Subgroups — C₂×C₃×#1950 #10639783

Order 768.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#108	C₂	1	2	yes	maximal
2	C₂×C₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₃×#1950	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#341	C₂	1	2	yes	maximal
7	C₂×#1950	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×#108	—	2	8	no	—
14	C₂×C₃×#108	C₂²	1	8	yes	—
15	C₃×#423	—	2	2	no	—
16	C₃×#423	C₂²	1	4	yes	—
17	C₂×C₃×C₄⋊C₈	—	2	1	no	—
18	C₂×C₃×C₄⋊C₈	—	2	1	no	—
19	C₂×C₃×C₄⋊C₈	C₄	1	2	yes	—
20	C₂×C₃×C₄⋊C₈	C₄	1	4	yes	—
21	C₂×C₃×C₄⋊C₈	C₄	1	2	yes	—
22	C₂×C₃×C₄⋊C₈	C₂²	1	4	yes	—
23	C₃×C₄×M₁₆	—	2	2	no	—
24	C₃×C₄×M₁₆	C₂²	1	4	yes	—
25	C₂×C₃×#97	—	2	1	no	—
26	C₂×C₃×C₄×C₈	—	2	1	no	—
27	C₃×#341	C₂²	1	8	yes	—
28	C₂²×#108	C₂×C₃	1	2	yes	—
29	C₂×#423	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
31	C₂×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
32	#1950	C₂×C₃	1	8	yes	direct product factor
33	C₂×#341	C₂×C₃	1	2	yes	—
34	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
35	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
36	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₃×M₁₆	—	2	1	no	—
38	C₂×C₃×M₁₆	—	2	1	no	—
39	C₂×C₃×M₁₆	—	2	2	no	—
40	C₂×C₃×M₁₆	—	2	2	no	—
41	C₂×C₃×M₁₆	—	2	2	no	—
42	C₂×C₃×M₁₆	—	2	4	no	—
43	C₂×C₃×M₁₆	—	2	4	no	—
44	C₂×C₃×M₁₆	D₄	1	4	yes	—
45	C₂×C₃×M₁₆	Q₈	1	4	yes	—
46	C₂×C₃×M₁₆	C₂³	1	4	yes	—
47	C₂×C₃×M₁₆	C₂³	1	2	yes	—
48	C₂×C₃×M₁₆	C₂³	1	2	yes	—
49	C₂²×C₃×C₈	—	2	4	no	—
50	C₂²×C₃×C₈	—	2	1	no	—
51	C₂²×C₃×C₈	—	2	1	no	—
52	C₂²×C₃×C₈	—	2	4	no	—
53	C₂²×C₃×C₈	—	2	2	no	—
54	C₂²×C₃×C₈	C₂×C₄	1	4	yes	—
55	C₂²×C₃×C₈	C₂×C₄	1	4	yes	—
56	C₂²×C₃×C₈	C₂³	1	4	yes	—
57	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄²	D₄	1	2	yes	—
61	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
62	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
63	C₂×C₃×C₄²	Q₈	1	2	yes	—
64	C₂×C₃×C₄²	C₂³	1	2	yes	—
65	C₃×#108	—	2	16	no	—
66	C₃×C₄⋊C₈	—	2	4	no	—
67	C₃×C₄⋊C₈	—	2	4	no	—
68	C₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
69	C₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
70	C₃×#97	—	2	4	no	—
71	C₃×C₄×C₈	—	2	4	no	—
72	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
73	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
74	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₈	C₂²×C₃	1	2	yes	—
76	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
77	C₂×#108	—	2	8	no	—
78	C₂×#108	C₂²×C₃	1	8	yes	—
79	#423	—	2	2	no	—
80	#423	C₂²×C₃	1	4	yes	—
81	C₂×C₄⋊C₈	—	2	1	no	—
82	C₂×C₄⋊C₈	—	2	1	no	—
83	C₂×C₄⋊C₈	C₃×C₄	1	2	yes	—
84	C₂×C₄⋊C₈	C₃×C₄	1	4	yes	—
85	C₂×C₄⋊C₈	C₃×C₄	1	2	yes	—
86	C₂×C₄⋊C₈	C₂²×C₃	1	4	yes	—
87	C₄×M₁₆	—	2	2	no	—
88	C₄×M₁₆	C₂²×C₃	1	4	yes	—
89	C₂×#97	—	2	1	no	—
90	C₂×C₄×C₈	—	2	1	no	—
91	#341	C₂²×C₃	1	8	yes	—
92	C₂⁴×C₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₃×C₄	—	2	4	no	—
94	C₂²×C₃×C₄	—	4	2	no	—
95	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
99	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
100	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
105	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
107	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
108	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
110	C₂²×C₃×C₄	#41	1	2	yes	—
111	C₂²×C₃×C₄	#41	1	2	yes	—
112	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
113	C₃×M₁₆	—	2	4	no	—
114	C₃×M₁₆	—	2	4	no	—
115	C₃×M₁₆	—	2	2	no	—
116	C₃×M₁₆	—	2	2	no	—
117	C₃×M₁₆	—	2	4	no	—
118	C₃×M₁₆	—	2	4	no	—
119	C₃×M₁₆	—	4	4	no	—
120	C₃×M₁₆	C₂×D₄	1	4	yes	—
121	C₃×M₁₆	C₂×Q₈	1	4	yes	—
