Subgroups — C₂×C₃×#65982 #14480468

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 640 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
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4081	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65982	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4042	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4034	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4032	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4031	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4024	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65982	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
20	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#711	—	2	8	no	—
22	C₂×C₃×#711	C₂²	1	8	yes	—
23	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₁₀	—	2	8	no	—
25	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
26	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
27	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
28	C₂²×C₃×Dic₁₀	C₂²	1	8	yes	complemented
29	C₃×C₅×#123	C₂²	1	8	yes	complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
35	C₃×#4081	C₂²	1	8	yes	complemented
36	C₃×#4075	C₂²	1	8	yes	complemented
37	C₂×C₃×#685	C₂²	1	2	yes	—
38	C₂×C₃×#685	C₂²	1	2	yes	—
39	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
40	C₂×C₃×#683	C₂²	1	2	yes	—
41	C₂×C₃×#683	C₂²	1	2	yes	—
42	C₂×C₃×#683	C₂²	1	2	yes	—
43	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
44	C₃×#4042	C₂²	1	16	yes	complemented
45	C₃×#4034	C₂²	1	16	yes	complemented
46	C₃×#4032	C₂²	1	8	yes	complemented
47	C₃×#4031	C₂²	1	16	yes	complemented
48	C₃×#4024	C₂²	1	16	yes	complemented
49	C₃×#4023	C₂²	1	8	yes	complemented
50	C₂×C₃×#536	—	5	1	no	maximal, Hall
51	C₂²×#711	C₂×C₃	1	1	yes	characteristic
52	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4081	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4075	C₂×C₃	1	1	yes	characteristic, complemented
56	#65982	C₂×C₃	1	16	yes	direct product factor
57	C₂×#4042	C₂×C₃	1	2	yes	complemented
58	C₂×#4034	C₂×C₃	1	2	yes	complemented
59	C₂×#4032	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4031	C₂×C₃	1	2	yes	complemented
61	C₂×#4024	C₂×C₃	1	2	yes	complemented
62	C₂×#4023	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	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	—	2	4	no	—
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
74	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
75	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
76	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
77	C₂²×C₃×Dic₅	—	2	4	no	—
78	C₂²×C₃×Dic₅	—	2	4	no	—
79	C₂²×C₃×Dic₅	D₄	1	8	yes	—
80	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
81	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
82	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
83	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
85	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
88	C₃×#711	—	2	32	no	—
89	C₂×C₃×C₄×D₅	—	2	4	no	—
90	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
91	C₂×C₃×Dic₁₀	—	2	8	no	—
92	C₂×C₃×Dic₁₀	—	2	8	no	—
93	C₂×C₃×Dic₁₀	—	2	32	no	—
94	C₂×C₃×Dic₁₀	—	2	4	no	—
95	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
