Subgroups — C₃×#10601269 #14297465

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3952	C₂	1	2	yes	maximal
4	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64770	C₂	1	2	yes	maximal, complemented
6	#10601269	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×#685	C₄	1	1	yes	characteristic
11	C₂×C₃×#685	C₄	1	1	yes	characteristic
12	C₂×C₃×#683	C₄	1	1	yes	characteristic
13	C₂×C₃×#683	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	2	yes	—
16	C₃×#4018	—	2	2	no	—
17	C₃×#4018	—	2	2	no	—
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₃×#3952	—	2	4	no	—
20	C₃×C₄⋊#168	—	2	2	no	—
21	C₃×#1798	—	5	1	no	maximal, Hall
22	C₂×#4018	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×#3952	C₂×C₃	1	2	yes	—
25	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
26	#64770	C₂×C₃	1	2	yes	complemented
27	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	—	2	1	no	—
35	C₂×C₃×C₄×D₅	—	2	1	no	—
36	C₂×C₃×C₄×D₅	—	2	1	no	—
37	C₂×C₃×C₄×D₅	—	2	1	no	—
38	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
39	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₃×C₄²×C₅	D₄	1	2	yes	—
45	C₃×#685	—	2	2	no	—
46	C₃×#685	—	2	2	no	—
47	C₃×#683	—	2	2	no	—
48	C₃×#683	—	2	2	no	—
49	C₃×C₄×Dic₅	—	2	1	no	—
50	C₃×C₄×Dic₅	—	2	1	no	—
51	C₂×C₃×#168	—	2	2	no	—
52	C₂×C₃×#168	—	2	2	no	—
53	C₂×C₃×#168	—	2	2	no	—
54	C₂×C₃×#117	—	5	1	no	—
55	C₂×C₃×C₄⋊C₈	—	5	1	no	—
56	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
57	C₂×C₃×C₂²⋊C₈	—	5	2	no	—
58	C₃×#336	—	5	2	no	—
59	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
61	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂×#685	C₃×C₄	1	1	yes	characteristic
63	C₂×#685	C₃×C₄	1	1	yes	characteristic
64	C₂×#683	C₃×C₄	1	1	yes	characteristic
65	C₂×#683	C₃×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
67	C₂²×#168	C₂²×C₃	1	2	yes	—
68	#4018	—	2	2	no	—
69	#4018	—	2	2	no	—
70	C₅×C₄⋊C₈	—	2	2	no	—
71	#3952	—	2	4	no	—
72	C₄⋊#168	—	2	2	no	—
73	#1798	—	5	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₃×D₅	—	2	1	no	—
76	C₂²×C₃×D₅	—	2	1	no	—
77	C₂²×C₃×D₅	—	2	2	no	—
78	C₂²×C₃×D₅	—	2	2	no	—
79	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
90	C₂×C₃×Dic₅	—	2	1	no	—
91	C₂×C₃×Dic₅	—	2	1	no	—
92	C₂×C₃×Dic₅	—	2	1	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	2	no	—
95	C₂×C₃×Dic₅	—	2	2	no	—
96	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
97	C₃×C₄×D₅	—	2	2	no	—
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×C₄×D₅	—	2	2	no	—
100	C₃×C₄×D₅	—	2	2	no	—
101	C₃×C₅×C₈	—	4	2	no	—
102	C₃×#168	—	4	2	no	—
103	C₂³×C₃×C₄	—	5	1	no	—
104	C₂²×C₃×C₈	—	5	2	no	—
105	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
106	C₃×#117	—	10	2	no	—
107	C₃×#117	—	10	2	no	—
108	C₂×C₃×C₄⋊C₄	—	5	1	no	—
109	C₂×C₃×C₄⋊C₄	—	5	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
111	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
112	C₂×C₃×C₄²	—	5	1	no	—
113	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
114	C₃×C₄⋊C₈	—	2	2	no	—
115	C₃×C₄⋊C₈	—	10	2	no	—
116	C₃×C₂²⋊C₈	—	10	4	no	—
117	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂×C₄×D₅	—	2	1	no	—
125	C₂×C₄×D₅	—	2	1	no	—
126	C₂×C₄×D₅	—	2	1	no	—
127	C₂×C₄×D₅	—	2	1	no	—
128	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
129	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₄²×C₅	C₃×D₄	1	2	yes	—
134	C₄²×C₅	C₃×D₄	1	2	yes	—
135	#685	—	2	2	no	—
136	#685	—	2	2	no	—
137	#683	—	2	2	no	—
138	#683	—	2	2	no	—
139	C₄×Dic₅	—	2	1	no	—
140	C₄×Dic₅	—	2	1	no	—
141	C₂×#168	—	2	2	no	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	—	2	2	no	—
144	C₂×#117	—	5	1	no	—
145	C₂×C₄⋊C₈	—	5	1	no	—
146	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
147	C₂×C₂²⋊C₈	—	5	2	no	—
148	#336	—	5	2	no	—
149	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	#117	1	1	yes	characteristic
152	C₂²×C₃×C₅	#131	1	2	yes	—