122	C₂×C₃×C₈	—	2	8	no	—
123	C₂×C₃×C₈	—	2	8	no	—
124	C₂×C₃×C₈	—	2	4	no	—
125	C₂×C₃×C₈	—	2	4	no	—
126	C₂×C₃×C₈	—	2	2	no	—
127	C₂×C₃×C₈	—	2	2	no	—
128	C₂×C₃×C₈	—	2	4	no	—
129	C₂×C₃×C₈	—	2	4	no	—
130	C₂×C₃×C₈	—	2	4	no	—
131	C₂×C₃×C₈	—	4	4	no	—
132	C₂×C₃×C₈	C₂²×C₄	1	8	yes	—
133	C₃×C₄²	C₄⋊C₄	1	2	yes	—
134	C₃×C₄²	C₄⋊C₄	1	2	yes	—
135	C₃×C₄²	C₄⋊C₄	1	2	yes	—
136	C₃×C₄²	C₄⋊C₄	1	2	yes	—
137	C₃×C₄²	C₂²×C₄	1	2	yes	—
138	C₃×C₄²	C₂²×C₄	1	2	yes	—
139	C₃×C₄²	C₂×D₄	1	2	yes	—
140	C₃×C₄²	C₂×D₄	1	2	yes	—
141	C₂³×C₄	C₃×Q₈	1	1	yes	characteristic
142	C₂³×C₄	C₃×Q₈	1	1	yes	characteristic
143	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	2	1	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	4	no	—
150	C₂×M₁₆	—	2	4	no	—
151	C₂×M₁₆	C₃×D₄	1	4	yes	—
152	C₂×M₁₆	C₃×Q₈	1	4	yes	—
153	C₂×M₁₆	C₂³×C₃	1	4	yes	—
154	C₂×M₁₆	C₂³×C₃	1	2	yes	—
155	C₂×M₁₆	C₂³×C₃	1	2	yes	—
156	C₂²×C₈	—	2	4	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	4	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	C₂×C₃×C₄	1	4	yes	—
162	C₂²×C₈	C₂×C₃×C₄	1	4	yes	—
163	C₂²×C₈	C₂³×C₃	1	4	yes	—
164	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
168	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
169	C₂×C₄²	C₃×D₄	1	2	yes	—
170	C₂×C₄²	C₃×Q₈	1	2	yes	—
171	C₂×C₄²	C₂³×C₃	1	2	yes	—
172	#108	—	2	16	no	—
173	C₄⋊C₈	—	2	4	no	—
174	C₄⋊C₈	—	2	4	no	—
175	C₄⋊C₈	C₂×C₃×C₄	1	8	yes	—
176	C₄⋊C₈	C₂×C₃×C₄	1	8	yes	—
177	#97	—	2	4	no	—
178	C₄×C₈	—	2	4	no	—
179	C₂³×C₃	—	2	2	no	—
180	C₂³×C₃	—	2	2	no	—
181	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₃	#125	1	2	yes	—
184	C₂³×C₃	C₄⋊Q₈	1	2	yes	—
185	C₂³×C₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	2	2	no	—
189	C₂×C₃×C₄	—	2	4	no	—
190	C₂×C₃×C₄	—	2	4	no	—
191	C₂×C₃×C₄	—	4	2	no	—
192	C₂×C₃×C₄	—	4	2	no	—
193	C₂×C₃×C₄	#108	1	4	yes	complemented
194	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
196	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
201	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
202	C₂×C₃×C₄	C₄×Q₈	1	2	yes	—
203	C₂×C₃×C₄	C₄×Q₈	1	2	yes	—
204	C₂×C₃×C₄	#121	1	2	yes	—
205	C₂×C₃×C₄	#121	1	2	yes	—
206	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₃×C₄	#125	1	2	yes	—
209	C₂×C₃×C₄	C₄⋊Q₈	1	2	yes	—
210	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
216	C₃×C₈	—	2	8	no	—
217	C₃×C₈	—	2	4	no	—
218	C₃×C₈	—	2	4	no	—
219	C₃×C₈	—	4	4	no	—
220	C₂⁴	C₂×C₃×Q₈	1	1	yes	characteristic
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	4	2	no	—
223	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
225	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₄	C₃×C₄⋊C₄	1	2	yes	—
227	C₂²×C₄	C₃×C₄⋊C₄	1	2	yes	—
228	C₂²×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
234	C₂²×C₄	C₂×C₃×Q₈	1	2	yes	—
235	C₂²×C₄	C₂×C₃×Q₈	1	2	yes	—
236	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₃×Q₈	1	2	yes	—
238	C₂²×C₄	C₃×#41	1	2	yes	—
239	C₂²×C₄	C₃×#41	1	2	yes	—
240	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
241	M₁₆	—	2	4	no	—
242	M₁₆	—	2	4	no	—
243	M₁₆	—	2	2	no	—
244	M₁₆	—	2	2	no	—
245	M₁₆	—	2	4	no	—
246	M₁₆	—	2	4	no	—
247	M₁₆	—	4	4	no	—
248	M₁₆	C₂×C₃×D₄	1	4	yes	—
249	M₁₆	C₂×C₃×Q₈	1	4	yes	—
250	C₂×C₈	—	2	8	no	—
251	C₂×C₈	—	2	8	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	4	4	no	—
260	C₂×C₈	C₂²×C₃×C₄	1	8	yes	—
261	C₄²	C₃×C₄⋊C₄	1	2	yes	—
262	C₄²	C₃×C₄⋊C₄	1	2	yes	—
263	C₄²	C₃×C₄⋊C₄	1	2	yes	—
264	C₄²	C₃×C₄⋊C₄	1	2	yes	—
265	C₄²	C₂²×C₃×C₄	1	2	yes	—
266	C₄²	C₂²×C₃×C₄	1	2	yes	—
267	C₄²	C₂×C₃×D₄	1	2	yes	—
268	C₄²	C₂×C₃×D₄	1	2	yes	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	4	no	—
