Subgroups — C₃×#10610756 #14430232

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65402	C₂	1	2	yes	maximal
5	C₃×#65395	C₂	1	2	yes	maximal, complemented
6	C₃×#65140	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65139	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65136	C₂	1	2	yes	maximal, complemented
9	C₃×#65135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65118	C₂	1	2	yes	maximal, complemented
12	#10610756	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
17	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
18	C₃×#4072	C₂²	1	1	yes	characteristic
19	C₃×#4072	C₂²	1	2	yes	—
20	C₃×#4070	—	2	1	no	—
21	C₃×#4070	—	2	1	no	—
22	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
23	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
24	C₃×#4018	—	2	1	no	—
25	C₃×C₄²×D₅	—	2	1	no	—
26	C₃×#4016	C₂²	1	2	yes	—
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	—	2	1	no	—
30	C₃×C₄×Dic₁₀	—	2	1	no	—
31	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
32	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×#3953	C₂²	1	2	yes	—
37	C₃×#3953	C₂²	1	2	yes	—
38	C₃×#3950	C₂²	1	2	yes	—
39	C₃×#3950	C₂²	1	2	yes	—
40	C₃×#3949	C₂²	1	2	yes	—
41	C₃×#3949	C₂²	1	2	yes	—
42	C₃×#3948	C₂²	1	2	yes	—
43	C₃×#3948	C₂²	1	2	yes	—
44	C₃×#3076	—	5	1	no	maximal, Hall
45	C₄×#709	C₂×C₃	1	1	yes	characteristic
46	#65804	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
48	#65402	C₂×C₃	1	2	yes	—
49	#65395	C₂×C₃	1	2	yes	complemented
50	#65140	C₂×C₃	1	1	yes	characteristic, complemented
51	#65139	C₂×C₃	1	1	yes	characteristic, complemented
52	#65136	C₂×C₃	1	2	yes	complemented
53	#65135	C₂×C₃	1	1	yes	characteristic, complemented
54	#65131	C₂×C₃	1	1	yes	characteristic, complemented
55	#65118	C₂×C₃	1	2	yes	complemented
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₃×#709	—	2	2	no	—
61	C₃×#709	Q₈	1	4	yes	complemented
62	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	—	2	1	no	—
64	C₂×C₃×C₄×D₅	—	2	1	no	—
65	C₂×C₃×C₄×D₅	—	2	1	no	—
66	C₂×C₃×Dic₁₀	—	2	1	no	—
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₂²⋊Dic₅	—	2	2	no	—
77	C₃×C₂²⋊Dic₅	—	2	1	no	—
78	C₃×#685	—	2	1	no	—
79	C₃×#685	—	2	1	no	—
80	C₃×C₄⋊Dic₅	—	2	1	no	—
81	C₃×C₄⋊Dic₅	—	2	1	no	—
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
84	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
86	C₃×#683	—	2	2	no	—
87	C₃×#683	—	2	2	no	—
88	C₃×#683	—	2	1	no	—
89	C₃×#683	—	2	1	no	—
90	C₃×C₄×Dic₅	—	2	2	no	—
91	C₃×C₄×Dic₅	—	2	1	no	—
92	C₃×C₄×Dic₅	—	2	1	no	—
93	C₃×C₄×Dic₅	—	2	1	no	—
94	C₃×#533	—	5	1	no	—
95	C₃×C₄×#41	—	5	1	no	—
96	C₃×#479	—	5	2	no	—
97	C₃×#478	—	5	2	no	—
98	C₃×#477	—	5	1	no	—
99	C₃×#476	—	5	1	no	—
100	C₃×#475	—	5	1	no	—
101	C₃×#474	—	5	1	no	—
102	C₃×#427	—	5	2	no	—
103	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
104	C₃×#416	—	5	2	no	—
105	C₂×#709	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
107	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
108	C₄×C₂²⋊D₅	—	2	1	no	—
109	C₄×C₂²⋊D₅	—	2	1	no	—
110	#4072	C₂²×C₃	1	2	yes	—
