Subgroups — C₂×C₃×#66163 #14482479

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66163	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4085	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4083	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4075	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₃×#685	C₂	1	2	yes	maximal, complemented
13	C₂×#66163	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
15	C₂×C₃×C₅×#41	—	2	8	no	—
16	C₂×C₃×C₅×#41	C₂²	1	8	yes	complemented
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
20	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
25	C₂³×C₃×Dic₅	C₂²	1	2	yes	complemented
26	C₂×C₃×D₄×D₅	—	2	8	no	—
27	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
28	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
32	C₃×#4093	C₂²	1	8	yes	complemented
33	C₃×#4092	C₂²	1	8	yes	complemented
34	C₃×#4085	C₂²	1	16	yes	complemented
35	C₃×#4083	C₂²	1	16	yes	complemented
36	C₃×D₄×Dic₅	C₂²	1	8	yes	complemented
37	C₃×#4076	C₂²	1	8	yes	complemented
38	C₃×#4075	C₂²	1	16	yes	complemented
39	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
40	C₂×C₃×#685	C₂²	1	1	yes	characteristic
41	C₂×C₃×#685	C₂²	1	2	yes	—
42	C₂×C₃×#685	C₂²	1	16	yes	complemented
43	C₂×C₃×#685	C₂²	1	2	yes	complemented
44	C₂×C₃×#685	C₂²	1	2	yes	complemented
45	C₂×C₃×#685	C₂²	1	2	yes	complemented
46	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#683	C₂²	1	2	yes	complemented
49	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×#546	—	5	1	no	maximal, Hall
51	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
53	#66163	C₂×C₃	1	16	yes	direct product factor
54	C₂×#4093	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4092	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4085	C₂×C₃	1	2	yes	complemented
57	C₂×#4083	C₂×C₃	1	2	yes	complemented
58	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4075	C₂×C₃	1	2	yes	complemented
61	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂²×#685	C₂×C₃	1	2	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
65	C₂³×C₃×D₅	—	2	8	no	—
66	C₂³×C₃×D₅	—	2	8	no	—
67	C₂³×C₃×D₅	—	4	4	no	—
68	C₂³×C₃×D₅	C₂³	1	2	yes	—
69	C₂³×C₃×D₅	C₂³	1	8	yes	—
70	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×#41	—	2	32	no	—
72	C₂×C₃×C₅×Q₈	—	2	4	no	—
73	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
74	C₂×C₃×C₅×D₄	—	2	8	no	—
75	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
78	C₂²×C₃×C₄×C₅	—	2	8	no	—
79	C₂²×C₃×C₄×C₅	—	2	4	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	complemented
84	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
85	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
86	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
87	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
88	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
89	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
90	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
91	C₂²×C₃×Dic₅	—	4	4	no	—
92	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
96	C₂²×C₃×Dic₅	C₂³	1	8	yes	complemented
97	C₃×D₄×D₅	—	2	32	no	—
98	C₂×C₃×D₂₀	—	2	4	no	—
99	C₂×C₃×D₂₀	C₂³	1	4	yes	—
100	C₂×C₃×C₄×D₅	—	2	4	no	—
101	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
102	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
103	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
104	C₃×#685	C₂³	1	8	yes	—
105	C₃×#685	C₂³	1	4	yes	—
106	C₃×#685	C₂³	1	8	yes	complemented
107	C₃×#685	C₂³	1	8	yes	complemented
108	C₃×#685	C₂³	1	8	yes	complemented
109	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
