Subgroups — C₂×C₃×#65941 #14480372

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4086	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4083	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65941	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#4041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4031	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×#4028	C₂	1	2	yes	maximal, complemented
13	C₂×#65941	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
20	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₂×C₃×D₄×D₅	—	2	8	no	—
24	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
25	C₂×C₃×#709	—	2	8	no	—
26	C₂×C₃×#709	C₂²	1	8	yes	complemented
27	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
28	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
29	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
30	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
37	C₃×#4086	C₂²	1	16	yes	complemented
38	C₃×#4084	C₂²	1	8	yes	complemented
39	C₃×#4083	C₂²	1	16	yes	complemented
40	C₃×#4076	C₂²	1	8	yes	complemented
41	C₂×C₃×#685	C₂²	1	2	yes	—
42	C₂×C₃×#685	C₂²	1	2	yes	complemented
43	C₂×C₃×#685	C₂²	1	2	yes	complemented
44	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
46	C₃×#4041	C₂²	1	8	yes	complemented
47	C₃×#4038	C₂²	1	8	yes	complemented
48	C₃×#4031	C₂²	1	16	yes	complemented
49	C₃×#4028	C₂²	1	16	yes	complemented
50	C₂×C₃×#535	—	5	1	no	maximal, Hall
51	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂²×#709	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4086	C₂×C₃	1	2	yes	complemented
55	C₂×#4084	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4083	C₂×C₃	1	2	yes	complemented
57	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
58	#65941	C₂×C₃	1	16	yes	direct product factor
59	C₂×#4041	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4038	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×#4031	C₂×C₃	1	2	yes	complemented
62	C₂×#4028	C₂×C₃	1	2	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₃×D₅	—	2	8	no	—
66	C₂³×C₃×D₅	—	4	4	no	—
67	C₂³×C₃×D₅	—	4	4	no	—
68	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×D₅	C₂³	1	2	yes	—
70	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
71	C₂³×C₃×D₅	C₂³	1	8	yes	—
72	C₂×C₃×C₅×D₄	—	2	4	no	—
73	C₂×C₃×C₅×D₄	—	4	4	no	—
74	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
75	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
76	C₂²×C₃×C₄×C₅	—	2	4	no	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
81	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
82	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
83	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
84	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
85	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
86	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
87	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
88	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
89	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
90	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
91	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
93	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
94	C₃×D₄×D₅	—	2	32	no	—
95	C₃×#709	—	2	32	no	—
96	C₂×C₃×D₂₀	—	2	4	no	—
97	C₂×C₃×D₂₀	—	2	4	no	—
98	C₂×C₃×D₂₀	—	4	4	no	—
99	C₂×C₃×D₂₀	C₂³	1	4	yes	—
100	C₂×C₃×D₂₀	C₂³	1	4	yes	—
101	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
102	C₂×C₃×C₄×D₅	—	2	4	no	—
103	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
104	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
105	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
