Subgroups — C₂²×D₃×#683 #14478714

Order 1920.

4976 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×D₃×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂³×D₃×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6712	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6669	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃×#683	C₂	1	24	yes	maximal, direct product factor
9	C₂³×#683	—	3	1	no	maximal, Hall
10	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂³×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	8	no	—
16	C₂²×C₄×C₅×D₃	C₂²	1	12	yes	—
17	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×D₃×Dic₅	—	2	8	no	—
20	C₂²×D₃×Dic₅	C₄	1	16	yes	complemented
21	C₂²×D₃×Dic₅	C₂²	1	12	yes	—
22	C₂²×D₃×Dic₅	C₂²	1	12	yes	—
23	C₂×#6712	C₂²	1	12	yes	complemented
24	C₂×C₃×#683	C₂²	1	12	yes	complemented
25	C₂×#6669	C₂²	1	12	yes	complemented
26	C₂×#6668	C₂²	1	12	yes	complemented
27	D₃×#683	C₂²	1	64	yes	direct product factor
28	C₂²×D₃×C₄⋊C₄	—	5	1	no	maximal, Hall
29	C₂⁴×C₄×C₅	—	3	1	no	—
30	C₂⁴×Dic₅	—	3	1	no	—
31	C₂⁴×Dic₅	—	3	1	no	—
32	C₂²×#683	—	3	24	no	—
33	C₂²×#683	—	3	1	no	—
34	C₂²×#683	—	3	1	no	—
35	C₂²×#683	—	3	1	no	—
36	C₂²×#683	D₃	1	1	yes	characteristic, direct product factor
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂³×C₅×D₃	C₂×C₄	1	8	yes	—
39	C₂³×C₅×D₃	D₄	1	8	yes	—
40	C₂³×C₅×D₃	Q₈	1	8	yes	—
41	C₂³×C₅×D₃	C₂³	1	6	yes	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
44	C₂²×Dic₁₅	—	2	4	no	—
45	C₂²×Dic₁₅	C₂×C₄	1	8	yes	complemented
46	C₂²×Dic₁₅	C₂³	1	6	yes	—
47	C₂²×Dic₁₅	C₂³	1	6	yes	—
48	C₂²×C₅×Dic₃	—	2	4	no	—
49	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
50	C₂×C₄×C₅×D₃	—	2	48	no	—
51	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
52	C₂²×C₃×Dic₅	—	2	4	no	—
53	C₂²×C₃×Dic₅	C₂×C₄	1	8	yes	complemented
54	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
56	C₂×D₃×Dic₅	—	2	48	no	—
57	C₂×D₃×Dic₅	C₂×C₄	1	96	yes	complemented
58	C₂×D₃×Dic₅	C₂³	1	16	yes	—
59	C₂×D₃×Dic₅	C₂³	1	16	yes	—
60	#6712	C₂³	1	16	yes	complemented
61	C₃×#683	C₂³	1	16	yes	complemented
62	#6669	C₂³	1	16	yes	complemented
63	#6668	C₂³	1	16	yes	complemented
64	C₂³×C₄×D₃	—	5	1	no	—
65	C₂³×C₄×D₃	—	5	1	no	—
66	C₂³×C₄×D₃	D₅	1	1	yes	characteristic
67	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
68	C₂²×C₄⋊Dic₃	—	5	1	no	—
69	C₂²×Dic₃⋊C₄	—	5	1	no	—