110	C₃×#683	C₂³	1	8	yes	complemented
111	C₃×#683	C₂³	1	4	yes	complemented
112	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
113	C₂²×C₃×#41	D₅	1	1	yes	characteristic, complemented
114	C₂³×C₃×D₄	—	5	1	no	—
115	C₃×#546	—	5	16	no	—
116	C₂×C₃×#124	—	5	1	no	—
117	C₂×C₃×#123	—	5	2	no	—
118	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
119	C₂×C₃×#121	—	5	2	no	—
120	C₂×C₃×#121	—	5	1	no	—
121	C₂×C₃×#120	—	5	2	no	—
122	C₂×C₃×C₄×D₄	—	5	1	no	—
123	C₂×C₃×C₄×D₄	—	5	1	no	—
124	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
125	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
126	C₂×C₅×#41	—	2	8	no	—
127	C₂×C₅×#41	C₂²×C₃	1	8	yes	complemented
128	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
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	2	yes	complemented
132	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
134	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
135	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
136	C₂³×Dic₅	C₂²×C₃	1	2	yes	complemented
137	C₂×D₄×D₅	—	2	8	no	—
138	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
139	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
140	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
143	#4093	C₂²×C₃	1	8	yes	complemented
144	#4092	C₂²×C₃	1	8	yes	complemented
145	#4085	C₂²×C₃	1	16	yes	complemented
146	#4083	C₂²×C₃	1	16	yes	complemented
147	D₄×Dic₅	C₂²×C₃	1	8	yes	complemented
148	#4076	C₂²×C₃	1	8	yes	complemented
149	#4075	C₂²×C₃	1	16	yes	complemented
150	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
151	C₂×#685	C₂²×C₃	1	1	yes	characteristic
152	C₂×#685	C₂²×C₃	1	2	yes	—
153	C₂×#685	C₂²×C₃	1	16	yes	complemented
154	C₂×#685	C₂²×C₃	1	2	yes	complemented
155	C₂×#685	C₂²×C₃	1	2	yes	complemented
156	C₂×#685	C₂²×C₃	1	2	yes	complemented
157	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂×#683	C₂²×C₃	1	2	yes	complemented
160	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×#546	—	5	1	no	Sylow
162	C₂³×C₃×C₅	—	2	4	no	—
163	C₂³×C₃×C₅	—	2	4	no	—
164	C₂³×C₃×C₅	—	2	2	no	—
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
168	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
169	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
170	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
171	C₂²×C₃×D₅	—	2	2	no	—
172	C₂²×C₃×D₅	—	2	2	no	—
173	C₂²×C₃×D₅	—	2	4	no	—
174	C₂²×C₃×D₅	—	2	16	no	—
175	C₂²×C₃×D₅	—	2	4	no	—
176	C₂²×C₃×D₅	—	2	4	no	—
177	C₂²×C₃×D₅	—	2	16	no	—
178	C₂²×C₃×D₅	—	4	8	no	—
179	C₂²×C₃×D₅	—	4	32	no	—
180	C₂²×C₃×D₅	#41	1	4	yes	complemented
181	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
182	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
183	C₃×C₅×Q₈	—	2	8	no	—
184	C₃×C₅×D₄	—	2	16	no	—
185	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
186	C₂×C₃×C₄×C₅	—	2	2	no	—
187	C₂×C₃×C₄×C₅	—	2	4	no	—
188	C₂×C₃×C₄×C₅	—	2	16	no	—
189	C₂×C₃×C₄×C₅	—	2	8	no	—
190	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
191	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
192	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
193	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
194	C₃×C₂²⋊D₅	—	2	16	no	—
195	C₃×C₂²⋊D₅	—	2	8	no	—
196	C₃×C₂²⋊D₅	—	4	8	no	—
197	C₂×C₃×Dic₅	—	2	2	no	—
198	C₂×C₃×Dic₅	—	2	2	no	—
199	C₂×C₃×Dic₅	—	2	2	no	—
200	C₂×C₃×Dic₅	—	2	4	no	—
201	C₂×C₃×Dic₅	—	4	8	no	—
202	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
203	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
204	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
205	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
206	C₃×D₂₀	—	2	8	no	—
