Subgroups — C₂×C₃×#65012 #14431612

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4070	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65012	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65012	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
15	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
16	C₃×#4072	—	2	2	no	—
17	C₃×#4072	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
21	C₃×#4070	—	2	2	no	—
22	C₃×#4070	C₂²	1	4	yes	—
23	C₂×C₃×#683	—	2	1	no	—
24	C₂×C₃×C₄×Dic₅	—	2	1	no	—
25	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
26	C₃×#3950	C₂²	1	4	yes	complemented
27	C₃×#3949	C₂²	1	4	yes	complemented
28	C₃×#3948	C₂²	1	4	yes	complemented
29	C₃×#3948	C₂²	1	4	yes	complemented
30	C₂×C₃×#485	—	5	1	no	maximal, Hall
31	C₂×#4072	C₂×C₃	1	1	yes	characteristic
32	C₂×#4070	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
34	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3949	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#3948	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3948	C₂×C₃	1	1	yes	characteristic, complemented
38	#65012	C₂×C₃	1	8	yes	direct product factor
39	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	—	2	1	no	—
47	C₂²×C₃×Dic₅	—	2	1	no	—
48	C₂²×C₃×Dic₅	—	2	1	no	—
49	C₂²×C₃×Dic₅	—	2	1	no	—
50	C₂×C₃×Dic₁₀	—	2	2	no	—
51	C₂×C₃×Dic₁₀	—	2	2	no	—
52	C₂×C₃×Dic₁₀	—	2	1	no	—
53	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₂²⋊Dic₅	—	2	4	no	—
59	C₃×C₂²⋊Dic₅	—	2	4	no	—
60	C₃×C₄⋊Dic₅	—	2	1	no	—
61	C₃×C₄⋊Dic₅	—	2	1	no	—
62	C₃×C₄⋊Dic₅	—	2	1	no	—
63	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
64	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
65	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
66	C₃×#683	—	2	4	no	—
67	C₃×C₄×Dic₅	—	2	4	no	—
68	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
69	C₂×C₃×#117	—	5	1	no	—
70	C₃×#485	—	5	8	no	—
71	C₂×C₃×#107	—	5	1	no	—
72	C₂×C₃×#106	—	5	1	no	—
73	C₂×C₃×#103	—	5	1	no	—
74	C₂×C₃×#103	—	5	1	no	—
75	C₂×C₃×C₂²⋊C₈	D₅	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₅	—	2	1	no	—
81	C₂×C₂²⋊Dic₅	—	2	1	no	—
82	#4072	—	2	2	no	—
83	#4072	C₂²×C₃	1	4	yes	—
84	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
87	#4070	—	2	2	no	—
88	#4070	C₂²×C₃	1	4	yes	—
89	C₂×#683	—	2	1	no	—
90	C₂×C₄×Dic₅	—	2	1	no	—
91	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
92	#3950	C₂²×C₃	1	4	yes	complemented
93	#3949	C₂²×C₃	1	4	yes	complemented
94	#3948	C₂²×C₃	1	4	yes	complemented
95	#3948	C₂²×C₃	1	4	yes	complemented
96	C₂×#485	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	4	2	no	—
116	C₂×C₃×Dic₅	—	4	2	no	—
117	C₂×C₃×Dic₅	—	4	2	no	—
118	C₂×C₃×Dic₅	—	4	2	no	—
119	C₃×Dic₁₀	—	2	2	no	—
120	C₃×Dic₁₀	—	2	2	no	—
121	C₃×Dic₁₀	—	4	2	no	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₂²×C₃×Q₈	—	5	1	no	—
125	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
