Subgroups — C₂×C₃×#65987 #14480300

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 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	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65987	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4041	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4040	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4030	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4028	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65987	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
15	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic, complemented
16	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂×C₃×D₄×D₅	—	2	8	no	—
23	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
24	C₂²×C₃×D₂₀	—	2	8	no	—
25	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
26	C₂²×C₃×D₂₀	C₂²	1	8	yes	complemented
27	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
28	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
30	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
32	C₃×C₅×#123	C₂²	1	8	yes	complemented
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₃×C₅×C₂²⋊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	1	yes	characteristic, complemented
37	C₃×#4083	C₂²	1	8	yes	complemented
38	C₃×#4075	C₂²	1	8	yes	complemented
39	C₂×C₃×#685	C₂²	1	2	yes	complemented
40	C₂×C₃×#685	C₂²	1	2	yes	complemented
41	C₂×C₃×#685	C₂²	1	2	yes	complemented
42	C₂×C₃×#685	C₂²	1	2	yes	complemented
43	C₂×C₃×#683	C₂²	1	2	yes	complemented
44	C₃×#4041	C₂²	1	16	yes	complemented
45	C₃×#4040	C₂²	1	16	yes	complemented
46	C₃×#4030	C₂²	1	16	yes	complemented
47	C₃×#4028	C₂²	1	16	yes	complemented
48	C₃×#4028	C₂²	1	8	yes	complemented
49	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂×C₃×#534	—	5	1	no	maximal, Hall
51	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4075	C₂×C₃	1	1	yes	characteristic, complemented
56	#65987	C₂×C₃	1	16	yes	direct product factor
57	C₂×#4041	C₂×C₃	1	2	yes	complemented
58	C₂×#4040	C₂×C₃	1	2	yes	complemented
59	C₂×#4030	C₂×C₃	1	2	yes	complemented
60	C₂×#4028	C₂×C₃	1	2	yes	complemented
61	C₂×#4028	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₃×D₅	—	2	4	no	—
66	C₂³×C₃×D₅	—	2	4	no	—
67	C₂³×C₃×D₅	—	4	4	no	—
68	C₂³×C₃×D₅	—	4	4	no	—
69	C₂³×C₃×D₅	—	4	4	no	—
70	C₂³×C₃×D₅	D₄	1	8	yes	complemented
71	C₂³×C₃×D₅	C₂³	1	2	yes	—
72	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
73	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
74	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
75	C₂³×C₃×D₅	C₂³	1	4	yes	—
76	C₂³×C₃×D₅	C₂³	1	4	yes	complemented
77	C₂³×C₃×D₅	C₂³	1	4	yes	complemented
78	C₂×C₃×C₅×D₄	—	2	4	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
80	C₂²×C₃×C₄×C₅	—	2	4	no	—
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	2	yes	—
84	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
85	C₂×C₃×C₂²⋊D₅	—	2	4	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	4	yes	complemented
90	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
91	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
92	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₃×D₄×D₅	—	2	32	no	—
94	C₂×C₃×D₂₀	—	2	8	no	—
95	C₂×C₃×D₂₀	—	2	8	no	—
96	C₂×C₃×D₂₀	—	2	4	no	—
97	C₂×C₃×D₂₀	—	2	32	no	—
98	C₂×C₃×D₂₀	—	4	4	no	—
99	C₂×C₃×D₂₀	C₂³	1	8	yes	—
100	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
101	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
102	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
103	C₂×C₃×C₄×D₅	—	2	4	no	—
104	C₂×C₃×C₄×D₅	—	4	4	no	—
105	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
106	C₂×C₃×C₄×D₅	C₂³	1	8	yes	complemented
