Subgroups — C₂×C₃×#65926 #14480369

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4086	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4085	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65926	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#4031	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4030	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65926	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
15	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₂²⋊D₅	—	2	8	no	—
19	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
20	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
21	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₂²⋊D₅	C₂²	1	8	yes	complemented
23	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
25	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
26	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
27	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#711	—	2	8	no	—
29	C₂×C₃×#711	C₂²	1	8	yes	complemented
30	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
31	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#120	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₃×#4099	C₂²	1	8	yes	complemented
37	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
39	C₃×#4086	C₂²	1	16	yes	complemented
40	C₃×#4085	C₂²	1	16	yes	complemented
41	C₃×#4083	C₂²	1	8	yes	complemented
42	C₂×C₃×#685	C₂²	1	2	yes	complemented
43	C₂×C₃×#685	C₂²	1	2	yes	complemented
44	C₂×C₃×#683	C₂²	1	2	yes	complemented
45	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
46	C₃×#4031	C₂²	1	16	yes	complemented
47	C₃×#4030	C₂²	1	16	yes	complemented
48	C₃×#4028	C₂²	1	8	yes	complemented
49	C₃×#4023	C₂²	1	8	yes	complemented
50	C₂×C₃×#535	—	5	1	no	maximal, Hall
51	C₂³×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂²×#711	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4099	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4086	C₂×C₃	1	2	yes	complemented
56	C₂×#4085	C₂×C₃	1	2	yes	complemented
57	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
58	#65926	C₂×C₃	1	16	yes	direct product factor
59	C₂×#4031	C₂×C₃	1	2	yes	complemented
60	C₂×#4030	C₂×C₃	1	2	yes	complemented
61	C₂×#4028	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×#4023	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂⁴×C₃×C₅	—	2	4	no	—
64	C₂⁴×C₃×C₅	—	4	4	no	—
65	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
66	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
67	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
68	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
69	C₂³×C₃×D₅	—	2	4	no	—
70	C₂³×C₃×D₅	—	4	4	no	—
71	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
72	C₂³×C₃×D₅	C₂³	1	2	yes	—
73	C₂³×C₃×D₅	C₂³	1	4	yes	—
74	C₂×C₃×C₅×D₄	—	2	4	no	—
75	C₂×C₃×C₅×D₄	—	4	4	no	—
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
80	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
81	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
82	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
83	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
84	C₂×C₃×C₂²⋊D₅	—	2	32	no	—
85	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
86	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
87	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
88	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
89	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
90	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