128	C₃×C₂²⋊Q₈	—	5	4	no	—
129	C₃×C₂²⋊Q₈	—	10	2	no	—
130	C₃×#117	—	5	4	no	—
131	C₃×#117	—	10	2	no	—
132	C₂×C₃×C₄⋊C₄	—	5	1	no	—
133	C₂×C₃×C₄⋊C₄	—	5	1	no	—
134	C₂×C₃×C₄⋊C₄	—	5	1	no	—
135	C₂×C₃×C₄⋊C₄	—	10	1	no	—
136	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
137	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
138	C₂×C₃×C₄²	—	10	1	no	—
139	C₃×#107	—	5	4	no	—
140	C₃×#106	—	5	4	no	—
141	C₃×#103	—	5	4	no	—
142	C₃×#103	—	5	4	no	—
143	C₃×C₂²⋊C₈	C₂×D₅	1	4	yes	—
144	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂²×Dic₅	—	2	1	no	—
152	C₂²×Dic₅	—	2	1	no	—
153	C₂²×Dic₅	—	2	1	no	—
154	C₂²×Dic₅	—	2	1	no	—
155	C₂×Dic₁₀	—	2	2	no	—
156	C₂×Dic₁₀	—	2	2	no	—
157	C₂×Dic₁₀	—	2	1	no	—
158	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
162	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
163	C₂²⋊Dic₅	—	2	4	no	—
164	C₂²⋊Dic₅	—	2	4	no	—
165	C₄⋊Dic₅	—	2	1	no	—
166	C₄⋊Dic₅	—	2	1	no	—
167	C₄⋊Dic₅	—	2	1	no	—
168	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
169	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
170	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
171	#683	—	2	4	no	—
172	C₄×Dic₅	—	2	4	no	—
173	C₂×C₂²⋊Q₈	—	5	1	no	—
174	C₂×#117	—	5	1	no	—
175	#485	—	5	8	no	—
176	C₂×#107	—	5	1	no	—
177	C₂×#106	—	5	1	no	—
178	C₂×#103	—	5	1	no	—
179	C₂×#103	—	5	1	no	—
180	C₂×C₂²⋊C₈	C₃×D₅	1	1	yes	characteristic
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	2	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	4	4	no	—
185	C₂²×C₃×C₅	#123	1	2	yes	—
186	C₂²×C₃×C₅	#135	1	2	yes	—
187	C₂²×C₃×C₅	#137	1	2	yes	—
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	#123	1	2	yes	—
191	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
193	C₃×Dic₅	—	4	2	no	—
194	C₃×Dic₅	—	4	2	no	—
195	C₃×Dic₅	—	4	2	no	—
196	C₃×Dic₅	—	4	2	no	—
197	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
198	C₂×C₃×Q₈	—	5	2	no	—
199	C₂×C₃×Q₈	—	10	1	no	—
200	C₂×C₃×Q₈	—	10	2	no	—
201	C₂×C₃×Q₈	—	10	2	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	10	1	no	—
205	C₂²×C₃×C₄	—	10	1	no	—
206	C₂²×C₃×C₄	—	10	1	no	—
207	C₂²×C₃×C₄	—	10	1	no	—
208	C₂²×C₃×C₄	D₂₀	1	2	yes	—
209	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	2	2	no	—
214	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
215	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
216	C₃×C₄⋊C₄	—	5	2	no	—
217	C₃×C₄⋊C₄	—	5	2	no	—
218	C₃×C₄⋊C₄	—	5	2	no	—
219	C₃×C₄⋊C₄	—	10	4	no	—
220	C₃×C₄⋊C₄	—	10	1	no	—
221	C₃×C₄⋊C₄	—	10	1	no	—
222	C₃×C₄⋊C₄	—	10	1	no	—
223	C₃×C₂²⋊C₄	—	10	4	no	—
224	C₃×C₂²⋊C₄	—	10	4	no	—
225	C₃×C₄²	—	10	4	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
230	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₃×#41	1	2	yes	—
238	C₂×C₄×C₅	C₃×#41	1	2	yes	—
239	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
240	C₂×Dic₅	—	2	2	no	—
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	4	2	no	—