111	#4072	C₂²×C₃	1	1	yes	characteristic
112	#4070	—	2	1	no	—
113	#4070	—	2	1	no	—
114	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
115	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	#4018	—	2	1	no	—
117	C₄²×D₅	—	2	1	no	—
118	#4016	C₂²×C₃	1	2	yes	—
119	#4015	C₂²×C₃	1	1	yes	characteristic
120	#4015	C₂²×C₃	1	1	yes	characteristic
121	C₄×Dic₁₀	—	2	1	no	—
122	C₄×Dic₁₀	—	2	1	no	—
123	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
124	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
125	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
126	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
128	#3953	C₂²×C₃	1	2	yes	—
129	#3953	C₂²×C₃	1	2	yes	—
130	#3950	C₂²×C₃	1	2	yes	—
131	#3950	C₂²×C₃	1	2	yes	—
132	#3949	C₂²×C₃	1	2	yes	—
133	#3949	C₂²×C₃	1	2	yes	—
134	#3948	C₂²×C₃	1	2	yes	—
135	#3948	C₂²×C₃	1	2	yes	—
136	#3076	—	5	1	no	Sylow
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	4	1	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₂²⋊D₅	—	2	4	no	—
150	C₂×C₃×Dic₅	—	2	1	no	—
151	C₂×C₃×Dic₅	—	2	1	no	—
152	C₂×C₃×Dic₅	—	2	1	no	—
153	C₂×C₃×Dic₅	—	2	2	no	—
154	C₂×C₃×Dic₅	—	2	2	no	—
155	C₃×D₂₀	—	2	1	no	—
156	C₃×D₂₀	C₂×Q₈	1	2	yes	—
157	C₃×C₄×D₅	—	2	4	no	—
158	C₃×C₄×D₅	—	4	2	no	—
159	C₃×C₄×D₅	—	4	2	no	—
160	C₃×Dic₁₀	—	2	1	no	—
161	C₃×Dic₁₀	—	4	2	no	—
162	C₃×Dic₁₀	—	4	2	no	—
163	C₃×Dic₁₀	C₂×Q₈	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
168	C₃×C₄⋊Q₈	—	5	1	no	—
169	C₃×C₄⋊Q₈	—	5	1	no	—
170	C₃×#125	—	5	2	no	—
171	C₃×C₂²⋊Q₈	—	10	1	no	—
172	C₃×C₂²⋊Q₈	—	10	1	no	—
173	C₃×C₄×Q₈	—	5	1	no	—
174	C₃×C₄×Q₈	—	5	1	no	—
175	C₃×C₄×Q₈	—	10	1	no	—
176	C₃×C₄×Q₈	—	10	1	no	—
177	C₃×C₄×D₄	—	5	1	no	—
178	C₃×C₄×D₄	—	5	1	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×C₄×D₄	—	10	1	no	—
181	C₃×#117	—	5	2	no	—
182	C₃×#117	—	5	1	no	—
183	C₃×#117	—	10	1	no	—
184	C₂×C₃×C₄²	—	10	1	no	—
185	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
186	C₃×#107	—	5	2	no	—
187	C₃×#107	—	5	2	no	—
188	C₃×#106	—	5	2	no	—
189	C₃×#106	—	5	2	no	—
190	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
191	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
193	C₃×#103	—	5	2	no	—
194	C₃×#103	—	5	2	no	—
195	C₃×#102	—	5	2	no	—
196	C₃×#102	—	5	2	no	—
197	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	—	2	1	no	—
201	#709	—	2	2	no	—
202	#709	C₃×Q₈	1	4	yes	complemented
203	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₄×D₅	—	2	1	no	—
205	C₂×C₄×D₅	—	2	1	no	—
206	C₂×C₄×D₅	—	2	1	no	—
207	C₂×Dic₁₀	—	2	1	no	—
208	C₂×Dic₁₀	—	2	1	no	—
209	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	—	2	4	no	—
211	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
214	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
215	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₂²⋊Dic₅	—	2	2	no	—
218	C₂²⋊Dic₅	—	2	1	no	—
219	#685	—	2	1	no	—
220	#685	—	2	1	no	—
221	C₄⋊Dic₅	—	2	1	no	—
222	C₄⋊Dic₅	—	2	1	no	—
223	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
224	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