91	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
92	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
93	C₂²×C₃×Dic₅	—	2	4	no	—
94	C₂²×C₃×Dic₅	D₄	1	8	yes	complemented
95	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
96	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
100	C₂²×C₃×Dic₅	C₂³	1	4	yes	complemented
101	C₃×#711	—	2	32	no	—
102	C₂×C₃×D₂₀	—	4	4	no	—
103	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
104	C₂×C₃×C₄×D₅	—	2	4	no	—
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×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
111	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
112	C₃×#685	C₂³	1	8	yes	complemented
113	C₃×#685	C₂³	1	8	yes	complemented
114	C₃×#683	C₂³	1	8	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	2	no	—
122	C₂×C₃×#121	—	5	2	no	—
123	C₂×C₃×#120	—	5	1	no	—
124	C₂×C₃×#120	—	5	1	no	—
125	C₂×C₃×#120	—	5	1	no	—
126	C₂×C₃×#120	D₅	1	1	yes	characteristic, complemented
127	C₂×C₃×#117	—	5	1	no	—
128	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
131	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
132	C₂²×C₂²⋊D₅	—	2	8	no	—
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	—
136	C₂²×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
137	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
139	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
140	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
141	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂×#711	—	2	8	no	—
143	C₂×#711	C₂²×C₃	1	8	yes	complemented
144	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
145	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₅×#120	C₂²×C₃	1	8	yes	complemented
148	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
150	#4099	C₂²×C₃	1	8	yes	complemented
151	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
153	#4086	C₂²×C₃	1	16	yes	complemented
154	#4085	C₂²×C₃	1	16	yes	complemented
155	#4083	C₂²×C₃	1	8	yes	complemented
156	C₂×#685	C₂²×C₃	1	2	yes	complemented
157	C₂×#685	C₂²×C₃	1	2	yes	complemented
158	C₂×#683	C₂²×C₃	1	2	yes	complemented
159	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
160	#4031	C₂²×C₃	1	16	yes	complemented
161	#4030	C₂²×C₃	1	16	yes	complemented
162	#4028	C₂²×C₃	1	8	yes	complemented
163	#4023	C₂²×C₃	1	8	yes	complemented
164	C₂×#535	—	5	1	no	Sylow
165	C₂³×C₃×C₅	—	2	4	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	—	2	8	no	—
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	2	4	no	—
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	—	2	4	no	—
172	C₂³×C₃×C₅	—	4	8	no	—
173	C₂³×C₃×C₅	—	4	16	no	—
174	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
175	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
176	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
177	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
178	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₃×D₅	—	2	2	no	—
180	C₂²×C₃×D₅	—	2	8	no	—
181	C₂²×C₃×D₅	—	2	4	no	—
182	C₂²×C₃×D₅	—	2	4	no	—
183	C₂²×C₃×D₅	—	2	4	no	—
184	C₂²×C₃×D₅	—	2	4	no	—
185	C₂²×C₃×D₅	—	4	8	no	—
186	C₂²×C₃×D₅	—	4	16	no	—
187	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
188	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
189	C₃×C₅×D₄	—	2	8	no	—
190	C₃×C₅×D₄	—	4	8	no	—
191	C₂×C₃×C₄×C₅	—	2	2	no	—
192	C₂×C₃×C₄×C₅	—	2	4	no	—
193	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
194	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
