—
350	C₂×C₂²⋊C₄	—	5	2	no	—
351	C₂×C₂²⋊C₄	—	5	2	no	—
352	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
353	C₂×C₄²	—	5	2	no	—
354	C₂×C₃×C₅	—	2	4	no	—
355	C₂×C₃×C₅	#539	1	4	yes	complemented
356	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
357	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
359	C₃×D₅	—	4	4	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	2	no	—
362	C₂³×C₃	—	5	4	no	—
363	C₂³×C₃	—	10	4	no	—
364	C₂³×C₃	—	10	4	no	—
365	C₂³×C₃	—	10	4	no	—
366	C₂³×C₃	#713	1	4	yes	—
367	C₂³×C₃	C₂³×D₅	1	2	yes	—
368	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
369	C₃×Q₈	—	4	4	no	—
370	C₃×D₄	—	10	16	no	—
371	C₃×D₄	—	20	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	4	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	—	4	4	no	—
377	C₂×C₃×C₄	—	5	4	no	—
378	C₂×C₃×C₄	—	5	4	no	—
379	C₂×C₃×C₄	—	5	4	no	—
380	C₂×C₃×C₄	—	10	4	no	—
381	C₂×C₃×C₄	—	10	8	no	—
382	C₂×C₃×C₄	—	10	4	no	—
383	C₂×C₃×C₄	—	10	4	no	—
384	C₂×C₃×C₄	—	20	8	no	—
385	C₂×C₃×C₄	—	20	4	no	—
386	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
387	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
388	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
389	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	8	no	—
393	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
394	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
395	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
396	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
397	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
398	C₂×D₅	—	2	4	no	—
399	C₂×D₅	—	2	4	no	—
400	C₂×D₅	—	2	4	no	—
401	C₂×D₅	—	4	8	no	—
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	4	no	—
406	Dic₅	—	2	4	no	—
407	Dic₅	—	2	4	no	—
408	Dic₅	—	2	4	no	—
409	C₂⁴	—	5	2	no	—
410	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
413	C₂×D₄	—	5	8	no	—
414	C₂×D₄	—	5	4	no	—
415	C₂×D₄	—	10	8	no	—
416	C₂×D₄	—	20	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	5	2	no	—
419	C₂²×C₄	—	5	2	no	—
420	C₂²×C₄	—	5	2	no	—
421	C₂²×C₄	—	5	4	no	—
422	C₂²×C₄	—	5	4	no	—
423	C₂²×C₄	—	5	8	no	—
424	C₂²×C₄	—	10	4	no	—
425	C₂²×C₄	—	20	4	no	—
426	C₂²×C₄	—	20	2	no	—
427	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
428	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
430	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
432	C₄⋊C₄	—	5	8	no	—
433	C₄⋊C₄	—	5	8	no	—
434	C₄⋊C₄	—	5	8	no	—
435	C₄⋊C₄	—	5	4	no	—
436	C₄⋊C₄	—	5	8	no	—
437	C₄⋊C₄	—	5	8	no	—
438	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
439	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
440	C₂²⋊C₄	—	5	8	no	—
441	C₂²⋊C₄	—	5	8	no	—
442	C₂²⋊C₄	—	5	8	no	—
443	C₂²⋊C₄	—	5	8	no	—
444	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
445	C₄²	—	5	8	no	—
446	C₃×C₅	C₂×#539	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	8	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	10	4	no	—
451	C₂²×C₃	—	10	4	no	—
452	C₂²×C₃	—	10	4	no	—
453	C₂²×C₃	—	20	8	no	—
454	C₂²×C₃	#4144	1	2	yes	—
455	C₂²×C₃	C₂×#713	1	4	yes	—
456	C₂²×C₃	C₂×#713	1	2	yes	—
457	C₂²×C₃	#4150	1	2	yes	—
458	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	4	no	—
462	C₃×C₄	—	2	4	no	—
463	C₃×C₄	—	10	4	no	—
464	C₃×C₄	—	10	4	no	—
465	C₃×C₄	—	10	4	no	—
466	C₂×C₅	—	2	4	no	—
467	C₂×C₅	C₃×#539	1	4	yes	complemented
468	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
469	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
471	D₅	—	4	4	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	5	4	no	—
475	C₂³	—	10	4	no	—
476	C₂³	—	10	4	no	—
