Subgroups — C₂×C₃×#65966 #14482900

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
6	C₃×#65966	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4042	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4034	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4027	C₂	1	2	yes	maximal
12	C₂×C₃×#4024	C₂	1	2	yes	maximal, complemented
13	C₂×#65966	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×Q₈×D₅	—	2	8	no	—
19	C₂×C₃×Q₈×D₅	C₂²	1	8	yes	complemented
20	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
22	C₂²×C₃×Dic₁₀	—	2	8	no	—
23	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
25	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
26	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
27	C₂²×C₃×Dic₁₀	C₂²	1	8	yes	complemented
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
33	C₃×#4090	C₂²	1	8	yes	complemented
34	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	—
35	C₂×C₃×#685	C₂²	1	2	yes	—
36	C₂×C₃×#685	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
38	C₂×C₃×#683	C₂²	1	1	yes	characteristic
39	C₂×C₃×#683	C₂²	1	2	yes	—
40	C₂×C₃×#683	C₂²	1	2	yes	—
41	C₂×C₃×#683	C₂²	1	2	yes	—
42	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
44	C₃×#4043	C₂²	1	8	yes	complemented
45	C₃×#4042	C₂²	1	16	yes	complemented
46	C₃×#4034	C₂²	1	16	yes	complemented
47	C₃×#4033	C₂²	1	8	yes	complemented
48	C₃×#4027	C₂²	1	16	yes	—
49	C₃×#4024	C₂²	1	16	yes	complemented
50	C₂×C₃×D₄×Q₈	—	5	1	no	maximal, Hall
51	C₂²×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4090	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic
56	#65966	C₂×C₃	1	16	yes	direct product factor
57	C₂×#4043	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#4042	C₂×C₃	1	2	yes	complemented
59	C₂×#4034	C₂×C₃	1	2	yes	complemented
60	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×#4027	C₂×C₃	1	2	yes	—
62	C₂×#4024	C₂×C₃	1	2	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×Q₈	—	2	4	no	—
66	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
67	C₂²×C₃×C₄×C₅	—	2	4	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₂²⋊D₅	Q₈	1	8	yes	complemented
74	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
75	C₂²×C₃×Dic₅	—	2	8	no	—
76	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
79	C₂²×C₃×Dic₅	C₂³	1	8	yes	—
80	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
81	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
82	C₃×Q₈×D₅	—	2	32	no	—
83	C₂×C₃×C₄×D₅	—	2	4	no	—
84	C₂×C₃×C₄×D₅	—	2	8	no	—
85	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
86	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
87	C₂×C₃×Dic₁₀	—	2	4	no	—
88	C₂×C₃×Dic₁₀	—	2	8	no	—
89	C₂×C₃×Dic₁₀	—	2	8	no	—
90	C₂×C₃×Dic₁₀	—	2	32	no	—
91	C₂×C₃×Dic₁₀	D₄	1	8	yes	complemented
92	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
93	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
94	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
95	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
96	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
98	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
100	C₃×#685	C₂³	1	8	yes	—
101	C₃×#685	C₂³	1	4	yes	—
102	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
103	C₃×#683	C₂³	1	8	yes	—
104	C₃×#683	C₂³	1	8	yes	—
105	C₃×#683	C₂³	1	8	yes	—
106	C₃×#683	C₂³	1	4	yes	—
107	C₃×C₄×Dic₅	C₂³	1	4	yes	—
108	C₃×C₄×Dic₅	C₂³	1	8	yes	—
109	C₂³×C₃×Q₈	—	5	1	no	—
110	C₂³×C₃×Q₈	—	5	1	no	—
111	C₃×D₄×Q₈	—	5	16	no	—