70	C₂²×Dic₃⋊C₄	—	5	1	no	—
71	C₂×D₃×C₄⋊C₄	—	5	24	no	—
72	C₂⁵×C₅	—	3	1	no	—
73	C₂³×C₄×C₅	—	3	1	no	—
74	C₂³×C₄×C₅	—	3	12	no	—
75	C₂³×C₄×C₅	—	6	8	no	—
76	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
77	C₂³×Dic₅	—	3	1	no	—
78	C₂³×Dic₅	—	3	16	no	—
79	C₂³×Dic₅	—	3	12	no	—
80	C₂³×Dic₅	—	3	1	no	—
81	C₂³×Dic₅	—	3	12	no	—
82	C₂³×Dic₅	—	6	8	no	—
83	C₂³×Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂³×Dic₅	C₂×D₃	1	1	yes	characteristic
85	C₂×#683	—	3	12	no	—
86	C₂×#683	—	3	12	no	—
87	C₂×#683	—	3	12	no	—
88	C₂×#683	—	3	64	no	—
89	C₂×#683	C₂×D₃	1	12	yes	direct product factor
90	C₂³×C₄⋊C₄	—	15	1	no	Sylow
91	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
92	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
93	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
94	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
95	C₂²×C₅×D₃	C₄⋊C₄	1	64	yes	complemented
96	C₂²×C₅×D₃	C₂²×C₄	1	24	yes	—
97	C₂²×C₅×D₃	C₂×D₄	1	24	yes	—
98	C₂²×C₅×D₃	C₂×Q₈	1	24	yes	—
99	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
100	C₂×C₃×C₄×C₅	—	2	12	no	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
102	C₂×Dic₁₅	—	2	12	no	—
103	C₂×Dic₁₅	C₂²×C₄	1	24	yes	complemented
104	C₂×Dic₁₅	C₂⁴	1	4	yes	—
105	C₂×Dic₁₅	C₂⁴	1	4	yes	—
106	C₂×C₅×Dic₃	—	2	12	no	—
107	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
108	C₄×C₅×D₃	—	2	32	no	—
109	C₂×C₃×Dic₅	—	2	12	no	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	24	yes	complemented
111	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
112	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
113	D₃×Dic₅	—	2	32	no	—
114	D₃×Dic₅	C₂²×C₄	1	64	yes	complemented
115	C₂⁴×D₃	C₂×D₅	1	1	yes	characteristic
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	1	no	—
118	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
119	C₂³×Dic₃	—	5	1	no	—
120	C₂³×Dic₃	—	5	1	no	—
121	C₂³×Dic₃	C₂×D₅	1	1	yes	characteristic
122	C₂²×C₄×D₃	—	2	8	no	—
123	C₂²×C₄×D₃	—	5	16	no	—
124	C₂²×C₄×D₃	—	5	12	no	—
125	C₂²×C₄×D₃	—	5	12	no	—
126	C₂²×C₄×D₃	—	10	8	no	—
127	C₂²×C₄×D₃	C₂×D₅	1	12	yes	—
128	C₂×C₃×C₄⋊C₄	—	5	12	no	—
129	C₂×C₄⋊Dic₃	—	5	12	no	—
130	C₂×Dic₃⋊C₄	—	5	12	no	—
131	C₂×Dic₃⋊C₄	—	5	12	no	—
132	D₃×C₄⋊C₄	—	5	64	no	—
133	C₂⁴×C₅	—	3	8	no	—
134	C₂⁴×C₅	—	3	8	no	—
135	C₂⁴×C₅	—	3	8	no	—
136	C₂⁴×C₅	—	3	6	no	—
137	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	4	no	—