225	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
226	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
227	#683	—	2	2	no	—
228	#683	—	2	2	no	—
229	#683	—	2	1	no	—
230	#683	—	2	1	no	—
231	C₄×Dic₅	—	2	2	no	—
232	C₄×Dic₅	—	2	1	no	—
233	C₄×Dic₅	—	2	1	no	—
234	C₄×Dic₅	—	2	1	no	—
235	#533	—	5	1	no	—
236	C₄×#41	—	5	1	no	—
237	#479	—	5	2	no	—
238	#478	—	5	2	no	—
239	#477	—	5	1	no	—
240	#476	—	5	1	no	—
241	#475	—	5	1	no	—
242	#474	—	5	1	no	—
243	#427	—	5	2	no	—
244	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
245	#416	—	5	2	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₃×D₅	—	2	2	no	—
251	C₂×C₃×D₅	—	4	1	no	—
252	C₂×C₃×D₅	—	4	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
257	C₃×C₄×C₅	#135	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₃×Dic₅	—	2	2	no	—
261	C₃×Dic₅	—	4	2	no	—
262	C₃×Dic₅	—	4	1	no	—
263	C₃×Dic₅	—	4	2	no	—
264	C₃×Dic₅	—	4	1	no	—
265	C₃×#41	—	5	4	no	—
266	C₃×#41	—	10	2	no	—
267	C₂×C₃×Q₈	—	5	1	no	—
268	C₂×C₃×Q₈	—	10	1	no	—
269	C₂×C₃×Q₈	—	10	1	no	—
270	C₂×C₃×D₄	—	5	1	no	—
271	C₂×C₃×D₄	—	10	1	no	—
272	C₂²×C₃×C₄	—	10	1	no	—
273	C₂²×C₃×C₄	—	10	1	no	—
274	C₂²×C₃×C₄	—	10	1	no	—
275	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
276	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
278	C₂×C₃×C₈	—	2	4	no	—
279	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
280	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
281	C₃×C₄⋊C₄	—	5	2	no	—
282	C₃×C₄⋊C₄	—	5	2	no	—
283	C₃×C₄⋊C₄	—	5	1	no	—
284	C₃×C₄⋊C₄	—	5	1	no	—
285	C₃×C₄⋊C₄	—	10	1	no	—
286	C₃×C₄⋊C₄	—	10	1	no	—
287	C₃×C₄⋊C₄	—	10	2	no	—
288	C₃×C₄⋊C₄	—	10	2	no	—
289	C₃×C₄⋊C₄	—	10	1	no	—
290	C₃×C₄⋊C₄	—	10	1	no	—
291	C₃×C₂²⋊C₄	—	10	1	no	—
292	C₃×C₂²⋊C₄	—	10	2	no	—
293	C₃×C₂²⋊C₄	—	10	1	no	—
294	C₃×C₂²⋊C₄	—	10	1	no	—
295	C₃×C₄²	—	10	1	no	—
296	C₃×C₄²	—	10	1	no	—
297	C₃×C₄²	—	10	1	no	—
298	C₃×C₄²	—	10	2	no	—
299	C₃×C₄²	D₂₀	1	1	yes	characteristic
300	C₃×C₄²	D₂₀	1	1	yes	characteristic
301	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
302	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂²×D₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
313	C₂×C₄×C₅	C₃×#41	1	2	yes	—
314	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
315	C₂²⋊D₅	—	2	4	no	—
316	C₂×Dic₅	—	2	1	no	—
317	C₂×Dic₅	—	2	1	no	—
318	C₂×Dic₅	—	2	1	no	—
319	C₂×Dic₅	—	2	2	no	—
320	C₂×Dic₅	—	2	2	no	—
321	D₂₀	—	2	1	no	—
322	D₂₀	C₂×C₃×Q₈	1	2	yes	—
323	C₄×D₅	—	2	4	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	2	no	—
326	Dic₁₀	—	2	1	no	—
327	Dic₁₀	—	4	2	no	—
328	Dic₁₀	—	4	2	no	—
329	Dic₁₀	C₂×C₃×Q₈	1	2	yes	—
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₂×#41	—	5	1	no	—
333	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
334	C₄⋊Q₈	—	5	1	no	—
335	C₄⋊Q₈	—	5	1	no	—
336	#125	—	5	2	no	—
337	C₂²⋊Q₈	—	10	1	no	—
338	C₂²⋊Q₈	—	10	1	no	—
339	C₄×Q₈	—	5	1	no	—
340	C₄×Q₈	—	5	1	no	—
341	C₄×Q₈	—	10	1	no	—
342	C₄×Q₈	—	10	1	no	—
343	C₄×D₄	—	5	1	no	—
344	C₄×D₄	—	5	1	no	—
345	C₄×D₄	—	10	1	no	—
346	C₄×D₄	—	10	1	no	—
347	#117	—	5	1	no	—
348	#117	—	5	2	no	—
349	#117	—	10	1	no	—
