Subgroups — C₃×#10600287 #14297817

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 464 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×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3937	C₂	1	2	yes	maximal
4	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64743	C₂	1	2	yes	maximal, complemented
6	#10600287	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#709	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
12	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
13	C₃×#4072	C₂²	1	1	yes	characteristic
14	C₂×C₃×#681	C₂²	1	2	yes	—
15	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic, complemented
16	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic, complemented
17	C₃×#4018	—	2	1	no	—
18	C₃×C₄²×D₅	—	2	1	no	—
19	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
20	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
21	C₃×C₅×#95	—	2	1	no	—
22	C₃×#3937	—	2	4	no	—
23	C₃×C₄⋊#168	—	2	1	no	—
24	C₃×C₄⋊#168	—	2	1	no	—
25	C₃×#1806	—	5	1	no	maximal, Hall
26	C₄×#709	C₂×C₃	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3937	C₂×C₃	1	2	yes	—
29	#65213	C₂×C₃	1	1	yes	characteristic, complemented
30	#64743	C₂×C₃	1	2	yes	complemented
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
36	C₃×#709	—	2	1	no	—
37	C₃×#709	—	2	1	no	—
38	C₃×#709	D₄	1	2	yes	—
39	C₃×#709	Q₈	1	2	yes	—
40	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	—	2	1	no	—
42	C₂×C₃×C₄×D₅	—	2	1	no	—
43	C₂×C₃×C₄×D₅	—	2	1	no	—
44	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	2	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₂²⋊Dic₅	—	2	1	no	—
53	C₃×#685	—	2	1	no	—
54	C₃×#685	—	2	1	no	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₃×#683	—	2	1	no	—
58	C₃×#683	—	2	1	no	—
59	C₃×C₄×Dic₅	—	2	1	no	—
60	C₃×C₄×Dic₅	—	2	1	no	—
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×#681	—	2	2	no	—
63	C₃×#681	—	2	2	no	—
64	C₂×C₃×#168	—	2	2	no	—
65	C₃×C₄×#41	—	5	1	no	—
66	C₃×#423	—	5	1	no	—
67	C₂×C₃×#104	—	5	2	no	—
68	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
69	C₃×#339	—	5	2	no	—
70	C₂×#709	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₄×C₂²⋊D₅	—	2	1	no	—
75	C₄×C₂²⋊D₅	—	2	1	no	—
76	#4072	C₂²×C₃	1	1	yes	characteristic
77	C₂×#681	C₂²×C₃	1	2	yes	—
78	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
79	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
80	#4018	—	2	1	no	—
81	C₄²×D₅	—	2	1	no	—
82	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
83	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
84	C₅×#95	—	2	1	no	—
85	#3937	—	2	4	no	—
86	C₄⋊#168	—	2	1	no	—
87	C₄⋊#168	—	2	1	no	—
88	#1806	—	5	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₃×C₂²⋊D₅	—	2	2	no	—
107	C₃×C₂²⋊D₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	1	no	—
109	C₂×C₃×Dic₅	—	2	1	no	—
110	C₂×C₃×Dic₅	—	2	1	no	—
111	C₃×D₂₀	—	2	1	no	—
112	C₃×D₂₀	C₄⋊C₄	1	2	yes	complemented
113	C₃×C₄×D₅	—	2	2	no	—
114	C₃×C₄×D₅	—	2	2	no	—
115	C₃×C₄×D₅	—	4	2	no	—
116	C₃×C₄×D₅	—	4	2	no	—
117	C₃×Dic₁₀	—	2	1	no	—
118	C₃×Dic₁₀	C₄⋊C₄	1	2	yes	complemented
119	C₃×#168	—	4	2	no	—
120	C₂×C₃×#41	—	5	1	no	—
121	C₂×C₃×M₁₆	—	5	2	no	—
122	C₃×C₄×Q₈	—	5	1	no	—
123	C₃×C₄×Q₈	—	5	1	no	—
124	C₃×C₄×D₄	—	5	1	no	—
125	C₃×C₄×D₄	—	5	1	no	—
126	C₃×C₄×D₄	—	10	1	no	—
127	C₃×C₄×D₄	—	10	1	no	—
128	C₃×#117	—	5	1	no	—
129	C₃×#117	—	10	1	no	—
130	C₂×C₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₃×C₄²	—	10	1	no	—