107	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
108	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
111	C₃×#685	C₂³	1	8	yes	complemented
112	C₃×#685	C₂³	1	8	yes	complemented
113	C₃×#685	C₂³	1	8	yes	complemented
114	C₃×#685	C₂³	1	8	yes	complemented
115	C₃×#683	C₂³	1	8	yes	complemented
116	C₂³×C₃×D₄	—	5	1	no	—
117	C₂³×C₃×D₄	—	5	1	no	—
118	C₃×#534	—	5	16	no	—
119	C₂×C₃×#123	—	5	1	no	—
120	C₂×C₃×#123	—	5	2	no	—
121	C₂×C₃×#123	D₅	1	1	yes	characteristic, complemented
122	C₂×C₃×#121	—	5	2	no	—
123	C₂×C₃×#121	—	5	2	no	—
124	C₂×C₃×#120	—	5	1	no	—
125	C₂×C₃×#120	—	5	2	no	—
126	C₂×C₃×#120	—	5	1	no	—
127	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
128	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic, complemented
135	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
136	C₂×D₄×D₅	—	2	8	no	—
137	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
138	C₂²×D₂₀	—	2	8	no	—
139	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
140	C₂²×D₂₀	C₂²×C₃	1	8	yes	complemented
141	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
142	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
144	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
146	C₅×#123	C₂²×C₃	1	8	yes	complemented
147	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
148	C₂×C₅×C₂²⋊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	1	yes	characteristic, complemented
151	#4083	C₂²×C₃	1	8	yes	complemented
152	#4075	C₂²×C₃	1	8	yes	complemented
153	C₂×#685	C₂²×C₃	1	2	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×#683	C₂²×C₃	1	2	yes	complemented
158	#4041	C₂²×C₃	1	16	yes	complemented
159	#4040	C₂²×C₃	1	16	yes	complemented
160	#4030	C₂²×C₃	1	16	yes	complemented
161	#4028	C₂²×C₃	1	16	yes	complemented
162	#4028	C₂²×C₃	1	8	yes	complemented
163	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
164	C₂×#534	—	5	1	no	Sylow
165	C₂³×C₃×C₅	—	2	4	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	—	2	4	no	—
168	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
169	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
170	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
171	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
172	C₂²×C₃×D₅	—	2	4	no	—
173	C₂²×C₃×D₅	—	2	4	no	—
174	C₂²×C₃×D₅	—	2	4	no	—
175	C₂²×C₃×D₅	—	2	8	no	—
176	C₂²×C₃×D₅	—	2	2	no	—
177	C₂²×C₃×D₅	—	2	4	no	—
178	C₂²×C₃×D₅	—	2	4	no	—
179	C₂²×C₃×D₅	—	2	4	no	—
180	C₂²×C₃×D₅	—	2	8	no	—
181	C₂²×C₃×D₅	—	4	16	no	—
182	C₂²×C₃×D₅	—	4	8	no	—
183	C₂²×C₃×D₅	—	4	8	no	—
184	C₂²×C₃×D₅	—	4	8	no	—
185	C₂²×C₃×D₅	—	4	16	no	—
186	C₂²×C₃×D₅	—	4	16	no	—
187	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
188	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
189	C₂²×C₃×D₅	C₂×D₄	1	16	yes	complemented
190	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
191	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
192	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
193	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
194	C₃×C₅×D₄	—	2	8	no	—
195	C₂×C₃×C₄×C₅	—	2	2	no	—
196	C₂×C₃×C₄×C₅	—	2	4	no	—
197	C₂×C₃×C₄×C₅	—	2	8	no	—
198	C₂×C₃×C₄×C₅	—	2	4	no	—
199	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
200	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
201	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
202	C₃×C₂²⋊D₅	—	2	8	no	—
203	C₃×C₂²⋊D₅	—	2	8	no	—
204	C₃×C₂²⋊D₅	—	4	8	no	—
205	C₂×C₃×Dic₅	—	2	2	no	—
206	C₂×C₃×Dic₅	—	2	4	no	—
207	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
208	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
209	C₃×D₂₀	—	2	16	no	—
210	C₃×D₂₀	—	2	16	no	—
211	C₃×D₂₀	—	2	8	no	—
212	C₃×D₂₀	—	4	8	no	—
213	C₃×C₄×D₅	—	2	8	no	—
214	C₃×C₄×D₅	—	4	8	no	—