207	C₃×C₄×D₅	—	2	8	no	—
208	C₂⁵×C₃	—	5	2	no	—
209	C₂×C₃×#41	—	2	8	no	—
210	C₂×C₃×#41	C₂×D₅	1	8	yes	complemented
211	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
212	C₂²×C₃×D₄	—	5	2	no	—
213	C₂²×C₃×D₄	—	5	1	no	—
214	C₂²×C₃×D₄	—	5	2	no	—
215	C₂²×C₃×D₄	—	5	8	no	—
216	C₂²×C₃×D₄	—	5	1	no	—
217	C₂²×C₃×D₄	—	10	8	no	—
218	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
219	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
220	C₂³×C₃×C₄	—	5	2	no	—
221	C₂³×C₃×C₄	—	5	1	no	—
222	C₂³×C₃×C₄	C₂×D₅	1	2	yes	complemented
223	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
224	C₃×#124	—	5	8	no	—
225	C₃×#123	—	5	16	no	—
226	C₃×C₂²⋊Q₈	—	5	8	no	—
227	C₃×#121	—	5	16	no	—
228	C₃×#121	—	5	8	no	—
229	C₃×#120	—	5	16	no	—
230	C₃×C₄×D₄	—	5	8	no	—
231	C₃×C₄×D₄	—	5	8	no	—
232	C₂×C₃×C₄⋊C₄	—	5	1	no	—
233	C₂×C₃×C₄⋊C₄	—	5	1	no	—
234	C₂×C₃×C₄⋊C₄	—	5	2	no	—
235	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
236	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
237	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
238	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
239	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
240	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
241	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
242	C₂×C₃×C₂²⋊C₄	—	5	16	no	—
243	C₂×C₃×C₄²	—	5	1	no	—
244	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
246	C₂³×D₅	—	2	8	no	—
247	C₂³×D₅	—	2	8	no	—
248	C₂³×D₅	—	4	4	no	—
249	C₂³×D₅	C₂³×C₃	1	2	yes	—
250	C₂³×D₅	C₂³×C₃	1	8	yes	—
251	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
252	C₅×#41	—	2	32	no	—
253	C₂×C₅×Q₈	—	2	4	no	—
254	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	complemented
255	C₂×C₅×D₄	—	2	8	no	—
256	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
257	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
258	C₂×C₅×D₄	C₂³×C₃	1	8	yes	complemented
259	C₂²×C₄×C₅	—	2	8	no	—
260	C₂²×C₄×C₅	—	2	4	no	—
261	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
263	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	complemented
265	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
266	C₂×C₂²⋊D₅	—	2	8	no	—
267	C₂×C₂²⋊D₅	—	2	4	no	—
268	C₂×C₂²⋊D₅	—	4	4	no	—
269	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
270	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
271	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
272	C₂²×Dic₅	—	4	4	no	—
273	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
274	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
275	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
276	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
277	C₂²×Dic₅	C₂³×C₃	1	8	yes	complemented
278	D₄×D₅	—	2	32	no	—
279	C₂×D₂₀	—	2	4	no	—
280	C₂×D₂₀	C₂³×C₃	1	4	yes	—
281	C₂×C₄×D₅	—	2	4	no	—
282	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
283	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
284	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
285	#685	C₂³×C₃	1	4	yes	—
286	#685	C₂³×C₃	1	8	yes	—
287	#685	C₂³×C₃	1	8	yes	complemented
288	#685	C₂³×C₃	1	8	yes	complemented
289	#685	C₂³×C₃	1	8	yes	complemented
290	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
291	#683	C₂³×C₃	1	4	yes	complemented
292	#683	C₂³×C₃	1	8	yes	complemented
293	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
294	C₂²×#41	C₃×D₅	1	1	yes	characteristic, complemented
295	C₂³×D₄	—	5	1	no	—
296	#546	—	5	16	no	—
297	C₂×#124	—	5	1	no	—
298	C₂×#123	—	5	2	no	—
299	C₂×C₂²⋊Q₈	—	5	1	no	—
300	C₂×#121	—	5	2	no	—
301	C₂×#121	—	5	1	no	—
302	C₂×#120	—	5	2	no	—
303	C₂×C₄×D₄	—	5	1	no	—