96	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
97	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
98	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
99	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
102	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
103	C₃×#685	C₂³	1	8	yes	—
104	C₃×#685	C₂³	1	8	yes	—
105	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
106	C₃×#683	C₂³	1	8	yes	—
107	C₃×#683	C₂³	1	8	yes	—
108	C₃×#683	C₂³	1	8	yes	—
109	C₃×C₄×Dic₅	C₂³	1	8	yes	—
110	C₂²×C₃×#41	—	5	1	no	—
111	C₂³×C₃×Q₈	—	5	1	no	—
112	C₃×#536	—	5	16	no	—
113	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
114	C₂×C₃×#124	—	5	2	no	—
115	C₂×C₃×#123	—	5	1	no	—
116	C₂×C₃×#123	—	5	1	no	—
117	C₂×C₃×#123	—	5	1	no	—
118	C₂×C₃×#123	D₅	1	1	yes	characteristic, complemented
119	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
120	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
121	C₂×C₃×#117	—	5	1	no	—
122	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
126	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
127	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
128	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×#711	—	2	8	no	—
130	C₂×#711	C₂²×C₃	1	8	yes	—
131	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
132	C₂²×Dic₁₀	—	2	8	no	—
133	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
134	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
135	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
136	C₂²×Dic₁₀	C₂²×C₃	1	8	yes	complemented
137	C₅×#123	C₂²×C₃	1	8	yes	complemented
138	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
141	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
143	#4081	C₂²×C₃	1	8	yes	complemented
144	#4075	C₂²×C₃	1	8	yes	complemented
145	C₂×#685	C₂²×C₃	1	2	yes	—
146	C₂×#685	C₂²×C₃	1	2	yes	—
147	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
148	C₂×#683	C₂²×C₃	1	2	yes	—
149	C₂×#683	C₂²×C₃	1	2	yes	—
150	C₂×#683	C₂²×C₃	1	2	yes	—
151	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
152	#4042	C₂²×C₃	1	16	yes	complemented
153	#4034	C₂²×C₃	1	16	yes	complemented
154	#4032	C₂²×C₃	1	8	yes	complemented
155	#4031	C₂²×C₃	1	16	yes	complemented
156	#4024	C₂²×C₃	1	16	yes	complemented
157	#4023	C₂²×C₃	1	8	yes	complemented
158	C₂×#536	—	5	1	no	Sylow
159	C₂³×C₃×C₅	—	2	4	no	—
160	C₂³×C₃×C₅	—	2	2	no	—
161	C₂³×C₃×C₅	—	2	4	no	—
162	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
163	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
164	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
165	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
166	C₂²×C₃×D₅	—	2	2	no	—
167	C₂²×C₃×D₅	—	2	4	no	—
168	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
169	C₃×C₅×D₄	—	2	8	no	—
170	C₂×C₃×C₄×C₅	—	2	8	no	—
171	C₂×C₃×C₄×C₅	—	2	4	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	4	no	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
177	C₃×C₂²⋊D₅	—	2	8	no	—
178	C₃×C₂²⋊D₅	—	2	8	no	—
179	C₂×C₃×Dic₅	—	2	8	no	—
180	C₂×C₃×Dic₅	—	2	4	no	—
181	C₂×C₃×Dic₅	—	2	2	no	—
182	C₂×C₃×Dic₅	—	2	4	no	—
183	C₂×C₃×Dic₅	—	2	8	no	—
184	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
185	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
186	C₂×C₃×Dic₅	C₂×D₄	1	16	yes	—
187	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