215	C₂⁵×C₃	—	5	1	no	—
216	C₂⁵×C₃	—	5	1	no	—
217	C₂⁵×C₃	—	5	1	no	—
218	C₂²×C₃×D₄	—	5	1	no	—
219	C₂²×C₃×D₄	—	5	1	no	—
220	C₂²×C₃×D₄	—	5	2	no	—
221	C₂²×C₃×D₄	—	5	8	no	—
222	C₂²×C₃×D₄	—	5	2	no	—
223	C₂²×C₃×D₄	—	5	1	no	—
224	C₂²×C₃×D₄	—	5	2	no	—
225	C₂²×C₃×D₄	—	5	2	no	—
226	C₂²×C₃×D₄	—	5	8	no	—
227	C₂²×C₃×D₄	—	10	8	no	—
228	C₂²×C₃×D₄	—	10	8	no	—
229	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
230	C₂³×C₃×C₄	—	5	1	no	—
231	C₂³×C₃×C₄	—	5	2	no	—
232	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
233	C₃×#123	—	5	8	no	—
234	C₃×#123	—	5	16	no	—
235	C₃×#123	C₂×D₅	1	8	yes	complemented
236	C₃×#121	—	5	16	no	—
237	C₃×#121	—	5	16	no	—
238	C₃×#120	—	5	8	no	—
239	C₃×#120	—	5	16	no	—
240	C₃×#120	—	5	8	no	—
241	C₂×C₃×C₄⋊C₄	—	5	2	no	—
242	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
243	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
244	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
245	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
246	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
247	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
249	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
251	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂³×D₅	—	2	4	no	—
254	C₂³×D₅	—	2	4	no	—
255	C₂³×D₅	—	4	4	no	—
256	C₂³×D₅	—	4	4	no	—
257	C₂³×D₅	—	4	4	no	—
258	C₂³×D₅	C₃×D₄	1	8	yes	complemented
259	C₂³×D₅	C₂³×C₃	1	2	yes	—
260	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
261	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
262	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
263	C₂³×D₅	C₂³×C₃	1	4	yes	—
264	C₂³×D₅	C₂³×C₃	1	4	yes	complemented
265	C₂³×D₅	C₂³×C₃	1	4	yes	complemented
266	C₂×C₅×D₄	—	2	4	no	—
267	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
268	C₂²×C₄×C₅	—	2	4	no	—
269	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
270	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
271	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
273	C₂×C₂²⋊D₅	—	2	4	no	—
274	C₂×C₂²⋊D₅	—	2	4	no	—
275	C₂×C₂²⋊D₅	—	4	4	no	—
276	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
277	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
278	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
279	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
280	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
281	D₄×D₅	—	2	32	no	—
282	C₂×D₂₀	—	2	8	no	—
283	C₂×D₂₀	—	2	8	no	—
284	C₂×D₂₀	—	2	4	no	—
285	C₂×D₂₀	—	2	32	no	—
286	C₂×D₂₀	—	4	4	no	—
287	C₂×D₂₀	C₂³×C₃	1	8	yes	—
288	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
289	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
290	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
291	C₂×C₄×D₅	—	2	4	no	—
292	C₂×C₄×D₅	—	4	4	no	—
293	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
294	C₂×C₄×D₅	C₂³×C₃	1	8	yes	complemented
295	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
296	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
297	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
298	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
299	#685	C₂³×C₃	1	8	yes	complemented
300	#685	C₂³×C₃	1	8	yes	complemented
301	#685	C₂³×C₃	1	8	yes	complemented
302	#685	C₂³×C₃	1	8	yes	complemented
303	#683	C₂³×C₃	1	8	yes	complemented
304	C₂³×D₄	—	5	1	no	—
305	C₂³×D₄	—	5	1	no	—
306	#534	—	5	16	no	—
307	C₂×#123	—	5	1	no	—
308	C₂×#123	—	5	2	no	—
309	C₂×#123	C₃×D₅	1	1	yes	characteristic, complemented
310	C₂×#121	—	5	2	no	—
311	C₂×#121	—	5	2	no	—
312	C₂×#120	—	5	1	no	—
313	C₂×#120	—	5	2	no	—
314	C₂×#120	—	5	1	no	—
315	C₂²×C₂²⋊C₄	—	5	1	no	—
316	C₂²×C₃×C₅	—	2	8	no	—
317	C₂²×C₃×C₅	—	2	4	no	—
318	C₂²×C₃×C₅	—	2	2	no	—
319	C₂²×C₃×C₅	—	2	4	no	—