304	C₂×C₄×D₄	—	5	1	no	—
305	C₂²×C₂²⋊C₄	—	5	2	no	—
306	C₂²×C₃×C₅	—	2	16	no	—
307	C₂²×C₃×C₅	—	2	4	no	—
308	C₂²×C₃×C₅	—	2	4	no	—
309	C₂²×C₃×C₅	—	2	2	no	—
310	C₂²×C₃×C₅	—	2	2	no	—
311	C₂²×C₃×C₅	—	2	2	no	—
312	C₂²×C₃×C₅	—	4	4	no	—
313	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
314	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
315	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
316	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
318	C₂×C₃×D₅	—	2	8	no	—
319	C₂×C₃×D₅	—	2	2	no	—
320	C₂×C₃×D₅	—	2	2	no	—
321	C₂×C₃×D₅	—	2	4	no	—
322	C₂×C₃×D₅	—	2	4	no	—
323	C₂×C₃×D₅	—	2	4	no	—
324	C₂×C₃×D₅	—	4	32	no	—
325	C₂×C₃×D₅	—	4	8	no	—
326	C₂×C₃×D₅	C₂×#41	1	4	yes	complemented
327	C₃×C₄×C₅	—	2	2	no	—
328	C₃×C₄×C₅	—	2	4	no	—
329	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
330	C₃×Dic₅	—	2	2	no	—
331	C₃×Dic₅	—	2	2	no	—
332	C₃×Dic₅	—	2	2	no	—
333	C₃×Dic₅	—	2	4	no	—
334	C₂⁴×C₃	—	5	1	no	—
335	C₂⁴×C₃	—	5	2	no	—
336	C₂⁴×C₃	—	5	8	no	—
337	C₂⁴×C₃	—	10	8	no	—
338	C₂⁴×C₃	—	10	8	no	—
339	C₂⁴×C₃	—	20	4	no	—
340	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
341	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
342	C₃×#41	—	2	32	no	—
343	C₂×C₃×Q₈	—	2	4	no	—
344	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
345	C₂×C₃×D₄	—	2	8	no	—
346	C₂×C₃×D₄	—	5	4	no	—
347	C₂×C₃×D₄	—	5	8	no	—
348	C₂×C₃×D₄	—	5	8	no	—
349	C₂×C₃×D₄	—	5	4	no	—
350	C₂×C₃×D₄	—	10	4	no	—
351	C₂×C₃×D₄	—	10	8	no	—
352	C₂×C₃×D₄	—	10	32	no	—
353	C₂×C₃×D₄	—	10	4	no	—
354	C₂×C₃×D₄	—	20	4	no	—
355	C₂×C₃×D₄	C₂²⋊D₅	1	8	yes	complemented
356	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
357	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
358	C₂²×C₃×C₄	—	2	8	no	—
359	C₂²×C₃×C₄	—	2	4	no	—
360	C₂²×C₃×C₄	—	5	1	no	—
361	C₂²×C₃×C₄	—	5	1	no	—
362	C₂²×C₃×C₄	—	5	2	no	—
363	C₂²×C₃×C₄	—	5	1	no	—
364	C₂²×C₃×C₄	—	5	8	no	—
365	C₂²×C₃×C₄	—	5	4	no	—
366	C₂²×C₃×C₄	—	10	4	no	—
367	C₂²×C₃×C₄	—	20	4	no	—
368	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
370	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	complemented
372	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
373	C₃×C₄⋊C₄	—	5	4	no	—
374	C₃×C₄⋊C₄	—	5	8	no	—
375	C₃×C₄⋊C₄	—	5	4	no	—
376	C₃×C₂²⋊C₄	—	5	8	no	—
377	C₃×C₂²⋊C₄	—	5	4	no	—
378	C₃×C₂²⋊C₄	—	5	4	no	—
379	C₃×C₂²⋊C₄	—	5	8	no	—
380	C₃×C₂²⋊C₄	—	5	8	no	—
381	C₃×C₂²⋊C₄	—	5	8	no	—
382	C₃×C₂²⋊C₄	—	5	8	no	—
383	C₃×C₄²	—	5	4	no	—
384	C₂³×C₅	—	2	4	no	—
385	C₂³×C₅	—	2	4	no	—
386	C₂³×C₅	—	2	2	no	—
387	C₂³×C₅	—	2	2	no	—
388	C₂³×C₅	—	2	2	no	—
389	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
390	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
391	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
392	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
393	C₂²×D₅	—	2	2	no	—
394	C₂²×D₅	—	2	2	no	—
395	C₂²×D₅	—	2	4	no	—
396	C₂²×D₅	—	2	16	no	—
397	C₂²×D₅	—	2	4	no	—
398	C₂²×D₅	—	2	4	no	—
399	C₂²×D₅	—	2	16	no	—
400	C₂²×D₅	—	4	8	no	—
401	C₂²×D₅	—	4	32	no	—
402	C₂²×D₅	C₃×#41	1	4	yes	complemented
403	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
404	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
405	C₅×Q₈	—	2	8	no	—
406	C₅×D₄	—	2	16	no	—
407	C₅×D₄	C₂×C₃×D₄	1	16	yes	complemented
408	C₂×C₄×C₅	—	2	2	no	—
409	C₂×C₄×C₅	—	2	4	no	—
410	C₂×C₄×C₅	—	2	16	no	—
411	C₂×C₄×C₅	—	2	8	no	—
412	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
413	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
414	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
415	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
416	C₂²⋊D₅	—	2	16	no	—
417	C₂²⋊D₅	—	2	8	no	—
418	C₂²⋊D₅	—	4	8	no	—
