Subgroups — C₃×#10601423 #14297900

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65276	C₂	1	2	yes	maximal
5	C₃×#64749	C₂	1	2	yes	maximal, complemented
6	#10601423	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	1	yes	characteristic
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₃×#685	—	2	2	no	—
11	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
12	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈×D₅	—	2	2	no	—
14	C₂×C₃×C₈×D₅	—	2	2	no	—
15	C₂×C₃×C₈×D₅	C₄	1	4	yes	complemented
16	C₃×C₅×#107	—	2	2	no	—
17	C₃×#3963	—	2	2	no	—
18	C₃×#3950	—	2	2	no	—
19	C₃×#1808	—	5	1	no	maximal, Hall
20	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
23	#65276	C₂×C₃	1	2	yes	—
24	#64749	C₂×C₃	1	2	yes	complemented
25	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₂²×C₃×Dic₅	—	2	2	no	—
29	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	—	2	1	no	—
31	C₂×C₃×C₄×D₅	—	2	1	no	—
32	C₂×C₃×C₄×D₅	—	2	1	no	—
33	C₂×C₃×C₄×D₅	—	2	1	no	—
34	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
35	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
36	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
39	C₃×C₅×C₄⋊C₄	—	2	2	no	—
40	C₃×C₅×C₄⋊C₄	—	2	2	no	—
41	C₃×#685	—	4	4	no	—
42	C₃×C₄⋊Dic₅	—	2	2	no	—
43	C₃×C₄⋊Dic₅	—	2	2	no	—
44	C₂×C₃×#168	—	2	1	no	—
45	C₂×C₃×#168	—	2	1	no	—
46	C₂×C₃×#168	C₂×C₄	1	2	yes	—
47	C₃×C₈×D₅	—	2	8	no	—
48	C₂³×C₃×C₈	—	5	1	no	—
49	C₂×C₃×#107	—	5	1	no	—
50	C₂×C₃×#107	D₅	1	1	yes	characteristic, complemented
51	C₃×#380	—	5	2	no	—
52	C₃×#340	—	5	2	no	—
53	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
56	C₂×#685	—	2	2	no	—
57	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
58	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₈×D₅	—	2	2	no	—
60	C₂×C₈×D₅	—	2	2	no	—
61	C₂×C₈×D₅	C₃×C₄	1	4	yes	complemented
62	C₅×#107	—	2	2	no	—
63	#3963	—	2	2	no	—
64	#3950	—	2	2	no	—
65	#1808	—	5	1	no	Sylow
66	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₃×D₅	—	2	1	no	—
68	C₂²×C₃×D₅	—	2	1	no	—
69	C₂²×C₃×D₅	—	2	1	no	—
70	C₂²×C₃×D₅	—	2	1	no	—
71	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
72	C₂²×C₃×D₅	D₈	1	2	yes	—
73	C₂²×C₃×D₅	Q₁₆	1	2	yes	—
74	C₂×C₃×C₄×C₅	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	4	2	no	—
76	C₂×C₃×C₄×C₅	—	4	2	no	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
83	C₂×C₃×Dic₅	—	2	1	no	—
84	C₂×C₃×Dic₅	—	2	1	no	—
85	C₂×C₃×Dic₅	—	4	2	no	—
86	C₂×C₃×Dic₅	—	4	2	no	—
87	C₂×C₃×Dic₅	—	4	2	no	—
88	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
89	C₃×C₄×D₅	—	2	2	no	—
90	C₃×C₄×D₅	—	2	2	no	—
91	C₃×C₄×D₅	—	2	2	no	—
92	C₃×C₄×D₅	—	2	2	no	—
93	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
94	C₃×#168	—	2	2	no	—
95	C₂³×C₃×C₄	—	5	1	no	—
96	C₂²×C₃×C₈	—	5	1	no	—
97	C₂²×C₃×C₈	—	5	4	no	—
98	C₂²×C₃×C₈	—	10	2	no	—
99	C₂²×C₃×C₈	—	10	2	no	—
100	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
101	C₂×C₃×C₄⋊C₄	—	5	2	no	—
102	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
104	C₃×#107	—	2	2	no	—
105	C₃×#107	—	10	2	no	—
106	C₃×#95	—	10	2	no	—
107	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
110	C₂²×Dic₅	—	2	2	no	—
111	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅	—	2	1	no	—
113	C₂×C₄×D₅	—	2	1	no	—