106	C₂×C₃×Dic₁₀	—	2	4	no	—
107	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
108	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
111	C₃×#685	C₂³	1	8	yes	—
112	C₃×#685	C₂³	1	8	yes	complemented
113	C₃×#685	C₂³	1	8	yes	complemented
114	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
115	C₃×C₄×Dic₅	C₂³	1	8	yes	complemented
116	C₂²×C₃×#41	—	5	1	no	—
117	C₂³×C₃×D₄	—	5	1	no	—
118	C₃×#535	—	5	16	no	—
119	C₂×C₃×#127	—	5	2	no	—
120	C₂×C₃×#124	—	5	2	no	—
121	C₂×C₃×#121	—	5	1	no	—
122	C₂×C₃×#121	—	5	1	no	—
123	C₂×C₃×#121	—	5	1	no	—
124	C₂×C₃×#121	D₅	1	1	yes	characteristic, complemented
125	C₂×C₃×#120	—	5	2	no	—
126	C₂×C₃×#120	—	5	2	no	—
127	C₂×C₃×#117	—	5	1	no	—
128	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
129	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
131	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
133	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
134	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
136	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
137	C₂×D₄×D₅	—	2	8	no	—
138	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
139	C₂×#709	—	2	8	no	—
140	C₂×#709	C₂²×C₃	1	8	yes	complemented
141	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
142	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
143	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
144	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₅×#121	C₂²×C₃	1	8	yes	complemented
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
150	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
151	#4086	C₂²×C₃	1	16	yes	complemented
152	#4084	C₂²×C₃	1	8	yes	complemented
153	#4083	C₂²×C₃	1	16	yes	complemented
154	#4076	C₂²×C₃	1	8	yes	complemented
155	C₂×#685	C₂²×C₃	1	2	yes	—
156	C₂×#685	C₂²×C₃	1	2	yes	complemented
157	C₂×#685	C₂²×C₃	1	2	yes	complemented
158	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
160	#4041	C₂²×C₃	1	8	yes	complemented
161	#4038	C₂²×C₃	1	8	yes	complemented
162	#4031	C₂²×C₃	1	16	yes	complemented
163	#4028	C₂²×C₃	1	16	yes	complemented
164	C₂×#535	—	5	1	no	Sylow
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	4	no	—
167	C₂³×C₃×C₅	—	2	2	no	—
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	2	2	no	—
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
172	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
173	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
174	C₂²×C₃×D₅	—	2	2	no	—
175	C₂²×C₃×D₅	—	2	2	no	—
176	C₂²×C₃×D₅	—	2	2	no	—
177	C₂²×C₃×D₅	—	2	4	no	—
178	C₂²×C₃×D₅	—	2	2	no	—
179	C₂²×C₃×D₅	—	2	4	no	—
180	C₂²×C₃×D₅	—	2	2	no	—
181	C₂²×C₃×D₅	—	2	4	no	—
182	C₂²×C₃×D₅	—	2	16	no	—
183	C₂²×C₃×D₅	—	4	8	no	—
184	C₂²×C₃×D₅	—	4	8	no	—
185	C₂²×C₃×D₅	—	4	32	no	—
186	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
187	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
188	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
189	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
190	C₃×C₅×D₄	—	2	8	no	—
191	C₃×C₅×D₄	—	4	8	no	—
192	C₂×C₃×C₄×C₅	—	2	2	no	—
193	C₂×C₃×C₄×C₅	—	2	4	no	—
194	C₂×C₃×C₄×C₅	—	2	8	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
196	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
197	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
198	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
199	C₃×C₂²⋊D₅	—	2	8	no	—
200	C₃×C₂²⋊D₅	—	2	8	no	—
201	C₃×C₂²⋊D₅	—	2	16	no	—
202	C₃×C₂²⋊D₅	—	4	8	no	—
203	C₃×C₂²⋊D₅	—	4	8	no	—
204	C₂×C₃×Dic₅	—	2	2	no	—
205	C₂×C₃×Dic₅	—	2	4	no	—
206	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
207	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