419	C₂×Dic₅	—	2	2	no	—
420	C₂×Dic₅	—	2	2	no	—
421	C₂×Dic₅	—	2	2	no	—
422	C₂×Dic₅	—	2	4	no	—
423	C₂×Dic₅	—	4	8	no	—
424	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
425	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
426	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
427	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
428	D₂₀	—	2	8	no	—
429	C₄×D₅	—	2	8	no	—
430	C₂⁵	—	5	2	no	—
431	C₂×#41	—	2	8	no	—
432	C₂×#41	C₂×C₃×D₅	1	8	yes	complemented
433	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
434	C₂²×D₄	—	5	1	no	—
435	C₂²×D₄	—	5	2	no	—
436	C₂²×D₄	—	5	2	no	—
437	C₂²×D₄	—	5	8	no	—
438	C₂²×D₄	—	5	1	no	—
439	C₂²×D₄	—	10	8	no	—
440	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
441	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
442	C₂³×C₄	—	5	2	no	—
443	C₂³×C₄	—	5	1	no	—
444	C₂³×C₄	C₂×C₃×D₅	1	2	yes	complemented
445	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
446	#124	—	5	8	no	—
447	#123	—	5	16	no	—
448	C₂²⋊Q₈	—	5	8	no	—
449	#121	—	5	16	no	—
450	#121	—	5	8	no	—
451	#120	—	5	16	no	—
452	C₄×D₄	—	5	8	no	—
453	C₄×D₄	—	5	8	no	—
454	C₂×C₄⋊C₄	—	5	1	no	—
455	C₂×C₄⋊C₄	—	5	1	no	—
456	C₂×C₄⋊C₄	—	5	2	no	—
457	C₂×C₂²⋊C₄	—	5	2	no	—
458	C₂×C₂²⋊C₄	—	5	1	no	—
459	C₂×C₂²⋊C₄	—	5	1	no	—
460	C₂×C₂²⋊C₄	—	5	2	no	—
461	C₂×C₂²⋊C₄	—	5	2	no	—
462	C₂×C₂²⋊C₄	—	5	2	no	—
463	C₂×C₂²⋊C₄	—	5	2	no	—
464	C₂×C₂²⋊C₄	—	5	16	no	—
465	C₂×C₄²	—	5	1	no	—
466	C₂×C₃×C₅	—	2	8	no	—
467	C₂×C₃×C₅	—	4	2	no	—
468	C₂×C₃×C₅	#546	1	4	yes	complemented
469	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
470	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₃×D₅	—	2	4	no	—
473	C₃×D₅	—	4	4	no	—
474	C₂³×C₃	—	2	4	no	—
475	C₂³×C₃	—	2	4	no	—
476	C₂³×C₃	—	2	2	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	—	5	4	no	—
480	C₂³×C₃	—	5	2	no	—
481	C₂³×C₃	—	5	4	no	—
482	C₂³×C₃	—	10	16	no	—
483	C₂³×C₃	—	10	2	no	—
484	C₂³×C₃	—	10	2	no	—
485	C₂³×C₃	—	10	4	no	—
486	C₂³×C₃	—	10	4	no	—
487	C₂³×C₃	—	10	16	no	—
488	C₂³×C₃	—	10	4	no	—
489	C₂³×C₃	—	20	8	no	—
490	C₂³×C₃	—	20	32	no	—
491	C₂³×C₃	C₂×C₂²⋊D₅	1	8	yes	—
492	C₂³×C₃	C₂³×D₅	1	2	yes	—
493	C₂³×C₃	C₂³×D₅	1	4	yes	—
494	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
495	C₃×Q₈	—	2	8	no	—
496	C₃×D₄	—	2	16	no	—
497	C₃×D₄	—	10	8	no	—
498	C₃×D₄	—	10	16	no	—
499	C₃×D₄	—	10	8	no	—
500	C₃×D₄	—	20	8	no	—
501	C₃×D₄	C₂×C₂²⋊D₅	1	16	yes	complemented
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	4	no	—
504	C₂×C₃×C₄	—	2	16	no	—
505	C₂×C₃×C₄	—	2	8	no	—
506	C₂×C₃×C₄	—	5	2	no	—
507	C₂×C₃×C₄	—	5	2	no	—
508	C₂×C₃×C₄	—	5	4	no	—
509	C₂×C₃×C₄	—	5	2	no	—
510	C₂×C₃×C₄	—	10	2	no	—
511	C₂×C₃×C₄	—	10	2	no	—
512	C₂×C₃×C₄	—	10	4	no	—
513	C₂×C₃×C₄	—	10	2	no	—
514	C₂×C₃×C₄	—	10	8	no	—
515	C₂×C₃×C₄	—	20	8	no	—
516	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
517	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
518	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
519	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
520	C₂²×C₅	—	2	4	no	—
521	C₂²×C₅	—	2	4	no	—
522	C₂²×C₅	—	2	16	no	—
523	C₂²×C₅	—	2	2	no	—
524	C₂²×C₅	—	2	2	no	—
525	C₂²×C₅	—	2	2	no	—
526	C₂²×C₅	—	4	4	no	—
527	C₂²×C₅	C₂²×C₃×D₄	1	8	yes	—
528	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
529	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
530	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
531	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
532	C₂×D₅	—	2	2	no	—
533	C₂×D₅	—	2	2	no	—
534	C₂×D₅	—	2	8	no	—
535	C₂×D₅	—	2	4	no	—
536	C₂×D₅	—	2	4	no	—
537	C₂×D₅	—	2	4	no	—
538	C₂×D₅	—	4	32	no	—
539	C₂×D₅	—	4	8	no	—
540	C₂×D₅	C₂×C₃×#41	1	4	yes	complemented