139	C₂²×C₄×C₅	—	3	6	no	—
140	C₂²×C₄×C₅	—	3	16	no	—
141	C₂²×C₄×C₅	—	6	48	no	—
142	C₂²×C₄×C₅	—	6	4	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
144	C₂²×Dic₅	—	2	4	no	—
145	C₂²×Dic₅	—	3	8	no	—
146	C₂²×Dic₅	—	3	6	no	—
147	C₂²×Dic₅	—	3	96	no	—
148	C₂²×Dic₅	—	3	16	no	—
149	C₂²×Dic₅	—	3	6	no	—
150	C₂²×Dic₅	—	3	16	no	—
151	C₂²×Dic₅	—	6	48	no	—
152	C₂²×Dic₅	—	6	4	no	—
153	C₂²×Dic₅	C₄×D₃	1	8	yes	complemented
154	C₂²×Dic₅	C₂²×D₃	1	6	yes	—
155	C₂²×Dic₅	C₂²×D₃	1	6	yes	—
156	#683	—	3	16	no	—
157	#683	—	3	16	no	—
158	#683	—	3	16	no	—
159	#683	C₂²×D₃	1	16	yes	direct product factor
160	C₂⁴×C₄	—	3	1	no	—
161	C₂⁴×C₄	—	15	1	no	—
162	C₂⁴×C₄	—	15	1	no	—
163	C₂²×C₄⋊C₄	—	5	1	no	—
164	C₂²×C₄⋊C₄	—	15	24	no	—
165	C₂²×C₄⋊C₄	—	15	1	no	—
166	C₂²×C₄⋊C₄	—	15	1	no	—
167	C₂²×C₄⋊C₄	—	15	1	no	—
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	16	yes	complemented
169	C₂²×C₃×C₅	C₂³×C₄	1	6	yes	—
170	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
171	C₂²×C₃×C₅	C₂²×Q₈	1	6	yes	—
172	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
173	C₂×C₅×D₃	C₂×C₄⋊C₄	1	96	yes	complemented
174	C₂×C₅×D₃	C₂³×C₄	1	8	yes	—
175	C₂×C₅×D₃	C₂²×D₄	1	8	yes	—
176	C₂×C₅×D₃	C₂²×Q₈	1	8	yes	—
177	C₃×C₄×C₅	—	2	4	no	—
178	Dic₁₅	—	2	4	no	—
179	Dic₁₅	C₂³×C₄	1	8	yes	complemented
180	C₃×Dic₅	—	2	4	no	—
181	C₃×Dic₅	C₂³×C₄	1	8	yes	complemented
182	C₅×Dic₃	—	2	4	no	—
183	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
184	C₂³×D₃	Dic₁₀	1	8	yes	—
185	C₂³×D₃	C₄×D₅	1	8	yes	—
186	C₂³×D₃	C₂²⋊D₅	1	8	yes	—
187	C₂³×D₃	C₂²×D₅	1	6	yes	—
188	C₂²×C₃×C₄	—	2	4	no	—
189	C₂²×C₃×C₄	—	5	8	no	—
190	C₂²×C₃×C₄	—	5	6	no	—
191	C₂²×C₃×C₄	—	5	6	no	—
192	C₂²×C₃×C₄	—	10	4	no	—
193	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
194	C₂²×Dic₃	—	2	4	no	—
195	C₂²×Dic₃	—	5	8	no	—
196	C₂²×Dic₃	—	5	6	no	—
197	C₂²×Dic₃	—	5	6	no	—
198	C₂²×Dic₃	—	10	4	no	—
199	C₂²×Dic₃	C₂²×D₅	1	6	yes	—
200	C₂×C₄×D₃	—	2	48	no	—
201	C₂×C₄×D₃	—	5	96	no	—
202	C₂×C₄×D₃	—	5	16	no	—
203	C₂×C₄×D₃	—	5	16	no	—
204	C₂×C₄×D₃	—	10	48	no	—
205	C₂×C₄×D₃	C₂²×D₅	1	16	yes	—
206	C₃×C₄⋊C₄	—	5	16	no	—
207	C₄⋊Dic₃	—	5	16	no	—
208	Dic₃⋊C₄	—	5	16	no	—
209	Dic₃⋊C₄	—	5	16	no	—
210	C₂³×C₅	—	3	64	no	—
211	C₂³×C₅	—	3	24	no	—
212	C₂³×C₅	—	3	24	no	—
213	C₂³×C₅	—	3	24	no	—
214	C₂³×C₅	—	3	4	no	—
215	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
216	C₂³×C₅	D₃×D₄	1	4	yes	—
217	C₂³×C₅	D₃×Q₈	1	4	yes	—