275	C₂²×C₃	#389	1	2	yes	—
276	C₂²×C₃	#389	1	2	yes	—
277	C₂²×C₃	C₂×#108	1	2	yes	—
278	C₂²×C₃	#430	1	2	yes	—
279	C₂²×C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×C₃	C₂×#125	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
282	C₃×C₄	—	2	2	no	—
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	#389	1	2	yes	—
286	C₃×C₄	#389	1	2	yes	—
287	C₃×C₄	C₂×#108	1	4	yes	complemented
288	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
289	C₃×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
290	C₃×C₄	C₂×#121	1	1	yes	characteristic
291	C₃×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
295	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
296	C₂³	C₃×#125	1	2	yes	—
297	C₂³	C₃×C₄⋊Q₈	1	2	yes	—
298	C₂³	C₂²×C₃×Q₈	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	C₃×#108	1	4	yes	complemented
307	C₂×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
308	C₂×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
309	C₂×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
310	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
312	C₂×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
313	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
314	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
315	C₂×C₄	C₃×C₄×Q₈	1	2	yes	—
316	C₂×C₄	C₃×C₄×Q₈	1	2	yes	—
317	C₂×C₄	C₃×#121	1	2	yes	—
318	C₂×C₄	C₃×#121	1	2	yes	—
319	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
320	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
321	C₂×C₄	C₃×#125	1	2	yes	—
322	C₂×C₄	C₃×C₄⋊Q₈	1	2	yes	—
323	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
327	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
328	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
329	C₈	—	2	8	no	—
330	C₈	—	2	4	no	—
331	C₈	—	2	4	no	—
332	C₈	—	4	4	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	#1950	1	4	yes	direct product factor
337	C₂×C₃	C₂×#389	1	1	yes	characteristic
338	C₂×C₃	C₂²×#108	1	1	yes	characteristic
339	C₂×C₃	C₂×#430	1	1	yes	characteristic
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	C₃×#389	1	2	yes	—
347	C₂²	C₃×#389	1	2	yes	—
348	C₂²	C₂×C₃×#108	1	2	yes	—
349	C₂²	C₃×#430	1	2	yes	—
350	C₂²	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
351	C₂²	C₂×C₃×#125	1	1	yes	characteristic
352	C₂²	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	C₃×#389	1	2	yes	—
357	C₄	C₃×#389	1	2	yes	—
358	C₄	C₂×C₃×#108	1	4	yes	complemented
359	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
360	C₄	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
361	C₄	C₂×C₃×#121	1	1	yes	characteristic
362	C₄	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
363	C₃	C₂×#1950	1	1	yes	characteristic, direct product factor, Sylow
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	C₃×#1950	1	4	yes	direct product factor
368	C₂	C₂×C₃×#389	1	1	yes	characteristic
369	C₂	C₂²×C₃×#108	1	1	yes	characteristic
370	C₂	C₂×C₃×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×#1950	C₂	direct (N × H)
7. C₂×#1950	C₃	direct (N × H)
32. #1950	C₂×C₃	direct (N × H)
193. C₂×C₃×C₄	#108	semidirect
287. C₃×C₄	C₂×#108	semidirect
306. C₂×C₄	C₃×#108	semidirect
336. C₂×C₃	#1950	direct (N × H)
358. C₄	C₂×C₃×#108	semidirect
363. C₃	C₂×#1950	direct (N × H)
367. C₂	C₃×#1950	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×#108	2
C₂×C₃×#423	2
C₂²×C₃×C₄⋊C₈	2
C₂×C₃×C₄×M₁₆	2
C₃×#1950	2
C₂×C₃×#341	2
C₂×#1950	3

Subgroups — C2×C3×#1950 #10639783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#1950 #10639783