208	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
209	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
210	C₃×D₂₀	—	2	8	no	—
211	C₃×D₂₀	—	2	8	no	—
212	C₃×D₂₀	—	4	8	no	—
213	C₃×C₄×D₅	—	2	8	no	—
214	C₃×C₄×D₅	C₂×D₄	1	16	yes	complemented
215	C₃×Dic₁₀	—	2	8	no	—
216	C₂⁵×C₃	—	5	2	no	—
217	C₂×C₃×#41	—	5	8	no	—
218	C₂×C₃×#41	—	10	8	no	—
219	C₂²×C₃×Q₈	—	5	1	no	—
220	C₂²×C₃×D₄	—	5	2	no	—
221	C₂²×C₃×D₄	—	5	1	no	—
222	C₂²×C₃×D₄	—	5	1	no	—
223	C₂²×C₃×D₄	—	5	2	no	—
224	C₂²×C₃×D₄	—	5	2	no	—
225	C₂²×C₃×D₄	—	5	8	no	—
226	C₂²×C₃×D₄	—	5	1	no	—
227	C₂²×C₃×D₄	—	5	1	no	—
228	C₂²×C₃×D₄	—	5	2	no	—
229	C₂²×C₃×D₄	—	10	8	no	—
230	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
231	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
232	C₂³×C₃×C₄	—	5	1	no	—
233	C₂³×C₃×C₄	—	5	1	no	—
234	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
235	C₃×#127	—	5	16	no	—
236	C₃×#124	—	5	16	no	—
237	C₃×#121	—	5	8	no	—
238	C₃×#121	—	5	8	no	—
239	C₃×#121	—	5	8	no	—
240	C₃×#121	C₂×D₅	1	8	yes	complemented
241	C₃×#120	—	5	16	no	—
242	C₃×#120	—	5	16	no	—
243	C₃×#117	—	5	8	no	—
244	C₂×C₃×C₄⋊C₄	—	5	1	no	—
245	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
246	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
247	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
249	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
250	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
251	C₂×C₃×C₄²	—	5	2	no	—
252	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
253	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂³×D₅	—	2	8	no	—
255	C₂³×D₅	—	4	4	no	—
256	C₂³×D₅	—	4	4	no	—
257	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
258	C₂³×D₅	C₂³×C₃	1	2	yes	—
259	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
260	C₂³×D₅	C₂³×C₃	1	8	yes	—
261	C₂×C₅×D₄	—	2	4	no	—
262	C₂×C₅×D₄	—	4	4	no	—
263	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
264	C₂×C₅×D₄	C₂³×C₃	1	8	yes	complemented
265	C₂²×C₄×C₅	—	2	4	no	—
266	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
268	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
270	C₂×C₂²⋊D₅	—	2	4	no	—
271	C₂×C₂²⋊D₅	—	2	4	no	—
272	C₂×C₂²⋊D₅	—	2	8	no	—
273	C₂×C₂²⋊D₅	—	4	4	no	—
274	C₂×C₂²⋊D₅	—	4	4	no	—
275	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
276	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
277	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
278	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
279	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
280	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
281	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
282	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
283	D₄×D₅	—	2	32	no	—
284	#709	—	2	32	no	—
285	C₂×D₂₀	—	2	4	no	—
286	C₂×D₂₀	—	2	4	no	—
287	C₂×D₂₀	—	4	4	no	—
288	C₂×D₂₀	C₂³×C₃	1	4	yes	—
289	C₂×D₂₀	C₂³×C₃	1	4	yes	—
290	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
291	C₂×C₄×D₅	—	2	4	no	—
292	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
293	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
294	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
295	C₂×Dic₁₀	—	2	4	no	—
296	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
297	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
298	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
299	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
300	#685	C₂³×C₃	1	8	yes	—
301	#685	C₂³×C₃	1	8	yes	complemented
302	#685	C₂³×C₃	1	8	yes	complemented
303	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
304	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
305	C₂²×#41	—	5	1	no	—
306	C₂³×D₄	—	5	1	no	—
307	#535	—	5	16	no	—