188	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
189	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
190	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
191	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
192	C₃×C₄×D₅	—	2	8	no	—
193	C₃×Dic₁₀	—	2	16	no	—
194	C₃×Dic₁₀	—	2	16	no	—
195	C₃×Dic₁₀	—	2	8	no	—
196	C₂×C₃×#41	—	5	8	no	—
197	C₂×C₃×#41	—	10	8	no	—
198	C₂²×C₃×Q₈	—	5	2	no	—
199	C₂²×C₃×Q₈	—	5	2	no	—
200	C₂²×C₃×Q₈	—	5	8	no	—
201	C₂²×C₃×Q₈	—	5	1	no	—
202	C₂²×C₃×Q₈	—	10	8	no	—
203	C₂²×C₃×D₄	—	5	1	no	—
204	C₂²×C₃×D₄	—	5	1	no	—
205	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
206	C₂³×C₃×C₄	—	5	1	no	—
207	C₂³×C₃×C₄	—	5	1	no	—
208	C₂³×C₃×C₄	—	5	1	no	—
209	C₂³×C₃×C₄	—	5	1	no	—
210	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
211	C₃×C₄⋊Q₈	—	5	16	no	—
212	C₃×#124	—	5	16	no	—
213	C₃×#123	—	5	8	no	—
214	C₃×#123	—	5	8	no	—
215	C₃×#123	—	5	8	no	—
216	C₃×#123	C₂×D₅	1	8	yes	complemented
217	C₃×C₂²⋊Q₈	—	5	16	no	—
218	C₃×C₂²⋊Q₈	—	5	16	no	—
219	C₃×#117	—	5	8	no	—
220	C₂×C₃×C₄⋊C₄	—	5	2	no	—
221	C₂×C₃×C₄⋊C₄	—	5	2	no	—
222	C₂×C₃×C₄⋊C₄	—	5	2	no	—
223	C₂×C₃×C₄⋊C₄	—	5	2	no	—
224	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
226	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
227	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
228	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
229	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
231	C₂×C₃×C₄²	—	5	2	no	—
232	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₅×D₄	—	2	4	no	—
236	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
237	C₂²×C₄×C₅	—	2	4	no	—
238	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
239	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
240	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
242	C₂×C₂²⋊D₅	—	2	4	no	—
243	C₂×C₂²⋊D₅	—	2	4	no	—
244	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
245	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
246	C₂²×Dic₅	—	2	4	no	—
247	C₂²×Dic₅	—	2	4	no	—
248	C₂²×Dic₅	C₃×D₄	1	8	yes	—
249	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
250	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
251	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
252	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
253	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
254	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
255	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
256	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
257	#711	—	2	32	no	—
258	C₂×C₄×D₅	—	2	4	no	—
259	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
260	C₂×Dic₁₀	—	2	8	no	—
261	C₂×Dic₁₀	—	2	8	no	—
262	C₂×Dic₁₀	—	2	32	no	—
263	C₂×Dic₁₀	—	2	4	no	—
264	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
265	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
266	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
267	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
268	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
269	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
270	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
271	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
272	#685	C₂³×C₃	1	8	yes	—
273	#685	C₂³×C₃	1	8	yes	—