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	—	2	4	no	—
543	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
544	Dic₅	—	2	2	no	—
545	Dic₅	—	2	2	no	—
546	Dic₅	—	2	2	no	—
547	Dic₅	—	2	4	no	—
548	C₂⁴	—	5	1	no	—
549	C₂⁴	—	5	2	no	—
550	C₂⁴	—	5	8	no	—
551	C₂⁴	—	10	8	no	—
552	C₂⁴	—	10	8	no	—
553	C₂⁴	—	20	4	no	—
554	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
555	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
556	#41	—	2	32	no	—
557	C₂×Q₈	—	2	4	no	—
558	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	complemented
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	5	4	no	—
561	C₂×D₄	—	5	8	no	—
562	C₂×D₄	—	5	8	no	—
563	C₂×D₄	—	5	4	no	—
564	C₂×D₄	—	10	4	no	—
565	C₂×D₄	—	10	8	no	—
566	C₂×D₄	—	10	32	no	—
567	C₂×D₄	—	10	4	no	—
568	C₂×D₄	—	20	4	no	—
569	C₂×D₄	C₃×C₂²⋊D₅	1	8	yes	complemented
570	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
571	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
572	C₂²×C₄	—	2	8	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	5	1	no	—
575	C₂²×C₄	—	5	1	no	—
576	C₂²×C₄	—	5	2	no	—
577	C₂²×C₄	—	5	1	no	—
578	C₂²×C₄	—	5	8	no	—
579	C₂²×C₄	—	5	4	no	—
580	C₂²×C₄	—	10	4	no	—
581	C₂²×C₄	—	20	4	no	—
582	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
584	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
585	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	complemented
586	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
587	C₄⋊C₄	—	5	4	no	—
588	C₄⋊C₄	—	5	4	no	—
589	C₄⋊C₄	—	5	8	no	—
590	C₂²⋊C₄	—	5	8	no	—
591	C₂²⋊C₄	—	5	4	no	—
592	C₂²⋊C₄	—	5	4	no	—
593	C₂²⋊C₄	—	5	8	no	—
594	C₂²⋊C₄	—	5	8	no	—
595	C₂²⋊C₄	—	5	8	no	—
596	C₂²⋊C₄	—	5	8	no	—
597	C₄²	—	5	4	no	—
598	C₃×C₅	C₂×#546	1	1	yes	characteristic, complemented, Hall
599	C₂²×C₃	—	2	16	no	—
600	C₂²×C₃	—	2	4	no	—
601	C₂²×C₃	—	2	4	no	—
602	C₂²×C₃	—	2	2	no	—
603	C₂²×C₃	—	2	2	no	—
604	C₂²×C₃	—	2	2	no	—
605	C₂²×C₃	—	4	4	no	—
606	C₂²×C₃	—	5	4	no	—
607	C₂²×C₃	—	10	8	no	—
608	C₂²×C₃	—	10	2	no	—
609	C₂²×C₃	—	10	2	no	—
610	C₂²×C₃	—	10	4	no	—
611	C₂²×C₃	—	10	4	no	—
612	C₂²×C₃	—	10	4	no	—
613	C₂²×C₃	—	20	32	no	—
614	C₂²×C₃	—	20	8	no	—
615	C₂²×C₃	D₅×#41	1	2	yes	—
616	C₂²×C₃	#4149	1	2	yes	—
617	C₂²×C₃	C₂²×C₂²⋊D₅	1	8	yes	—
618	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
619	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
620	C₃×C₄	—	2	2	no	—
621	C₃×C₄	—	2	4	no	—
622	C₃×C₄	—	10	2	no	—
623	C₃×C₄	—	10	2	no	—
624	C₃×C₄	—	10	4	no	—
625	C₃×C₄	—	10	2	no	—
626	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
627	C₂×C₅	—	2	8	no	—
628	C₂×C₅	—	4	2	no	—
629	C₂×C₅	C₃×#546	1	4	yes	complemented
630	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
631	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
632	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
633	D₅	—	2	4	no	—
634	D₅	—	4	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	5	4	no	—
641	C₂³	—	5	2	no	—
642	C₂³	—	5	4	no	—
643	C₂³	—	10	16	no	—
644	C₂³	—	10	2	no	—
645	C₂³	—	10	2	no	—
646	C₂³	—	10	4	no	—
647	C₂³	—	10	4	no	—
648	C₂³	—	10	16	no	—
649	C₂³	—	10	4	no	—
650	C₂³	—	20	8	no	—
651	C₂³	—	20	32	no	—
652	C₂³	C₂×C₃×C₂²⋊D₅	1	8	yes	—
653	C₂³	C₂³×C₃×D₅	1	2	yes	—
654	C₂³	C₂³×C₃×D₅	1	4	yes	—
655	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
656	Q₈	—	2	8	no	—
657	D₄	—	2	16	no	—
658	D₄	—	10	8	no	—
659	D₄	—	10	16	no	—
660	D₄	—	10	8	no	—
661	D₄	—	20	8	no	—
662	D₄	C₂×C₃×C₂²⋊D₅	1	16	yes	complemented
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	16	no	—
666	C₂×C₄	—	2	8	no	—
667	C₂×C₄	—	5	2	no	—
668	C₂×C₄	—	5	2	no	—
669	C₂×C₄	—	5	4	no	—
670	C₂×C₄	—	5	2	no	—