308	C₂×#127	—	5	2	no	—
309	C₂×#124	—	5	2	no	—
310	C₂×#121	—	5	1	no	—
311	C₂×#121	—	5	1	no	—
312	C₂×#121	—	5	1	no	—
313	C₂×#121	C₃×D₅	1	1	yes	characteristic, complemented
314	C₂×#120	—	5	2	no	—
315	C₂×#120	—	5	2	no	—
316	C₂×#117	—	5	1	no	—
317	C₂²×C₃×C₅	—	2	2	no	—
318	C₂²×C₃×C₅	—	2	4	no	—
319	C₂²×C₃×C₅	—	2	2	no	—
320	C₂²×C₃×C₅	—	2	4	no	—
321	C₂²×C₃×C₅	—	2	2	no	—
322	C₂²×C₃×C₅	—	2	4	no	—
323	C₂²×C₃×C₅	—	4	8	no	—
324	C₂²×C₃×C₅	—	4	4	no	—
325	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
326	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
328	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
329	C₂×C₃×D₅	—	2	8	no	—
330	C₂×C₃×D₅	—	2	2	no	—
331	C₂×C₃×D₅	—	2	2	no	—
332	C₂×C₃×D₅	—	2	2	no	—
333	C₂×C₃×D₅	—	2	4	no	—
334	C₂×C₃×D₅	—	2	2	no	—
335	C₂×C₃×D₅	—	2	4	no	—
336	C₂×C₃×D₅	—	2	2	no	—
337	C₂×C₃×D₅	—	2	4	no	—
338	C₂×C₃×D₅	—	4	32	no	—
339	C₂×C₃×D₅	—	4	4	no	—
340	C₂×C₃×D₅	—	4	8	no	—
341	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
342	C₃×C₄×C₅	—	2	2	no	—
343	C₃×C₄×C₅	—	2	4	no	—
344	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
345	C₃×Dic₅	—	2	2	no	—
346	C₃×Dic₅	—	2	4	no	—
347	C₃×Dic₅	C₂²×D₄	1	4	yes	—
348	C₂⁴×C₃	—	5	1	no	—
349	C₂⁴×C₃	—	5	2	no	—
350	C₂⁴×C₃	—	5	1	no	—
351	C₂⁴×C₃	—	5	8	no	—
352	C₂⁴×C₃	—	10	8	no	—
353	C₂⁴×C₃	—	20	4	no	—
354	C₂⁴×C₃	—	20	4	no	—
355	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
356	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
357	C₃×#41	—	10	32	no	—
358	C₂×C₃×Q₈	—	5	4	no	—
359	C₂×C₃×Q₈	—	10	4	no	—
360	C₂×C₃×D₄	—	2	4	no	—
361	C₂×C₃×D₄	—	4	4	no	—
362	C₂×C₃×D₄	—	5	4	no	—
363	C₂×C₃×D₄	—	5	8	no	—
364	C₂×C₃×D₄	—	5	4	no	—
365	C₂×C₃×D₄	—	5	8	no	—
366	C₂×C₃×D₄	—	5	8	no	—
367	C₂×C₃×D₄	—	5	4	no	—
368	C₂×C₃×D₄	—	5	4	no	—
369	C₂×C₃×D₄	—	5	8	no	—
370	C₂×C₃×D₄	—	10	4	no	—
371	C₂×C₃×D₄	—	10	32	no	—
372	C₂×C₃×D₄	—	10	8	no	—
373	C₂×C₃×D₄	—	10	4	no	—
374	C₂×C₃×D₄	—	10	4	no	—
375	C₂×C₃×D₄	—	10	4	no	—
376	C₂×C₃×D₄	—	20	4	no	—
377	C₂×C₃×D₄	—	20	4	no	—
378	C₂×C₃×D₄	—	20	4	no	—
379	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
380	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	5	1	no	—
383	C₂²×C₃×C₄	—	5	8	no	—
384	C₂²×C₃×C₄	—	5	4	no	—
385	C₂²×C₃×C₄	—	5	2	no	—
386	C₂²×C₃×C₄	—	5	1	no	—
387	C₂²×C₃×C₄	—	5	4	no	—
388	C₂²×C₃×C₄	—	10	4	no	—
389	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
390	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
393	C₃×C₄⋊C₄	—	5	4	no	—
394	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
395	C₃×C₂²⋊C₄	—	5	8	no	—
396	C₃×C₂²⋊C₄	—	5	8	no	—
397	C₃×C₂²⋊C₄	—	5	8	no	—
398	C₃×C₂²⋊C₄	—	5	8	no	—
399	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
400	C₃×C₄²	—	5	8	no	—
401	C₂³×C₅	—	2	2	no	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	2	2	no	—
404	C₂³×C₅	—	2	4	no	—
405	C₂³×C₅	—	2	2	no	—
406	C₂³×C₅	—	2	4	no	—
407	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
408	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
409	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
410	C₂²×D₅	—	2	2	no	—
411	C₂²×D₅	—	2	2	no	—
412	C₂²×D₅	—	2	2	no	—
413	C₂²×D₅	—	2	4	no	—
414	C₂²×D₅	—	2	2	no	—
415	C₂²×D₅	—	2	4	no	—
416	C₂²×D₅	—	2	2	no	—
417	C₂²×D₅	—	2	4	no	—
418	C₂²×D₅	—	2	16	no	—
419	C₂²×D₅	—	4	8	no	—
420	C₂²×D₅	—	4	8	no	—
421	C₂²×D₅	—	4	32	no	—
422	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
423	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
424	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
425	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
426	C₅×D₄	—	2	8	no	—
427	C₅×D₄	—	4	8	no	—
428	C₂×C₄×C₅	—	2	2	no	—
429	C₂×C₄×C₅	—	2	4	no	—
430	C₂×C₄×C₅	—	2	8	no	—
431	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