112	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
113	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
114	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
115	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
116	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
117	C₂×C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, complemented
118	C₂×C₃×C₄×Q₈	—	5	1	no	—
119	C₂×C₃×C₄×D₄	—	5	1	no	—
120	C₂×C₃×C₄×D₄	—	5	2	no	—
121	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
122	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
124	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
125	C₂×Q₈×D₅	—	2	8	no	—
126	C₂×Q₈×D₅	C₂²×C₃	1	8	yes	complemented
127	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
128	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂²×Dic₁₀	—	2	8	no	—
130	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
131	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
132	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
133	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
134	C₂²×Dic₁₀	C₂²×C₃	1	8	yes	complemented
135	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
136	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
139	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
140	#4090	C₂²×C₃	1	8	yes	complemented
141	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	—
142	C₂×#685	C₂²×C₃	1	2	yes	—
143	C₂×#685	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
145	C₂×#683	C₂²×C₃	1	2	yes	—
146	C₂×#683	C₂²×C₃	1	2	yes	—
147	C₂×#683	C₂²×C₃	1	2	yes	—
148	C₂×#683	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
150	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
151	#4043	C₂²×C₃	1	8	yes	complemented
152	#4042	C₂²×C₃	1	16	yes	complemented
153	#4034	C₂²×C₃	1	16	yes	complemented
154	#4033	C₂²×C₃	1	8	yes	complemented
155	#4027	C₂²×C₃	1	16	yes	—
156	#4024	C₂²×C₃	1	16	yes	complemented
157	C₂×D₄×Q₈	—	5	1	no	Sylow
158	C₂³×C₃×C₅	—	2	2	no	—
159	C₂³×C₃×C₅	—	2	2	no	—
160	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	complemented
161	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
162	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
163	C₂²×C₃×D₅	—	2	2	no	—
164	C₂²×C₃×D₅	—	2	2	no	—
165	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	complemented
166	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
167	C₃×C₅×Q₈	—	2	8	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	4	no	—
170	C₂×C₃×C₄×C₅	—	2	4	no	—
171	C₂×C₃×C₄×C₅	—	2	8	no	—
172	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
173	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
177	C₃×C₂²⋊D₅	C₂×Q₈	1	16	yes	complemented
178	C₂×C₃×Dic₅	—	2	2	no	—
179	C₂×C₃×Dic₅	—	2	4	no	—
180	C₂×C₃×Dic₅	—	2	2	no	—
181	C₂×C₃×Dic₅	—	2	16	no	—
182	C₂×C₃×Dic₅	C₂×D₄	1	8	yes	—
183	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	complemented
184	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
185	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
186	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
187	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
188	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
189	C₃×C₄×D₅	—	2	8	no	—
190	C₃×C₄×D₅	—	2	16	no	—
191	C₃×Dic₁₀	—	2	8	no	—
192	C₃×Dic₁₀	—	2	16	no	—
193	C₃×Dic₁₀	—	2	16	no	—
194	C₃×Dic₁₀	C₂×D₄	1	16	yes	complemented
195	C₂²×C₃×Q₈	—	5	8	no	—
196	C₂²×C₃×Q₈	—	5	1	no	—
197	C₂²×C₃×Q₈	—	5	2	no	—
198	C₂²×C₃×Q₈	—	5	2	no	—
199	C₂²×C₃×Q₈	—	5	1	no	—