320	C₂²×C₃×C₅	—	4	4	no	—
321	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
322	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
323	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
324	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
325	C₂×C₃×D₅	—	2	8	no	—
326	C₂×C₃×D₅	—	2	8	no	—
327	C₂×C₃×D₅	—	2	4	no	—
328	C₂×C₃×D₅	—	2	4	no	—
329	C₂×C₃×D₅	—	2	4	no	—
330	C₂×C₃×D₅	—	2	2	no	—
331	C₂×C₃×D₅	—	2	4	no	—
332	C₂×C₃×D₅	—	2	4	no	—
333	C₂×C₃×D₅	—	2	4	no	—
334	C₂×C₃×D₅	—	4	16	no	—
335	C₂×C₃×D₅	—	4	16	no	—
336	C₂×C₃×D₅	—	4	16	no	—
337	C₂×C₃×D₅	—	4	8	no	—
338	C₂×C₃×D₅	—	4	4	no	—
339	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
340	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
341	C₃×C₄×C₅	—	2	2	no	—
342	C₃×C₄×C₅	—	2	4	no	—
343	C₃×C₄×C₅	—	2	4	no	—
344	C₃×Dic₅	—	2	2	no	—
345	C₃×Dic₅	—	2	4	no	—
346	C₂⁴×C₃	—	5	1	no	—
347	C₂⁴×C₃	—	5	1	no	—
348	C₂⁴×C₃	—	5	8	no	—
349	C₂⁴×C₃	—	5	4	no	—
350	C₂⁴×C₃	—	5	2	no	—
351	C₂⁴×C₃	—	5	1	no	—
352	C₂⁴×C₃	—	5	4	no	—
353	C₂⁴×C₃	—	5	4	no	—
354	C₂⁴×C₃	—	10	4	no	—
355	C₂⁴×C₃	—	10	4	no	—
356	C₂⁴×C₃	—	20	4	no	—
357	C₂⁴×C₃	—	20	4	no	—
358	C₂⁴×C₃	—	20	4	no	—
359	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
360	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
361	C₂×C₃×D₄	—	2	4	no	—
362	C₂×C₃×D₄	—	5	4	no	—
363	C₂×C₃×D₄	—	5	4	no	—
364	C₂×C₃×D₄	—	5	8	no	—
365	C₂×C₃×D₄	—	5	8	no	—
366	C₂×C₃×D₄	—	5	4	no	—
367	C₂×C₃×D₄	—	5	8	no	—
368	C₂×C₃×D₄	—	5	8	no	—
369	C₂×C₃×D₄	—	10	8	no	—
370	C₂×C₃×D₄	—	10	8	no	—
371	C₂×C₃×D₄	—	10	32	no	—
372	C₂×C₃×D₄	—	10	4	no	—
373	C₂×C₃×D₄	—	10	32	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	C₂²×D₅	1	4	yes	—
379	C₂²×C₃×C₄	—	2	4	no	—
380	C₂²×C₃×C₄	—	5	2	no	—
381	C₂²×C₃×C₄	—	5	1	no	—
382	C₂²×C₃×C₄	—	5	4	no	—
383	C₂²×C₃×C₄	—	5	8	no	—
384	C₂²×C₃×C₄	—	10	4	no	—
385	C₂²×C₃×C₄	—	20	4	no	—
386	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
387	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
389	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
390	C₃×C₄⋊C₄	—	5	8	no	—
391	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	complemented
392	C₃×C₂²⋊C₄	—	5	4	no	—
393	C₃×C₂²⋊C₄	—	5	8	no	—
394	C₃×C₂²⋊C₄	—	5	8	no	—
395	C₃×C₂²⋊C₄	—	5	8	no	—
396	C₃×C₂²⋊C₄	—	5	8	no	—
397	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
398	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
399	C₂³×C₅	—	2	4	no	—
400	C₂³×C₅	—	2	2	no	—
401	C₂³×C₅	—	2	4	no	—
402	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
403	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
404	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
405	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
406	C₂²×D₅	—	2	4	no	—
407	C₂²×D₅	—	2	4	no	—
408	C₂²×D₅	—	2	4	no	—
409	C₂²×D₅	—	2	8	no	—
410	C₂²×D₅	—	2	2	no	—
411	C₂²×D₅	—	2	4	no	—
412	C₂²×D₅	—	2	4	no	—
413	C₂²×D₅	—	2	4	no	—
414	C₂²×D₅	—	2	8	no	—
415	C₂²×D₅	—	4	16	no	—
416	C₂²×D₅	—	4	8	no	—
417	C₂²×D₅	—	4	8	no	—
418	C₂²×D₅	—	4	8	no	—
419	C₂²×D₅	—	4	16	no	—
420	C₂²×D₅	—	4	16	no	—
421	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
422	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
423	C₂²×D₅	C₂×C₃×D₄	1	16	yes	complemented
424	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
425	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
426	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
427	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
428	C₅×D₄	—	2	8	no	—
429	C₂×C₄×C₅	—	2	2	no	—
430	C₂×C₄×C₅	—	2	4	no	—
431	C₂×C₄×C₅	—	2	8	no	—
432	C₂×C₄×C₅	—	2	4	no	—
433	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
434	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
435	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