218	C₂³×C₅	C₂³×D₃	1	3	yes	—
219	C₂×C₄×C₅	—	2	12	no	—
220	C₂×C₄×C₅	—	3	4	no	—
221	C₂×C₄×C₅	—	6	32	no	—
222	C₂×C₄×C₅	—	6	12	no	—
223	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
224	C₂×Dic₅	—	2	12	no	—
225	C₂×Dic₅	—	3	24	no	—
226	C₂×Dic₅	—	3	4	no	—
227	C₂×Dic₅	—	3	64	no	—
228	C₂×Dic₅	—	3	4	no	—
229	C₂×Dic₅	—	6	32	no	—
230	C₂×Dic₅	—	6	12	no	—
231	C₂×Dic₅	C₂×C₄×D₃	1	24	yes	complemented
232	C₂×Dic₅	C₂³×D₃	1	4	yes	—
233	C₂×Dic₅	C₂³×D₃	1	4	yes	—
234	C₂⁵	—	3	1	no	—
235	C₂³×C₄	—	3	1	no	—
236	C₂³×C₄	—	3	12	no	—
237	C₂³×C₄	—	5	1	no	—
238	C₂³×C₄	—	5	1	no	—
239	C₂³×C₄	—	6	8	no	—
240	C₂³×C₄	—	15	12	no	—
241	C₂³×C₄	—	15	16	no	—
242	C₂³×C₄	—	15	12	no	—
243	C₂³×C₄	—	15	1	no	—
244	C₂³×C₄	—	15	1	no	—
245	C₂³×C₄	—	30	8	no	—
246	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
247	C₂×C₄⋊C₄	—	5	12	no	—
248	C₂×C₄⋊C₄	—	15	64	no	—
249	C₂×C₄⋊C₄	—	15	12	no	—
250	C₂×C₄⋊C₄	—	15	12	no	—
251	C₂×C₄⋊C₄	—	15	12	no	—
252	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	12	yes	complemented
253	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
254	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
255	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
256	C₅×D₃	C₂²×C₄⋊C₄	1	16	yes	complemented
257	C₂³×C₃	C₂×Dic₁₀	1	4	yes	—
258	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
259	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
260	C₂³×C₃	C₂³×D₅	1	3	yes	—
261	C₂²×D₃	#683	1	64	yes	direct product factor
262	C₂²×D₃	C₂×Dic₁₀	1	24	yes	—
263	C₂²×D₃	C₂×C₄×D₅	1	24	yes	—
264	C₂²×D₃	C₂×C₂²⋊D₅	1	24	yes	—
265	C₂²×D₃	C₂³×D₅	1	4	yes	—
266	C₂×C₃×C₄	—	2	12	no	—
267	C₂×C₃×C₄	—	5	24	no	—
268	C₂×C₃×C₄	—	5	4	no	—
269	C₂×C₃×C₄	—	5	4	no	—
270	C₂×C₃×C₄	—	10	12	no	—
271	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
272	C₂×Dic₃	—	2	12	no	—
273	C₂×Dic₃	—	5	24	no	—
274	C₂×Dic₃	—	5	4	no	—
275	C₂×Dic₃	—	5	4	no	—
276	C₂×Dic₃	—	10	12	no	—
277	C₂×Dic₃	C₂³×D₅	1	4	yes	—
278	C₄×D₃	—	2	32	no	—
279	C₄×D₃	—	5	64	no	—
280	C₄×D₃	—	10	32	no	—
281	C₂²×C₅	—	3	8	no	—
282	C₂²×C₅	—	3	8	no	—
283	C₂²×C₅	—	3	8	no	—
284	C₂²×C₅	—	3	96	no	—
285	C₂²×C₅	D₃×C₄⋊C₄	1	16	yes	complemented
286	C₂²×C₅	C₂²×C₄×D₃	1	6	yes	—
287	C₂²×C₅	C₂×D₃×D₄	1	6	yes	—
288	C₂²×C₅	C₂×D₃×Q₈	1	6	yes	—
289	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
290	C₄×C₅	—	2	4	no	—
291	C₄×C₅	—	6	4	no	—
292	Dic₅	—	2	4	no	—
293	Dic₅	—	3	8	no	—