114	C₂×C₄×D₅	—	2	1	no	—
115	C₂×C₄×D₅	—	2	1	no	—
116	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
117	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
118	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
119	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
120	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	#685	—	4	4	no	—
124	C₄⋊Dic₅	—	2	2	no	—
125	C₄⋊Dic₅	—	2	2	no	—
126	C₂×#168	—	2	1	no	—
127	C₂×#168	—	2	1	no	—
128	C₂×#168	C₂×C₃×C₄	1	2	yes	—
129	C₈×D₅	—	2	8	no	—
130	C₂³×C₈	—	5	1	no	—
131	C₂×#107	—	5	1	no	—
132	C₂×#107	C₃×D₅	1	1	yes	characteristic, complemented
133	#380	—	5	2	no	—
134	#340	—	5	2	no	—
135	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂²×C₃×C₅	#121	1	1	yes	characteristic
137	C₂²×C₃×C₅	#121	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
140	C₂²×C₃×C₅	#135	1	1	yes	characteristic
141	C₂²×C₃×C₅	#135	1	1	yes	characteristic
142	C₂×C₃×D₅	—	2	2	no	—
143	C₂×C₃×D₅	—	2	2	no	—
144	C₂×C₃×D₅	—	2	2	no	—
145	C₂×C₃×D₅	—	2	2	no	—
146	C₂×C₃×D₅	—	2	2	no	—
147	C₂×C₃×D₅	—	2	2	no	—
148	C₂×C₃×D₅	#107	1	4	yes	complemented
149	C₃×C₄×C₅	—	8	2	no	—
150	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₃×C₄×C₅	#117	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
154	C₃×Dic₅	—	2	2	no	—
155	C₃×Dic₅	—	8	2	no	—
156	C₂⁴×C₃	—	5	1	no	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	5	1	no	—
159	C₂²×C₃×C₄	—	5	2	no	—
160	C₂²×C₃×C₄	—	5	2	no	—
161	C₂²×C₃×C₄	—	10	1	no	—
162	C₂²×C₃×C₄	—	10	1	no	—
163	C₂²×C₃×C₄	—	10	1	no	—
164	C₂²×C₃×C₄	—	10	1	no	—
165	C₂²×C₃×C₄	—	10	2	no	—
166	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
167	C₂×C₃×C₈	—	5	2	no	—
168	C₂×C₃×C₈	—	10	1	no	—
169	C₂×C₃×C₈	—	10	1	no	—
170	C₂×C₃×C₈	—	10	8	no	—
171	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
172	C₂×C₃×C₈	D₂₀	1	2	yes	—
173	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	10	2	no	—
177	C₃×C₄⋊C₄	—	10	2	no	—
178	C₃×C₂²⋊C₄	—	20	4	no	—
179	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂²×D₅	—	2	1	no	—
181	C₂²×D₅	—	2	1	no	—
182	C₂²×D₅	—	2	1	no	—
183	C₂²×D₅	—	2	1	no	—
184	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
185	C₂²×D₅	C₃×D₈	1	2	yes	—
186	C₂²×D₅	C₃×Q₁₆	1	2	yes	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
195	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
196	C₂×Dic₅	—	2	1	no	—
197	C₂×Dic₅	—	2	1	no	—
198	C₂×Dic₅	—	4	2	no	—
199	C₂×Dic₅	—	4	2	no	—
200	C₂×Dic₅	—	4	2	no	—
201	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
202	C₄×D₅	—	2	2	no	—
203	C₄×D₅	—	2	2	no	—
204	C₄×D₅	—	2	2	no	—
205	C₄×D₅	—	2	2	no	—
206	C₅×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
207	#168	—	2	2	no	—
208	C₂³×C₄	—	5	1	no	—
209	C₂²×C₈	—	5	1	no	—
210	C₂²×C₈	—	5	4	no	—
211	C₂²×C₈	—	10	2	no	—
212	C₂²×C₈	—	10	2	no	—
213	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
214	C₂×C₄⋊C₄	—	5	2	no	—
215	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
216	C₂×C₂²⋊C₄	—	10	2	no	—
217	#107	—	2	2	no	—
218	#107	—	10	2	no	—
219	#95	—	10	2	no	—
220	C₂×C₃×C₅	#380	1	1	yes	characteristic
221	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
222	C₂×C₃×C₅	#427	1	1	yes	characteristic
223	C₂×C₃×C₅	#466	1	1	yes	characteristic
224	C₂×C₃×C₅	#466	1	1	yes	characteristic
