Subgroups — C₂×C₃×#66049 #14480363

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4085	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4083	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#66049	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#66049	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	complemented
19	C₂³×C₃×Dic₅	C₂²	1	2	yes	complemented
20	C₂×C₃×#711	—	2	8	no	—
21	C₂×C₃×#711	C₂²	1	8	yes	complemented
22	C₂×C₃×D₄×D₅	—	2	8	no	—
23	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
24	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#127	C₂²	1	8	yes	complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
30	C₃×#4086	C₂²	1	8	yes	complemented
31	C₃×#4085	C₂²	1	32	yes	complemented
32	C₃×#4083	C₂²	1	32	yes	complemented
33	C₃×#4082	C₂²	1	8	yes	complemented
34	C₂×C₃×#685	C₂²	1	2	yes	—
35	C₂×C₃×#685	C₂²	1	4	yes	complemented
36	C₂×C₃×#683	C₂²	1	2	yes	complemented
37	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#4021	C₂²	1	8	yes	complemented
39	C₃×#4018	C₂²	1	8	yes	complemented
40	C₂×C₃×#535	—	5	1	no	maximal, Hall
41	C₂²×#711	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4085	C₂×C₃	1	4	yes	complemented
46	C₂×#4083	C₂×C₃	1	4	yes	complemented
47	C₂×#4082	C₂×C₃	1	1	yes	characteristic, complemented
48	#66049	C₂×C₃	1	16	yes	direct product factor
49	C₂×#4021	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
53	C₂³×C₃×D₅	—	2	8	no	—
54	C₂³×C₃×D₅	—	4	8	no	—
55	C₂³×C₃×D₅	C₂³	1	2	yes	—
56	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
57	C₂³×C₃×D₅	C₂³	1	8	yes	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	4	8	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
62	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
63	C₂×C₃×C₅×D₄	C₂³	1	16	yes	complemented
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
67	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
68	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
69	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
70	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
71	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	complemented
72	C₂²×C₃×Dic₅	—	2	8	no	—
73	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
74	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
75	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×Dic₅	C₂³	1	8	yes	complemented
77	C₃×#711	—	2	32	no	—
78	C₃×D₄×D₅	—	2	32	no	—
79	C₂×C₃×D₂₀	—	2	4	no	—
80	C₂×C₃×D₂₀	C₂³	1	4	yes	—
81	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
82	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
83	C₂×C₃×Dic₁₀	—	2	4	no	—
84	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
85	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
86	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
87	C₃×#685	C₂³	1	8	yes	—
88	C₃×#685	C₂³	1	16	yes	complemented
89	C₃×#683	C₂³	1	8	yes	complemented
90	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
91	C₂²×C₃×#41	—	5	1	no	—
92	C₂³×C₃×D₄	—	5	1	no	—
93	C₃×#535	—	5	16	no	—
94	C₂×C₃×#127	—	5	1	no	—
95	C₂×C₃×#127	D₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#124	—	5	1	no	—