436	C₂²⋊D₅	—	2	8	no	—
437	C₂²⋊D₅	—	2	8	no	—
438	C₂²⋊D₅	—	4	8	no	—
439	C₂×Dic₅	—	2	2	no	—
440	C₂×Dic₅	—	2	4	no	—
441	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
442	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
443	D₂₀	—	2	16	no	—
444	D₂₀	—	2	16	no	—
445	D₂₀	—	2	8	no	—
446	D₂₀	—	4	8	no	—
447	C₄×D₅	—	2	8	no	—
448	C₄×D₅	—	4	8	no	—
449	C₂⁵	—	5	1	no	—
450	C₂⁵	—	5	1	no	—
451	C₂⁵	—	5	1	no	—
452	C₂²×D₄	—	5	1	no	—
453	C₂²×D₄	—	5	1	no	—
454	C₂²×D₄	—	5	2	no	—
455	C₂²×D₄	—	5	8	no	—
456	C₂²×D₄	—	5	2	no	—
457	C₂²×D₄	—	5	1	no	—
458	C₂²×D₄	—	5	2	no	—
459	C₂²×D₄	—	5	2	no	—
460	C₂²×D₄	—	5	8	no	—
461	C₂²×D₄	—	10	8	no	—
462	C₂²×D₄	—	10	8	no	—
463	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
464	C₂³×C₄	—	5	1	no	—
465	C₂³×C₄	—	5	2	no	—
466	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
467	#123	—	5	8	no	—
468	#123	—	5	16	no	—
469	#123	C₂×C₃×D₅	1	8	yes	complemented
470	#121	—	5	16	no	—
471	#121	—	5	16	no	—
472	#120	—	5	8	no	—
473	#120	—	5	16	no	—
474	#120	—	5	8	no	—
475	C₂×C₄⋊C₄	—	5	2	no	—
476	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
477	C₂×C₂²⋊C₄	—	5	1	no	—
478	C₂×C₂²⋊C₄	—	5	2	no	—
479	C₂×C₂²⋊C₄	—	5	2	no	—
480	C₂×C₂²⋊C₄	—	5	2	no	—
481	C₂×C₂²⋊C₄	—	5	2	no	—
482	C₂×C₂²⋊C₄	—	5	8	no	—
483	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
485	C₂×C₃×C₅	—	2	4	no	—
486	C₂×C₃×C₅	—	4	2	no	—
487	C₂×C₃×C₅	#534	1	4	yes	complemented
488	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
489	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
490	C₃×D₅	—	2	4	no	—
491	C₃×D₅	—	2	4	no	—
492	C₃×D₅	—	4	4	no	—
493	C₃×D₅	—	4	2	no	—
494	C₂³×C₃	—	2	4	no	—
495	C₂³×C₃	—	2	2	no	—
496	C₂³×C₃	—	2	4	no	—
497	C₂³×C₃	—	5	4	no	—
498	C₂³×C₃	—	5	4	no	—
499	C₂³×C₃	—	5	2	no	—
500	C₂³×C₃	—	5	2	no	—
501	C₂³×C₃	—	5	16	no	—
502	C₂³×C₃	—	5	4	no	—
503	C₂³×C₃	—	5	2	no	—
504	C₂³×C₃	—	10	8	no	—
505	C₂³×C₃	—	10	4	no	—
506	C₂³×C₃	—	10	4	no	—
507	C₂³×C₃	—	10	8	no	—
508	C₂³×C₃	—	10	4	no	—
509	C₂³×C₃	—	10	2	no	—
510	C₂³×C₃	—	10	4	no	—
511	C₂³×C₃	—	10	4	no	—
512	C₂³×C₃	—	10	4	no	—
513	C₂³×C₃	—	20	16	no	—
514	C₂³×C₃	—	20	8	no	—
515	C₂³×C₃	—	20	8	no	—
516	C₂³×C₃	—	20	8	no	—
517	C₂³×C₃	—	20	16	no	—
518	C₂³×C₃	—	20	16	no	—
519	C₂³×C₃	D₄×D₅	1	4	yes	—
520	C₂³×C₃	C₂³×D₅	1	2	yes	—
521	C₂³×C₃	C₂³×D₅	1	2	yes	—
522	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
523	C₃×D₄	—	2	8	no	—
524	C₃×D₄	—	10	16	no	—
525	C₃×D₄	—	10	16	no	—
526	C₃×D₄	—	10	8	no	—
527	C₃×D₄	—	10	8	no	—
528	C₃×D₄	—	10	8	no	—
529	C₃×D₄	—	20	8	no	—
530	C₃×D₄	—	20	8	no	—
531	C₂×C₃×C₄	—	2	4	no	—
532	C₂×C₃×C₄	—	2	8	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	4	no	—
535	C₂×C₃×C₄	—	5	4	no	—
536	C₂×C₃×C₄	—	5	2	no	—
537	C₂×C₃×C₄	—	10	8	no	—
538	C₂×C₃×C₄	—	10	2	no	—
539	C₂×C₃×C₄	—	10	4	no	—
540	C₂×C₃×C₄	—	20	8	no	—
541	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
542	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
543	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
544	C₂²×C₅	—	2	4	no	—
545	C₂²×C₅	—	2	8	no	—
546	C₂²×C₅	—	2	2	no	—
547	C₂²×C₅	—	2	4	no	—
548	C₂²×C₅	—	4	4	no	—
549	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
550	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
551	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
552	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
553	C₂×D₅	—	2	4	no	—
554	C₂×D₅	—	2	4	no	—
555	C₂×D₅	—	2	8	no	—
556	C₂×D₅	—	2	8	no	—
557	C₂×D₅	—	2	4	no	—
558	C₂×D₅	—	2	2	no	—
559	C₂×D₅	—	2	4	no	—
560	C₂×D₅	—	2	4	no	—
561	C₂×D₅	—	2	4	no	—
562	C₂×D₅	—	4	16	no	—
563	C₂×D₅	—	4	16	no	—
564	C₂×D₅	—	4	16	no	—
565	C₂×D₅	—	4	8	no	—
566	C₂×D₅	—	4	4	no	—
567	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