195	C₃×C₂²⋊D₅	—	2	8	no	—
196	C₃×C₂²⋊D₅	—	2	8	no	—
197	C₃×C₂²⋊D₅	—	2	16	no	—
198	C₃×C₂²⋊D₅	—	2	16	no	—
199	C₃×C₂²⋊D₅	—	4	8	no	—
200	C₃×C₂²⋊D₅	—	4	8	no	—
201	C₂×C₃×Dic₅	—	2	2	no	—
202	C₂×C₃×Dic₅	—	2	4	no	—
203	C₂×C₃×Dic₅	—	2	8	no	—
204	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
205	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
206	C₂×C₃×Dic₅	C₂×D₄	1	16	yes	complemented
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	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
211	C₃×D₂₀	—	4	8	no	—
212	C₃×C₄×D₅	—	2	8	no	—
213	C₃×Dic₁₀	—	2	8	no	—
214	C₂⁵×C₃	—	5	1	no	—
215	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
216	C₂×C₃×#41	—	5	8	no	—
217	C₂×C₃×#41	—	10	8	no	—
218	C₂²×C₃×Q₈	—	5	1	no	—
219	C₂²×C₃×D₄	—	5	2	no	—
220	C₂²×C₃×D₄	—	5	2	no	—
221	C₂²×C₃×D₄	—	5	8	no	—
222	C₂²×C₃×D₄	—	5	1	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	2	no	—
227	C₂²×C₃×D₄	—	10	8	no	—
228	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
229	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
230	C₂³×C₃×C₄	—	5	1	no	—
231	C₂³×C₃×C₄	—	5	1	no	—
232	C₂³×C₃×C₄	—	5	1	no	—
233	C₃×#127	—	5	16	no	—
234	C₃×#124	—	5	16	no	—
235	C₃×#121	—	5	16	no	—
236	C₃×#121	—	5	16	no	—
237	C₃×#120	—	5	8	no	—
238	C₃×#120	—	5	8	no	—
239	C₃×#120	—	5	8	no	—
240	C₃×#120	C₂×D₅	1	8	yes	complemented
241	C₃×#117	—	5	8	no	—
242	C₂×C₃×C₄⋊C₄	—	5	2	no	—
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	C₂×D₅	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
249	C₂×C₃×C₄²	—	5	2	no	—
250	C₂⁴×C₅	—	2	4	no	—
251	C₂⁴×C₅	—	4	4	no	—
252	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
253	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
256	C₂³×D₅	—	2	4	no	—
257	C₂³×D₅	—	4	4	no	—
258	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
259	C₂³×D₅	C₂³×C₃	1	2	yes	—
260	C₂³×D₅	C₂³×C₃	1	4	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	C₂³×C₃	1	2	yes	—
266	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₂²⋊D₅	—	2	4	no	—
268	C₂×C₂²⋊D₅	—	2	4	no	—
269	C₂×C₂²⋊D₅	—	2	8	no	—
270	C₂×C₂²⋊D₅	—	2	8	no	—
271	C₂×C₂²⋊D₅	—	2	32	no	—
272	C₂×C₂²⋊D₅	—	4	4	no	—
273	C₂×C₂²⋊D₅	—	4	4	no	—
274	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
275	C₂×C₂²⋊D₅	C₂³×C₃	1	8	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	—	2	4	no	—
281	C₂²×Dic₅	C₃×D₄	1	8	yes	complemented
282	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
283	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
284	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
285	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
286	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
287	C₂²×Dic₅	C₂³×C₃	1	4	yes	complemented
288	#711	—	2	32	no	—
289	C₂×D₂₀	—	4	4	no	—
290	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
291	C₂×C₄×D₅	—	2	4	no	—
292	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
293	C₂×Dic₁₀	—	2	4	no	—
294	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
295	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
296	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
297	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
298	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
299	#685	C₂³×C₃	1	8	yes	complemented
300	#685	C₂³×C₃	1	8	yes	complemented
301	#683	C₂³×C₃	1	8	yes	complemented
302	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
303	C₂²×#41	—	5	1	no	—
304	C₂³×D₄	—	5	1	no	—
305	#535	—	5	16	no	—
306	C₂×#127	—	5	2	no	—
307	C₂×#124	—	5	2	no	—