225	C₂×C₃×C₅	#467	1	1	yes	characteristic
226	C₂×C₃×C₅	#467	1	1	yes	characteristic
227	C₃×D₅	—	2	4	no	—
228	C₂³×C₃	—	5	2	no	—
229	C₂³×C₃	—	5	2	no	—
230	C₂³×C₃	—	5	2	no	—
231	C₂³×C₃	—	10	1	no	—
232	C₂³×C₃	—	10	1	no	—
233	C₂³×C₃	—	10	1	no	—
234	C₂³×C₃	—	10	1	no	—
235	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	5	2	no	—
240	C₂×C₃×C₄	—	10	1	no	—
241	C₂×C₃×C₄	—	10	1	no	—
242	C₂×C₃×C₄	—	10	2	no	—
243	C₂×C₃×C₄	—	10	2	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	10	2	no	—
246	C₂×C₃×C₄	—	20	2	no	—
247	C₂×C₃×C₄	—	20	2	no	—
248	C₂×C₃×C₄	—	20	2	no	—
249	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
251	C₂×C₃×C₄	#711	1	1	yes	characteristic
252	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
253	C₂×C₃×C₄	#713	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
255	C₃×C₈	—	10	2	no	—
256	C₃×C₈	#685	1	4	yes	complemented
257	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₅	C₃×#121	1	1	yes	characteristic
259	C₂²×C₅	C₃×#121	1	1	yes	characteristic
260	C₂²×C₅	C₂×C₃×D₈	1	1	yes	characteristic
261	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
262	C₂²×C₅	C₃×#135	1	1	yes	characteristic
263	C₂²×C₅	C₃×#135	1	1	yes	characteristic
264	C₂×D₅	—	2	2	no	—
265	C₂×D₅	—	2	2	no	—
266	C₂×D₅	—	2	2	no	—
267	C₂×D₅	—	2	2	no	—
268	C₂×D₅	—	2	2	no	—
269	C₂×D₅	—	2	2	no	—
270	C₂×D₅	C₃×#107	1	4	yes	complemented
271	C₄×C₅	—	8	2	no	—
272	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₅	C₃×#117	1	1	yes	characteristic
274	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
275	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
276	Dic₅	—	2	2	no	—
277	Dic₅	—	8	2	no	—
278	C₂⁴	—	5	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	5	1	no	—
281	C₂²×C₄	—	5	2	no	—
282	C₂²×C₄	—	5	2	no	—
283	C₂²×C₄	—	10	1	no	—
284	C₂²×C₄	—	10	1	no	—
285	C₂²×C₄	—	10	1	no	—
286	C₂²×C₄	—	10	1	no	—
287	C₂²×C₄	—	10	2	no	—
288	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
289	C₂×C₈	—	5	2	no	—
290	C₂×C₈	—	10	1	no	—
291	C₂×C₈	—	10	1	no	—
292	C₂×C₈	—	10	8	no	—
293	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
294	C₂×C₈	C₃×D₂₀	1	2	yes	—
295	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	10	2	no	—
299	C₄⋊C₄	—	10	2	no	—
300	C₂²⋊C₄	—	20	4	no	—
301	C₃×C₅	#1808	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	5	4	no	—
303	C₂²×C₃	—	10	2	no	—
304	C₂²×C₃	—	10	2	no	—
305	C₂²×C₃	—	10	2	no	—
306	C₂²×C₃	—	10	2	no	—
307	C₂²×C₃	—	10	2	no	—
308	C₂²×C₃	—	10	2	no	—
309	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
310	C₂²×C₃	#4041	1	1	yes	characteristic
311	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
312	C₂²×C₃	#4058	1	1	yes	characteristic
313	C₂²×C₃	D₅×Q₁₆	1	1	yes	characteristic
314	C₂²×C₃	#4065	1	1	yes	characteristic
315	C₂²×C₃	#4084	1	1	yes	characteristic
316	C₃×C₄	—	8	2	no	—
317	C₃×C₄	—	10	2	no	—
318	C₃×C₄	—	40	2	no	—
319	C₃×C₄	#4038	1	1	yes	characteristic
320	C₃×C₄	#4043	1	1	yes	characteristic
321	C₃×C₄	C₂×#685	1	1	yes	characteristic
322	C₃×C₄	#4092	1	1	yes	characteristic
323	C₂×C₅	C₃×#380	1	1	yes	characteristic
324	C₂×C₅	C₂×C₃×#107	1	1	yes	characteristic
325	C₂×C₅	C₃×#427	1	1	yes	characteristic
326	C₂×C₅	C₃×#466	1	1	yes	characteristic
327	C₂×C₅	C₃×#466	1	1	yes	characteristic