432	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
433	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
434	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
435	C₂²⋊D₅	—	2	8	no	—
436	C₂²⋊D₅	—	2	8	no	—
437	C₂²⋊D₅	—	2	16	no	—
438	C₂²⋊D₅	—	4	8	no	—
439	C₂²⋊D₅	—	4	8	no	—
440	C₂×Dic₅	—	2	2	no	—
441	C₂×Dic₅	—	2	4	no	—
442	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
443	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
444	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
445	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
446	D₂₀	—	2	8	no	—
447	D₂₀	—	2	8	no	—
448	D₂₀	—	4	8	no	—
449	C₄×D₅	—	2	8	no	—
450	C₄×D₅	C₂×C₃×D₄	1	16	yes	complemented
451	Dic₁₀	—	2	8	no	—
452	C₂⁵	—	5	2	no	—
453	C₂×#41	—	5	8	no	—
454	C₂×#41	—	10	8	no	—
455	C₂²×Q₈	—	5	1	no	—
456	C₂²×D₄	—	5	1	no	—
457	C₂²×D₄	—	5	2	no	—
458	C₂²×D₄	—	5	1	no	—
459	C₂²×D₄	—	5	2	no	—
460	C₂²×D₄	—	5	2	no	—
461	C₂²×D₄	—	5	8	no	—
462	C₂²×D₄	—	5	1	no	—
463	C₂²×D₄	—	5	1	no	—
464	C₂²×D₄	—	5	2	no	—
465	C₂²×D₄	—	10	8	no	—
466	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
467	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
468	C₂³×C₄	—	5	1	no	—
469	C₂³×C₄	—	5	1	no	—
470	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
471	#127	—	5	16	no	—
472	#124	—	5	16	no	—
473	#121	—	5	8	no	—
474	#121	—	5	8	no	—
475	#121	—	5	8	no	—
476	#121	C₂×C₃×D₅	1	8	yes	complemented
477	#120	—	5	16	no	—
478	#120	—	5	16	no	—
479	#117	—	5	8	no	—
480	C₂×C₄⋊C₄	—	5	1	no	—
481	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
482	C₂×C₂²⋊C₄	—	5	2	no	—
483	C₂×C₂²⋊C₄	—	5	2	no	—
484	C₂×C₂²⋊C₄	—	5	2	no	—
485	C₂×C₂²⋊C₄	—	5	2	no	—
486	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
487	C₂×C₄²	—	5	2	no	—
488	C₂×C₃×C₅	—	4	4	no	—
489	C₂×C₃×C₅	—	4	2	no	—
490	C₂×C₃×C₅	#535	1	4	yes	complemented
491	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
492	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₃×D₅	—	2	4	no	—
495	C₃×D₅	—	4	2	no	—
496	C₃×D₅	—	4	4	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	4	no	—
499	C₂³×C₃	—	2	2	no	—
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	2	2	no	—
502	C₂³×C₃	—	2	4	no	—
503	C₂³×C₃	—	5	4	no	—
504	C₂³×C₃	—	5	2	no	—
505	C₂³×C₃	—	5	4	no	—
506	C₂³×C₃	—	5	2	no	—
507	C₂³×C₃	—	10	16	no	—
508	C₂³×C₃	—	10	2	no	—
509	C₂³×C₃	—	10	2	no	—
510	C₂³×C₃	—	10	2	no	—
511	C₂³×C₃	—	10	4	no	—
512	C₂³×C₃	—	10	2	no	—
513	C₂³×C₃	—	10	4	no	—
514	C₂³×C₃	—	10	2	no	—
515	C₂³×C₃	—	10	4	no	—
516	C₂³×C₃	—	20	8	no	—
517	C₂³×C₃	—	20	8	no	—
518	C₂³×C₃	—	20	32	no	—
519	C₂³×C₃	C₂³×D₅	1	4	yes	—
520	C₂³×C₃	C₂³×D₅	1	2	yes	—
521	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
522	C₃×Q₈	—	10	8	no	—
523	C₃×D₄	—	2	8	no	—
524	C₃×D₄	—	4	8	no	—
525	C₃×D₄	—	10	8	no	—
526	C₃×D₄	—	10	16	no	—
527	C₃×D₄	—	10	8	no	—
528	C₃×D₄	—	10	8	no	—
529	C₃×D₄	—	10	8	no	—
530	C₃×D₄	—	20	8	no	—
531	C₃×D₄	—	20	8	no	—
532	C₃×D₄	—	20	8	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	4	no	—
535	C₂×C₃×C₄	—	2	8	no	—
536	C₂×C₃×C₄	—	5	4	no	—
537	C₂×C₃×C₄	—	5	2	no	—
538	C₂×C₃×C₄	—	5	16	no	—
539	C₂×C₃×C₄	—	5	4	no	—
540	C₂×C₃×C₄	—	5	2	no	—
541	C₂×C₃×C₄	—	10	2	no	—
542	C₂×C₃×C₄	—	10	4	no	—
543	C₂×C₃×C₄	—	10	8	no	—
544	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
545	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
546	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
547	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
548	C₂²×C₅	—	2	2	no	—
549	C₂²×C₅	—	2	4	no	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	2	4	no	—
552	C₂²×C₅	—	2	2	no	—
553	C₂²×C₅	—	2	4	no	—
554	C₂²×C₅	—	4	8	no	—
555	C₂²×C₅	—	4	4	no	—