245	C₂×Dic₅	—	4	2	no	—
246	C₂×Dic₅	—	4	2	no	—
247	C₂×Dic₅	—	4	2	no	—
248	Dic₁₀	—	2	2	no	—
249	Dic₁₀	—	2	2	no	—
250	Dic₁₀	—	4	2	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	2	2	no	—
253	C₂²×Q₈	—	5	1	no	—
254	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
255	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
256	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
257	C₂²⋊Q₈	—	5	4	no	—
258	C₂²⋊Q₈	—	10	2	no	—
259	#117	—	5	4	no	—
260	#117	—	10	2	no	—
261	C₂×C₄⋊C₄	—	5	1	no	—
262	C₂×C₄⋊C₄	—	5	1	no	—
263	C₂×C₄⋊C₄	—	5	1	no	—
264	C₂×C₄⋊C₄	—	10	1	no	—
265	C₂×C₂²⋊C₄	—	10	1	no	—
266	C₂×C₂²⋊C₄	—	10	1	no	—
267	C₂×C₄²	—	10	1	no	—
268	#107	—	5	4	no	—
269	#106	—	5	4	no	—
270	#103	—	5	4	no	—
271	#103	—	5	4	no	—
272	C₂²⋊C₈	C₂×C₃×D₅	1	4	yes	—
273	C₂×C₃×C₅	—	4	2	no	—
274	C₂×C₃×C₅	#485	1	4	yes	complemented
275	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	C₂×D₂₀	1	2	yes	—
282	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
283	C₃×Q₈	—	10	2	no	—
284	C₃×Q₈	—	10	2	no	—
285	C₃×Q₈	—	20	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	20	2	no	—
295	C₂×C₃×C₄	—	20	2	no	—
296	C₂×C₃×C₄	—	20	2	no	—
297	C₂×C₃×C₄	—	20	2	no	—
298	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
299	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
300	C₂×C₃×C₄	#711	1	2	yes	—
301	C₂×C₃×C₄	#711	1	2	yes	—
302	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	4	4	no	—
309	C₂²×C₅	C₃×#123	1	2	yes	—
310	C₂²×C₅	C₃×#135	1	2	yes	—
311	C₂²×C₅	C₃×#137	1	2	yes	—
312	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	C₃×#123	1	2	yes	—
315	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
316	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
317	Dic₅	—	4	2	no	—
318	Dic₅	—	4	2	no	—
319	Dic₅	—	4	2	no	—
320	Dic₅	—	4	2	no	—
321	C₂⁴	C₃×D₂₀	1	1	yes	characteristic
322	C₂×Q₈	—	5	2	no	—
323	C₂×Q₈	—	10	1	no	—
324	C₂×Q₈	—	10	2	no	—
325	C₂×Q₈	—	10	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	10	1	no	—
329	C₂²×C₄	—	10	1	no	—
330	C₂²×C₄	—	10	1	no	—
331	C₂²×C₄	—	10	1	no	—
332	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
333	C₂²×C₄	C₃×D₂₀	1	2	yes	—
334	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
335	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
339	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
340	C₄⋊C₄	—	5	2	no	—
341	C₄⋊C₄	—	5	2	no	—
342	C₄⋊C₄	—	5	2	no	—
343	C₄⋊C₄	—	10	1	no	—
344	C₄⋊C₄	—	10	1	no	—
345	C₄⋊C₄	—	10	1	no	—
346	C₄⋊C₄	—	10	4	no	—
347	C₂²⋊C₄	—	10	4	no	—
348	C₂²⋊C₄	—	10	4	no	—
349	C₄²	—	10	4	no	—
350	C₃×C₅	C₂×#485	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	#4032	1	2	yes	—
356	C₂²×C₃	#4050	1	2	yes	—
357	C₂²×C₃	#4055	1	2	yes	—
358	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	20	2	no	—
361	C₃×C₄	—	20	2	no	—
362	C₃×C₄	—	20	2	no	—
363	C₃×C₄	—	20	2	no	—
364	C₃×C₄	#4032	1	2	yes	—
365	C₃×C₄	C₂×#711	1	1	yes	characteristic