274	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
275	#683	C₂³×C₃	1	8	yes	—
276	#683	C₂³×C₃	1	8	yes	—
277	#683	C₂³×C₃	1	8	yes	—
278	C₄×Dic₅	C₂³×C₃	1	8	yes	—
279	C₂²×#41	—	5	1	no	—
280	C₂³×Q₈	—	5	1	no	—
281	#536	—	5	16	no	—
282	C₂×C₄⋊Q₈	—	5	2	no	—
283	C₂×#124	—	5	2	no	—
284	C₂×#123	—	5	1	no	—
285	C₂×#123	—	5	1	no	—
286	C₂×#123	—	5	1	no	—
287	C₂×#123	C₃×D₅	1	1	yes	characteristic, complemented
288	C₂×C₂²⋊Q₈	—	5	2	no	—
289	C₂×C₂²⋊Q₈	—	5	2	no	—
290	C₂×#117	—	5	1	no	—
291	C₂²×C₃×C₅	—	2	8	no	—
292	C₂²×C₃×C₅	—	2	4	no	—
293	C₂²×C₃×C₅	—	2	2	no	—
294	C₂²×C₃×C₅	—	2	4	no	—
295	C₂²×C₃×C₅	—	4	4	no	—
296	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
297	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
298	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
299	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
300	C₂×C₃×D₅	—	2	2	no	—
301	C₂×C₃×D₅	—	2	4	no	—
302	C₂×C₃×D₅	—	4	4	no	—
303	C₃×C₄×C₅	—	2	4	no	—
304	C₃×C₄×C₅	—	2	2	no	—
305	C₃×C₄×C₅	—	2	4	no	—
306	C₃×Dic₅	—	2	4	no	—
307	C₃×Dic₅	—	2	2	no	—
308	C₃×Dic₅	—	2	4	no	—
309	C₃×Dic₅	C₂²×D₄	1	4	yes	—
310	C₃×Dic₅	C₂²×D₄	1	4	yes	—
311	C₂⁴×C₃	—	5	1	no	—
312	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
313	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
314	C₃×#41	—	10	32	no	—
315	C₂×C₃×Q₈	—	5	8	no	—
316	C₂×C₃×Q₈	—	5	8	no	—
317	C₂×C₃×Q₈	—	5	4	no	—
318	C₂×C₃×Q₈	—	10	8	no	—
319	C₂×C₃×Q₈	—	10	8	no	—
320	C₂×C₃×Q₈	—	10	32	no	—
321	C₂×C₃×Q₈	—	10	4	no	—
322	C₂×C₃×D₄	—	2	4	no	—
323	C₂×C₃×D₄	—	5	4	no	—
324	C₂×C₃×D₄	—	5	4	no	—
325	C₂×C₃×D₄	—	10	4	no	—
326	C₂×C₃×D₄	—	10	4	no	—
327	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
328	C₂²×C₃×C₄	—	2	4	no	—
329	C₂²×C₃×C₄	—	5	8	no	—
330	C₂²×C₃×C₄	—	5	4	no	—
331	C₂²×C₃×C₄	—	5	1	no	—
332	C₂²×C₃×C₄	—	5	1	no	—
333	C₂²×C₃×C₄	—	5	4	no	—
334	C₂²×C₃×C₄	—	5	4	no	—
335	C₂²×C₃×C₄	—	5	2	no	—
336	C₂²×C₃×C₄	—	5	2	no	—
337	C₂²×C₃×C₄	—	5	1	no	—
338	C₂²×C₃×C₄	—	5	4	no	—
339	C₂²×C₃×C₄	—	10	4	no	—
340	C₂²×C₃×C₄	—	10	4	no	—
341	C₂²×C₃×C₄	—	10	4	no	—
342	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
343	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
344	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
345	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
346	C₃×C₄⋊C₄	—	5	8	no	—
347	C₃×C₄⋊C₄	—	5	8	no	—
348	C₃×C₄⋊C₄	—	5	8	no	—
349	C₃×C₄⋊C₄	—	5	8	no	—
350	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
351	C₃×C₂²⋊C₄	—	5	4	no	—
352	C₃×C₂²⋊C₄	—	5	8	no	—
353	C₃×C₂²⋊C₄	—	5	8	no	—
354	C₃×C₂²⋊C₄	—	5	8	no	—
355	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
356	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
357	C₃×C₄²	—	5	8	no	—
358	C₂³×C₅	—	2	4	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	—	2	4	no	—
361	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
362	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
363	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
364	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
365	C₂²×D₅	—	2	2	no	—
366	C₂²×D₅	—	2	4	no	—
367	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
368	C₅×D₄	—	2	8	no	—
369	C₂×C₄×C₅	—	2	8	no	—
370	C₂×C₄×C₅	—	2	4	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	4	no	—
373	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