556	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
557	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
558	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
559	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
560	C₂×D₅	—	2	2	no	—
561	C₂×D₅	—	2	2	no	—
562	C₂×D₅	—	2	8	no	—
563	C₂×D₅	—	2	2	no	—
564	C₂×D₅	—	2	4	no	—
565	C₂×D₅	—	2	2	no	—
566	C₂×D₅	—	2	4	no	—
567	C₂×D₅	—	2	2	no	—
568	C₂×D₅	—	2	4	no	—
569	C₂×D₅	—	4	32	no	—
570	C₂×D₅	—	4	4	no	—
571	C₂×D₅	—	4	8	no	—
572	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	2	4	no	—
575	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
576	Dic₅	—	2	2	no	—
577	Dic₅	—	2	4	no	—
578	Dic₅	C₂²×C₃×D₄	1	4	yes	—
579	C₂⁴	—	5	1	no	—
580	C₂⁴	—	5	2	no	—
581	C₂⁴	—	5	1	no	—
582	C₂⁴	—	5	8	no	—
583	C₂⁴	—	10	8	no	—
584	C₂⁴	—	20	4	no	—
585	C₂⁴	—	20	4	no	—
586	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
587	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
588	#41	—	10	32	no	—
589	C₂×Q₈	—	5	4	no	—
590	C₂×Q₈	—	10	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	5	4	no	—
594	C₂×D₄	—	5	8	no	—
595	C₂×D₄	—	5	4	no	—
596	C₂×D₄	—	5	8	no	—
597	C₂×D₄	—	5	8	no	—
598	C₂×D₄	—	5	4	no	—
599	C₂×D₄	—	5	4	no	—
600	C₂×D₄	—	5	8	no	—
601	C₂×D₄	—	10	4	no	—
602	C₂×D₄	—	10	32	no	—
603	C₂×D₄	—	10	8	no	—
604	C₂×D₄	—	10	4	no	—
605	C₂×D₄	—	10	4	no	—
606	C₂×D₄	—	10	4	no	—
607	C₂×D₄	—	20	4	no	—
608	C₂×D₄	—	20	4	no	—
609	C₂×D₄	—	20	4	no	—
610	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
611	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	5	1	no	—
614	C₂²×C₄	—	5	8	no	—
615	C₂²×C₄	—	5	4	no	—
616	C₂²×C₄	—	5	2	no	—
617	C₂²×C₄	—	5	1	no	—
618	C₂²×C₄	—	5	4	no	—
619	C₂²×C₄	—	10	4	no	—
620	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
621	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
624	C₄⋊C₄	—	5	4	no	—
625	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
626	C₂²⋊C₄	—	5	8	no	—
627	C₂²⋊C₄	—	5	8	no	—
628	C₂²⋊C₄	—	5	8	no	—
629	C₂²⋊C₄	—	5	8	no	—
630	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
631	C₄²	—	5	8	no	—
632	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	2	2	no	—
636	C₂²×C₃	—	2	4	no	—
637	C₂²×C₃	—	2	2	no	—
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	4	4	no	—
640	C₂²×C₃	—	4	8	no	—
641	C₂²×C₃	—	5	4	no	—
642	C₂²×C₃	—	10	8	no	—
643	C₂²×C₃	—	10	2	no	—
644	C₂²×C₃	—	10	2	no	—
645	C₂²×C₃	—	10	2	no	—
646	C₂²×C₃	—	10	4	no	—
647	C₂²×C₃	—	10	2	no	—
648	C₂²×C₃	—	10	4	no	—
649	C₂²×C₃	—	10	2	no	—
650	C₂²×C₃	—	10	4	no	—
651	C₂²×C₃	—	20	32	no	—
652	C₂²×C₃	—	20	4	no	—
653	C₂²×C₃	—	20	8	no	—
654	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
655	C₂²×C₃	#4144	1	2	yes	—
656	C₂²×C₃	#4149	1	2	yes	—
657	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	4	no	—
660	C₃×C₄	—	5	4	no	—
661	C₃×C₄	—	10	2	no	—
662	C₃×C₄	—	10	4	no	—
663	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
664	C₂×C₅	—	4	4	no	—
665	C₂×C₅	—	4	2	no	—
666	C₂×C₅	C₃×#535	1	4	yes	complemented
667	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
668	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
670	D₅	—	2	4	no	—
671	D₅	—	4	4	no	—
672	D₅	—	4	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	5	4	no	—
680	C₂³	—	5	2	no	—
681	C₂³	—	5	4	no	—
682	C₂³	—	5	2	no	—
683	C₂³	—	10	16	no	—
684	C₂³	—	10	2	no	—
685	C₂³	—	10	2	no	—
686	C₂³	—	10	2	no	—
687	C₂³	—	10	4	no	—
688	C₂³	—	10	2	no	—
689	C₂³	—	10	4	no	—
690	C₂³	—	10	2	no	—
691	C₂³	—	10	4	no	—
692	C₂³	—	20	8	no	—
693	C₂³	—	20	8	no	—
694	C₂³	—	20	32	no	—
695	C₂³	C₂³×C₃×D₅	1	4	yes	—
696	C₂³	C₂³×C₃×D₅	1	2	yes	—
697	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
698	Q₈	—	10	8	no	—
699	D₄	—	2	8	no	—
700	D₄	—	4	8	no	—
701	D₄	—	10	8	no	—