350	C₂×C₄²	—	10	1	no	—
351	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
352	#107	—	5	2	no	—
353	#107	—	5	2	no	—
354	#106	—	5	2	no	—
355	#106	—	5	2	no	—
356	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
357	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
358	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
359	#103	—	5	2	no	—
360	#103	—	5	2	no	—
361	#102	—	5	2	no	—
362	#102	—	5	2	no	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	C₃×D₅	—	4	2	no	—
368	C₂³×C₃	—	10	1	no	—
369	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
370	C₃×Q₈	—	5	2	no	—
371	C₃×Q₈	—	10	1	no	—
372	C₃×Q₈	—	20	2	no	—
373	C₃×Q₈	—	20	2	no	—
374	C₃×D₄	—	5	2	no	—
375	C₃×D₄	—	10	4	no	—
376	C₃×D₄	—	10	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	4	1	no	—
379	C₂×C₃×C₄	—	10	1	no	—
380	C₂×C₃×C₄	—	10	4	no	—
381	C₂×C₃×C₄	—	10	1	no	—
382	C₂×C₃×C₄	—	10	1	no	—
383	C₂×C₃×C₄	—	10	2	no	—
384	C₂×C₃×C₄	—	10	2	no	—
385	C₂×C₃×C₄	—	20	2	no	—
386	C₂×C₃×C₄	—	20	2	no	—
387	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
392	C₂×C₃×C₄	#711	1	2	yes	—
393	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
394	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	2	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
400	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₂×D₅	—	2	2	no	—
402	C₂×D₅	—	4	1	no	—
403	C₂×D₅	—	4	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
408	C₄×C₅	C₃×#135	1	2	yes	—
409	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
410	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
411	Dic₅	—	2	2	no	—
412	Dic₅	—	4	2	no	—
413	Dic₅	—	4	1	no	—
414	Dic₅	—	4	2	no	—
415	Dic₅	—	4	1	no	—
416	#41	—	5	4	no	—
417	#41	—	10	2	no	—
418	C₂×Q₈	—	5	1	no	—
419	C₂×Q₈	—	10	1	no	—
420	C₂×Q₈	—	10	1	no	—
421	C₂×D₄	—	5	1	no	—
422	C₂×D₄	—	10	1	no	—
423	C₂²×C₄	—	10	1	no	—
424	C₂²×C₄	—	10	1	no	—
425	C₂²×C₄	—	10	1	no	—
426	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
427	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
431	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
432	C₄⋊C₄	—	5	2	no	—
433	C₄⋊C₄	—	5	2	no	—
434	C₄⋊C₄	—	5	1	no	—
435	C₄⋊C₄	—	5	1	no	—
436	C₄⋊C₄	—	10	1	no	—
437	C₄⋊C₄	—	10	1	no	—
438	C₄⋊C₄	—	10	2	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₄⋊C₄	—	10	1	no	—
441	C₄⋊C₄	—	10	1	no	—
442	C₂²⋊C₄	—	10	1	no	—
443	C₂²⋊C₄	—	10	2	no	—
444	C₂²⋊C₄	—	10	1	no	—
445	C₂²⋊C₄	—	10	1	no	—
446	C₄²	—	10	1	no	—
447	C₄²	—	10	1	no	—
448	C₄²	—	10	1	no	—
449	C₄²	—	10	2	no	—
450	C₄²	C₃×D₂₀	1	1	yes	characteristic
451	C₄²	C₃×D₂₀	1	1	yes	characteristic
452	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
453	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	10	2	no	—
458	C₂²×C₃	—	20	1	no	—
459	C₂²×C₃	—	20	1	no	—
460	C₂²×C₃	#4043	1	2	yes	—
461	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	10	2	no	—
466	C₃×C₄	—	20	1	no	—
467	C₃×C₄	—	20	2	no	—
468	C₃×C₄	—	20	1	no	—
469	C₃×C₄	—	20	2	no	—
470	C₃×C₄	#4043	1	2	yes	—
471	C₃×C₄	#4050	1	2	yes	—
472	C₃×C₄	C₂×#711	1	1	yes	characteristic