568	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
569	C₄×C₅	—	2	2	no	—
570	C₄×C₅	—	2	4	no	—
571	C₄×C₅	—	2	4	no	—
572	Dic₅	—	2	2	no	—
573	Dic₅	—	2	4	no	—
574	C₂⁴	—	5	1	no	—
575	C₂⁴	—	5	1	no	—
576	C₂⁴	—	5	8	no	—
577	C₂⁴	—	5	4	no	—
578	C₂⁴	—	5	1	no	—
579	C₂⁴	—	5	2	no	—
580	C₂⁴	—	5	4	no	—
581	C₂⁴	—	5	4	no	—
582	C₂⁴	—	10	4	no	—
583	C₂⁴	—	10	4	no	—
584	C₂⁴	—	20	4	no	—
585	C₂⁴	—	20	4	no	—
586	C₂⁴	—	20	4	no	—
587	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
588	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	5	4	no	—
591	C₂×D₄	—	5	4	no	—
592	C₂×D₄	—	5	8	no	—
593	C₂×D₄	—	5	8	no	—
594	C₂×D₄	—	5	4	no	—
595	C₂×D₄	—	5	8	no	—
596	C₂×D₄	—	5	8	no	—
597	C₂×D₄	—	10	8	no	—
598	C₂×D₄	—	10	8	no	—
599	C₂×D₄	—	10	32	no	—
600	C₂×D₄	—	10	4	no	—
601	C₂×D₄	—	10	32	no	—
602	C₂×D₄	—	10	4	no	—
603	C₂×D₄	—	10	4	no	—
604	C₂×D₄	—	20	4	no	—
605	C₂×D₄	—	20	4	no	—
606	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	5	2	no	—
609	C₂²×C₄	—	5	1	no	—
610	C₂²×C₄	—	5	4	no	—
611	C₂²×C₄	—	5	8	no	—
612	C₂²×C₄	—	10	4	no	—
613	C₂²×C₄	—	20	4	no	—
614	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
615	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
617	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
618	C₄⋊C₄	—	5	8	no	—
619	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
620	C₂²⋊C₄	—	5	4	no	—
621	C₂²⋊C₄	—	5	8	no	—
622	C₂²⋊C₄	—	5	8	no	—
623	C₂²⋊C₄	—	5	8	no	—
624	C₂²⋊C₄	—	5	8	no	—
625	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
626	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
627	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
628	C₂²×C₃	—	2	8	no	—
629	C₂²×C₃	—	2	4	no	—
630	C₂²×C₃	—	2	2	no	—
631	C₂²×C₃	—	2	4	no	—
632	C₂²×C₃	—	4	4	no	—
633	C₂²×C₃	—	5	4	no	—
634	C₂²×C₃	—	5	4	no	—
635	C₂²×C₃	—	10	8	no	—
636	C₂²×C₃	—	10	8	no	—
637	C₂²×C₃	—	10	4	no	—
638	C₂²×C₃	—	10	4	no	—
639	C₂²×C₃	—	10	4	no	—
640	C₂²×C₃	—	10	2	no	—
641	C₂²×C₃	—	10	4	no	—
642	C₂²×C₃	—	10	4	no	—
643	C₂²×C₃	—	10	4	no	—
644	C₂²×C₃	—	20	16	no	—
645	C₂²×C₃	—	20	16	no	—
646	C₂²×C₃	—	20	16	no	—
647	C₂²×C₃	—	20	8	no	—
648	C₂²×C₃	—	20	4	no	—
649	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
650	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
651	C₂²×C₃	#4149	1	4	yes	—
652	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
653	C₃×C₄	—	2	4	no	—
654	C₃×C₄	—	2	2	no	—
655	C₃×C₄	—	2	4	no	—
656	C₃×C₄	—	10	2	no	—
657	C₃×C₄	—	10	4	no	—
658	C₂×C₅	—	2	4	no	—
659	C₂×C₅	—	4	2	no	—
660	C₂×C₅	C₃×#534	1	4	yes	complemented
661	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
662	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
663	D₅	—	2	4	no	—
664	D₅	—	2	4	no	—
665	D₅	—	4	4	no	—
666	D₅	—	4	2	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	5	4	no	—
671	C₂³	—	5	4	no	—
672	C₂³	—	5	2	no	—
673	C₂³	—	5	2	no	—
674	C₂³	—	5	16	no	—
675	C₂³	—	5	2	no	—
676	C₂³	—	5	4	no	—
677	C₂³	—	10	8	no	—
678	C₂³	—	10	4	no	—
679	C₂³	—	10	4	no	—
680	C₂³	—	10	8	no	—
681	C₂³	—	10	4	no	—
682	C₂³	—	10	2	no	—
683	C₂³	—	10	4	no	—
684	C₂³	—	10	4	no	—
685	C₂³	—	10	4	no	—
686	C₂³	—	20	8	no	—
687	C₂³	—	20	8	no	—
688	C₂³	—	20	16	no	—
689	C₂³	—	20	8	no	—
690	C₂³	—	20	16	no	—
691	C₂³	—	20	16	no	—
692	C₂³	C₃×D₄×D₅	1	4	yes	—
693	C₂³	C₂³×C₃×D₅	1	2	yes	—
694	C₂³	C₂³×C₃×D₅	1	2	yes	—
695	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
696	D₄	—	2	8	no	—
697	D₄	—	10	16	no	—
698	D₄	—	10	16	no	—
699	D₄	—	10	8	no	—
700	D₄	—	10	8	no	—
701	D₄	—	10	8	no	—
702	D₄	—	20	8	no	—
703	D₄	—	20	8	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	5	4	no	—
709	C₂×C₄	—	5	2	no	—
710	C₂×C₄	—	10	8	no	—
711	C₂×C₄	—	10	2	no	—
712	C₂×C₄	—	10	4	no	—
713	C₂×C₄	—	20	8	no	—
714	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