374	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
375	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
376	C₂²⋊D₅	—	2	8	no	—
377	C₂²⋊D₅	—	2	8	no	—
378	C₂×Dic₅	—	2	8	no	—
379	C₂×Dic₅	—	2	4	no	—
380	C₂×Dic₅	—	2	2	no	—
381	C₂×Dic₅	—	2	4	no	—
382	C₂×Dic₅	—	2	8	no	—
383	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
384	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
385	C₂×Dic₅	C₂×C₃×D₄	1	16	yes	—
386	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
387	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
388	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
389	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
390	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
391	C₄×D₅	—	2	8	no	—
392	Dic₁₀	—	2	16	no	—
393	Dic₁₀	—	2	16	no	—
394	Dic₁₀	—	2	8	no	—
395	C₂×#41	—	5	8	no	—
396	C₂×#41	—	10	8	no	—
397	C₂²×Q₈	—	5	2	no	—
398	C₂²×Q₈	—	5	2	no	—
399	C₂²×Q₈	—	5	1	no	—
400	C₂²×Q₈	—	5	8	no	—
401	C₂²×Q₈	—	10	8	no	—
402	C₂²×D₄	—	5	1	no	—
403	C₂²×D₄	—	5	1	no	—
404	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
405	C₂³×C₄	—	5	1	no	—
406	C₂³×C₄	—	5	1	no	—
407	C₂³×C₄	—	5	1	no	—
408	C₂³×C₄	—	5	1	no	—
409	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
410	C₄⋊Q₈	—	5	16	no	—
411	#124	—	5	16	no	—
412	#123	—	5	8	no	—
413	#123	—	5	8	no	—
414	#123	—	5	8	no	—
415	#123	C₂×C₃×D₅	1	8	yes	complemented
416	C₂²⋊Q₈	—	5	16	no	—
417	C₂²⋊Q₈	—	5	16	no	—
418	#117	—	5	8	no	—
419	C₂×C₄⋊C₄	—	5	2	no	—
420	C₂×C₄⋊C₄	—	5	2	no	—
421	C₂×C₄⋊C₄	—	5	2	no	—
422	C₂×C₄⋊C₄	—	5	2	no	—
423	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
424	C₂×C₂²⋊C₄	—	5	1	no	—
425	C₂×C₂²⋊C₄	—	5	2	no	—
426	C₂×C₂²⋊C₄	—	5	2	no	—
427	C₂×C₂²⋊C₄	—	5	2	no	—
428	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
430	C₂×C₄²	—	5	2	no	—
431	C₂×C₃×C₅	—	2	4	no	—
432	C₂×C₃×C₅	—	4	2	no	—
433	C₂×C₃×C₅	#536	1	4	yes	complemented
434	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
435	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
436	C₃×D₅	—	4	2	no	—
437	C₂³×C₃	—	2	4	no	—
438	C₂³×C₃	—	2	2	no	—
439	C₂³×C₃	—	2	4	no	—
440	C₂³×C₃	—	5	2	no	—
441	C₂³×C₃	—	10	2	no	—
442	C₂³×C₃	—	10	4	no	—
443	C₂³×C₃	D₄×D₅	1	4	yes	—
444	C₂³×C₃	C₂³×D₅	1	2	yes	—
445	C₂³×C₃	C₂³×D₅	1	2	yes	—
446	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
447	C₃×Q₈	—	10	16	no	—
448	C₃×Q₈	—	10	16	no	—
449	C₃×Q₈	—	10	8	no	—
450	C₃×D₄	—	2	8	no	—
451	C₃×D₄	—	10	8	no	—
452	C₃×D₄	—	10	8	no	—
453	C₂×C₃×C₄	—	2	8	no	—
454	C₂×C₃×C₄	—	2	4	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	4	no	—
457	C₂×C₃×C₄	—	5	4	no	—
458	C₂×C₃×C₄	—	5	4	no	—
459	C₂×C₃×C₄	—	5	16	no	—
460	C₂×C₃×C₄	—	5	2	no	—
461	C₂×C₃×C₄	—	5	2	no	—
462	C₂×C₃×C₄	—	5	4	no	—
463	C₂×C₃×C₄	—	5	4	no	—
464	C₂×C₃×C₄	—	5	2	no	—
465	C₂×C₃×C₄	—	10	8	no	—
466	C₂×C₃×C₄	—	10	8	no	—
467	C₂×C₃×C₄	—	10	2	no	—
468	C₂×C₃×C₄	—	10	8	no	—
469	C₂×C₃×C₄	—	10	4	no	—
470	C₂×C₃×C₄	—	10	4	no	—
471	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
472	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
473	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
474	C₂²×C₅	—	2	4	no	—
475	C₂²×C₅	—	2	8	no	—
476	C₂²×C₅	—	2	2	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	4	4	no	—
479	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
480	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