97	C₂×C₃×#124	—	5	1	no	—
98	C₂×C₃×#121	—	5	4	no	—
99	C₂×C₃×#120	—	5	4	no	—
100	C₂×C₃×#117	—	5	1	no	—
101	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
102	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
105	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
106	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
107	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
108	C₂³×Dic₅	C₂²×C₃	1	2	yes	complemented
109	C₂×#711	—	2	8	no	—
110	C₂×#711	C₂²×C₃	1	8	yes	complemented
111	C₂×D₄×D₅	—	2	8	no	—
112	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
113	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₅×#127	C₂²×C₃	1	8	yes	complemented
117	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	complemented
119	#4086	C₂²×C₃	1	8	yes	complemented
120	#4085	C₂²×C₃	1	32	yes	complemented
121	#4083	C₂²×C₃	1	32	yes	complemented
122	#4082	C₂²×C₃	1	8	yes	complemented
123	C₂×#685	C₂²×C₃	1	2	yes	—
124	C₂×#685	C₂²×C₃	1	4	yes	complemented
125	C₂×#683	C₂²×C₃	1	2	yes	complemented
126	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
127	#4021	C₂²×C₃	1	8	yes	complemented
128	#4018	C₂²×C₃	1	8	yes	complemented
129	C₂×#535	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	4	no	—
131	C₂³×C₃×C₅	—	2	4	no	—
132	C₂³×C₃×C₅	—	2	8	no	—
133	C₂³×C₃×C₅	—	2	8	no	—
134	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
135	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₂²×C₃×D₅	—	2	4	no	—
138	C₂²×C₃×D₅	—	2	4	no	—
139	C₂²×C₃×D₅	—	2	8	no	—
140	C₂²×C₃×D₅	—	2	16	no	—
141	C₂²×C₃×D₅	—	4	16	no	—
142	C₂²×C₃×D₅	—	4	32	no	—
143	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
144	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
145	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
146	C₃×C₅×D₄	—	2	8	no	—
147	C₃×C₅×D₄	—	2	8	no	—
148	C₃×C₅×D₄	—	4	16	no	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
153	C₃×C₂²⋊D₅	—	2	16	no	—
154	C₃×C₂²⋊D₅	—	2	16	no	—
155	C₃×C₂²⋊D₅	—	4	16	no	—
156	C₂×C₃×Dic₅	—	2	4	no	—
157	C₂×C₃×Dic₅	—	2	4	no	—
158	C₂×C₃×Dic₅	—	2	16	no	—
159	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
160	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
161	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
162	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
163	C₃×D₂₀	—	2	8	no	—
164	C₃×C₄×D₅	C₂×D₄	1	16	yes	complemented
165	C₃×Dic₁₀	—	2	8	no	—
166	C₂⁵×C₃	—	5	2	no	—
167	C₂×C₃×#41	—	5	8	no	—
168	C₂×C₃×#41	—	10	8	no	—
169	C₂²×C₃×Q₈	—	5	1	no	—
170	C₂²×C₃×D₄	—	5	2	no	—
171	C₂²×C₃×D₄	—	5	2	no	—
172	C₂²×C₃×D₄	—	5	4	no	—
173	C₂²×C₃×D₄	—	5	8	no	—
174	C₂²×C₃×D₄	—	5	1	no	—
175	C₂²×C₃×D₄	—	10	8	no	—
176	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
177	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
178	C₂²×C₃×D₄	C₂×D₅	1	4	yes	complemented
179	C₂³×C₃×C₄	—	5	1	no	—
180	C₂³×C₃×C₄	—	5	2	no	—
181	C₃×#127	—	5	8	no	—
182	C₃×#127	C₂×D₅	1	8	yes	complemented
183	C₃×#124	—	5	8	no	—
184	C₃×#124	—	5	8	no	—
185	C₃×#121	—	5	32	no	—
186	C₃×#120	—	5	32	no	—
187	C₃×#117	—	5	8	no	—
188	C₂×C₃×C₄⋊C₄	—	5	2	no	—
189	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