132	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
133	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
134	C₃×C₄⋊C₈	—	10	1	no	—
135	C₃×C₄⋊C₈	—	10	1	no	—
136	C₃×#104	—	10	4	no	—
137	C₃×#95	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	—	2	1	no	—
143	#709	—	2	1	no	—
144	#709	—	2	1	no	—
145	#709	C₃×D₄	1	2	yes	—
146	#709	C₃×Q₈	1	2	yes	—
147	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	—	2	1	no	—
150	C₂×C₄×D₅	—	2	1	no	—
151	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
156	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
157	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
159	C₂²⋊Dic₅	—	2	1	no	—
160	#685	—	2	1	no	—
161	#685	—	2	1	no	—
162	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
164	#683	—	2	1	no	—
165	#683	—	2	1	no	—
166	C₄×Dic₅	—	2	1	no	—
167	C₄×Dic₅	—	2	1	no	—
168	C₄×Dic₅	—	2	1	no	—
169	#681	—	2	2	no	—
170	#681	—	2	2	no	—
171	C₂×#168	—	2	2	no	—
172	C₄×#41	—	5	1	no	—
173	#423	—	5	1	no	—
174	C₂×#104	—	5	2	no	—
175	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
176	#339	—	5	2	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	—	2	1	no	—
179	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	#121	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₃×D₅	—	2	2	no	—
183	C₂×C₃×D₅	—	4	1	no	—
184	C₂×C₃×D₅	—	4	1	no	—
185	C₃×C₄×C₅	—	2	1	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	4	4	no	—
189	C₃×C₄×C₅	#104	1	2	yes	complemented
190	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	#117	1	1	yes	characteristic
192	C₃×C₄×C₅	#121	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	C₃×Dic₅	—	2	2	no	—
195	C₃×Dic₅	—	4	1	no	—
196	C₃×Dic₅	—	4	1	no	—
197	C₃×#41	—	5	2	no	—
198	C₃×#41	—	5	2	no	—
199	C₃×#41	—	10	1	no	—
200	C₃×#41	—	10	1	no	—
201	C₂×C₃×Q₈	—	5	1	no	—
202	C₂×C₃×D₄	—	5	1	no	—
203	C₂×C₃×D₄	—	10	1	no	—
204	C₂²×C₃×C₄	—	2	2	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	C₂²⋊D₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₃×M₁₆	—	10	2	no	—
212	C₃×M₁₆	—	10	2	no	—
213	C₂×C₃×C₈	—	10	2	no	—
214	C₃×C₄⋊C₄	—	2	4	no	—
215	C₃×C₄⋊C₄	—	5	1	no	—
216	C₃×C₄⋊C₄	—	5	1	no	—
217	C₃×C₄⋊C₄	—	10	1	no	—
218	C₃×C₄⋊C₄	—	10	1	no	—
219	C₃×C₂²⋊C₄	—	10	1	no	—
220	C₃×C₂²⋊C₄	—	10	1	no	—
221	C₃×C₂²⋊C₄	—	10	1	no	—
222	C₃×C₄²	—	2	2	no	—
223	C₃×C₄²	—	2	2	no	—
224	C₃×C₄²	—	10	1	no	—
225	C₃×C₄²	—	10	1	no	—
226	C₃×C₄²	—	10	1	no	—
227	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
228	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
229	C₃×C₄²	D₂₀	1	1	yes	characteristic
230	C₃×C₄²	D₂₀	1	1	yes	characteristic
231	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂²×D₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
246	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
247	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
248	C₂²⋊D₅	—	2	2	no	—
249	C₂²⋊D₅	—	2	2	no	—
250	C₂×Dic₅	—	2	1	no	—
251	C₂×Dic₅	—	2	1	no	—
252	C₂×Dic₅	—	2	1	no	—
253	D₂₀	—	2	1	no	—
254	D₂₀	C₃×C₄⋊C₄	1	2	yes	complemented
255	C₄×D₅	—	2	2	no	—
256	C₄×D₅	—	2	2	no	—
257	C₄×D₅	—	4	2	no	—
258	C₄×D₅	—	4	2	no	—
259	Dic₁₀	—	2	1	no	—
260	Dic₁₀	C₃×C₄⋊C₄	1	2	yes	complemented
261	#168	—	4	2	no	—
262	C₂×#41	—	5	1	no	—
263	C₂×M₁₆	—	5	2	no	—
264	C₄×Q₈	—	5	1	no	—
265	C₄×Q₈	—	5	1	no	—
266	C₄×D₄	—	5	1	no	—
267	C₄×D₄	—	5	1	no	—
268	C₄×D₄	—	10	1	no	—
269	C₄×D₄	—	10	1	no	—
270	#117	—	5	1	no	—