481	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
482	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
483	C₂×D₅	—	2	2	no	—
484	C₂×D₅	—	2	4	no	—
485	C₂×D₅	—	4	4	no	—
486	C₄×C₅	—	2	4	no	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	2	4	no	—
489	Dic₅	—	2	4	no	—
490	Dic₅	—	2	2	no	—
491	Dic₅	—	2	4	no	—
492	Dic₅	C₂²×C₃×D₄	1	4	yes	—
493	Dic₅	C₂²×C₃×D₄	1	4	yes	—
494	C₂⁴	—	5	1	no	—
495	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
496	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
497	#41	—	10	32	no	—
498	C₂×Q₈	—	5	8	no	—
499	C₂×Q₈	—	5	8	no	—
500	C₂×Q₈	—	5	4	no	—
501	C₂×Q₈	—	10	8	no	—
502	C₂×Q₈	—	10	8	no	—
503	C₂×Q₈	—	10	32	no	—
504	C₂×Q₈	—	10	4	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	5	4	no	—
507	C₂×D₄	—	5	4	no	—
508	C₂×D₄	—	10	4	no	—
509	C₂×D₄	—	10	4	no	—
510	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	5	8	no	—
513	C₂²×C₄	—	5	1	no	—
514	C₂²×C₄	—	5	1	no	—
515	C₂²×C₄	—	5	4	no	—
516	C₂²×C₄	—	5	2	no	—
517	C₂²×C₄	—	5	2	no	—
518	C₂²×C₄	—	5	1	no	—
519	C₂²×C₄	—	5	4	no	—
520	C₂²×C₄	—	5	4	no	—
521	C₂²×C₄	—	5	4	no	—
522	C₂²×C₄	—	10	4	no	—
523	C₂²×C₄	—	10	4	no	—
524	C₂²×C₄	—	10	4	no	—
525	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
526	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
527	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
529	C₄⋊C₄	—	5	8	no	—
530	C₄⋊C₄	—	5	8	no	—
531	C₄⋊C₄	—	5	8	no	—
532	C₄⋊C₄	—	5	8	no	—
533	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
534	C₂²⋊C₄	—	5	4	no	—
535	C₂²⋊C₄	—	5	8	no	—
536	C₂²⋊C₄	—	5	8	no	—
537	C₂²⋊C₄	—	5	8	no	—
538	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
539	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
540	C₄²	—	5	8	no	—
541	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
542	C₂²×C₃	—	2	8	no	—
543	C₂²×C₃	—	2	4	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	4	no	—
546	C₂²×C₃	—	4	4	no	—
547	C₂²×C₃	—	10	2	no	—
548	C₂²×C₃	—	10	4	no	—
549	C₂²×C₃	—	20	4	no	—
550	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
551	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
552	C₂²×C₃	#4150	1	4	yes	—
553	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	2	2	no	—
556	C₃×C₄	—	2	4	no	—
557	C₃×C₄	—	5	4	no	—
558	C₃×C₄	—	5	4	no	—
559	C₃×C₄	—	10	2	no	—
560	C₃×C₄	—	10	4	no	—
561	C₃×C₄	—	10	4	no	—
562	C₂×C₅	—	2	4	no	—
563	C₂×C₅	—	4	2	no	—
564	C₂×C₅	C₃×#536	1	4	yes	complemented
565	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
566	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
567	D₅	—	4	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	5	2	no	—
572	C₂³	—	10	2	no	—
573	C₂³	—	10	4	no	—
574	C₂³	C₃×D₄×D₅	1	4	yes	—
575	C₂³	C₂³×C₃×D₅	1	2	yes	—
576	C₂³	C₂³×C₃×D₅	1	2	yes	—
577	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
578	Q₈	—	10	16	no	—
579	Q₈	—	10	16	no	—
580	Q₈	—	10	8	no	—
581	D₄	—	2	8	no	—
582	D₄	—	10	8	no	—
583	D₄	—	10	8	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	5	4	no	—
589	C₂×C₄	—	5	4	no	—
590	C₂×C₄	—	5	16	no	—
591	C₂×C₄	—	5	2	no	—
592	C₂×C₄	—	5	2	no	—
593	C₂×C₄	—	5	4	no	—
594	C₂×C₄	—	5	4	no	—
595	C₂×C₄	—	5	2	no	—
596	C₂×C₄	—	10	8	no	—
597	C₂×C₄	—	10	8	no	—
598	C₂×C₄	—	10	2	no	—
599	C₂×C₄	—	10	8	no	—
600	C₂×C₄	—	10	4	no	—
601	C₂×C₄	—	10	4	no	—