671	C₂×C₄	—	10	2	no	—
672	C₂×C₄	—	10	2	no	—
673	C₂×C₄	—	10	4	no	—
674	C₂×C₄	—	10	2	no	—
675	C₂×C₄	—	10	8	no	—
676	C₂×C₄	—	20	8	no	—
677	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
678	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
679	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
680	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
681	C₂×C₃	—	2	8	no	—
682	C₂×C₃	—	4	2	no	—
683	C₂×C₃	—	10	4	no	—
684	C₂×C₃	—	20	4	no	—
685	C₂×C₃	#66163	1	4	yes	direct product factor
686	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
687	C₂×C₃	C₂×#4149	1	1	yes	characteristic
688	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
689	C₅	C₂×C₃×#546	1	1	yes	characteristic, complemented, Sylow
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	16	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	5	4	no	—
698	C₂²	—	10	2	no	—
699	C₂²	—	10	2	no	—
700	C₂²	—	10	8	no	—
701	C₂²	—	10	4	no	—
702	C₂²	—	10	4	no	—
703	C₂²	—	10	4	no	—
704	C₂²	—	20	32	no	—
705	C₂²	—	20	8	no	—
706	C₂²	C₃×D₅×#41	1	2	yes	—
707	C₂²	C₃×#4149	1	2	yes	—
708	C₂²	C₂²×C₃×C₂²⋊D₅	1	8	yes	—
709	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
710	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	2	4	no	—
713	C₄	—	10	2	no	—
714	C₄	—	10	2	no	—
715	C₄	—	10	4	no	—
716	C₄	—	10	2	no	—
717	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
718	C₃	C₂×#66163	1	1	yes	characteristic, direct product factor, Sylow
719	C₂	—	2	8	no	—
720	C₂	—	4	2	no	—
721	C₂	—	10	4	no	—
722	C₂	—	20	4	no	—
723	C₂	C₃×#66163	1	4	yes	direct product factor
724	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
725	C₂	C₂×C₃×#4149	1	1	yes	characteristic
726	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	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₃×#41	D₅
hypocenter	C₅	C₂×C₃×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₃×D₄×D₅	C₂	semidirect
3. C₃×#66163	C₂	direct (N × H)
4. C₂×C₃×#4093	C₂	semidirect
5. C₂×C₃×#4092	C₂	semidirect
6. C₂×C₃×#4085	C₂	semidirect
7. C₂×C₃×#4083	C₂	semidirect
8. C₂×C₃×D₄×Dic₅	C₂	semidirect
9. C₂×C₃×#4076	C₂	semidirect
10. C₂×C₃×#4075	C₂	semidirect
11. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
12. C₂²×C₃×#685	C₂	semidirect
13. C₂×#66163	C₃	direct (N × H)
16. C₂×C₃×C₅×#41	C₂²	semidirect
17. C₂²×C₃×C₅×Q₈	C₂²	semidirect
19. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂³×C₃×C₄×C₅	C₂²	semidirect
21. C₂³×C₃×C₄×C₅	C₂²	semidirect
24. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
25. C₂³×C₃×Dic₅	C₂²	semidirect
27. C₂×C₃×D₄×D₅	C₂²	semidirect
30. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
31. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
32. C₃×#4093	C₂²	semidirect
33. C₃×#4092	C₂²	semidirect
34. C₃×#4085	C₂²	semidirect
35. C₃×#4083	C₂²	semidirect
36. C₃×D₄×Dic₅	C₂²	semidirect
37. C₃×#4076	C₂²	semidirect
38. C₃×#4075	C₂²	semidirect
39. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
42. C₂×C₃×#685	C₂²	semidirect
43. C₂×C₃×#685	C₂²	semidirect
44. C₂×C₃×#685	C₂²	semidirect
45. C₂×C₃×#685	C₂²	semidirect
46. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
47. C₂×C₃×#683	C₂²	semidirect
48. C₂×C₃×#683	C₂²	semidirect
49. C₂×C₃×C₄×Dic₅	C₂²	semidirect
51. C₂²×C₅×#41	C₂×C₃	semidirect
52. C₂²×D₄×D₅	C₂×C₃	semidirect
53. #66163	C₂×C₃	direct (N × H)
54. C₂×#4093	C₂×C₃	semidirect
55. C₂×#4092	C₂×C₃	semidirect
56. C₂×#4085	C₂×C₃	semidirect
57. C₂×#4083	C₂×C₃	semidirect
58. C₂×D₄×Dic₅	C₂×C₃	semidirect
59. C₂×#4076	C₂×C₃	semidirect
60. C₂×#4075	C₂×C₃	semidirect
61. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
62. C₂²×#685	C₂×C₃	semidirect
