Subgroups — C₂×C₃×#65517 #14423353

Order 1920.

1480 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	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#689	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4070	C₂	1	1	yes	maximal, characteristic
4	C₃×#65517	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3967	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic
7	C₂×#65517	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	—	2	8	no	—
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂²×C₃×C₅×Q₈	—	2	2	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	4	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	—	2	1	no	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
17	C₂×C₃×#689	—	2	8	no	—
18	C₂×C₃×#689	C₂²	1	8	yes	complemented
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₃×#4070	—	2	2	no	—
21	C₃×#4070	C₂²	1	4	yes	—
22	C₂×C₃×#683	—	2	1	no	—
23	C₂²×C₃×#168	C₂²	1	2	yes	—
24	C₃×#3967	C₂²	1	8	yes	complemented
25	C₃×C₂²⋊#168	C₂²	1	4	yes	—
26	C₂×C₃×#451	—	5	1	no	maximal, Hall
27	C₂³×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₂²×#689	C₂×C₃	1	2	yes	complemented
29	C₂×#4070	C₂×C₃	1	1	yes	characteristic
30	#65517	C₂×C₃	1	8	yes	direct product factor
31	C₂×#3967	C₂×C₃	1	2	yes	complemented
32	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂×C₃×C₅×Q₈	—	2	16	no	—
35	C₂×C₃×C₅×Q₈	—	2	8	no	—
36	C₂×C₃×C₅×Q₈	—	2	16	no	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	—	2	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	D₄	1	8	yes	—
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	—	2	8	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	—	2	1	no	—
51	C₂²×C₃×Dic₅	—	2	1	no	—
52	C₂×C₃×Dic₁₀	—	2	4	no	—
53	C₂×C₃×Dic₁₀	—	2	1	no	—
54	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
55	C₃×C₂²⋊Dic₅	—	2	4	no	—
56	C₃×#689	—	2	16	no	—
57	C₃×C₄⋊Dic₅	—	2	1	no	—
58	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
59	C₃×#683	—	2	4	no	—
60	C₂×C₃×#168	—	2	4	no	—
61	C₂×C₃×#168	C₂³	1	4	yes	—
62	C₂³×C₃×Q₈	D₅	1	1	yes	characteristic
63	C₂²×C₃×Q₁₆	—	5	2	no	—
64	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
65	C₃×#451	—	5	8	no	—
66	C₂×C₃×#103	—	5	2	no	—
67	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
68	C₂²×C₅×Q₈	—	2	8	no	—
69	C₂²×C₅×Q₈	—	2	1	no	—
70	C₂²×C₅×Q₈	—	2	2	no	—
71	C₂²×C₅×Q₈	C₂²×C₃	1	4	yes	—
72	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₅	—	2	1	no	—
77	C₂×#689	—	2	8	no	—
78	C₂×#689	C₂²×C₃	1	8	yes	complemented
79	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
80	#4070	—	2	2	no	—
81	#4070	C₂²×C₃	1	4	yes	—
82	C₂×#683	—	2	1	no	—
83	C₂²×#168	C₂²×C₃	1	2	yes	—
84	#3967	C₂²×C₃	1	8	yes	complemented
85	C₂²⋊#168	C₂²×C₃	1	4	yes	—
86	C₂×#451	—	5	1	no	Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	Q₁₆	1	4	yes	complemented
90	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	16	no	—
93	C₃×C₅×Q₈	—	2	8	no	—
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	C₂×D₄	1	8	yes	—
96	C₂×C₃×C₄×C₅	—	2	16	no	—
97	C₂×C₃×C₄×C₅	—	2	8	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	4	2	no	—
109	C₂×C₃×Dic₅	—	4	2	no	—