477	C₂³	—	10	4	no	—
478	C₂³	C₃×#713	1	4	yes	—
479	C₂³	C₂³×C₃×D₅	1	2	yes	—
480	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
481	Q₈	—	4	4	no	—
482	D₄	—	10	16	no	—
483	D₄	—	20	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	5	4	no	—
490	C₂×C₄	—	5	4	no	—
491	C₂×C₄	—	5	4	no	—
492	C₂×C₄	—	10	4	no	—
493	C₂×C₄	—	10	8	no	—
494	C₂×C₄	—	10	4	no	—
495	C₂×C₄	—	10	4	no	—
496	C₂×C₄	—	20	8	no	—
497	C₂×C₄	—	20	4	no	—
498	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
499	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
500	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
501	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
502	C₂×C₃	—	2	4	no	—
503	C₂×C₃	—	20	4	no	—
504	C₂×C₃	#65979	1	4	yes	direct product factor
505	C₂×C₃	C₂×#4144	1	1	yes	characteristic
506	C₂×C₃	C₂²×#713	1	1	yes	characteristic
507	C₂×C₃	C₂×#4150	1	1	yes	characteristic
508	C₅	C₂×C₃×#539	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	10	4	no	—
513	C₂²	—	10	4	no	—
514	C₂²	—	10	4	no	—
515	C₂²	—	20	8	no	—
516	C₂²	C₃×#4144	1	2	yes	—
517	C₂²	C₂×C₃×#713	1	4	yes	—
518	C₂²	C₂×C₃×#713	1	2	yes	—
519	C₂²	C₃×#4150	1	2	yes	—
520	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	10	4	no	—
526	C₄	—	10	4	no	—
527	C₄	—	10	4	no	—
528	C₃	C₂×#65979	1	1	yes	characteristic, direct product factor, Sylow
529	C₂	—	2	4	no	—
530	C₂	—	20	4	no	—
531	C₂	C₃×#65979	1	4	yes	direct product factor
532	C₂	C₂×C₃×#4144	1	1	yes	characteristic
533	C₂	C₂²×C₃×#713	1	1	yes	characteristic
534	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×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×#4076	C₂
hypercenter	C₂×C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#539
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₃×#4092	C₂	semidirect
4. C₂²×C₃×#683	C₂	semidirect
5. C₃×#65979	C₂	direct (N × H)
6. C₂×C₃×#4044	C₂	semidirect
7. C₂×C₃×#4040	C₂	semidirect
8. C₂×C₃×#4036	C₂	semidirect
9. C₂×C₃×#4032	C₂	semidirect
10. C₂×C₃×#4027	C₂	semidirect
11. C₂×#65979	C₃	direct (N × H)
19. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
23. C₃×#4092	C₂²	semidirect
35. C₂×C₃×#683	C₂²	semidirect
37. C₃×#4044	C₂²	semidirect
38. C₃×#4040	C₂²	semidirect
39. C₃×#4036	C₂²	semidirect
40. C₃×#4032	C₂²	semidirect
41. C₃×#4027	C₂²	semidirect
43. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
44. C₂×#4092	C₂×C₃	semidirect
46. C₂²×#683	C₂×C₃	semidirect
47. #65979	C₂×C₃	direct (N × H)
48. C₂×#4044	C₂×C₃	semidirect
49. C₂×#4040	C₂×C₃	semidirect
50. C₂×#4036	C₂×C₃	semidirect
51. C₂×#4032	C₂×C₃	semidirect
52. C₂×#4027	C₂×C₃	semidirect
96. C₂×C₃×C₂²⋊Q₈	D₅	semidirect
107. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
111. #4092	C₂²×C₃	semidirect
123. C₂×#683	C₂²×C₃	semidirect
125. #4044	C₂²×C₃	semidirect
126. #4040	C₂²×C₃	semidirect
127. #4036	C₂²×C₃	semidirect
128. #4032	C₂²×C₃	semidirect
129. #4027	C₂²×C₃	semidirect
173. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
234. C₂×C₂²⋊Q₈	C₃×D₅	semidirect
336. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
355. C₂×C₃×C₅	#539	semidirect
446. C₃×C₅	C₂×#539	semidirect
467. C₂×C₅	C₃×#539	semidirect
504. C₂×C₃	#65979	direct (N × H)
508. C₅	C₂×C₃×#539	semidirect
528. C₃	C₂×#65979	direct (N × H)
531. C₂	C₃×#65979	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×C₂²⋊Q₈	2
C₂×C₃×#4092	2
C₂×C₃×#4076	2
C₂²×C₃×#683	2
C₃×#65979	2
C₂×C₃×#4044	2
C₂×C₃×#4040	2
C₂×C₃×#4036	2
C₂×C₃×#4032	2
C₂×C₃×#4027	2
C₂×#65979	3
C₂×C₃×#539	5

Subgroups — C2×C3×#65979 #14480939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65979 #14480939