294	Dic₅	—	6	4	no	—
295	Dic₅	C₂²×C₄×D₃	1	8	yes	complemented
296	C₂⁴	—	3	8	no	—
297	C₂⁴	—	3	8	no	—
298	C₂⁴	—	3	8	no	—
299	C₂⁴	—	3	6	no	—
300	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	3	6	no	—
303	C₂²×C₄	—	3	16	no	—
304	C₂²×C₄	—	5	8	no	—
305	C₂²×C₄	—	5	6	no	—
306	C₂²×C₄	—	5	6	no	—
307	C₂²×C₄	—	6	48	no	—
308	C₂²×C₄	—	6	4	no	—
309	C₂²×C₄	—	10	4	no	—
310	C₂²×C₄	—	15	16	no	—
311	C₂²×C₄	—	15	96	no	—
312	C₂²×C₄	—	15	16	no	—
313	C₂²×C₄	—	15	8	no	—
314	C₂²×C₄	—	15	6	no	—
315	C₂²×C₄	—	15	6	no	—
316	C₂²×C₄	—	30	48	no	—
317	C₂²×C₄	—	30	4	no	—
318	C₂²×C₄	C₂×D₃×D₅	1	6	yes	—
319	C₄⋊C₄	—	5	16	no	—
320	C₄⋊C₄	—	15	16	no	—
321	C₄⋊C₄	—	15	16	no	—
322	C₄⋊C₄	—	15	16	no	—
323	C₃×C₅	C₂³×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
324	C₂²×C₃	C₂×#683	1	16	yes	complemented
325	C₂²×C₃	C₂²×Dic₁₀	1	6	yes	—
326	C₂²×C₃	C₂²×C₄×D₅	1	6	yes	—
327	C₂²×C₃	C₂²×C₂²⋊D₅	1	6	yes	—
328	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
329	C₂×D₃	C₂×#683	1	96	yes	direct product factor
330	C₂×D₃	C₂²×Dic₁₀	1	8	yes	—
331	C₂×D₃	C₂²×C₄×D₅	1	8	yes	—
332	C₂×D₃	C₂²×C₂²⋊D₅	1	8	yes	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	5	8	no	—
335	C₃×C₄	—	10	4	no	—
336	Dic₃	—	2	4	no	—
337	Dic₃	—	5	8	no	—
338	Dic₃	—	10	4	no	—
339	C₂×C₅	—	3	16	no	—
340	C₂×C₅	C₂×D₃×C₄⋊C₄	1	12	yes	complemented
341	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
342	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
343	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
344	C₂³	—	3	64	no	—
345	C₂³	—	3	24	no	—
346	C₂³	—	3	24	no	—
347	C₂³	—	3	24	no	—
348	C₂³	—	3	4	no	—
349	C₂³	D₃×Dic₁₀	1	4	yes	—
350	C₂³	C₄×D₃×D₅	1	4	yes	—
351	C₂³	D₃×C₂²⋊D₅	1	4	yes	—
352	C₂³	C₂²×D₃×D₅	1	3	yes	—
353	C₂×C₄	—	2	12	no	—
354	C₂×C₄	—	3	4	no	—
355	C₂×C₄	—	5	24	no	—
356	C₂×C₄	—	5	4	no	—
357	C₂×C₄	—	5	4	no	—
358	C₂×C₄	—	6	32	no	—
359	C₂×C₄	—	6	12	no	—
360	C₂×C₄	—	10	12	no	—
361	C₂×C₄	—	15	64	no	—
362	C₂×C₄	—	15	24	no	—
363	C₂×C₄	—	15	4	no	—
364	C₂×C₄	—	15	4	no	—
365	C₂×C₄	—	30	32	no	—
366	C₂×C₄	—	30	12	no	—
367	C₂×C₄	C₂²×D₃×D₅	1	4	yes	—
368	C₂×C₃	C₂²×#683	1	12	yes	complemented
369	C₂×C₃	C₂³×Dic₁₀	1	1	yes	characteristic
370	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
371	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
372	D₃	C₂²×#683	1	16	yes	direct product factor
373	C₅	C₂²×D₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