200	C₂²×C₃×Q₈	—	5	8	no	—
201	C₂²×C₃×Q₈	—	10	8	no	—
202	C₂²×C₃×Q₈	—	10	8	no	—
203	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
204	C₂²×C₃×D₄	—	5	1	no	—
205	C₂³×C₃×C₄	—	5	2	no	—
206	C₂³×C₃×C₄	—	5	2	no	—
207	C₂³×C₃×C₄	—	5	1	no	—
208	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
209	C₃×C₄⋊Q₈	—	5	8	no	—
210	C₃×C₄⋊Q₈	—	5	16	no	—
211	C₃×C₂²⋊Q₈	—	5	16	no	—
212	C₃×C₂²⋊Q₈	—	5	8	no	—
213	C₃×C₂²⋊Q₈	—	5	16	no	—
214	C₃×C₂²⋊Q₈	C₂×D₅	1	8	yes	complemented
215	C₃×C₄×Q₈	—	5	8	no	—
216	C₃×C₄×D₄	—	5	8	no	—
217	C₃×C₄×D₄	—	5	16	no	—
218	C₂×C₃×C₄⋊C₄	—	5	1	no	—
219	C₂×C₃×C₄⋊C₄	—	5	2	no	—
220	C₂×C₃×C₄⋊C₄	—	5	2	no	—
221	C₂×C₃×C₄⋊C₄	—	5	2	no	—
222	C₂×C₃×C₄⋊C₄	—	5	2	no	—
223	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
226	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
227	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
228	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
229	C₂×C₃×C₄²	—	5	2	no	—
230	C₂×C₃×C₄²	—	5	1	no	—
231	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₅×Q₈	—	2	4	no	—
234	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
235	C₂²×C₄×C₅	—	2	4	no	—
236	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
237	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
238	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
240	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₂²⋊D₅	C₃×Q₈	1	8	yes	complemented
242	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
243	C₂²×Dic₅	—	2	8	no	—
244	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
245	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
246	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
247	C₂²×Dic₅	C₂³×C₃	1	8	yes	—
248	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
249	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
250	Q₈×D₅	—	2	32	no	—
251	C₂×C₄×D₅	—	2	4	no	—
252	C₂×C₄×D₅	—	2	8	no	—
253	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
254	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
255	C₂×Dic₁₀	—	2	4	no	—
256	C₂×Dic₁₀	—	2	8	no	—
257	C₂×Dic₁₀	—	2	8	no	—
258	C₂×Dic₁₀	—	2	32	no	—
259	C₂×Dic₁₀	C₃×D₄	1	8	yes	complemented
260	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
261	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
262	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
263	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
264	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
265	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
266	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
267	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
268	#685	C₂³×C₃	1	8	yes	—
269	#685	C₂³×C₃	1	4	yes	—
270	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
271	#683	C₂³×C₃	1	8	yes	—
272	#683	C₂³×C₃	1	8	yes	—
273	#683	C₂³×C₃	1	8	yes	—
274	#683	C₂³×C₃	1	4	yes	—
275	C₄×Dic₅	C₂³×C₃	1	8	yes	—
276	C₄×Dic₅	C₂³×C₃	1	4	yes	—
277	C₂³×Q₈	—	5	1	no	—
278	C₂³×Q₈	—	5	1	no	—
279	D₄×Q₈	—	5	16	no	—
280	C₂×C₄⋊Q₈	—	5	1	no	—
281	C₂×C₄⋊Q₈	—	5	2	no	—
282	C₂×C₂²⋊Q₈	—	5	2	no	—
283	C₂×C₂²⋊Q₈	—	5	1	no	—
284	C₂×C₂²⋊Q₈	—	5	2	no	—
285	C₂×C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
286	C₂×C₄×Q₈	—	5	1	no	—
287	C₂×C₄×D₄	—	5	1	no	—
288	C₂×C₄×D₄	—	5	2	no	—
289	C₂²×C₃×C₅	—	2	8	no	—
290	C₂²×C₃×C₅	—	2	2	no	—
291	C₂²×C₃×C₅	—	2	2	no	—
292	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
293	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
294	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