308	C₂×#121	—	5	2	no	—
309	C₂×#121	—	5	2	no	—
310	C₂×#120	—	5	1	no	—
311	C₂×#120	—	5	1	no	—
312	C₂×#120	—	5	1	no	—
313	C₂×#120	C₃×D₅	1	1	yes	characteristic, complemented
314	C₂×#117	—	5	1	no	—
315	C₂²×C₃×C₅	—	2	8	no	—
316	C₂²×C₃×C₅	—	2	4	no	—
317	C₂²×C₃×C₅	—	2	2	no	—
318	C₂²×C₃×C₅	—	2	4	no	—
319	C₂²×C₃×C₅	—	2	4	no	—
320	C₂²×C₃×C₅	—	2	4	no	—
321	C₂²×C₃×C₅	—	2	4	no	—
322	C₂²×C₃×C₅	—	4	16	no	—
323	C₂²×C₃×C₅	—	4	4	no	—
324	C₂²×C₃×C₅	—	4	8	no	—
325	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
326	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
327	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
328	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
329	C₂×C₃×D₅	—	2	2	no	—
330	C₂×C₃×D₅	—	2	4	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	4	no	—
336	C₂×C₃×D₅	—	4	8	no	—
337	C₃×C₄×C₅	—	2	2	no	—
338	C₃×C₄×C₅	—	2	4	no	—
339	C₃×Dic₅	—	2	2	no	—
340	C₃×Dic₅	—	2	4	no	—
341	C₃×Dic₅	C₂²×D₄	1	4	yes	—
342	C₃×Dic₅	C₂²×D₄	1	4	yes	—
343	C₂⁴×C₃	—	2	4	no	—
344	C₂⁴×C₃	—	4	4	no	—
345	C₂⁴×C₃	—	5	2	no	—
346	C₂⁴×C₃	—	5	1	no	—
347	C₂⁴×C₃	—	5	4	no	—
348	C₂⁴×C₃	—	10	4	no	—
349	C₂⁴×C₃	—	20	4	no	—
350	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
351	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
352	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
353	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
354	C₃×#41	—	10	32	no	—
355	C₂×C₃×Q₈	—	5	4	no	—
356	C₂×C₃×Q₈	—	10	4	no	—
357	C₂×C₃×D₄	—	2	4	no	—
358	C₂×C₃×D₄	—	4	4	no	—
359	C₂×C₃×D₄	—	5	4	no	—
360	C₂×C₃×D₄	—	5	8	no	—
361	C₂×C₃×D₄	—	5	8	no	—
362	C₂×C₃×D₄	—	5	4	no	—
363	C₂×C₃×D₄	—	5	8	no	—
364	C₂×C₃×D₄	—	5	8	no	—
365	C₂×C₃×D₄	—	5	8	no	—
366	C₂×C₃×D₄	—	10	8	no	—
367	C₂×C₃×D₄	—	10	8	no	—
368	C₂×C₃×D₄	—	10	32	no	—
369	C₂×C₃×D₄	—	10	4	no	—
370	C₂×C₃×D₄	—	10	4	no	—
371	C₂×C₃×D₄	—	20	4	no	—
372	C₂×C₃×D₄	—	20	4	no	—
373	C₂×C₃×D₄	—	20	4	no	—
374	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
375	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
376	C₂²×C₃×C₄	—	5	8	no	—
377	C₂²×C₃×C₄	—	5	4	no	—
378	C₂²×C₃×C₄	—	5	1	no	—
379	C₂²×C₃×C₄	—	5	1	no	—
380	C₂²×C₃×C₄	—	5	4	no	—
381	C₂²×C₃×C₄	—	5	2	no	—
382	C₂²×C₃×C₄	—	5	1	no	—
383	C₂²×C₃×C₄	—	5	4	no	—
384	C₂²×C₃×C₄	—	10	4	no	—
385	C₂²×C₃×C₄	—	10	4	no	—
386	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
387	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
388	C₃×C₄⋊C₄	—	5	8	no	—
389	C₃×C₂²⋊C₄	—	5	4	no	—
390	C₃×C₂²⋊C₄	—	5	8	no	—
391	C₃×C₂²⋊C₄	—	5	8	no	—
392	C₃×C₂²⋊C₄	—	5	8	no	—
393	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
394	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
395	C₃×C₄²	—	5	8	no	—
396	C₂³×C₅	—	2	4	no	—
397	C₂³×C₅	—	2	2	no	—
398	C₂³×C₅	—	2	8	no	—
399	C₂³×C₅	—	2	4	no	—
400	C₂³×C₅	—	2	4	no	—
401	C₂³×C₅	—	2	4	no	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	4	8	no	—
404	C₂³×C₅	—	4	16	no	—
405	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
406	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
407	C₂³×C₅	C₂⁴×C₃	1	2	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	8	no	—
412	C₂²×D₅	—	2	4	no	—
413	C₂²×D₅	—	2	4	no	—
414	C₂²×D₅	—	2	4	no	—
415	C₂²×D₅	—	2	4	no	—
416	C₂²×D₅	—	4	8	no	—
417	C₂²×D₅	—	4	16	no	—
418	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
419	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
420	C₅×D₄	—	2	8	no	—
421	C₅×D₄	—	4	8	no	—
422	C₂×C₄×C₅	—	2	2	no	—
423	C₂×C₄×C₅	—	2	4	no	—
424	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