602	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
603	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
604	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
605	C₂×C₃	—	2	4	no	—
606	C₂×C₃	—	4	2	no	—
607	C₂×C₃	—	20	2	no	—
608	C₂×C₃	#65982	1	4	yes	direct product factor
609	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
610	C₂×C₃	C₂×#4150	1	2	yes	—
611	C₅	C₂×C₃×#536	1	1	yes	characteristic, complemented, Sylow
612	C₂²	—	2	4	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	10	2	no	—
618	C₂²	—	10	4	no	—
619	C₂²	—	20	4	no	—
620	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
621	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
622	C₂²	C₃×#4150	1	4	yes	—
623	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	5	4	no	—
628	C₄	—	5	4	no	—
629	C₄	—	10	2	no	—
630	C₄	—	10	4	no	—
631	C₄	—	10	4	no	—
632	C₃	C₂×#65982	1	1	yes	characteristic, direct product factor, Sylow
633	C₂	—	2	4	no	—
634	C₂	—	4	2	no	—
635	C₂	—	20	2	no	—
636	C₂	C₃×#65982	1	4	yes	direct product factor
637	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
638	C₂	C₂×C₃×#4150	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
prime radical	C₂²×C₃×#711	C₂
hypercenter	C₂×C₃×#123	D₅
hypocenter	C₅	C₂×C₃×#536
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
2. C₂³×C₃×Dic₁₀	C₂	semidirect
3. C₂×C₃×C₅×#123	C₂	semidirect
4. C₂×C₃×#4081	C₂	semidirect
5. C₂×C₃×#4075	C₂	semidirect
6. C₃×#65982	C₂	direct (N × H)
7. C₂×C₃×#4042	C₂	semidirect
8. C₂×C₃×#4034	C₂	semidirect
9. C₂×C₃×#4032	C₂	semidirect
10. C₂×C₃×#4031	C₂	semidirect
11. C₂×C₃×#4024	C₂	semidirect
12. C₂×C₃×#4023	C₂	semidirect
13. C₂×#65982	C₃	direct (N × H)
28. C₂²×C₃×Dic₁₀	C₂²	semidirect
29. C₃×C₅×#123	C₂²	semidirect
35. C₃×#4081	C₂²	semidirect
36. C₃×#4075	C₂²	semidirect
44. C₃×#4042	C₂²	semidirect
45. C₃×#4034	C₂²	semidirect
46. C₃×#4032	C₂²	semidirect
47. C₃×#4031	C₂²	semidirect
48. C₃×#4024	C₂²	semidirect
49. C₃×#4023	C₂²	semidirect
52. C₂³×Dic₁₀	C₂×C₃	semidirect
53. C₂×C₅×#123	C₂×C₃	semidirect
54. C₂×#4081	C₂×C₃	semidirect
55. C₂×#4075	C₂×C₃	semidirect
56. #65982	C₂×C₃	direct (N × H)
57. C₂×#4042	C₂×C₃	semidirect
58. C₂×#4034	C₂×C₃	semidirect
59. C₂×#4032	C₂×C₃	semidirect
60. C₂×#4031	C₂×C₃	semidirect
61. C₂×#4024	C₂×C₃	semidirect
62. C₂×#4023	C₂×C₃	semidirect
118. C₂×C₃×#123	D₅	semidirect
136. C₂²×Dic₁₀	C₂²×C₃	semidirect
137. C₅×#123	C₂²×C₃	semidirect
143. #4081	C₂²×C₃	semidirect
144. #4075	C₂²×C₃	semidirect
152. #4042	C₂²×C₃	semidirect
153. #4034	C₂²×C₃	semidirect
154. #4032	C₂²×C₃	semidirect
155. #4031	C₂²×C₃	semidirect
156. #4024	C₂²×C₃	semidirect
157. #4023	C₂²×C₃	semidirect
216. C₃×#123	C₂×D₅	semidirect
287. C₂×#123	C₃×D₅	semidirect
415. #123	C₂×C₃×D₅	semidirect
433. C₂×C₃×C₅	#536	semidirect
541. C₃×C₅	C₂×#536	semidirect
564. C₂×C₅	C₃×#536	semidirect
608. C₂×C₃	#65982	direct (N × H)
611. C₅	C₂×C₃×#536	semidirect
632. C₃	C₂×#65982	direct (N × H)
636. C₂	C₃×#65982	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
C₂³×C₃×Dic₁₀	2
C₂×C₃×C₅×#123	2
C₂×C₃×#4081	2
C₂×C₃×#4075	2
C₃×#65982	2
C₂×C₃×#4042	2
C₂×C₃×#4034	2
C₂×C₃×#4032	2
C₂×C₃×#4031	2
C₂×C₃×#4024	2
C₂×C₃×#4023	2
C₂×#65982	3
C₂×C₃×#536	5

Subgroups — C2×C3×#65982 #14480468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65982 #14480468