715	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
716	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
717	C₂×C₃	—	2	4	no	—
718	C₂×C₃	—	4	2	no	—
719	C₂×C₃	—	10	4	no	—
720	C₂×C₃	—	10	4	no	—
721	C₂×C₃	—	20	4	no	—
722	C₂×C₃	—	20	2	no	—
723	C₂×C₃	#65987	1	4	yes	direct product factor
724	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
725	C₂×C₃	C₂×#4149	1	2	yes	—
726	C₅	C₂×C₃×#534	1	1	yes	characteristic, complemented, Sylow
727	C₂²	—	2	4	no	—
728	C₂²	—	2	8	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	5	4	no	—
733	C₂²	—	5	4	no	—
734	C₂²	—	10	4	no	—
735	C₂²	—	10	4	no	—
736	C₂²	—	10	8	no	—
737	C₂²	—	10	8	no	—
738	C₂²	—	10	4	no	—
739	C₂²	—	10	2	no	—
740	C₂²	—	10	4	no	—
741	C₂²	—	10	4	no	—
742	C₂²	—	10	4	no	—
743	C₂²	—	20	16	no	—
744	C₂²	—	20	16	no	—
745	C₂²	—	20	16	no	—
746	C₂²	—	20	8	no	—
747	C₂²	—	20	4	no	—
748	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
749	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
750	C₂²	C₃×#4149	1	4	yes	—
751	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
752	C₄	—	2	4	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	10	2	no	—
756	C₄	—	10	4	no	—
757	C₃	C₂×#65987	1	1	yes	characteristic, direct product factor, Sylow
758	C₂	—	2	4	no	—
759	C₂	—	4	2	no	—
760	C₂	—	10	4	no	—
761	C₂	—	10	4	no	—
762	C₂	—	20	4	no	—
763	C₂	—	20	2	no	—
764	C₂	C₃×#65987	1	4	yes	direct product factor
765	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
766	C₂	C₂×C₃×#4149	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#123	D₅
hypocenter	C₅	C₂×C₃×#534
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄×D₅	C₂	semidirect
2. C₂³×C₃×D₂₀	C₂	semidirect
3. C₂×C₃×C₅×#123	C₂	semidirect
4. C₂×C₃×#4083	C₂	semidirect
5. C₂×C₃×#4075	C₂	semidirect
6. C₃×#65987	C₂	direct (N × H)
7. C₂×C₃×#4041	C₂	semidirect
8. C₂×C₃×#4040	C₂	semidirect
9. C₂×C₃×#4030	C₂	semidirect
10. C₂×C₃×#4028	C₂	semidirect
11. C₂×C₃×#4028	C₂	semidirect
12. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
13. C₂×#65987	C₃	direct (N × H)
15. C₂⁴×C₃×D₅	C₂²	semidirect
16. C₂⁴×C₃×D₅	C₂²	semidirect
18. C₂³×C₃×C₄×C₅	C₂²	semidirect
20. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
21. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
23. C₂×C₃×D₄×D₅	C₂²	semidirect
26. C₂²×C₃×D₂₀	C₂²	semidirect
27. C₂²×C₃×D₂₀	C₂²	semidirect
28. C₂²×C₃×D₂₀	C₂²	semidirect
29. C₂²×C₃×D₂₀	C₂²	semidirect
30. C₂²×C₃×C₄×D₅	C₂²	semidirect
31. C₂²×C₃×C₄×D₅	C₂²	semidirect
32. C₃×C₅×#123	C₂²	semidirect
33. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
37. C₃×#4083	C₂²	semidirect
38. C₃×#4075	C₂²	semidirect
39. C₂×C₃×#685	C₂²	semidirect
40. C₂×C₃×#685	C₂²	semidirect
41. C₂×C₃×#685	C₂²	semidirect
42. C₂×C₃×#685	C₂²	semidirect
43. C₂×C₃×#683	C₂²	semidirect
44. C₃×#4041	C₂²	semidirect
45. C₃×#4040	C₂²	semidirect
46. C₃×#4030	C₂²	semidirect
47. C₃×#4028	C₂²	semidirect
48. C₃×#4028	C₂²	semidirect
49. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
51. C₂²×D₄×D₅	C₂×C₃	semidirect
52. C₂³×D₂₀	C₂×C₃	semidirect
53. C₂×C₅×#123	C₂×C₃	semidirect
54. C₂×#4083	C₂×C₃	semidirect
55. C₂×#4075	C₂×C₃	semidirect
56. #65987	C₂×C₃	direct (N × H)
57. C₂×#4041	C₂×C₃	semidirect
58. C₂×#4040	C₂×C₃	semidirect
59. C₂×#4030	C₂×C₃	semidirect
60. C₂×#4028	C₂×C₃	semidirect
61. C₂×#4028	C₂×C₃	semidirect
62. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
70. C₂³×C₃×D₅	D₄	semidirect
76. C₂³×C₃×D₅	C₂³	semidirect
77. C₂³×C₃×D₅	C₂³	semidirect
84. C₂²×C₃×C₄×C₅	C₂³	semidirect
89. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
90. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
100. C₂×C₃×D₂₀	C₂³	semidirect
101. C₂×C₃×D₂₀	C₂³	semidirect