473	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
477	C₂×C₅	C₃×#575	1	1	yes	characteristic
478	D₅	—	4	2	no	—
479	C₂³	—	10	1	no	—
480	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
481	Q₈	—	5	2	no	—
482	Q₈	—	10	1	no	—
483	Q₈	—	20	2	no	—
484	Q₈	—	20	2	no	—
485	D₄	—	5	2	no	—
486	D₄	—	10	4	no	—
487	D₄	—	10	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	10	1	no	—
491	C₂×C₄	—	10	4	no	—
492	C₂×C₄	—	10	1	no	—
493	C₂×C₄	—	10	1	no	—
494	C₂×C₄	—	10	2	no	—
495	C₂×C₄	—	10	2	no	—
496	C₂×C₄	—	20	2	no	—
497	C₂×C₄	—	20	2	no	—
498	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
499	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
500	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
501	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
502	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
503	C₂×C₄	C₃×#711	1	2	yes	—
504	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
505	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	20	2	no	—
510	C₂×C₃	C₂×#4043	1	1	yes	characteristic
511	C₂×C₃	C₂×#4050	1	1	yes	characteristic
512	C₂×C₃	#66082	1	1	yes	characteristic
513	C₅	C₃×#3076	1	1	yes	characteristic, complemented, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	10	2	no	—
517	C₂²	—	20	1	no	—
518	C₂²	—	20	1	no	—
519	C₂²	C₃×#4043	1	2	yes	—
520	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	10	2	no	—
525	C₄	—	20	1	no	—
526	C₄	—	20	2	no	—
527	C₄	—	20	1	no	—
528	C₄	—	20	2	no	—
529	C₄	C₃×#4043	1	2	yes	—
530	C₄	C₃×#4050	1	2	yes	—
531	C₄	C₂×C₃×#711	1	1	yes	characteristic
532	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
533	C₃	#10610756	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	20	2	no	—
536	C₂	C₂×C₃×#4043	1	1	yes	characteristic
537	C₂	C₂×C₃×#4050	1	1	yes	characteristic
538	C₂	C₃×#66082	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#3076
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65804	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₃×#65395	C₂	semidirect
6. C₃×#65140	C₂	semidirect
7. C₃×#65139	C₂	semidirect
8. C₃×#65136	C₂	semidirect
9. C₃×#65135	C₂	semidirect
10. C₃×#65131	C₂	semidirect
11. C₃×#65118	C₂	semidirect
12. #10610756	C₃	direct (N × H)
46. #65804	C₂×C₃	semidirect
47. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
49. #65395	C₂×C₃	semidirect
50. #65140	C₂×C₃	semidirect
51. #65139	C₂×C₃	semidirect
52. #65136	C₂×C₃	semidirect
53. #65135	C₂×C₃	semidirect
54. #65131	C₂×C₃	semidirect
55. #65118	C₂×C₃	semidirect
61. C₃×#709	Q₈	semidirect
103. C₂×C₃×C₄⋊C₈	D₅	semidirect
202. #709	C₃×Q₈	semidirect
244. C₂×C₄⋊C₈	C₃×D₅	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	C₃×#3076	semidirect
533. C₃	#10610756	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#709	2
C₃×#65804	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×#65402	2
C₃×#65395	2
C₃×#65140	2
C₃×#65139	2
C₃×#65136	2
C₃×#65135	2
C₃×#65131	2
C₃×#65118	2
#10610756	3
C₃×#3076	5

Subgroups — C3×#10610756 #14430232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610756 #14430232