271	#117	—	10	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	10	1	no	—
274	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
275	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
276	C₄⋊C₈	—	10	1	no	—
277	C₄⋊C₈	—	10	1	no	—
278	#104	—	10	4	no	—
279	#95	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	#380	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
284	C₂×C₃×C₅	#421	1	1	yes	characteristic
285	C₃×D₅	—	4	2	no	—
286	C₂³×C₃	—	10	1	no	—
287	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
288	C₃×Q₈	—	5	2	no	—
289	C₃×Q₈	—	10	1	no	—
290	C₃×D₄	—	5	2	no	—
291	C₃×D₄	—	10	2	no	—
292	C₃×D₄	—	10	2	no	—
293	C₃×D₄	—	10	1	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	4	1	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	—	10	1	no	—
300	C₂×C₃×C₄	—	10	2	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	10	1	no	—
303	C₂×C₃×C₄	—	10	1	no	—
304	C₂×C₃×C₄	—	20	2	no	—
305	C₂×C₃×C₄	—	20	2	no	—
306	C₂×C₃×C₄	#685	1	1	yes	characteristic
307	C₂×C₃×C₄	#685	1	1	yes	characteristic
308	C₂×C₃×C₄	#685	1	1	yes	characteristic
309	C₂×C₃×C₄	#685	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
312	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
313	C₂×C₃×C₄	#711	1	1	yes	characteristic
314	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
315	C₂×C₃×C₄	#713	1	1	yes	characteristic
316	C₃×C₈	—	20	2	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×C₅	C₃×#121	1	1	yes	characteristic
321	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
322	C₂×D₅	—	2	2	no	—
323	C₂×D₅	—	4	1	no	—
324	C₂×D₅	—	4	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	4	4	no	—
329	C₄×C₅	C₃×#104	1	2	yes	complemented
330	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
331	C₄×C₅	C₃×#117	1	1	yes	characteristic
332	C₄×C₅	C₃×#121	1	1	yes	characteristic
333	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
334	Dic₅	—	2	2	no	—
335	Dic₅	—	4	1	no	—
336	Dic₅	—	4	1	no	—
337	#41	—	5	2	no	—
338	#41	—	5	2	no	—
339	#41	—	10	1	no	—
340	#41	—	10	1	no	—
341	C₂×Q₈	—	5	1	no	—
342	C₂×D₄	—	5	1	no	—
343	C₂×D₄	—	10	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	10	1	no	—
346	C₂²×C₄	—	10	1	no	—
347	C₂²×C₄	—	10	1	no	—
348	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
349	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
351	M₁₆	—	10	2	no	—
352	M₁₆	—	10	2	no	—
353	C₂×C₈	—	10	2	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	5	1	no	—
356	C₄⋊C₄	—	5	1	no	—
357	C₄⋊C₄	—	10	1	no	—
358	C₄⋊C₄	—	10	1	no	—
359	C₂²⋊C₄	—	10	1	no	—
360	C₂²⋊C₄	—	10	1	no	—
361	C₂²⋊C₄	—	10	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	10	1	no	—
365	C₄²	—	10	1	no	—
366	C₄²	—	10	1	no	—
367	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
368	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
369	C₄²	C₃×D₂₀	1	1	yes	characteristic
370	C₄²	C₃×D₂₀	1	1	yes	characteristic
371	C₃×C₅	#1806	1	1	yes	characteristic, complemented, Hall
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	10	2	no	—
375	C₂²×C₃	—	20	1	no	—
376	C₂²×C₃	—	20	1	no	—
377	C₂²×C₃	C₂×#685	1	1	yes	characteristic
378	C₂²×C₃	#4084	1	1	yes	characteristic
379	C₂²×C₃	#4092	1	1	yes	characteristic
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	4	4	no	—
384	C₃×C₄	—	10	2	no	—
385	C₃×C₄	—	20	1	no	—
386	C₃×C₄	—	20	1	no	—
387	C₃×C₄	#3937	1	2	yes	complemented
388	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