374	C₂²	—	3	8	no	—
375	C₂²	—	3	96	no	—
376	C₂²	—	3	8	no	—
377	C₂²	—	3	8	no	—
378	C₂²	D₃×#683	1	16	yes	direct product factor
379	C₂²	C₂×D₃×Dic₁₀	1	6	yes	—
380	C₂²	C₂×C₄×D₃×D₅	1	6	yes	—
381	C₂²	C₂×D₃×C₂²⋊D₅	1	6	yes	—
382	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	5	8	no	—
385	C₄	—	6	4	no	—
386	C₄	—	10	4	no	—
387	C₄	—	15	8	no	—
388	C₄	—	30	4	no	—
389	C₃	C₂³×#683	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	3	16	no	—
391	C₂	C₂×D₃×#683	1	12	yes	direct product factor
392	C₂	C₂²×D₃×Dic₁₀	1	1	yes	characteristic
393	C₂	C₂²×C₄×D₃×D₅	1	1	yes	characteristic
394	C₂	C₂²×D₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂²×#6712	C₂	semidirect
5. C₂²×C₃×#683	C₂	semidirect
6. C₂²×#6669	C₂	semidirect
7. C₂²×#6668	C₂	semidirect
8. C₂×D₃×#683	C₂	direct (N × H)
20. C₂²×D₃×Dic₅	C₄	semidirect
23. C₂×#6712	C₂²	semidirect
24. C₂×C₃×#683	C₂²	semidirect
25. C₂×#6669	C₂²	semidirect
26. C₂×#6668	C₂²	semidirect
27. D₃×#683	C₂²	direct (N × H)
36. C₂²×#683	D₃	direct (N × H)
45. C₂²×Dic₁₅	C₂×C₄	semidirect
53. C₂²×C₃×Dic₅	C₂×C₄	semidirect
57. C₂×D₃×Dic₅	C₂×C₄	semidirect
60. #6712	C₂³	semidirect
61. C₃×#683	C₂³	semidirect
62. #6669	C₂³	semidirect
63. #6668	C₂³	semidirect
89. C₂×#683	C₂×D₃	direct (N × H)
95. C₂²×C₅×D₃	C₄⋊C₄	semidirect
103. C₂×Dic₁₅	C₂²×C₄	semidirect
110. C₂×C₃×Dic₅	C₂²×C₄	semidirect
114. D₃×Dic₅	C₂²×C₄	semidirect
153. C₂²×Dic₅	C₄×D₃	semidirect
159. #683	C₂²×D₃	direct (N × H)
168. C₂²×C₃×C₅	C₂×C₄⋊C₄	semidirect
173. C₂×C₅×D₃	C₂×C₄⋊C₄	semidirect
179. Dic₁₅	C₂³×C₄	semidirect
181. C₃×Dic₅	C₂³×C₄	semidirect
231. C₂×Dic₅	C₂×C₄×D₃	semidirect
252. C₂×C₃×C₅	C₂²×C₄⋊C₄	semidirect
256. C₅×D₃	C₂²×C₄⋊C₄	semidirect
261. C₂²×D₃	#683	direct (N × H)
285. C₂²×C₅	D₃×C₄⋊C₄	semidirect
295. Dic₅	C₂²×C₄×D₃	semidirect
323. C₃×C₅	C₂³×C₄⋊C₄	semidirect
324. C₂²×C₃	C₂×#683	semidirect
329. C₂×D₃	C₂×#683	direct (N × H)
340. C₂×C₅	C₂×D₃×C₄⋊C₄	semidirect
368. C₂×C₃	C₂²×#683	semidirect
372. D₃	C₂²×#683	direct (N × H)
373. C₅	C₂²×D₃×C₄⋊C₄	semidirect
378. C₂²	D₃×#683	direct (N × H)
389. C₃	C₂³×#683	semidirect
391. C₂	C₂×D₃×#683	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂³×D₃×Dic₅	2
C₂²×#6712	2
C₂²×C₃×#683	2
C₂²×#6669	2
C₂²×#6668	2
C₂×D₃×#683	2
C₂³×#683	3
C₂²×D₃×C₄⋊C₄	5

Subgroups — C22×D3×#683 #14478714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×#683 #14478714