425	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
426	C₂²⋊D₅	—	2	8	no	—
427	C₂²⋊D₅	—	2	8	no	—
428	C₂²⋊D₅	—	2	16	no	—
429	C₂²⋊D₅	—	2	16	no	—
430	C₂²⋊D₅	—	4	8	no	—
431	C₂²⋊D₅	—	4	8	no	—
432	C₂×Dic₅	—	2	2	no	—
433	C₂×Dic₅	—	2	4	no	—
434	C₂×Dic₅	—	2	8	no	—
435	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
436	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
437	C₂×Dic₅	C₂×C₃×D₄	1	16	yes	complemented
438	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
439	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
440	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
441	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
442	D₂₀	—	4	8	no	—
443	C₄×D₅	—	2	8	no	—
444	Dic₁₀	—	2	8	no	—
445	C₂⁵	—	5	1	no	—
446	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
447	C₂×#41	—	5	8	no	—
448	C₂×#41	—	10	8	no	—
449	C₂²×Q₈	—	5	1	no	—
450	C₂²×D₄	—	5	1	no	—
451	C₂²×D₄	—	5	2	no	—
452	C₂²×D₄	—	5	2	no	—
453	C₂²×D₄	—	5	1	no	—
454	C₂²×D₄	—	5	8	no	—
455	C₂²×D₄	—	5	2	no	—
456	C₂²×D₄	—	5	2	no	—
457	C₂²×D₄	—	5	2	no	—
458	C₂²×D₄	—	10	8	no	—
459	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
460	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
461	C₂³×C₄	—	5	1	no	—
462	C₂³×C₄	—	5	1	no	—
463	C₂³×C₄	—	5	1	no	—
464	#127	—	5	16	no	—
465	#124	—	5	16	no	—
466	#121	—	5	16	no	—
467	#121	—	5	16	no	—
468	#120	—	5	8	no	—
469	#120	—	5	8	no	—
470	#120	—	5	8	no	—
471	#120	C₂×C₃×D₅	1	8	yes	complemented
472	#117	—	5	8	no	—
473	C₂×C₄⋊C₄	—	5	2	no	—
474	C₂×C₂²⋊C₄	—	5	1	no	—
475	C₂×C₂²⋊C₄	—	5	2	no	—
476	C₂×C₂²⋊C₄	—	5	2	no	—
477	C₂×C₂²⋊C₄	—	5	2	no	—
478	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
480	C₂×C₄²	—	5	2	no	—
481	C₂×C₃×C₅	—	2	4	no	—
482	C₂×C₃×C₅	—	4	2	no	—
483	C₂×C₃×C₅	—	4	4	no	—
484	C₂×C₃×C₅	#535	1	4	yes	complemented
485	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
486	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
487	C₃×D₅	—	4	2	no	—
488	C₃×D₅	—	4	4	no	—
489	C₂³×C₃	—	2	4	no	—
490	C₂³×C₃	—	2	2	no	—
491	C₂³×C₃	—	2	8	no	—
492	C₂³×C₃	—	2	4	no	—
493	C₂³×C₃	—	2	4	no	—
494	C₂³×C₃	—	2	4	no	—
495	C₂³×C₃	—	2	4	no	—
496	C₂³×C₃	—	4	8	no	—
497	C₂³×C₃	—	4	16	no	—
498	C₂³×C₃	—	5	4	no	—
499	C₂³×C₃	—	5	2	no	—
500	C₂³×C₃	—	10	2	no	—
501	C₂³×C₃	—	10	8	no	—
502	C₂³×C₃	—	10	4	no	—
503	C₂³×C₃	—	10	4	no	—
504	C₂³×C₃	—	10	4	no	—
505	C₂³×C₃	—	10	4	no	—
506	C₂³×C₃	—	20	8	no	—
507	C₂³×C₃	—	20	16	no	—
508	C₂³×C₃	D₄×D₅	1	4	yes	—
509	C₂³×C₃	C₂³×D₅	1	4	yes	—
510	C₂³×C₃	C₂³×D₅	1	2	yes	—
511	C₂³×C₃	C₂³×D₅	1	2	yes	—
512	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
513	C₃×Q₈	—	10	8	no	—
514	C₃×D₄	—	2	8	no	—
515	C₃×D₄	—	4	8	no	—
516	C₃×D₄	—	10	16	no	—
517	C₃×D₄	—	10	16	no	—
518	C₃×D₄	—	10	8	no	—
519	C₃×D₄	—	10	8	no	—
520	C₃×D₄	—	20	8	no	—
521	C₃×D₄	—	20	8	no	—
522	C₃×D₄	—	20	8	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	4	no	—
525	C₂×C₃×C₄	—	5	4	no	—
526	C₂×C₃×C₄	—	5	4	no	—
527	C₂×C₃×C₄	—	5	16	no	—
528	C₂×C₃×C₄	—	5	2	no	—
529	C₂×C₃×C₄	—	5	2	no	—
530	C₂×C₃×C₄	—	5	4	no	—
531	C₂×C₃×C₄	—	5	2	no	—
532	C₂×C₃×C₄	—	10	8	no	—
533	C₂×C₃×C₄	—	10	8	no	—
534	C₂×C₃×C₄	—	10	2	no	—
535	C₂×C₃×C₄	—	10	4	no	—
536	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
537	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
538	C₂²×C₅	—	2	4	no	—
539	C₂²×C₅	—	2	8	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	2	4	no	—
542	C₂²×C₅	—	2	4	no	—
543	C₂²×C₅	—	2	4	no	—
544	C₂²×C₅	—	2	4	no	—
545	C₂²×C₅	—	4	16	no	—
546	C₂²×C₅	—	4	4	no	—
547	C₂²×C₅	—	4	8	no	—