190	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
191	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
192	C₂×C₃×C₄²	—	5	1	no	—
193	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
194	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
195	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
196	C₂³×D₅	—	2	8	no	—
197	C₂³×D₅	—	4	8	no	—
198	C₂³×D₅	C₂³×C₃	1	2	yes	—
199	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
200	C₂³×D₅	C₂³×C₃	1	8	yes	—
201	C₂×C₅×D₄	—	2	4	no	—
202	C₂×C₅×D₄	—	2	4	no	—
203	C₂×C₅×D₄	—	4	8	no	—
204	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
205	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
206	C₂×C₅×D₄	C₂³×C₃	1	16	yes	complemented
207	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	8	no	—
210	C₂×C₂²⋊D₅	—	2	8	no	—
211	C₂×C₂²⋊D₅	—	4	8	no	—
212	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
213	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
214	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	complemented
215	C₂²×Dic₅	—	2	8	no	—
216	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
217	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
218	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
219	C₂²×Dic₅	C₂³×C₃	1	8	yes	complemented
220	#711	—	2	32	no	—
221	D₄×D₅	—	2	32	no	—
222	C₂×D₂₀	—	2	4	no	—
223	C₂×D₂₀	C₂³×C₃	1	4	yes	—
224	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
225	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
226	C₂×Dic₁₀	—	2	4	no	—
227	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
228	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
229	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	complemented
230	#685	C₂³×C₃	1	8	yes	—
231	#685	C₂³×C₃	1	16	yes	complemented
232	#683	C₂³×C₃	1	8	yes	complemented
233	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
234	C₂²×#41	—	5	1	no	—
235	C₂³×D₄	—	5	1	no	—
236	#535	—	5	16	no	—
237	C₂×#127	—	5	1	no	—
238	C₂×#127	C₃×D₅	1	1	yes	characteristic, complemented
239	C₂×#124	—	5	1	no	—
240	C₂×#124	—	5	1	no	—
241	C₂×#121	—	5	4	no	—
242	C₂×#120	—	5	4	no	—
243	C₂×#117	—	5	1	no	—
244	C₂²×C₃×C₅	—	2	4	no	—
245	C₂²×C₃×C₅	—	2	4	no	—
246	C₂²×C₃×C₅	—	2	8	no	—
247	C₂²×C₃×C₅	—	2	8	no	—
248	C₂²×C₃×C₅	—	4	8	no	—
249	C₂²×C₃×C₅	—	4	8	no	—
250	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
251	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
252	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
253	C₂×C₃×D₅	—	2	8	no	—
254	C₂×C₃×D₅	—	2	4	no	—
255	C₂×C₃×D₅	—	2	4	no	—
256	C₂×C₃×D₅	—	2	8	no	—
257	C₂×C₃×D₅	—	4	32	no	—
258	C₂×C₃×D₅	—	4	8	no	—
259	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
260	C₃×C₄×C₅	—	2	4	no	—
261	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
262	C₃×Dic₅	—	2	4	no	—
263	C₃×Dic₅	—	2	4	no	—
264	C₃×Dic₅	C₂²×D₄	1	4	yes	—
265	C₂⁴×C₃	—	5	1	no	—
266	C₂⁴×C₃	—	5	2	no	—
267	C₂⁴×C₃	—	5	8	no	—
268	C₂⁴×C₃	—	10	8	no	—
269	C₂⁴×C₃	—	20	8	no	—
270	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
271	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
272	C₃×#41	—	10	32	no	—
273	C₂×C₃×Q₈	—	5	4	no	—