295	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
296	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
297	C₂×C₃×D₅	—	2	8	no	—
298	C₂×C₃×D₅	—	2	2	no	—
299	C₂×C₃×D₅	—	2	2	no	—
300	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	complemented
301	C₃×C₄×C₅	—	2	2	no	—
302	C₃×C₄×C₅	—	2	4	no	—
303	C₃×C₄×C₅	—	2	4	no	—
304	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
305	C₃×Dic₅	—	2	2	no	—
306	C₃×Dic₅	—	2	4	no	—
307	C₃×Dic₅	—	2	2	no	—
308	C₃×Dic₅	C₂²×D₄	1	8	yes	—
309	C₃×Dic₅	C₂²×Q₈	1	4	yes	complemented
310	C₂⁴×C₃	—	5	1	no	—
311	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
312	C₂×C₃×Q₈	—	2	4	no	—
313	C₂×C₃×Q₈	—	5	8	no	—
314	C₂×C₃×Q₈	—	5	4	no	—
315	C₂×C₃×Q₈	—	5	8	no	—
316	C₂×C₃×Q₈	—	5	8	no	—
317	C₂×C₃×Q₈	—	5	4	no	—
318	C₂×C₃×Q₈	—	10	8	no	—
319	C₂×C₃×Q₈	—	10	8	no	—
320	C₂×C₃×Q₈	—	10	32	no	—
321	C₂×C₃×Q₈	—	10	32	no	—
322	C₂×C₃×Q₈	—	10	4	no	—
323	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
324	C₂×C₃×D₄	—	5	8	no	—
325	C₂×C₃×D₄	—	5	4	no	—
326	C₂²×C₃×C₄	—	2	4	no	—
327	C₂²×C₃×C₄	—	5	1	no	—
328	C₂²×C₃×C₄	—	5	2	no	—
329	C₂²×C₃×C₄	—	5	8	no	—
330	C₂²×C₃×C₄	—	5	1	no	—
331	C₂²×C₃×C₄	—	5	1	no	—
332	C₂²×C₃×C₄	—	5	2	no	—
333	C₂²×C₃×C₄	—	5	8	no	—
334	C₂²×C₃×C₄	—	5	4	no	—
335	C₂²×C₃×C₄	—	10	8	no	—
336	C₂²×C₃×C₄	—	10	8	no	—
337	C₂²×C₃×C₄	—	10	4	no	—
338	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
339	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
340	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
342	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
343	C₃×C₄⋊C₄	—	5	4	no	—
344	C₃×C₄⋊C₄	—	5	8	no	—
345	C₃×C₄⋊C₄	—	5	8	no	—
346	C₃×C₄⋊C₄	—	5	8	no	—
347	C₃×C₄⋊C₄	—	5	8	no	—
348	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
349	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
350	C₃×C₂²⋊C₄	—	5	4	no	—
351	C₃×C₂²⋊C₄	—	5	4	no	—
352	C₃×C₂²⋊C₄	—	5	8	no	—
353	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
354	C₃×C₄²	—	5	8	no	—
355	C₃×C₄²	—	5	4	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	complemented
359	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
360	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
361	C₂²×D₅	—	2	2	no	—
362	C₂²×D₅	—	2	2	no	—
363	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	complemented
364	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
365	C₅×Q₈	—	2	8	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	4	no	—
368	C₂×C₄×C₅	—	2	4	no	—
369	C₂×C₄×C₅	—	2	8	no	—
370	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
371	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
372	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
373	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
374	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
375	C₂²⋊D₅	C₂×C₃×Q₈	1	16	yes	complemented
376	C₂×Dic₅	—	2	2	no	—
377	C₂×Dic₅	—	2	4	no	—
378	C₂×Dic₅	—	2	2	no	—
379	C₂×Dic₅	—	2	16	no	—
380	C₂×Dic₅	C₂×C₃×D₄	1	8	yes	—
381	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	complemented
382	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
383	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
384	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
385	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
386	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
387	C₄×D₅	—	2	8	no	—
388	C₄×D₅	—	2	16	no	—
389	Dic₁₀	—	2	8	no	—
390	Dic₁₀	—	2	16	no	—
391	Dic₁₀	—	2	16	no	—
392	Dic₁₀	C₂×C₃×D₄	1	16	yes	complemented
393	C₂²×Q₈	—	5	8	no	—