548	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
549	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
550	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
551	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
552	C₂×D₅	—	2	2	no	—
553	C₂×D₅	—	2	4	no	—
554	C₂×D₅	—	2	4	no	—
555	C₂×D₅	—	2	4	no	—
556	C₂×D₅	—	2	4	no	—
557	C₂×D₅	—	4	16	no	—
558	C₂×D₅	—	4	4	no	—
559	C₂×D₅	—	4	8	no	—
560	C₄×C₅	—	2	2	no	—
561	C₄×C₅	—	2	4	no	—
562	Dic₅	—	2	2	no	—
563	Dic₅	—	2	4	no	—
564	Dic₅	C₂²×C₃×D₄	1	4	yes	—
565	Dic₅	C₂²×C₃×D₄	1	4	yes	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	4	4	no	—
568	C₂⁴	—	5	2	no	—
569	C₂⁴	—	5	1	no	—
570	C₂⁴	—	5	4	no	—
571	C₂⁴	—	10	4	no	—
572	C₂⁴	—	20	4	no	—
573	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
574	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
575	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
576	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
577	#41	—	10	32	no	—
578	C₂×Q₈	—	5	4	no	—
579	C₂×Q₈	—	10	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	—	5	4	no	—
583	C₂×D₄	—	5	8	no	—
584	C₂×D₄	—	5	8	no	—
585	C₂×D₄	—	5	4	no	—
586	C₂×D₄	—	5	8	no	—
587	C₂×D₄	—	5	8	no	—
588	C₂×D₄	—	5	8	no	—
589	C₂×D₄	—	10	8	no	—
590	C₂×D₄	—	10	8	no	—
591	C₂×D₄	—	10	32	no	—
592	C₂×D₄	—	10	4	no	—
593	C₂×D₄	—	10	4	no	—
594	C₂×D₄	—	20	4	no	—
595	C₂×D₄	—	20	4	no	—
596	C₂×D₄	—	20	4	no	—
597	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
598	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
599	C₂²×C₄	—	5	8	no	—
600	C₂²×C₄	—	5	1	no	—
601	C₂²×C₄	—	5	1	no	—
602	C₂²×C₄	—	5	4	no	—
603	C₂²×C₄	—	5	2	no	—
604	C₂²×C₄	—	5	1	no	—
605	C₂²×C₄	—	5	4	no	—
606	C₂²×C₄	—	5	4	no	—
607	C₂²×C₄	—	10	4	no	—
608	C₂²×C₄	—	10	4	no	—
609	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
610	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
611	C₄⋊C₄	—	5	8	no	—
612	C₂²⋊C₄	—	5	4	no	—
613	C₂²⋊C₄	—	5	8	no	—
614	C₂²⋊C₄	—	5	8	no	—
615	C₂²⋊C₄	—	5	8	no	—
616	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
617	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
618	C₄²	—	5	8	no	—
619	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
620	C₂²×C₃	—	2	8	no	—
621	C₂²×C₃	—	2	4	no	—
622	C₂²×C₃	—	2	2	no	—
623	C₂²×C₃	—	2	4	no	—
624	C₂²×C₃	—	2	4	no	—
625	C₂²×C₃	—	2	4	no	—
626	C₂²×C₃	—	2	4	no	—
627	C₂²×C₃	—	4	16	no	—
628	C₂²×C₃	—	4	4	no	—
629	C₂²×C₃	—	4	8	no	—
630	C₂²×C₃	—	10	2	no	—
631	C₂²×C₃	—	10	4	no	—
632	C₂²×C₃	—	10	4	no	—
633	C₂²×C₃	—	10	4	no	—
634	C₂²×C₃	—	10	4	no	—
635	C₂²×C₃	—	20	16	no	—
636	C₂²×C₃	—	20	4	no	—
637	C₂²×C₃	—	20	8	no	—
638	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
639	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
640	C₂²×C₃	#4144	1	4	yes	—
641	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	2	4	no	—
644	C₃×C₄	—	5	4	no	—
645	C₃×C₄	—	5	4	no	—
646	C₃×C₄	—	10	2	no	—
647	C₃×C₄	—	10	4	no	—
648	C₂×C₅	—	2	4	no	—
649	C₂×C₅	—	4	4	no	—
650	C₂×C₅	—	4	2	no	—
651	C₂×C₅	C₃×#535	1	4	yes	complemented
652	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
653	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
654	D₅	—	4	4	no	—
655	D₅	—	4	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	4	8	no	—
664	C₂³	—	4	16	no	—
665	C₂³	—	5	4	no	—
666	C₂³	—	5	2	no	—
667	C₂³	—	10	2	no	—
668	C₂³	—	10	8	no	—
669	C₂³	—	10	4	no	—
670	C₂³	—	10	4	no	—
671	C₂³	—	10	4	no	—
672	C₂³	—	10	4	no	—
673	C₂³	—	20	8	no	—
674	C₂³	—	20	16	no	—
675	C₂³	C₃×D₄×D₅	1	4	yes	—
676	C₂³	C₂³×C₃×D₅	1	4	yes	—
677	C₂³	C₂³×C₃×D₅	1	2	yes	—