702	D₄	—	10	16	no	—
703	D₄	—	10	8	no	—
704	D₄	—	10	8	no	—
705	D₄	—	10	8	no	—
706	D₄	—	20	8	no	—
707	D₄	—	20	8	no	—
708	D₄	—	20	8	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	5	4	no	—
713	C₂×C₄	—	5	2	no	—
714	C₂×C₄	—	5	16	no	—
715	C₂×C₄	—	5	4	no	—
716	C₂×C₄	—	5	2	no	—
717	C₂×C₄	—	10	2	no	—
718	C₂×C₄	—	10	4	no	—
719	C₂×C₄	—	10	8	no	—
720	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
721	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
722	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
723	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
724	C₂×C₃	—	4	4	no	—
725	C₂×C₃	—	4	2	no	—
726	C₂×C₃	—	10	4	no	—
727	C₂×C₃	—	20	4	no	—
728	C₂×C₃	—	20	2	no	—
729	C₂×C₃	#65941	1	4	yes	direct product factor
730	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
731	C₂×C₃	C₂×#4144	1	1	yes	characteristic
732	C₂×C₃	C₂×#4149	1	1	yes	characteristic
733	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	4	8	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	5	4	no	—
743	C₂²	—	10	2	no	—
744	C₂²	—	10	2	no	—
745	C₂²	—	10	8	no	—
746	C₂²	—	10	2	no	—
747	C₂²	—	10	4	no	—
748	C₂²	—	10	2	no	—
749	C₂²	—	10	4	no	—
750	C₂²	—	10	2	no	—
751	C₂²	—	10	4	no	—
752	C₂²	—	20	32	no	—
753	C₂²	—	20	8	no	—
754	C₂²	—	20	4	no	—
755	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
756	C₂²	C₃×#4144	1	2	yes	—
757	C₂²	C₃×#4149	1	2	yes	—
758	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
759	C₄	—	2	2	no	—
760	C₄	—	2	4	no	—
761	C₄	—	5	4	no	—
762	C₄	—	10	2	no	—
763	C₄	—	10	4	no	—
764	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
765	C₃	C₂×#65941	1	1	yes	characteristic, direct product factor, Sylow
766	C₂	—	4	4	no	—
767	C₂	—	4	2	no	—
768	C₂	—	10	4	no	—
769	C₂	—	20	4	no	—
770	C₂	—	20	2	no	—
771	C₂	C₃×#65941	1	4	yes	direct product factor
772	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
773	C₂	C₂×C₃×#4144	1	1	yes	characteristic
774	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×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#121	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄×D₅	C₂	semidirect
2. C₂²×C₃×#709	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×#4086	C₂	semidirect
5. C₂×C₃×#4084	C₂	semidirect
6. C₂×C₃×#4083	C₂	semidirect
7. C₂×C₃×#4076	C₂	semidirect
8. C₃×#65941	C₂	direct (N × H)
9. C₂×C₃×#4041	C₂	semidirect
10. C₂×C₃×#4038	C₂	semidirect
11. C₂×C₃×#4031	C₂	semidirect
12. C₂×C₃×#4028	C₂	semidirect
13. C₂×#65941	C₃	direct (N × H)
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
20. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
21. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
22. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
24. C₂×C₃×D₄×D₅	C₂²	semidirect
26. C₂×C₃×#709	C₂²	semidirect
29. C₂²×C₃×D₂₀	C₂²	semidirect
31. C₂²×C₃×C₄×D₅	C₂²	semidirect
32. C₂²×C₃×Dic₁₀	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
37. C₃×#4086	C₂²	semidirect
38. C₃×#4084	C₂²	semidirect
39. C₃×#4083	C₂²	semidirect
40. C₃×#4076	C₂²	semidirect
42. C₂×C₃×#685	C₂²	semidirect
43. C₂×C₃×#685	C₂²	semidirect
44. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
45. C₂×C₃×C₄×Dic₅	C₂²	semidirect
46. C₃×#4041	C₂²	semidirect
47. C₃×#4038	C₂²	semidirect
48. C₃×#4031	C₂²	semidirect
49. C₃×#4028	C₂²	semidirect
51. C₂²×D₄×D₅	C₂×C₃	semidirect
52. C₂²×#709	C₂×C₃	semidirect
53. C₂×C₅×#121	C₂×C₃	semidirect
54. C₂×#4086	C₂×C₃	semidirect
55. C₂×#4084	C₂×C₃	semidirect
56. C₂×#4083	C₂×C₃	semidirect
57. C₂×#4076	C₂×C₃	semidirect
58. #65941	C₂×C₃	direct (N × H)
59. C₂×#4041	C₂×C₃	semidirect
60. C₂×#4038	C₂×C₃	semidirect
61. C₂×#4031	C₂×C₃	semidirect
62. C₂×#4028	C₂×C₃	semidirect