73. C₂×C₃×C₅×Q₈	C₂³	semidirect
75. C₂×C₃×C₅×D₄	D₄	semidirect
77. C₂×C₃×C₅×D₄	C₂³	semidirect
83. C₂²×C₃×C₄×C₅	C₂³	semidirect
84. C₂²×C₃×C₄×C₅	C₂³	semidirect
90. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
96. C₂²×C₃×Dic₅	C₂³	semidirect
102. C₃×C₂²⋊Dic₅	C₂³	semidirect
103. C₃×C₂²⋊Dic₅	C₂³	semidirect
106. C₃×#685	C₂³	semidirect
107. C₃×#685	C₂³	semidirect
108. C₃×#685	C₂³	semidirect
109. C₃×C₄⋊Dic₅	C₂³	semidirect
110. C₃×#683	C₂³	semidirect
111. C₃×#683	C₂³	semidirect
112. C₃×C₄×Dic₅	C₂³	semidirect
113. C₂²×C₃×#41	D₅	semidirect
127. C₂×C₅×#41	C₂²×C₃	semidirect
128. C₂²×C₅×Q₈	C₂²×C₃	semidirect
130. C₂²×C₅×D₄	C₂²×C₃	semidirect
131. C₂³×C₄×C₅	C₂²×C₃	semidirect
132. C₂³×C₄×C₅	C₂²×C₃	semidirect
135. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
136. C₂³×Dic₅	C₂²×C₃	semidirect
138. C₂×D₄×D₅	C₂²×C₃	semidirect
141. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
142. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
143. #4093	C₂²×C₃	semidirect
144. #4092	C₂²×C₃	semidirect
145. #4085	C₂²×C₃	semidirect
146. #4083	C₂²×C₃	semidirect
147. D₄×Dic₅	C₂²×C₃	semidirect
148. #4076	C₂²×C₃	semidirect
149. #4075	C₂²×C₃	semidirect
150. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
153. C₂×#685	C₂²×C₃	semidirect
154. C₂×#685	C₂²×C₃	semidirect
155. C₂×#685	C₂²×C₃	semidirect
156. C₂×#685	C₂²×C₃	semidirect
157. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
158. C₂×#683	C₂²×C₃	semidirect
159. C₂×#683	C₂²×C₃	semidirect
160. C₂×C₄×Dic₅	C₂²×C₃	semidirect
180. C₂²×C₃×D₅	#41	semidirect
185. C₃×C₅×D₄	C₂×D₄	semidirect
210. C₂×C₃×#41	C₂×D₅	semidirect
211. C₂²×C₃×Q₈	C₂×D₅	semidirect
219. C₂²×C₃×D₄	C₂×D₅	semidirect
222. C₂³×C₃×C₄	C₂×D₅	semidirect
223. C₂³×C₃×C₄	C₂×D₅	semidirect
254. C₂×C₅×Q₈	C₂³×C₃	semidirect
256. C₂×C₅×D₄	C₃×D₄	semidirect
258. C₂×C₅×D₄	C₂³×C₃	semidirect
264. C₂²×C₄×C₅	C₂³×C₃	semidirect
265. C₂²×C₄×C₅	C₂³×C₃	semidirect
271. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
277. C₂²×Dic₅	C₂³×C₃	semidirect
283. C₂²⋊Dic₅	C₂³×C₃	semidirect
284. C₂²⋊Dic₅	C₂³×C₃	semidirect
287. #685	C₂³×C₃	semidirect
288. #685	C₂³×C₃	semidirect
289. #685	C₂³×C₃	semidirect
290. C₄⋊Dic₅	C₂³×C₃	semidirect
291. #683	C₂³×C₃	semidirect
292. #683	C₂³×C₃	semidirect
293. C₄×Dic₅	C₂³×C₃	semidirect
294. C₂²×#41	C₃×D₅	semidirect
326. C₂×C₃×D₅	C₂×#41	semidirect
344. C₂×C₃×Q₈	C₂²×D₅	semidirect
355. C₂×C₃×D₄	C₂²⋊D₅	semidirect
357. C₂×C₃×D₄	C₂²×D₅	semidirect
371. C₂²×C₃×C₄	C₂²×D₅	semidirect
372. C₂²×C₃×C₄	C₂²×D₅	semidirect
402. C₂²×D₅	C₃×#41	semidirect
407. C₅×D₄	C₂×C₃×D₄	semidirect
432. C₂×#41	C₂×C₃×D₅	semidirect
433. C₂²×Q₈	C₂×C₃×D₅	semidirect
441. C₂²×D₄	C₂×C₃×D₅	semidirect
444. C₂³×C₄	C₂×C₃×D₅	semidirect
445. C₂³×C₄	C₂×C₃×D₅	semidirect
468. C₂×C₃×C₅	#546	semidirect
501. C₃×D₄	C₂×C₂²⋊D₅	semidirect
540. C₂×D₅	C₂×C₃×#41	semidirect
558. C₂×Q₈	C₂²×C₃×D₅	semidirect
569. C₂×D₄	C₃×C₂²⋊D₅	semidirect
571. C₂×D₄	C₂²×C₃×D₅	semidirect
585. C₂²×C₄	C₂²×C₃×D₅	semidirect
586. C₂²×C₄	C₂²×C₃×D₅	semidirect
598. C₃×C₅	C₂×#546	semidirect
629. C₂×C₅	C₃×#546	semidirect
662. D₄	C₂×C₃×C₂²⋊D₅	semidirect
685. C₂×C₃	#66163	direct (N × H)
689. C₅	C₂×C₃×#546	semidirect
718. C₃	C₂×#66163	direct (N × H)
723. C₂	C₃×#66163	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×C₅×#41	2
C₂²×C₃×D₄×D₅	2
C₃×#66163	2
C₂×C₃×#4093	2
C₂×C₃×#4092	2
C₂×C₃×#4085	2
C₂×C₃×#4083	2
C₂×C₃×D₄×Dic₅	2
C₂×C₃×#4076	2
C₂×C₃×#4075	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂²×C₃×#685	2
C₂×#66163	3
C₂×C₃×#546	5

Subgroups — C2×C3×#66163 #14482479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66163 #14482479