274	C₂×C₃×Q₈	—	10	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂×C₃×D₄	—	4	8	no	—
278	C₂×C₃×D₄	—	5	8	no	—
279	C₂×C₃×D₄	—	5	8	no	—
280	C₂×C₃×D₄	—	5	16	no	—
281	C₂×C₃×D₄	—	5	4	no	—
282	C₂×C₃×D₄	—	10	32	no	—
283	C₂×C₃×D₄	—	10	8	no	—
284	C₂×C₃×D₄	—	10	8	no	—
285	C₂×C₃×D₄	—	10	4	no	—
286	C₂×C₃×D₄	—	20	8	no	—
287	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
288	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
289	C₂×C₃×D₄	C₂²×D₅	1	16	yes	complemented
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	8	no	—
292	C₂²×C₃×C₄	—	5	4	no	—
293	C₂²×C₃×C₄	—	5	8	no	—
294	C₂²×C₃×C₄	—	5	2	no	—
295	C₂²×C₃×C₄	—	5	2	no	—
296	C₂²×C₃×C₄	—	10	8	no	—
297	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
298	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
299	C₃×C₄⋊C₄	—	5	8	no	—
300	C₃×C₂²⋊C₄	—	5	16	no	—
301	C₃×C₂²⋊C₄	—	5	8	no	—
302	C₃×C₂²⋊C₄	—	5	16	no	—
303	C₃×C₄²	—	5	4	no	—
304	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	2	8	no	—
308	C₂³×C₅	—	2	8	no	—
309	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
310	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
311	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
312	C₂²×D₅	—	2	4	no	—
313	C₂²×D₅	—	2	4	no	—
314	C₂²×D₅	—	2	8	no	—
315	C₂²×D₅	—	2	16	no	—
316	C₂²×D₅	—	4	16	no	—
317	C₂²×D₅	—	4	32	no	—
318	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
319	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
320	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
321	C₅×D₄	—	2	8	no	—
322	C₅×D₄	—	2	8	no	—
323	C₅×D₄	—	4	16	no	—
324	C₂×C₄×C₅	—	2	4	no	—
325	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
326	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
327	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
328	C₂²⋊D₅	—	2	16	no	—
329	C₂²⋊D₅	—	2	16	no	—
330	C₂²⋊D₅	—	4	16	no	—
331	C₂×Dic₅	—	2	4	no	—
332	C₂×Dic₅	—	2	4	no	—
333	C₂×Dic₅	—	2	16	no	—
334	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
335	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
336	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
337	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
338	D₂₀	—	2	8	no	—
339	C₄×D₅	C₂×C₃×D₄	1	16	yes	complemented
340	Dic₁₀	—	2	8	no	—
341	C₂⁵	—	5	2	no	—
342	C₂×#41	—	5	8	no	—
343	C₂×#41	—	10	8	no	—
344	C₂²×Q₈	—	5	1	no	—
345	C₂²×D₄	—	5	2	no	—
346	C₂²×D₄	—	5	2	no	—
347	C₂²×D₄	—	5	4	no	—
348	C₂²×D₄	—	5	8	no	—
349	C₂²×D₄	—	5	1	no	—
350	C₂²×D₄	—	10	8	no	—
351	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
352	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
353	C₂²×D₄	C₂×C₃×D₅	1	4	yes	complemented
354	C₂³×C₄	—	5	1	no	—
355	C₂³×C₄	—	5	2	no	—
356	#127	—	5	8	no	—
357	#127	C₂×C₃×D₅	1	8	yes	complemented
358	#124	—	5	8	no	—
359	#124	—	5	8	no	—
360	#121	—	5	32	no	—
361	#120	—	5	32	no	—
362	#117	—	5	8	no	—
363	C₂×C₄⋊C₄	—	5	2	no	—
364	C₂×C₂²⋊C₄	—	5	4	no	—
365	C₂×C₂²⋊C₄	—	5	2	no	—
366	C₂×C₂²⋊C₄	—	5	4	no	—
367	C₂×C₄²	—	5	1	no	—
368	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
369	C₂×C₃×C₅	—	4	4	no	—
370	C₂×C₃×C₅	—	4	4	no	—
371	C₂×C₃×C₅	#535	1	4	yes	complemented