394	C₂²×Q₈	—	5	1	no	—
395	C₂²×Q₈	—	5	2	no	—
396	C₂²×Q₈	—	5	2	no	—
397	C₂²×Q₈	—	5	1	no	—
398	C₂²×Q₈	—	5	8	no	—
399	C₂²×Q₈	—	10	8	no	—
400	C₂²×Q₈	—	10	8	no	—
401	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
402	C₂²×D₄	—	5	1	no	—
403	C₂³×C₄	—	5	2	no	—
404	C₂³×C₄	—	5	2	no	—
405	C₂³×C₄	—	5	1	no	—
406	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
407	C₄⋊Q₈	—	5	8	no	—
408	C₄⋊Q₈	—	5	16	no	—
409	C₂²⋊Q₈	—	5	16	no	—
410	C₂²⋊Q₈	—	5	8	no	—
411	C₂²⋊Q₈	—	5	16	no	—
412	C₂²⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
413	C₄×Q₈	—	5	8	no	—
414	C₄×D₄	—	5	8	no	—
415	C₄×D₄	—	5	16	no	—
416	C₂×C₄⋊C₄	—	5	1	no	—
417	C₂×C₄⋊C₄	—	5	2	no	—
418	C₂×C₄⋊C₄	—	5	2	no	—
419	C₂×C₄⋊C₄	—	5	2	no	—
420	C₂×C₄⋊C₄	—	5	2	no	—
421	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
423	C₂×C₂²⋊C₄	—	5	1	no	—
424	C₂×C₂²⋊C₄	—	5	1	no	—
425	C₂×C₂²⋊C₄	—	5	2	no	—
426	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
427	C₂×C₄²	—	5	2	no	—
428	C₂×C₄²	—	5	1	no	—
429	C₂×C₃×C₅	—	2	4	no	—
430	C₂×C₃×C₅	D₄×Q₈	1	4	yes	complemented
431	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
432	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
433	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₃×D₅	—	2	4	no	—
435	C₂³×C₃	—	2	2	no	—
436	C₂³×C₃	—	2	2	no	—
437	C₂³×C₃	—	5	4	no	—
438	C₂³×C₃	—	5	2	no	—
439	C₂³×C₃	—	10	2	no	—
440	C₂³×C₃	—	10	2	no	—
441	C₂³×C₃	Q₈×D₅	1	4	yes	complemented
442	C₂³×C₃	C₂³×D₅	1	2	yes	—
443	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
444	C₃×Q₈	—	2	8	no	—
445	C₃×Q₈	—	5	16	no	—
446	C₃×Q₈	—	10	16	no	—
447	C₃×Q₈	—	10	16	no	—
448	C₃×Q₈	—	10	8	no	—
449	C₃×D₄	—	5	16	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	4	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	2	8	no	—
454	C₂×C₃×C₄	—	5	8	no	—
455	C₂×C₃×C₄	—	5	4	no	—
456	C₂×C₃×C₄	—	5	2	no	—
457	C₂×C₃×C₄	—	5	4	no	—
458	C₂×C₃×C₄	—	5	2	no	—
459	C₂×C₃×C₄	—	5	4	no	—
460	C₂×C₃×C₄	—	5	2	no	—
461	C₂×C₃×C₄	—	10	16	no	—
462	C₂×C₃×C₄	—	10	16	no	—
463	C₂×C₃×C₄	—	10	2	no	—
464	C₂×C₃×C₄	—	10	4	no	—
465	C₂×C₃×C₄	—	10	2	no	—
466	C₂×C₃×C₄	—	10	8	no	—
467	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
468	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
469	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
470	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
471	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	2	2	no	—
474	C₂²×C₅	—	2	8	no	—
475	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
476	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
477	C₂²×C₅	C₂²×C₃×Q₈	1	4	yes	complemented
478	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
479	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
480	C₂×D₅	—	2	2	no	—
481	C₂×D₅	—	2	2	no	—
482	C₂×D₅	—	2	8	no	—
483	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	complemented
484	C₄×C₅	—	2	2	no	—
485	C₄×C₅	—	2	4	no	—
486	C₄×C₅	—	2	4	no	—
487	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
488	Dic₅	—	2	2	no	—
489	Dic₅	—	2	4	no	—
490	Dic₅	—	2	2	no	—
491	Dic₅	C₂²×C₃×D₄	1	8	yes	—
492	Dic₅	C₂²×C₃×Q₈	1	4	yes	complemented
493	C₂⁴	—	5	1	no	—
494	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	5	8	no	—
497	C₂×Q₈	—	5	4	no	—
498	C₂×Q₈	—	5	8	no	—
499	C₂×Q₈	—	5	8	no	—
500	C₂×Q₈	—	5	4	no	—
501	C₂×Q₈	—	10	8	no	—
502	C₂×Q₈	—	10	8	no	—
503	C₂×Q₈	—	10	32	no	—
504	C₂×Q₈	—	10	32	no	—
505	C₂×Q₈	—	10	4	no	—
506	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
507	C₂×D₄	—	5	8	no	—