153	C₂²×C₃×C₅	#131	1	2	yes	—
154	C₂×C₃×D₅	—	2	2	no	—
155	C₂×C₃×D₅	—	2	4	no	—
156	C₂×C₃×D₅	—	4	1	no	—
157	C₂×C₃×D₅	—	4	1	no	—
158	C₂×C₃×D₅	—	4	2	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	2	2	no	—
161	C₃×C₄×C₅	#121	1	1	yes	characteristic
162	C₃×C₄×C₅	#121	1	1	yes	characteristic
163	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
164	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
165	C₃×Dic₅	—	2	2	no	—
166	C₃×Dic₅	—	4	1	no	—
167	C₃×Dic₅	—	4	1	no	—
168	C₂⁴×C₃	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	2	no	—
171	C₂²×C₃×C₄	—	5	2	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	—	5	1	no	—
174	C₂²×C₃×C₄	—	10	1	no	—
175	C₂²×C₃×C₄	—	10	1	no	—
176	C₂²×C₃×C₄	—	10	1	no	—
177	C₂²×C₃×C₄	—	10	1	no	—
178	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	2	2	no	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₂×C₃×C₈	—	10	2	no	—
185	C₂×C₃×C₈	—	10	2	no	—
186	C₂×C₃×C₈	—	10	2	no	—
187	C₃×C₄⋊C₄	—	10	2	no	—
188	C₃×C₄⋊C₄	—	10	2	no	—
189	C₃×C₂²⋊C₄	—	10	2	no	—
190	C₃×C₂²⋊C₄	—	10	2	no	—
191	C₃×C₄²	—	10	1	no	—
192	C₃×C₄²	—	10	1	no	—
193	C₃×C₄²	D₂₀	1	2	yes	—
194	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
195	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
196	C₂²×D₅	—	2	1	no	—
197	C₂²×D₅	—	2	1	no	—
198	C₂²×D₅	—	2	2	no	—
199	C₂²×D₅	—	2	2	no	—
200	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
210	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
211	C₂×Dic₅	—	2	1	no	—
212	C₂×Dic₅	—	2	1	no	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	2	1	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	2	2	no	—
217	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
218	C₄×D₅	—	2	2	no	—
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	—	2	2	no	—
221	C₄×D₅	—	2	2	no	—
222	C₅×C₈	—	4	2	no	—
223	#168	—	4	2	no	—
224	C₂³×C₄	—	5	1	no	—
225	C₂²×C₈	—	5	2	no	—
226	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
227	#117	—	10	2	no	—
228	#117	—	10	2	no	—
229	C₂×C₄⋊C₄	—	5	1	no	—
230	C₂×C₄⋊C₄	—	5	1	no	—
231	C₂×C₂²⋊C₄	—	5	1	no	—
232	C₂×C₂²⋊C₄	—	5	1	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	10	2	no	—
237	C₂²⋊C₈	—	10	4	no	—
238	C₂×C₃×C₅	#380	1	1	yes	characteristic
239	C₂×C₃×C₅	#408	1	1	yes	characteristic
240	C₂×C₃×C₅	#408	1	1	yes	characteristic
241	C₂×C₃×C₅	#424	1	2	yes	—
242	C₂×C₃×C₅	#433	1	2	yes	—
243	C₃×D₅	—	4	2	no	—
244	C₂³×C₃	—	5	2	no	—
245	C₂³×C₃	—	10	1	no	—
246	C₂³×C₃	—	10	2	no	—
247	C₂³×C₃	—	10	2	no	—
248	C₂³×C₃	—	10	1	no	—
249	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	5	2	no	—
253	C₂×C₃×C₄	—	10	1	no	—
254	C₂×C₃×C₄	—	10	1	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	—	10	2	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	—	10	2	no	—
261	C₂×C₃×C₄	—	10	1	no	—
262	C₂×C₃×C₄	—	10	1	no	—
263	C₂×C₃×C₄	#685	1	2	yes	—
264	C₂×C₃×C₄	#685	1	2	yes	—
265	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
266	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
267	C₂×C₃×C₄	#711	1	1	yes	characteristic
268	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
269	C₂×C₃×C₄	#713	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
271	C₃×C₈	—	4	2	no	—
272	C₃×C₈	—	20	2	no	—
273	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×C₅	C₃×#117	1	1	yes	characteristic
276	C₂²×C₅	C₃×#131	1	2	yes	—
277	C₂²×C₅	C₃×#131	1	2	yes	—
278	C₂×D₅	—	2	2	no	—
279	C₂×D₅	—	2	4	no	—
280	C₂×D₅	—	4	1	no	—
281	C₂×D₅	—	4	1	no	—
282	C₂×D₅	—	4	2	no	—
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	C₃×#121	1	1	yes	characteristic
286	C₄×C₅	C₃×#121	1	1	yes	characteristic
287	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
288	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
289	Dic₅	—	2	2	no	—
290	Dic₅	—	4	1	no	—
291	Dic₅	—	4	1	no	—
292	C₂⁴	—	5	1	no	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	2	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	10	1	no	—