372	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₃×D₅	—	2	4	no	—
375	C₃×D₅	—	4	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	4	no	—
378	C₂³×C₃	—	2	8	no	—
379	C₂³×C₃	—	2	8	no	—
380	C₂³×C₃	—	5	4	no	—
381	C₂³×C₃	—	5	2	no	—
382	C₂³×C₃	—	5	4	no	—
383	C₂³×C₃	—	10	16	no	—
384	C₂³×C₃	—	10	4	no	—
385	C₂³×C₃	—	10	4	no	—
386	C₂³×C₃	—	10	8	no	—
387	C₂³×C₃	—	20	16	no	—
388	C₂³×C₃	—	20	32	no	—
389	C₂³×C₃	C₂³×D₅	1	4	yes	—
390	C₂³×C₃	C₂³×D₅	1	4	yes	—
391	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
392	C₃×Q₈	—	10	8	no	—
393	C₃×D₄	—	2	8	no	—
394	C₃×D₄	—	2	8	no	—
395	C₃×D₄	—	4	16	no	—
396	C₃×D₄	—	10	16	no	—
397	C₃×D₄	—	10	16	no	—
398	C₃×D₄	—	10	8	no	—
399	C₃×D₄	—	20	16	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	5	4	no	—
402	C₂×C₃×C₄	—	5	2	no	—
403	C₂×C₃×C₄	—	5	16	no	—
404	C₂×C₃×C₄	—	5	4	no	—
405	C₂×C₃×C₄	—	5	4	no	—
406	C₂×C₃×C₄	—	10	16	no	—
407	C₂×C₃×C₄	—	10	4	no	—
408	C₂×C₃×C₄	—	10	4	no	—
409	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
410	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
411	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
412	C₂²×C₅	—	2	4	no	—
413	C₂²×C₅	—	2	4	no	—
414	C₂²×C₅	—	2	8	no	—
415	C₂²×C₅	—	2	8	no	—
416	C₂²×C₅	—	4	8	no	—
417	C₂²×C₅	—	4	8	no	—
418	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
419	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
420	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
421	C₂×D₅	—	2	4	no	—
422	C₂×D₅	—	2	8	no	—
423	C₂×D₅	—	2	4	no	—
424	C₂×D₅	—	2	8	no	—
425	C₂×D₅	—	4	32	no	—
426	C₂×D₅	—	4	8	no	—
427	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
428	C₄×C₅	—	2	4	no	—
429	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
430	Dic₅	—	2	4	no	—
431	Dic₅	—	2	4	no	—
432	Dic₅	C₂²×C₃×D₄	1	4	yes	—
433	C₂⁴	—	5	1	no	—
434	C₂⁴	—	5	2	no	—
435	C₂⁴	—	5	8	no	—
436	C₂⁴	—	10	8	no	—
437	C₂⁴	—	20	8	no	—
438	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
439	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
440	#41	—	10	32	no	—
441	C₂×Q₈	—	5	4	no	—
442	C₂×Q₈	—	10	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	5	8	no	—
447	C₂×D₄	—	5	8	no	—
448	C₂×D₄	—	5	16	no	—
449	C₂×D₄	—	5	4	no	—
450	C₂×D₄	—	10	32	no	—
451	C₂×D₄	—	10	8	no	—
452	C₂×D₄	—	10	8	no	—
453	C₂×D₄	—	10	4	no	—
454	C₂×D₄	—	20	8	no	—
455	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
456	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
457	C₂×D₄	C₂²×C₃×D₅	1	16	yes	complemented
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	8	no	—
460	C₂²×C₄	—	5	4	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	5	8	no	—
464	C₂²×C₄	—	10	8	no	—
465	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
466	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
467	C₄⋊C₄	—	5	8	no	—
468	C₂²⋊C₄	—	5	16	no	—
469	C₂²⋊C₄	—	5	8	no	—
470	C₂²⋊C₄	—	5	16	no	—
471	C₄²	—	5	4	no	—
472	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
473	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	2	8	no	—
477	C₂²×C₃	—	2	8	no	—
478	C₂²×C₃	—	4	8	no	—
479	C₂²×C₃	—	4	8	no	—
480	C₂²×C₃	—	5	4	no	—
481	C₂²×C₃	—	10	8	no	—
482	C₂²×C₃	—	10	4	no	—
483	C₂²×C₃	—	10	4	no	—