508	C₂×D₄	—	5	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	5	1	no	—
511	C₂²×C₄	—	5	2	no	—
512	C₂²×C₄	—	5	1	no	—
513	C₂²×C₄	—	5	1	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	8	no	—
516	C₂²×C₄	—	5	8	no	—
517	C₂²×C₄	—	5	4	no	—
518	C₂²×C₄	—	10	8	no	—
519	C₂²×C₄	—	10	8	no	—
520	C₂²×C₄	—	10	4	no	—
521	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
522	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
524	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
525	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
526	C₄⋊C₄	—	5	4	no	—
527	C₄⋊C₄	—	5	8	no	—
528	C₄⋊C₄	—	5	8	no	—
529	C₄⋊C₄	—	5	8	no	—
530	C₄⋊C₄	—	5	8	no	—
531	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
532	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
533	C₂²⋊C₄	—	5	4	no	—
534	C₂²⋊C₄	—	5	4	no	—
535	C₂²⋊C₄	—	5	8	no	—
536	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
537	C₄²	—	5	8	no	—
538	C₄²	—	5	4	no	—
539	C₃×C₅	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Hall
540	C₂²×C₃	—	2	8	no	—
541	C₂²×C₃	—	2	2	no	—
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	—	5	4	no	—
544	C₂²×C₃	—	10	8	no	—
545	C₂²×C₃	—	10	2	no	—
546	C₂²×C₃	—	10	2	no	—
547	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
548	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
549	C₂²×C₃	C₂×Q₈×D₅	1	4	yes	complemented
550	C₂²×C₃	#4150	1	2	yes	—
551	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	5	8	no	—
556	C₃×C₄	—	5	4	no	—
557	C₃×C₄	—	10	2	no	—
558	C₃×C₄	—	10	4	no	—
559	C₃×C₄	—	10	2	no	—
560	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
561	C₂×C₅	—	2	4	no	—
562	C₂×C₅	C₃×D₄×Q₈	1	4	yes	complemented
563	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
564	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
565	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
566	D₅	—	2	4	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	5	4	no	—
570	C₂³	—	5	2	no	—
571	C₂³	—	10	2	no	—
572	C₂³	—	10	2	no	—
573	C₂³	C₃×Q₈×D₅	1	4	yes	complemented
574	C₂³	C₂³×C₃×D₅	1	2	yes	—
575	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
576	Q₈	—	2	8	no	—
577	Q₈	—	5	16	no	—
578	Q₈	—	10	16	no	—
579	Q₈	—	10	16	no	—
580	Q₈	—	10	8	no	—
581	D₄	—	5	16	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	5	8	no	—
587	C₂×C₄	—	5	4	no	—
588	C₂×C₄	—	5	2	no	—
589	C₂×C₄	—	5	4	no	—
590	C₂×C₄	—	5	2	no	—
591	C₂×C₄	—	5	2	no	—
592	C₂×C₄	—	5	4	no	—
593	C₂×C₄	—	10	16	no	—
594	C₂×C₄	—	10	16	no	—
595	C₂×C₄	—	10	4	no	—
596	C₂×C₄	—	10	2	no	—
597	C₂×C₄	—	10	2	no	—
598	C₂×C₄	—	10	8	no	—
599	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
600	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
601	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
602	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
603	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
604	C₂×C₃	—	2	4	no	—
605	C₂×C₃	—	10	4	no	—
606	C₂×C₃	#65966	1	4	yes	direct product factor
607	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
608	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
609	C₂×C₃	C₂×#4150	1	1	yes	characteristic
610	C₅	C₂×C₃×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	5	4	no	—
615	C₂²	—	10	2	no	—
616	C₂²	—	10	2	no	—
617	C₂²	—	10	8	no	—
618	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
619	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
620	C₂²	C₂×C₃×Q₈×D₅	1	4	yes	complemented
621	C₂²	C₃×#4150	1	2	yes	—
622	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	5	8	no	—