110	C₃×Dic₁₀	—	2	4	no	—
111	C₃×Dic₁₀	—	4	2	no	—
112	C₃×#168	—	2	4	no	—
113	C₂²×C₃×Q₈	—	2	8	no	—
114	C₂²×C₃×Q₈	—	2	2	no	—
115	C₂²×C₃×Q₈	—	2	1	no	—
116	C₂²×C₃×Q₈	—	5	1	no	—
117	C₂²×C₃×Q₈	C₂×D₅	1	4	yes	—
118	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
119	C₂³×C₃×C₄	—	2	1	no	—
120	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×Q₁₆	—	5	8	no	—
122	C₂×C₃×Q₁₆	—	10	8	no	—
123	C₂²×C₃×C₈	—	5	2	no	—
124	C₃×C₂²⋊Q₈	—	5	4	no	—
125	C₃×C₂²⋊Q₈	—	10	2	no	—
126	C₂×C₃×C₄⋊C₄	—	5	1	no	—
127	C₂×C₃×C₄⋊C₄	—	10	1	no	—
128	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
129	C₃×#103	—	5	8	no	—
130	C₃×C₂²⋊C₈	—	5	4	no	—
131	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
132	C₂×C₅×Q₈	—	2	16	no	—
133	C₂×C₅×Q₈	—	2	8	no	—
134	C₂×C₅×Q₈	—	2	16	no	—
135	C₂×C₅×Q₈	—	2	4	no	—
136	C₂×C₅×Q₈	—	2	4	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	C₃×D₄	1	8	yes	—
139	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
140	C₂²×C₄×C₅	—	2	8	no	—
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×Dic₅	—	2	1	no	—
149	C₂²×Dic₅	—	2	1	no	—
150	C₂×Dic₁₀	—	2	4	no	—
151	C₂×Dic₁₀	—	2	1	no	—
152	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
153	C₂²⋊Dic₅	—	2	4	no	—
154	#689	—	2	16	no	—
155	C₄⋊Dic₅	—	2	1	no	—
156	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
157	#683	—	2	4	no	—
158	C₂×#168	—	2	4	no	—
159	C₂×#168	C₂³×C₃	1	4	yes	—
160	C₂³×Q₈	C₃×D₅	1	1	yes	characteristic
161	C₂²×Q₁₆	—	5	2	no	—
162	C₂×C₂²⋊Q₈	—	5	1	no	—
163	#451	—	5	8	no	—
164	C₂×#103	—	5	2	no	—
165	C₂×C₂²⋊C₈	—	5	1	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	2	8	no	—
169	C₂²×C₃×C₅	#120	1	2	yes	—
170	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
171	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	complemented
172	C₂²×C₃×C₅	#137	1	2	yes	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	—	2	8	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	#120	1	2	yes	—
177	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
178	C₃×Dic₅	—	4	2	no	—
179	C₃×Dic₅	—	4	2	no	—
180	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
181	C₂×C₃×Q₈	—	2	16	no	—
182	C₂×C₃×Q₈	—	2	8	no	—
183	C₂×C₃×Q₈	—	2	16	no	—
184	C₂×C₃×Q₈	—	2	4	no	—
185	C₂×C₃×Q₈	—	2	4	no	—
186	C₂×C₃×Q₈	—	2	2	no	—
187	C₂×C₃×Q₈	—	5	2	no	—
188	C₂×C₃×Q₈	—	10	1	no	—
189	C₂×C₃×Q₈	—	10	4	no	—
190	C₂×C₃×Q₈	C₂²⋊D₅	1	8	yes	—
191	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
192	C₂²×C₃×C₄	—	2	8	no	—
193	C₂²×C₃×C₄	—	2	4	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	10	1	no	—
197	C₂²×C₃×C₄	—	10	1	no	—
198	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₃×Q₁₆	—	10	16	no	—
203	C₂×C₃×C₈	—	5	4	no	—
204	C₂×C₃×C₈	—	10	4	no	—
205	C₃×C₄⋊C₄	—	5	2	no	—
206	C₃×C₄⋊C₄	—	10	4	no	—
207	C₃×C₄⋊C₄	—	10	1	no	—
208	C₃×C₂²⋊C₄	—	10	4	no	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	C₃×Q₁₆	1	4	yes	complemented
212	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
214	C₅×Q₈	—	2	16	no	—
215	C₅×Q₈	—	2	8	no	—
216	C₅×Q₈	—	2	4	no	—
217	C₅×Q₈	C₂×C₃×D₄	1	8	yes	—
218	C₂×C₄×C₅	—	2	16	no	—
219	C₂×C₄×C₅	—	2	8	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	4	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