328	C₂×C₅	C₃×#467	1	1	yes	characteristic
329	C₂×C₅	C₃×#467	1	1	yes	characteristic
330	D₅	—	2	4	no	—
331	C₂³	—	5	2	no	—
332	C₂³	—	5	2	no	—
333	C₂³	—	5	2	no	—
334	C₂³	—	10	1	no	—
335	C₂³	—	10	1	no	—
336	C₂³	—	10	1	no	—
337	C₂³	—	10	1	no	—
338	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	5	2	no	—
343	C₂×C₄	—	10	1	no	—
344	C₂×C₄	—	10	1	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	10	2	no	—
347	C₂×C₄	—	10	2	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	20	2	no	—
350	C₂×C₄	—	20	2	no	—
351	C₂×C₄	—	20	2	no	—
352	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
354	C₂×C₄	C₃×#711	1	1	yes	characteristic
355	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
356	C₂×C₄	C₃×#713	1	1	yes	characteristic
357	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
358	C₈	—	10	2	no	—
359	C₈	C₃×#685	1	4	yes	complemented
360	C₂×C₃	—	10	4	no	—
361	C₂×C₃	D₅×#107	1	1	yes	characteristic
362	C₂×C₃	#65169	1	1	yes	characteristic
363	C₂×C₃	#65172	1	1	yes	characteristic
364	C₂×C₃	#65176	1	1	yes	characteristic
365	C₂×C₃	#65276	1	1	yes	characteristic
366	C₂×C₃	#65446	1	1	yes	characteristic
367	C₂×C₃	#65477	1	1	yes	characteristic
368	C₅	C₃×#1808	1	1	yes	characteristic, complemented, Sylow
369	C₂²	—	5	4	no	—
370	C₂²	—	10	2	no	—
371	C₂²	—	10	2	no	—
372	C₂²	—	10	2	no	—
373	C₂²	—	10	2	no	—
374	C₂²	—	10	2	no	—
375	C₂²	—	10	2	no	—
376	C₂²	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
377	C₂²	C₃×#4041	1	1	yes	characteristic
378	C₂²	C₃×D₅×D₈	1	1	yes	characteristic
379	C₂²	C₃×#4058	1	1	yes	characteristic
380	C₂²	C₃×D₅×Q₁₆	1	1	yes	characteristic
381	C₂²	C₃×#4065	1	1	yes	characteristic
382	C₂²	C₃×#4084	1	1	yes	characteristic
383	C₄	—	8	2	no	—
384	C₄	—	10	2	no	—
385	C₄	—	40	2	no	—
386	C₄	C₃×#4038	1	1	yes	characteristic
387	C₄	C₃×#4043	1	1	yes	characteristic
388	C₄	C₂×C₃×#685	1	1	yes	characteristic
389	C₄	C₃×#4092	1	1	yes	characteristic
390	C₃	#10601423	1	1	yes	characteristic, direct product factor, Sylow
391	C₂	—	10	4	no	—
392	C₂	C₃×D₅×#107	1	1	yes	characteristic
393	C₂	C₃×#65169	1	1	yes	characteristic
394	C₂	C₃×#65172	1	1	yes	characteristic
395	C₂	C₃×#65176	1	1	yes	characteristic
396	C₂	C₃×#65276	1	1	yes	characteristic
397	C₂	C₃×#65446	1	1	yes	characteristic
398	C₂	C₃×#65477	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#107	D₅
hypocenter	C₅	C₃×#1808
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#107	C₂	semidirect
3. C₂×C₃×#3950	C₂	semidirect
5. C₃×#64749	C₂	semidirect
6. #10601423	C₃	direct (N × H)
15. C₂×C₃×C₈×D₅	C₄	semidirect
21. C₂×C₅×#107	C₂×C₃	semidirect
22. C₂×#3950	C₂×C₃	semidirect
24. #64749	C₂×C₃	semidirect
50. C₂×C₃×#107	D₅	semidirect
61. C₂×C₈×D₅	C₃×C₄	semidirect
93. C₃×C₅×C₈	C₂²⋊C₄	semidirect
132. C₂×#107	C₃×D₅	semidirect
148. C₂×C₃×D₅	#107	semidirect
206. C₅×C₈	C₃×C₂²⋊C₄	semidirect
256. C₃×C₈	#685	semidirect
270. C₂×D₅	C₃×#107	semidirect
301. C₃×C₅	#1808	semidirect
359. C₈	C₃×#685	semidirect
368. C₅	C₃×#1808	semidirect
390. C₃	#10601423	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×C₈×D₅	2
C₂×C₃×C₅×#107	2
C₂×C₃×#3950	2
C₃×#65276	2
C₃×#64749	2
#10601423	3
C₃×#1808	5

Subgroups — C3×#10601423 #14297900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601423 #14297900