484	C₂²×C₃	—	10	8	no	—
485	C₂²×C₃	—	20	32	no	—
486	C₂²×C₃	—	20	8	no	—
487	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
488	C₂²×C₃	#4144	1	4	yes	—
489	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
490	C₃×C₄	—	2	4	no	—
491	C₃×C₄	—	5	4	no	—
492	C₃×C₄	—	10	4	no	—
493	C₃×C₄	—	10	4	no	—
494	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
495	C₂×C₅	—	4	4	no	—
496	C₂×C₅	—	4	4	no	—
497	C₂×C₅	C₃×#535	1	4	yes	complemented
498	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
499	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
500	D₅	—	2	4	no	—
501	D₅	—	4	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	5	4	no	—
507	C₂³	—	5	2	no	—
508	C₂³	—	5	4	no	—
509	C₂³	—	10	16	no	—
510	C₂³	—	10	4	no	—
511	C₂³	—	10	4	no	—
512	C₂³	—	10	8	no	—
513	C₂³	—	20	16	no	—
514	C₂³	—	20	32	no	—
515	C₂³	C₂³×C₃×D₅	1	4	yes	—
516	C₂³	C₂³×C₃×D₅	1	4	yes	—
517	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
518	Q₈	—	10	8	no	—
519	D₄	—	2	8	no	—
520	D₄	—	2	8	no	—
521	D₄	—	4	16	no	—
522	D₄	—	10	16	no	—
523	D₄	—	10	16	no	—
524	D₄	—	10	8	no	—
525	D₄	—	20	16	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	5	4	no	—
528	C₂×C₄	—	5	2	no	—
529	C₂×C₄	—	5	16	no	—
530	C₂×C₄	—	5	4	no	—
531	C₂×C₄	—	5	4	no	—
532	C₂×C₄	—	10	16	no	—
533	C₂×C₄	—	10	4	no	—
534	C₂×C₄	—	10	4	no	—
535	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
536	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
537	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
538	C₂×C₃	—	4	4	no	—
539	C₂×C₃	—	4	4	no	—
540	C₂×C₃	—	10	4	no	—
541	C₂×C₃	—	20	4	no	—
542	C₂×C₃	#66049	1	4	yes	direct product factor
543	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
544	C₂×C₃	C₂×#4144	1	2	yes	—
545	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	4	8	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	5	4	no	—
553	C₂²	—	10	4	no	—
554	C₂²	—	10	8	no	—
555	C₂²	—	10	4	no	—
556	C₂²	—	10	8	no	—
557	C₂²	—	20	32	no	—
558	C₂²	—	20	8	no	—
559	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
560	C₂²	C₃×#4144	1	4	yes	—
561	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	5	4	no	—
564	C₄	—	10	4	no	—
565	C₄	—	10	4	no	—
566	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
567	C₃	C₂×#66049	1	1	yes	characteristic, direct product factor, Sylow
568	C₂	—	4	4	no	—
569	C₂	—	4	4	no	—
570	C₂	—	10	4	no	—
571	C₂	—	20	4	no	—
572	C₂	C₃×#66049	1	4	yes	direct product factor
573	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
574	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×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#711	C₂	semidirect
2. C₂²×C₃×D₄×D₅	C₂	semidirect
3. C₂×C₃×C₅×#127	C₂	semidirect
4. C₂×C₃×#4086	C₂	semidirect
5. C₂×C₃×#4085	C₂	semidirect
6. C₂×C₃×#4083	C₂	semidirect
7. C₂×C₃×#4082	C₂	semidirect
8. C₃×#66049	C₂	direct (N × H)
9. C₂×C₃×#4021	C₂	semidirect
10. C₂×C₃×#4018	C₂	semidirect
11. C₂×#66049	C₃	direct (N × H)
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
19. C₂³×C₃×Dic₅	C₂²	semidirect
21. C₂×C₃×#711	C₂²	semidirect
23. C₂×C₃×D₄×D₅	C₂²	semidirect
26. C₂²×C₃×Dic₁₀	C₂²	semidirect