227	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
228	C₂×Dic₅	—	2	2	no	—
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	4	2	no	—
231	C₂×Dic₅	—	4	2	no	—
232	Dic₁₀	—	2	4	no	—
233	Dic₁₀	—	4	2	no	—
234	#168	—	2	4	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	5	1	no	—
239	C₂²×Q₈	C₂×C₃×D₅	1	4	yes	—
240	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
243	C₂×Q₁₆	—	5	8	no	—
244	C₂×Q₁₆	—	10	8	no	—
245	C₂²×C₈	—	5	2	no	—
246	C₂²⋊Q₈	—	5	4	no	—
247	C₂²⋊Q₈	—	10	2	no	—
248	C₂×C₄⋊C₄	—	5	1	no	—
249	C₂×C₄⋊C₄	—	10	1	no	—
250	C₂×C₂²⋊C₄	—	10	1	no	—
251	#103	—	5	8	no	—
252	C₂²⋊C₈	—	5	4	no	—
253	C₂×C₃×C₅	—	2	4	no	—
254	C₂×C₃×C₅	#451	1	4	yes	complemented
255	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
256	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
257	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	#689	1	4	yes	complemented
261	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
262	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
263	C₃×Q₈	—	2	16	no	—
264	C₃×Q₈	—	2	8	no	—
265	C₃×Q₈	—	2	4	no	—
266	C₃×Q₈	—	10	4	no	—
267	C₃×Q₈	—	20	2	no	—
268	C₃×Q₈	C₂×C₂²⋊D₅	1	8	yes	—
269	C₂×C₃×C₄	—	2	16	no	—
270	C₂×C₃×C₄	—	2	8	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	20	2	no	—
278	C₂×C₃×C₄	—	20	2	no	—
279	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
282	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
283	C₃×C₈	—	10	4	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	8	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	C₃×#120	1	2	yes	—
288	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
289	C₂²×C₅	C₂×C₃×Q₁₆	1	4	yes	complemented
290	C₂²×C₅	C₃×#137	1	2	yes	—
291	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
292	C₄×C₅	—	2	8	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	C₃×#120	1	2	yes	—
295	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
296	Dic₅	—	4	2	no	—
297	Dic₅	—	4	2	no	—
298	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
299	C₂×Q₈	—	2	16	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	16	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	5	2	no	—
306	C₂×Q₈	—	10	1	no	—
307	C₂×Q₈	—	10	4	no	—
308	C₂×Q₈	C₃×C₂²⋊D₅	1	8	yes	—
309	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	10	1	no	—
315	C₂²×C₄	—	10	1	no	—
316	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
317	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
318	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
319	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
320	Q₁₆	—	10	16	no	—
321	C₂×C₈	—	5	4	no	—
322	C₂×C₈	—	10	4	no	—
323	C₄⋊C₄	—	5	2	no	—
324	C₄⋊C₄	—	10	1	no	—
325	C₄⋊C₄	—	10	4	no	—
326	C₂²⋊C₄	—	10	4	no	—
327	C₃×C₅	C₂×#451	1	1	yes	characteristic, complemented, Hall
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	8	no	—
331	C₂²×C₃	#4088	1	2	yes	—
332	C₂²×C₃	C₂×#689	1	2	yes	—
333	C₂²×C₃	C₂×#689	1	4	yes	complemented
334	C₂²×C₃	#4099	1	2	yes	—
335	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
336	C₃×C₄	—	2	8	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	20	2	no	—