627	C₄	—	5	4	no	—
628	C₄	—	10	4	no	—
629	C₄	—	10	2	no	—
630	C₄	—	10	2	no	—
631	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
632	C₃	C₂×#65966	1	1	yes	characteristic, direct product factor, Sylow
633	C₂	—	2	4	no	—
634	C₂	—	10	4	no	—
635	C₂	C₃×#65966	1	4	yes	direct product factor
636	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
637	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
638	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	C₂²×C₃×C₂²⋊D₅	C₂²
hypercenter	C₂×C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×D₄×Q₈
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. C₂²×C₃×Q₈×D₅	C₂	semidirect
2. C₂³×C₃×Dic₁₀	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₃×#4090	C₂	semidirect
6. C₃×#65966	C₂	direct (N × H)
7. C₂×C₃×#4043	C₂	semidirect
8. C₂×C₃×#4042	C₂	semidirect
9. C₂×C₃×#4034	C₂	semidirect
10. C₂×C₃×#4033	C₂	semidirect
12. C₂×C₃×#4024	C₂	semidirect
13. C₂×#65966	C₃	direct (N × H)
19. C₂×C₃×Q₈×D₅	C₂²	semidirect
27. C₂²×C₃×Dic₁₀	C₂²	semidirect
28. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₃×#4090	C₂²	semidirect
44. C₃×#4043	C₂²	semidirect
45. C₃×#4042	C₂²	semidirect
46. C₃×#4034	C₂²	semidirect
47. C₃×#4033	C₂²	semidirect
49. C₃×#4024	C₂²	semidirect
51. C₂²×Q₈×D₅	C₂×C₃	semidirect
52. C₂³×Dic₁₀	C₂×C₃	semidirect
53. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
54. C₂×#4090	C₂×C₃	semidirect
56. #65966	C₂×C₃	direct (N × H)
57. C₂×#4043	C₂×C₃	semidirect
58. C₂×#4042	C₂×C₃	semidirect
59. C₂×#4034	C₂×C₃	semidirect
60. C₂×#4033	C₂×C₃	semidirect
62. C₂×#4024	C₂×C₃	semidirect
73. C₂×C₃×C₂²⋊D₅	Q₈	semidirect
91. C₂×C₃×Dic₁₀	D₄	semidirect
117. C₂×C₃×C₂²⋊Q₈	D₅	semidirect
126. C₂×Q₈×D₅	C₂²×C₃	semidirect
134. C₂²×Dic₁₀	C₂²×C₃	semidirect
135. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
140. #4090	C₂²×C₃	semidirect
151. #4043	C₂²×C₃	semidirect
152. #4042	C₂²×C₃	semidirect
153. #4034	C₂²×C₃	semidirect
154. #4033	C₂²×C₃	semidirect
156. #4024	C₂²×C₃	semidirect
160. C₂³×C₃×C₅	C₂×Q₈	semidirect
165. C₂²×C₃×D₅	C₂×Q₈	semidirect
177. C₃×C₂²⋊D₅	C₂×Q₈	semidirect
183. C₂×C₃×Dic₅	C₂×Q₈	semidirect
194. C₃×Dic₁₀	C₂×D₄	semidirect
214. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
241. C₂×C₂²⋊D₅	C₃×Q₈	semidirect
259. C₂×Dic₁₀	C₃×D₄	semidirect
285. C₂×C₂²⋊Q₈	C₃×D₅	semidirect
294. C₂²×C₃×C₅	C₂²×Q₈	semidirect
300. C₂×C₃×D₅	C₂²×Q₈	semidirect
309. C₃×Dic₅	C₂²×Q₈	semidirect
358. C₂³×C₅	C₂×C₃×Q₈	semidirect
363. C₂²×D₅	C₂×C₃×Q₈	semidirect
375. C₂²⋊D₅	C₂×C₃×Q₈	semidirect
381. C₂×Dic₅	C₂×C₃×Q₈	semidirect
392. Dic₁₀	C₂×C₃×D₄	semidirect
412. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
430. C₂×C₃×C₅	D₄×Q₈	semidirect
441. C₂³×C₃	Q₈×D₅	semidirect
477. C₂²×C₅	C₂²×C₃×Q₈	semidirect
483. C₂×D₅	C₂²×C₃×Q₈	semidirect
492. Dic₅	C₂²×C₃×Q₈	semidirect
539. C₃×C₅	C₂×D₄×Q₈	semidirect
549. C₂²×C₃	C₂×Q₈×D₅	semidirect
562. C₂×C₅	C₃×D₄×Q₈	semidirect
573. C₂³	C₃×Q₈×D₅	semidirect
606. C₂×C₃	#65966	direct (N × H)
610. C₅	C₂×C₃×D₄×Q₈	semidirect
620. C₂²	C₂×C₃×Q₈×D₅	semidirect
632. C₃	C₂×#65966	direct (N × H)
635. C₂	C₃×#65966	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×Q₈×D₅	2
C₂³×C₃×Dic₁₀	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×#4090	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₃×#65966	2
C₂×C₃×#4043	2
C₂×C₃×#4042	2
C₂×C₃×#4034	2
C₂×C₃×#4033	2
C₂×C₃×#4027	2
C₂×C₃×#4024	2
C₂×#65966	3
C₂×C₃×D₄×Q₈	5

Subgroups — C2×C3×#65966 #14482900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65966 #14482900