389	C₃×C₄	#4038	1	1	yes	characteristic
390	C₃×C₄	#4041	1	1	yes	characteristic
391	C₃×C₄	#4043	1	1	yes	characteristic
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	C₃×#380	1	1	yes	characteristic
395	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
396	C₂×C₅	C₃×#421	1	1	yes	characteristic
397	D₅	—	4	2	no	—
398	C₂³	—	10	1	no	—
399	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
400	Q₈	—	5	2	no	—
401	Q₈	—	10	1	no	—
402	D₄	—	5	2	no	—
403	D₄	—	10	2	no	—
404	D₄	—	10	2	no	—
405	D₄	—	10	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	10	1	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	10	2	no	—
414	C₂×C₄	—	10	1	no	—
415	C₂×C₄	—	10	1	no	—
416	C₂×C₄	—	20	2	no	—
417	C₂×C₄	—	20	2	no	—
418	C₂×C₄	C₃×#685	1	1	yes	characteristic
419	C₂×C₄	C₃×#685	1	1	yes	characteristic
420	C₂×C₄	C₃×#685	1	1	yes	characteristic
421	C₂×C₄	C₃×#685	1	1	yes	characteristic
422	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
423	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
424	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
425	C₂×C₄	C₃×#711	1	1	yes	characteristic
426	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
427	C₂×C₄	C₃×#713	1	1	yes	characteristic
428	C₈	—	20	2	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	20	2	no	—
432	C₂×C₃	C₂×#3937	1	1	yes	characteristic
433	C₂×C₃	#65276	1	1	yes	characteristic
434	C₂×C₃	#65294	1	1	yes	characteristic
435	C₅	C₃×#1806	1	1	yes	characteristic, complemented, Sylow
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	10	2	no	—
439	C₂²	—	20	1	no	—
440	C₂²	—	20	1	no	—
441	C₂²	C₂×C₃×#685	1	1	yes	characteristic
442	C₂²	C₃×#4084	1	1	yes	characteristic
443	C₂²	C₃×#4092	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	10	2	no	—
449	C₄	—	20	1	no	—
450	C₄	—	20	1	no	—
451	C₄	C₃×#3937	1	2	yes	complemented
452	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
453	C₄	C₃×#4038	1	1	yes	characteristic
454	C₄	C₃×#4041	1	1	yes	characteristic
455	C₄	C₃×#4043	1	1	yes	characteristic
456	C₃	#10600287	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	20	2	no	—
460	C₂	C₂×C₃×#3937	1	1	yes	characteristic
461	C₂	C₃×#65276	1	1	yes	characteristic
462	C₂	C₃×#65294	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#1806
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×#65213	C₂	semidirect
5. C₃×#64743	C₂	semidirect
6. #10600287	C₃	direct (N × H)
15. C₃×C₄×D₂₀	C₄	semidirect
16. C₃×C₄×D₂₀	C₄	semidirect
19. C₃×C₄×Dic₁₀	C₄	semidirect
20. C₃×C₄×Dic₁₀	C₄	semidirect
27. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
29. #65213	C₂×C₃	semidirect
30. #64743	C₂×C₃	semidirect
68. C₃×C₄×C₄⋊C₄	D₅	semidirect
78. C₄×D₂₀	C₃×C₄	semidirect
79. C₄×D₂₀	C₃×C₄	semidirect
82. C₄×Dic₁₀	C₃×C₄	semidirect
83. C₄×Dic₁₀	C₃×C₄	semidirect
112. C₃×D₂₀	C₄⋊C₄	semidirect
118. C₃×Dic₁₀	C₄⋊C₄	semidirect
175. C₄×C₄⋊C₄	C₃×D₅	semidirect
189. C₃×C₄×C₅	#104	semidirect
254. D₂₀	C₃×C₄⋊C₄	semidirect
260. Dic₁₀	C₃×C₄⋊C₄	semidirect
329. C₄×C₅	C₃×#104	semidirect
371. C₃×C₅	#1806	semidirect
387. C₃×C₄	#3937	semidirect
435. C₅	C₃×#1806	semidirect
451. C₄	C₃×#3937	semidirect
456. C₃	#10600287	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×C₄×C₅×C₄⋊C₄	2
C₂×C₃×#3937	2
C₃×#65213	2
C₃×#64743	2
#10600287	3
C₃×#1806	5

Subgroups — C3×#10600287 #14297817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600287 #14297817