339	C₃×C₄	—	20	2	no	—
340	C₃×C₄	#4099	1	2	yes	—
341	C₃×C₄	C₂²×C₂²⋊D₅	1	2	yes	—
342	C₂×C₅	—	2	4	no	—
343	C₂×C₅	C₃×#451	1	4	yes	complemented
344	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
345	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
346	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₃×#689	1	4	yes	complemented
350	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
351	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
352	Q₈	—	2	16	no	—
353	Q₈	—	2	8	no	—
354	Q₈	—	2	4	no	—
355	Q₈	—	10	4	no	—
356	Q₈	—	20	2	no	—
357	Q₈	C₂×C₃×C₂²⋊D₅	1	8	yes	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	20	2	no	—
367	C₂×C₄	—	20	2	no	—
368	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
369	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
371	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
372	C₈	—	10	4	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	#65517	1	4	yes	direct product factor
375	C₂×C₃	C₂×#4088	1	1	yes	characteristic
376	C₂×C₃	C₂²×#689	1	1	yes	characteristic
377	C₂×C₃	C₂×#4099	1	1	yes	characteristic
378	C₅	C₂×C₃×#451	1	1	yes	characteristic, complemented, Sylow
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	8	no	—
382	C₂²	C₃×#4088	1	2	yes	—
383	C₂²	C₂×C₃×#689	1	2	yes	—
384	C₂²	C₂×C₃×#689	1	4	yes	complemented
385	C₂²	C₃×#4099	1	2	yes	—
386	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
387	C₄	—	2	8	no	—
388	C₄	—	2	2	no	—
389	C₄	—	20	2	no	—
390	C₄	—	20	2	no	—
391	C₄	C₃×#4099	1	2	yes	—
392	C₄	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
393	C₃	C₂×#65517	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	2	4	no	—
395	C₂	C₃×#65517	1	4	yes	direct product factor
396	C₂	C₂×C₃×#4088	1	1	yes	characteristic
397	C₂	C₂²×C₃×#689	1	1	yes	characteristic
398	C₂	C₂×C₃×#4099	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
hypercenter	C₂³×C₃×Q₈	D₅
hypocenter	C₅	C₂×C₃×#451
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂³×C₃×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#689	C₂	semidirect
4. C₃×#65517	C₂	direct (N × H)
5. C₂×C₃×#3967	C₂	semidirect
7. C₂×#65517	C₃	direct (N × H)
18. C₂×C₃×#689	C₂²	semidirect
24. C₃×#3967	C₂²	semidirect
28. C₂²×#689	C₂×C₃	semidirect
30. #65517	C₂×C₃	direct (N × H)
31. C₂×#3967	C₂×C₃	semidirect
78. C₂×#689	C₂²×C₃	semidirect
84. #3967	C₂²×C₃	semidirect
89. C₂³×C₃×C₅	Q₁₆	semidirect
171. C₂²×C₃×C₅	C₂×Q₁₆	semidirect
211. C₂³×C₅	C₃×Q₁₆	semidirect
254. C₂×C₃×C₅	#451	semidirect
260. C₂³×C₃	#689	semidirect
289. C₂²×C₅	C₂×C₃×Q₁₆	semidirect
327. C₃×C₅	C₂×#451	semidirect
333. C₂²×C₃	C₂×#689	semidirect
343. C₂×C₅	C₃×#451	semidirect
349. C₂³	C₃×#689	semidirect
374. C₂×C₃	#65517	direct (N × H)
378. C₅	C₂×C₃×#451	semidirect
384. C₂²	C₂×C₃×#689	semidirect
393. C₃	C₂×#65517	direct (N × H)
395. C₂	C₃×#65517	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×C₃×C₅×Q₈	2
C₂²×C₃×#689	2
C₂×C₃×#4070	2
C₃×#65517	2
C₂×C₃×#3967	2
C₂×C₃×C₂²⋊#168	2
C₂×#65517	3
C₂×C₃×#451	5

Subgroups — C2×C3×#65517 #14423353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65517 #14423353