299	C₂²×C₄	—	10	1	no	—
300	C₂²×C₄	—	10	1	no	—
301	C₂²×C₄	—	10	1	no	—
302	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
303	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	10	2	no	—
309	C₂×C₈	—	10	2	no	—
310	C₂×C₈	—	10	2	no	—
311	C₄⋊C₄	—	10	2	no	—
312	C₄⋊C₄	—	10	2	no	—
313	C₂²⋊C₄	—	10	2	no	—
314	C₂²⋊C₄	—	10	2	no	—
315	C₄²	—	10	1	no	—
316	C₄²	—	10	1	no	—
317	C₄²	C₃×D₂₀	1	2	yes	—
318	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
319	C₃×C₅	#1798	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	—	10	4	no	—
321	C₂²×C₃	—	10	2	no	—
322	C₂²×C₃	—	20	2	no	—
323	C₂²×C₃	—	20	1	no	—
324	C₂²×C₃	—	20	1	no	—
325	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
326	C₂²×C₃	#4038	1	1	yes	characteristic
327	C₂²×C₃	#4047	1	2	yes	—
328	C₂²×C₃	#4053	1	2	yes	—
329	C₂²×C₃	C₂×#685	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	10	2	no	—
333	C₃×C₄	—	20	1	no	—
334	C₃×C₄	—	20	1	no	—
335	C₃×C₄	#4041	1	1	yes	characteristic
336	C₃×C₄	#4043	1	1	yes	characteristic
337	C₃×C₄	#4084	1	1	yes	characteristic
338	C₃×C₄	#4092	1	1	yes	characteristic
339	C₂×C₅	C₃×#380	1	1	yes	characteristic
340	C₂×C₅	C₃×#408	1	1	yes	characteristic
341	C₂×C₅	C₃×#408	1	1	yes	characteristic
342	C₂×C₅	C₃×#424	1	2	yes	—
343	C₂×C₅	C₃×#433	1	2	yes	—
344	D₅	—	4	2	no	—
345	C₂³	—	5	2	no	—
346	C₂³	—	10	1	no	—
347	C₂³	—	10	2	no	—
348	C₂³	—	10	2	no	—
349	C₂³	—	10	1	no	—
350	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	5	2	no	—
354	C₂×C₄	—	10	1	no	—
355	C₂×C₄	—	10	1	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	10	2	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	10	2	no	—
362	C₂×C₄	—	10	1	no	—
363	C₂×C₄	—	10	1	no	—
364	C₂×C₄	C₃×#685	1	2	yes	—
365	C₂×C₄	C₃×#685	1	2	yes	—
366	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
367	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
368	C₂×C₄	C₃×#711	1	1	yes	characteristic
369	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
370	C₂×C₄	C₃×#713	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
372	C₈	—	4	2	no	—
373	C₈	—	20	2	no	—
374	C₂×C₃	—	20	2	no	—
375	C₂×C₃	#65128	1	2	yes	—
376	C₂×C₃	#65129	1	2	yes	—
377	C₂×C₃	#65276	1	1	yes	characteristic
378	C₂×C₃	#65399	1	1	yes	characteristic
379	C₂×C₃	#65418	1	1	yes	characteristic
380	C₅	C₃×#1798	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	10	4	no	—
382	C₂²	—	10	2	no	—
383	C₂²	—	20	2	no	—
384	C₂²	—	20	1	no	—
385	C₂²	—	20	1	no	—
386	C₂²	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
387	C₂²	C₃×#4038	1	1	yes	characteristic
388	C₂²	C₃×#4047	1	2	yes	—
389	C₂²	C₃×#4053	1	2	yes	—
390	C₂²	C₂×C₃×#685	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	10	2	no	—
394	C₄	—	20	1	no	—
395	C₄	—	20	1	no	—
396	C₄	C₃×#4041	1	1	yes	characteristic
397	C₄	C₃×#4043	1	1	yes	characteristic
398	C₄	C₃×#4084	1	1	yes	characteristic
399	C₄	C₃×#4092	1	1	yes	characteristic
400	C₃	#10601269	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	20	2	no	—
402	C₂	C₃×#65128	1	2	yes	—
403	C₂	C₃×#65129	1	2	yes	—
404	C₂	C₃×#65276	1	1	yes	characteristic
405	C₂	C₃×#65399	1	1	yes	characteristic
406	C₂	C₃×#65418	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#1798
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₃×C₄⋊#168	C₂	semidirect
5. C₃×#64770	C₂	semidirect
6. #10601269	C₃	direct (N × H)
23. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
25. C₂×C₄⋊#168	C₂×C₃	semidirect
26. #64770	C₂×C₃	semidirect
56. C₂×C₃×C₄⋊C₈	D₅	semidirect
146. C₂×C₄⋊C₈	C₃×D₅	semidirect
319. C₃×C₅	#1798	semidirect
380. C₅	C₃×#1798	semidirect
400. C₃	#10601269	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×#4018	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3952	2
C₂×C₃×C₄⋊#168	2
C₃×#64770	2
#10601269	3
C₃×#1798	5

Subgroups — C3×#10601269 #14297465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601269 #14297465