366	C₃×C₄	C₂×#711	1	1	yes	characteristic
367	C₂×C₅	—	4	2	no	—
368	C₂×C₅	C₃×#485	1	4	yes	complemented
369	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
370	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
371	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×C₃×D₂₀	1	2	yes	—
376	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
377	Q₈	—	10	2	no	—
378	Q₈	—	10	2	no	—
379	Q₈	—	20	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	20	2	no	—
389	C₂×C₄	—	20	2	no	—
390	C₂×C₄	—	20	2	no	—
391	C₂×C₄	—	20	2	no	—
392	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
393	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
394	C₂×C₄	C₃×#711	1	2	yes	—
395	C₂×C₄	C₃×#711	1	2	yes	—
396	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₂×C₃	—	4	2	no	—
400	C₂×C₃	#65012	1	4	yes	direct product factor
401	C₂×C₃	C₂×#4032	1	1	yes	characteristic
402	C₂×C₃	C₂×#4050	1	1	yes	characteristic
403	C₂×C₃	C₂×#4055	1	1	yes	characteristic
404	C₅	C₂×C₃×#485	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	C₃×#4032	1	2	yes	—
410	C₂²	C₃×#4050	1	2	yes	—
411	C₂²	C₃×#4055	1	2	yes	—
412	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	20	2	no	—
415	C₄	—	20	2	no	—
416	C₄	—	20	2	no	—
417	C₄	—	20	2	no	—
418	C₄	C₃×#4032	1	2	yes	—
419	C₄	C₂×C₃×#711	1	1	yes	characteristic
420	C₄	C₂×C₃×#711	1	1	yes	characteristic
421	C₃	C₂×#65012	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	4	2	no	—
423	C₂	C₃×#65012	1	4	yes	direct product factor
424	C₂	C₂×C₃×#4032	1	1	yes	characteristic
425	C₂	C₂×C₃×#4050	1	1	yes	characteristic
426	C₂	C₂×C₃×#4055	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
hypercenter	C₂×C₃×C₂²⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#485
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×#3950	C₂	semidirect
5. C₂×C₃×#3949	C₂	semidirect
6. C₂×C₃×#3948	C₂	semidirect
7. C₂×C₃×#3948	C₂	semidirect
8. C₃×#65012	C₂	direct (N × H)
9. C₂×#65012	C₃	direct (N × H)
26. C₃×#3950	C₂²	semidirect
27. C₃×#3949	C₂²	semidirect
28. C₃×#3948	C₂²	semidirect
29. C₃×#3948	C₂²	semidirect
34. C₂×#3950	C₂×C₃	semidirect
35. C₂×#3949	C₂×C₃	semidirect
36. C₂×#3948	C₂×C₃	semidirect
37. C₂×#3948	C₂×C₃	semidirect
38. #65012	C₂×C₃	direct (N × H)
92. #3950	C₂²×C₃	semidirect
93. #3949	C₂²×C₃	semidirect
94. #3948	C₂²×C₃	semidirect
95. #3948	C₂²×C₃	semidirect
274. C₂×C₃×C₅	#485	semidirect
350. C₃×C₅	C₂×#485	semidirect
368. C₂×C₅	C₃×#485	semidirect
400. C₂×C₃	#65012	direct (N × H)
404. C₅	C₂×C₃×#485	semidirect
421. C₃	C₂×#65012	direct (N × H)
423. C₂	C₃×#65012	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4072	2
C₂×C₃×#4070	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₃×#3950	2
C₂×C₃×#3949	2
C₂×C₃×#3948	2
C₃×#65012	2
C₂×#65012	3
C₂×C₃×#485	5

Subgroups — C2×C3×#65012 #14431612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65012 #14431612