678	C₂³	C₂³×C₃×D₅	1	2	yes	—
679	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
680	Q₈	—	10	8	no	—
681	D₄	—	2	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	10	16	no	—
684	D₄	—	10	16	no	—
685	D₄	—	10	8	no	—
686	D₄	—	10	8	no	—
687	D₄	—	20	8	no	—
688	D₄	—	20	8	no	—
689	D₄	—	20	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	5	4	no	—
693	C₂×C₄	—	5	4	no	—
694	C₂×C₄	—	5	16	no	—
695	C₂×C₄	—	5	2	no	—
696	C₂×C₄	—	5	2	no	—
697	C₂×C₄	—	5	4	no	—
698	C₂×C₄	—	5	2	no	—
699	C₂×C₄	—	10	8	no	—
700	C₂×C₄	—	10	8	no	—
701	C₂×C₄	—	10	2	no	—
702	C₂×C₄	—	10	4	no	—
703	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
704	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
705	C₂×C₃	—	2	4	no	—
706	C₂×C₃	—	4	4	no	—
707	C₂×C₃	—	4	2	no	—
708	C₂×C₃	—	20	4	no	—
709	C₂×C₃	—	20	2	no	—
710	C₂×C₃	#65926	1	4	yes	direct product factor
711	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
712	C₂×C₃	C₂×#4144	1	2	yes	—
713	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
714	C₂²	—	2	4	no	—
715	C₂²	—	2	8	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	4	16	no	—
722	C₂²	—	4	8	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	10	2	no	—
725	C₂²	—	10	4	no	—
726	C₂²	—	10	4	no	—
727	C₂²	—	10	4	no	—
728	C₂²	—	10	4	no	—
729	C₂²	—	20	16	no	—
730	C₂²	—	20	8	no	—
731	C₂²	—	20	4	no	—
732	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
733	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
734	C₂²	C₃×#4144	1	4	yes	—
735	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
736	C₄	—	2	2	no	—
737	C₄	—	2	4	no	—
738	C₄	—	5	4	no	—
739	C₄	—	5	4	no	—
740	C₄	—	10	2	no	—
741	C₄	—	10	4	no	—
742	C₃	C₂×#65926	1	1	yes	characteristic, direct product factor, Sylow
743	C₂	—	2	4	no	—
744	C₂	—	4	4	no	—
745	C₂	—	4	2	no	—
746	C₂	—	20	4	no	—
747	C₂	—	20	2	no	—
748	C₂	C₃×#65926	1	4	yes	direct product factor
749	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
750	C₂	C₂×C₃×#4144	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×#120	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#120	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₂²⋊D₅	C₂	semidirect
2. C₂²×C₃×#711	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×#4099	C₂	semidirect
5. C₂×C₃×#4086	C₂	semidirect
6. C₂×C₃×#4085	C₂	semidirect
7. C₂×C₃×#4083	C₂	semidirect
8. C₃×#65926	C₂	direct (N × H)
9. C₂×C₃×#4031	C₂	semidirect
10. C₂×C₃×#4030	C₂	semidirect
11. C₂×C₃×#4028	C₂	semidirect
12. C₂×C₃×#4023	C₂	semidirect
13. C₂×#65926	C₃	direct (N × H)
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
23. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
24. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
25. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
27. C₂³×C₃×Dic₅	C₂²	semidirect
29. C₂×C₃×#711	C₂²	semidirect
30. C₂²×C₃×D₂₀	C₂²	semidirect
31. C₂²×C₃×C₄×D₅	C₂²	semidirect
32. C₂²×C₃×Dic₁₀	C₂²	semidirect
33. C₃×C₅×#120	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₃×#4099	C₂²	semidirect
38. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
39. C₃×#4086	C₂²	semidirect
40. C₃×#4085	C₂²	semidirect
41. C₃×#4083	C₂²	semidirect
42. C₂×C₃×#685	C₂²	semidirect
43. C₂×C₃×#685	C₂²	semidirect
44. C₂×C₃×#683	C₂²	semidirect
45. C₂×C₃×C₄×Dic₅	C₂²	semidirect
46. C₃×#4031	C₂²	semidirect
47. C₃×#4030	C₂²	semidirect
48. C₃×#4028	C₂²	semidirect
49. C₃×#4023	C₂²	semidirect
51. C₂³×C₂²⋊D₅	C₂×C₃	semidirect
52. C₂²×#711	C₂×C₃	semidirect
53. C₂×C₅×#120	C₂×C₃	semidirect