75. C₂×C₃×C₅×D₄	C₂³	semidirect
80. C₂²×C₃×C₄×C₅	C₂³	semidirect
88. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
89. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
90. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
101. C₂×C₃×D₂₀	C₂³	semidirect
103. C₂×C₃×C₄×D₅	D₄	semidirect
105. C₂×C₃×C₄×D₅	C₂³	semidirect
107. C₂×C₃×Dic₁₀	C₂³	semidirect
108. C₃×C₅×C₄⋊C₄	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
110. C₃×C₂²⋊Dic₅	C₂³	semidirect
112. C₃×#685	C₂³	semidirect
113. C₃×#685	C₂³	semidirect
114. C₃×C₄⋊Dic₅	C₂³	semidirect
115. C₃×C₄×Dic₅	C₂³	semidirect
124. C₂×C₃×#121	D₅	semidirect
130. C₂²×C₅×D₄	C₂²×C₃	semidirect
131. C₂³×C₄×C₅	C₂²×C₃	semidirect
134. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
135. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
136. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
138. C₂×D₄×D₅	C₂²×C₃	semidirect
140. C₂×#709	C₂²×C₃	semidirect
143. C₂²×D₂₀	C₂²×C₃	semidirect
145. C₂²×C₄×D₅	C₂²×C₃	semidirect
146. C₂²×Dic₁₀	C₂²×C₃	semidirect
147. C₅×#121	C₂²×C₃	semidirect
148. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
149. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
150. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
151. #4086	C₂²×C₃	semidirect
152. #4084	C₂²×C₃	semidirect
153. #4083	C₂²×C₃	semidirect
154. #4076	C₂²×C₃	semidirect
156. C₂×#685	C₂²×C₃	semidirect
157. C₂×#685	C₂²×C₃	semidirect
158. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
159. C₂×C₄×Dic₅	C₂²×C₃	semidirect
160. #4041	C₂²×C₃	semidirect
161. #4038	C₂²×C₃	semidirect
162. #4031	C₂²×C₃	semidirect
163. #4028	C₂²×C₃	semidirect
214. C₃×C₄×D₅	C₂×D₄	semidirect
231. C₂²×C₃×D₄	C₂×D₅	semidirect
234. C₂³×C₃×C₄	C₂×D₅	semidirect
240. C₃×#121	C₂×D₅	semidirect
245. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
250. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
264. C₂×C₅×D₄	C₂³×C₃	semidirect
269. C₂²×C₄×C₅	C₂³×C₃	semidirect
277. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
278. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
279. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
290. C₂×D₂₀	C₂³×C₃	semidirect
292. C₂×C₄×D₅	C₃×D₄	semidirect
294. C₂×C₄×D₅	C₂³×C₃	semidirect
296. C₂×Dic₁₀	C₂³×C₃	semidirect
297. C₅×C₄⋊C₄	C₂³×C₃	semidirect
298. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
299. C₂²⋊Dic₅	C₂³×C₃	semidirect
301. #685	C₂³×C₃	semidirect
302. #685	C₂³×C₃	semidirect
303. C₄⋊Dic₅	C₂³×C₃	semidirect
304. C₄×Dic₅	C₂³×C₃	semidirect
313. C₂×#121	C₃×D₅	semidirect
380. C₂×C₃×D₄	C₂²×D₅	semidirect
392. C₂²×C₃×C₄	C₂²×D₅	semidirect
394. C₃×C₄⋊C₄	C₂²×D₅	semidirect
399. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
450. C₄×D₅	C₂×C₃×D₄	semidirect
467. C₂²×D₄	C₂×C₃×D₅	semidirect
470. C₂³×C₄	C₂×C₃×D₅	semidirect
476. #121	C₂×C₃×D₅	semidirect
481. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
486. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
490. C₂×C₃×C₅	#535	semidirect
611. C₂×D₄	C₂²×C₃×D₅	semidirect
623. C₂²×C₄	C₂²×C₃×D₅	semidirect
625. C₄⋊C₄	C₂²×C₃×D₅	semidirect
630. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
632. C₃×C₅	C₂×#535	semidirect
666. C₂×C₅	C₃×#535	semidirect
729. C₂×C₃	#65941	direct (N × H)
733. C₅	C₂×C₃×#535	semidirect
765. C₃	C₂×#65941	direct (N × H)
771. C₂	C₃×#65941	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×D₄×D₅	2
C₂²×C₃×#709	2
C₂×C₃×C₅×#121	2
C₂×C₃×#4086	2
C₂×C₃×#4084	2
C₂×C₃×#4083	2
C₂×C₃×#4076	2
C₃×#65941	2
C₂×C₃×#4041	2
C₂×C₃×#4038	2
C₂×C₃×#4031	2
C₂×C₃×#4028	2
C₂×#65941	3
C₂×C₃×#535	5

Subgroups — C2×C3×#65941 #14480372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65941 #14480372