27. C₃×C₅×#127	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
30. C₃×#4086	C₂²	semidirect
31. C₃×#4085	C₂²	semidirect
32. C₃×#4083	C₂²	semidirect
33. C₃×#4082	C₂²	semidirect
35. C₂×C₃×#685	C₂²	semidirect
36. C₂×C₃×#683	C₂²	semidirect
37. C₂×C₃×C₄×Dic₅	C₂²	semidirect
38. C₃×#4021	C₂²	semidirect
39. C₃×#4018	C₂²	semidirect
41. C₂²×#711	C₂×C₃	semidirect
42. C₂²×D₄×D₅	C₂×C₃	semidirect
43. C₂×C₅×#127	C₂×C₃	semidirect
44. C₂×#4086	C₂×C₃	semidirect
45. C₂×#4085	C₂×C₃	semidirect
46. C₂×#4083	C₂×C₃	semidirect
47. C₂×#4082	C₂×C₃	semidirect
48. #66049	C₂×C₃	direct (N × H)
49. C₂×#4021	C₂×C₃	semidirect
50. C₂×#4018	C₂×C₃	semidirect
62. C₂×C₃×C₅×D₄	C₂³	semidirect
63. C₂×C₃×C₅×D₄	C₂³	semidirect
71. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
76. C₂²×C₃×Dic₅	C₂³	semidirect
81. C₂×C₃×C₄×D₅	D₄	semidirect
84. C₂×C₃×Dic₁₀	C₂³	semidirect
85. C₃×C₄²×C₅	C₂³	semidirect
86. C₃×C₂²⋊Dic₅	C₂³	semidirect
88. C₃×#685	C₂³	semidirect
89. C₃×#683	C₂³	semidirect
90. C₃×C₄×Dic₅	C₂³	semidirect
95. C₂×C₃×#127	D₅	semidirect
103. C₂²×C₅×D₄	C₂²×C₃	semidirect
104. C₂²×C₅×D₄	C₂²×C₃	semidirect
107. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
108. C₂³×Dic₅	C₂²×C₃	semidirect
110. C₂×#711	C₂²×C₃	semidirect
112. C₂×D₄×D₅	C₂²×C₃	semidirect
115. C₂²×Dic₁₀	C₂²×C₃	semidirect
116. C₅×#127	C₂²×C₃	semidirect
117. C₂×C₄²×C₅	C₂²×C₃	semidirect
118. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
119. #4086	C₂²×C₃	semidirect
120. #4085	C₂²×C₃	semidirect
121. #4083	C₂²×C₃	semidirect
122. #4082	C₂²×C₃	semidirect
124. C₂×#685	C₂²×C₃	semidirect
125. C₂×#683	C₂²×C₃	semidirect
126. C₂×C₄×Dic₅	C₂²×C₃	semidirect
127. #4021	C₂²×C₃	semidirect
128. #4018	C₂²×C₃	semidirect
164. C₃×C₄×D₅	C₂×D₄	semidirect
177. C₂²×C₃×D₄	C₂×D₅	semidirect
178. C₂²×C₃×D₄	C₂×D₅	semidirect
182. C₃×#127	C₂×D₅	semidirect
193. C₂×C₃×C₄²	C₂×D₅	semidirect
205. C₂×C₅×D₄	C₂³×C₃	semidirect
206. C₂×C₅×D₄	C₂³×C₃	semidirect
214. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
219. C₂²×Dic₅	C₂³×C₃	semidirect
224. C₂×C₄×D₅	C₃×D₄	semidirect
227. C₂×Dic₁₀	C₂³×C₃	semidirect
228. C₄²×C₅	C₂³×C₃	semidirect
229. C₂²⋊Dic₅	C₂³×C₃	semidirect
231. #685	C₂³×C₃	semidirect
232. #683	C₂³×C₃	semidirect
233. C₄×Dic₅	C₂³×C₃	semidirect
238. C₂×#127	C₃×D₅	semidirect
288. C₂×C₃×D₄	C₂²×D₅	semidirect
289. C₂×C₃×D₄	C₂²×D₅	semidirect
304. C₃×C₄²	C₂²×D₅	semidirect
339. C₄×D₅	C₂×C₃×D₄	semidirect
352. C₂²×D₄	C₂×C₃×D₅	semidirect
353. C₂²×D₄	C₂×C₃×D₅	semidirect
357. #127	C₂×C₃×D₅	semidirect
368. C₂×C₄²	C₂×C₃×D₅	semidirect
371. C₂×C₃×C₅	#535	semidirect
456. C₂×D₄	C₂²×C₃×D₅	semidirect
457. C₂×D₄	C₂²×C₃×D₅	semidirect
472. C₄²	C₂²×C₃×D₅	semidirect
473. C₃×C₅	C₂×#535	semidirect
497. C₂×C₅	C₃×#535	semidirect
542. C₂×C₃	#66049	direct (N × H)
545. C₅	C₂×C₃×#535	semidirect
567. C₃	C₂×#66049	direct (N × H)
572. C₂	C₃×#66049	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×#711	2
C₂²×C₃×D₄×D₅	2
C₂×C₃×C₅×#127	2
C₂×C₃×#4086	2
C₂×C₃×#4085	2
C₂×C₃×#4083	2
C₂×C₃×#4082	2
C₃×#66049	2
C₂×C₃×#4021	2
C₂×C₃×#4018	2
C₂×#66049	3
C₂×C₃×#535	5

Subgroups — C2×C3×#66049 #14480363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66049 #14480363