54. C₂×#4099	C₂×C₃	semidirect
55. C₂×#4086	C₂×C₃	semidirect
56. C₂×#4085	C₂×C₃	semidirect
57. C₂×#4083	C₂×C₃	semidirect
58. #65926	C₂×C₃	direct (N × H)
59. C₂×#4031	C₂×C₃	semidirect
60. C₂×#4030	C₂×C₃	semidirect
61. C₂×#4028	C₂×C₃	semidirect
62. C₂×#4023	C₂×C₃	semidirect
77. C₂×C₃×C₅×D₄	C₂³	semidirect
90. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
91. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
92. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
94. C₂²×C₃×Dic₅	D₄	semidirect
100. C₂²×C₃×Dic₅	C₂³	semidirect
103. C₂×C₃×D₂₀	C₂³	semidirect
105. C₂×C₃×C₄×D₅	C₂³	semidirect
107. C₂×C₃×Dic₁₀	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
111. C₃×C₂²⋊Dic₅	C₂³	semidirect
112. C₃×#685	C₂³	semidirect
113. C₃×#685	C₂³	semidirect
114. C₃×#683	C₂³	semidirect
115. C₃×C₄×Dic₅	C₂³	semidirect
126. C₂×C₃×#120	D₅	semidirect
131. C₂²×C₅×D₄	C₂²×C₃	semidirect
136. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
137. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
138. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
139. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
141. C₂³×Dic₅	C₂²×C₃	semidirect
143. C₂×#711	C₂²×C₃	semidirect
144. C₂²×D₂₀	C₂²×C₃	semidirect
145. C₂²×C₄×D₅	C₂²×C₃	semidirect
146. C₂²×Dic₁₀	C₂²×C₃	semidirect
147. C₅×#120	C₂²×C₃	semidirect
149. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
150. #4099	C₂²×C₃	semidirect
152. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
153. #4086	C₂²×C₃	semidirect
154. #4085	C₂²×C₃	semidirect
155. #4083	C₂²×C₃	semidirect
156. C₂×#685	C₂²×C₃	semidirect
157. C₂×#685	C₂²×C₃	semidirect
158. C₂×#683	C₂²×C₃	semidirect
159. C₂×C₄×Dic₅	C₂²×C₃	semidirect
160. #4031	C₂²×C₃	semidirect
161. #4030	C₂²×C₃	semidirect
162. #4028	C₂²×C₃	semidirect
163. #4023	C₂²×C₃	semidirect
206. C₂×C₃×Dic₅	C₂×D₄	semidirect
229. C₂²×C₃×D₄	C₂×D₅	semidirect
240. C₃×#120	C₂×D₅	semidirect
248. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
264. C₂×C₅×D₄	C₂³×C₃	semidirect
277. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
278. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
279. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
281. C₂²×Dic₅	C₃×D₄	semidirect
287. C₂²×Dic₅	C₂³×C₃	semidirect
290. C₂×D₂₀	C₂³×C₃	semidirect
292. C₂×C₄×D₅	C₂³×C₃	semidirect
294. C₂×Dic₁₀	C₂³×C₃	semidirect
296. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
298. C₂²⋊Dic₅	C₂³×C₃	semidirect
299. #685	C₂³×C₃	semidirect
300. #685	C₂³×C₃	semidirect
301. #683	C₂³×C₃	semidirect
302. C₄×Dic₅	C₂³×C₃	semidirect
313. C₂×#120	C₃×D₅	semidirect
375. C₂×C₃×D₄	C₂²×D₅	semidirect
394. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
437. C₂×Dic₅	C₂×C₃×D₄	semidirect
460. C₂²×D₄	C₂×C₃×D₅	semidirect
471. #120	C₂×C₃×D₅	semidirect
479. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
484. C₂×C₃×C₅	#535	semidirect
598. C₂×D₄	C₂²×C₃×D₅	semidirect
617. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
619. C₃×C₅	C₂×#535	semidirect
651. C₂×C₅	C₃×#535	semidirect
710. C₂×C₃	#65926	direct (N × H)
713. C₅	C₂×C₃×#535	semidirect
742. C₃	C₂×#65926	direct (N × H)
748. C₂	C₃×#65926	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₂²⋊D₅	2
C₂²×C₃×#711	2
C₂×C₃×C₅×#120	2
C₂×C₃×#4099	2
C₂×C₃×#4086	2
C₂×C₃×#4085	2
C₂×C₃×#4083	2
C₃×#65926	2
C₂×C₃×#4031	2
C₂×C₃×#4030	2
C₂×C₃×#4028	2
C₂×C₃×#4023	2
C₂×#65926	3
C₂×C₃×#535	5

Subgroups — C2×C3×#65926 #14480369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65926 #14480369