102. C₂×C₃×D₂₀	C₂³	semidirect
105. C₂×C₃×C₄×D₅	C₂³	semidirect
106. C₂×C₃×C₄×D₅	C₂³	semidirect
107. C₃×C₅×C₄⋊C₄	C₂³	semidirect
108. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
110. C₃×C₂²⋊Dic₅	C₂³	semidirect
111. C₃×#685	C₂³	semidirect
112. C₃×#685	C₂³	semidirect
113. C₃×#685	C₂³	semidirect
114. C₃×#685	C₂³	semidirect
115. C₃×#683	C₂³	semidirect
121. C₂×C₃×#123	D₅	semidirect
129. C₂⁴×D₅	C₂²×C₃	semidirect
130. C₂⁴×D₅	C₂²×C₃	semidirect
132. C₂³×C₄×C₅	C₂²×C₃	semidirect
134. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
135. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
137. C₂×D₄×D₅	C₂²×C₃	semidirect
140. C₂²×D₂₀	C₂²×C₃	semidirect
141. C₂²×D₂₀	C₂²×C₃	semidirect
142. C₂²×D₂₀	C₂²×C₃	semidirect
143. C₂²×D₂₀	C₂²×C₃	semidirect
144. C₂²×C₄×D₅	C₂²×C₃	semidirect
145. C₂²×C₄×D₅	C₂²×C₃	semidirect
146. C₅×#123	C₂²×C₃	semidirect
147. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
148. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
149. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
150. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
151. #4083	C₂²×C₃	semidirect
152. #4075	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×#683	C₂²×C₃	semidirect
158. #4041	C₂²×C₃	semidirect
159. #4040	C₂²×C₃	semidirect
160. #4030	C₂²×C₃	semidirect
161. #4028	C₂²×C₃	semidirect
162. #4028	C₂²×C₃	semidirect
163. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
189. C₂²×C₃×D₅	C₂×D₄	semidirect
232. C₂³×C₃×C₄	C₂×D₅	semidirect
235. C₃×#123	C₂×D₅	semidirect
242. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
249. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
250. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
258. C₂³×D₅	C₃×D₄	semidirect
264. C₂³×D₅	C₂³×C₃	semidirect
265. C₂³×D₅	C₂³×C₃	semidirect
272. C₂²×C₄×C₅	C₂³×C₃	semidirect
277. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
278. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
288. C₂×D₂₀	C₂³×C₃	semidirect
289. C₂×D₂₀	C₂³×C₃	semidirect
290. C₂×D₂₀	C₂³×C₃	semidirect
293. C₂×C₄×D₅	C₂³×C₃	semidirect
294. C₂×C₄×D₅	C₂³×C₃	semidirect
295. C₅×C₄⋊C₄	C₂³×C₃	semidirect
296. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
297. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
298. C₂²⋊Dic₅	C₂³×C₃	semidirect
299. #685	C₂³×C₃	semidirect
300. #685	C₂³×C₃	semidirect
301. #685	C₂³×C₃	semidirect
302. #685	C₂³×C₃	semidirect
303. #683	C₂³×C₃	semidirect
309. C₂×#123	C₃×D₅	semidirect
389. C₂²×C₃×C₄	C₂²×D₅	semidirect
391. C₃×C₄⋊C₄	C₂²×D₅	semidirect
397. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
398. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
423. C₂²×D₅	C₂×C₃×D₄	semidirect
466. C₂³×C₄	C₂×C₃×D₅	semidirect
469. #123	C₂×C₃×D₅	semidirect
476. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
483. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
484. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
487. C₂×C₃×C₅	#534	semidirect
617. C₂²×C₄	C₂²×C₃×D₅	semidirect
619. C₄⋊C₄	C₂²×C₃×D₅	semidirect
625. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
626. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
627. C₃×C₅	C₂×#534	semidirect
660. C₂×C₅	C₃×#534	semidirect
723. C₂×C₃	#65987	direct (N × H)
726. C₅	C₂×C₃×#534	semidirect
757. C₃	C₂×#65987	direct (N × H)
764. C₂	C₃×#65987	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
C₂³×C₃×D₂₀	2
C₂×C₃×C₅×#123	2
C₂×C₃×#4083	2
C₂×C₃×#4075	2
C₃×#65987	2
C₂×C₃×#4041	2
C₂×C₃×#4040	2
C₂×C₃×#4030	2
C₂×C₃×#4028	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×#65987	3
C₂×C₃×#534	5

Subgroups — C2×C3×#65987 #14480300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65987 #14480300