Subgroups — C₂×C₃×#1953 #10639790

Order 768.

858 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	C₂×C₃×#430	C₂	1	2	yes	maximal
2	C₂²×C₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#108	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic
5	C₃×#1953	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#344	C₂	1	2	yes	maximal
7	C₂×#1953	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×#117	C₂²	1	1	yes	characteristic
13	C₃×#430	—	2	4	no	—
14	C₃×#430	C₂²	1	8	yes	—
15	C₂×C₃×#108	—	2	4	no	—
16	C₂×C₃×#108	—	2	1	no	—
17	C₂×C₃×#108	—	2	1	no	—
18	C₂×C₃×#108	—	2	2	no	—
19	C₂×C₃×#108	C₄	1	4	yes	complemented
20	C₂×C₃×#108	C₄	1	4	yes	complemented
21	C₂×C₃×#108	C₂²	1	4	yes	—
22	C₂×C₃×#108	C₂²	1	4	yes	—
23	C₃×#405	—	2	2	no	—
24	C₃×#405	C₂²	1	4	yes	—
25	C₂×C₃×#97	—	2	1	no	—
26	C₂×C₃×C₄×C₈	—	2	1	no	—
27	C₃×#344	C₂²	1	8	yes	—
28	C₂×#430	C₂×C₃	1	2	yes	—
29	C₂²×#108	C₂×C₃	1	1	yes	characteristic
30	C₂²×#108	C₂×C₃	1	1	yes	characteristic
31	C₂×#405	C₂×C₃	1	1	yes	characteristic
32	#1953	C₂×C₃	1	8	yes	direct product factor
33	C₂×#344	C₂×C₃	1	2	yes	—
34	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₂×C₃×M₁₆	—	2	1	no	—
36	C₂×C₃×M₁₆	—	2	2	no	—
37	C₂×C₃×M₁₆	—	2	2	no	—
38	C₂×C₃×M₁₆	—	2	2	no	—
39	C₂×C₃×M₁₆	—	2	1	no	—
40	C₂×C₃×M₁₆	—	2	1	no	—
41	C₂×C₃×M₁₆	—	2	2	no	—
42	C₂×C₃×M₁₆	—	2	2	no	—
43	C₂×C₃×M₁₆	—	2	2	no	—
44	C₂×C₃×M₁₆	—	2	2	no	—
45	C₂×C₃×M₁₆	—	2	2	no	—
46	C₂×C₃×M₁₆	C₂×C₄	1	4	yes	—
47	C₂×C₃×M₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₃×M₁₆	D₄	1	2	yes	—
49	C₂×C₃×M₁₆	D₄	1	2	yes	—
50	C₂×C₃×M₁₆	C₂³	1	4	yes	—
51	C₂×C₃×M₁₆	C₂³	1	4	yes	—
52	C₂×C₃×M₁₆	C₂³	1	2	yes	—
53	C₂²×C₃×C₈	—	2	1	no	—
54	C₂²×C₃×C₈	—	2	2	no	—
55	C₂²×C₃×C₈	—	2	2	no	—
56	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
57	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
58	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₈	D₄	1	2	yes	—
61	C₂²×C₃×C₈	Q₈	1	2	yes	—
62	C₂²×C₃×C₈	Q₈	1	2	yes	—
63	C₂²×C₃×C₈	C₂³	1	2	yes	—
64	C₃×#117	—	2	1	no	—
65	C₃×#117	—	2	1	no	—
66	C₃×#117	Q₈	1	2	yes	—
67	C₃×#117	C₂³	1	2	yes	—
68	C₂×C₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₃×C₂²⋊C₄	Q₈	1	2	yes	—
70	C₂×C₃×C₄²	—	2	1	no	—
71	C₃×#108	—	2	16	no	—
72	C₃×#108	—	2	4	no	—
73	C₃×#108	—	2	4	no	—
74	C₃×#108	C₂×C₄	1	16	yes	complemented
75	C₃×#97	—	2	4	no	—
76	C₃×C₄×C₈	—	2	4	no	—
77	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
78	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
79	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
81	C₂×#117	C₂²×C₃	1	1	yes	characteristic
82	#430	—	2	4	no	—
83	#430	C₂²×C₃	1	8	yes	—
84	C₂×#108	—	2	4	no	—
85	C₂×#108	—	2	1	no	—
86	C₂×#108	—	2	1	no	—
87	C₂×#108	—	2	2	no	—
88	C₂×#108	C₃×C₄	1	4	yes	complemented
89	C₂×#108	C₃×C₄	1	4	yes	complemented
90	C₂×#108	C₂²×C₃	1	4	yes	—
91	C₂×#108	C₂²×C₃	1	4	yes	—
92	#405	—	2	2	no	—
93	#405	C₂²×C₃	1	4	yes	—
94	C₂×#97	—	2	1	no	—
95	C₂×C₄×C₈	—	2	1	no	—
96	#344	C₂²×C₃	1	8	yes	—
97	C₂⁴×C₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₃×C₄	—	2	2	no	—
99	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₃×C₄	#41	1	1	yes	characteristic
109	C₂²×C₃×C₄	#41	1	1	yes	characteristic
110	C₂²×C₃×C₄	#41	1	1	yes	characteristic
111	C₂²×C₃×C₄	#41	1	1	yes	characteristic
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	2	no	—
119	C₃×M₁₆	—	2	4	no	—
120	C₃×M₁₆	—	2	4	no	—
121	C₃×M₁₆	—	4	2	no	—
122	C₃×M₁₆	—	4	2	no	—
123	C₃×M₁₆	C₂²×C₄	1	8	yes	—
124	C₃×M₁₆	C₂×D₄	1	4	yes	—
125	C₂×C₃×C₈	—	2	4	no	—
126	C₂×C₃×C₈	—	2	4	no	—
127	C₂×C₃×C₈	—	2	2	no	—
128	C₂×C₃×C₈	—	2	2	no	—
129	C₂×C₃×C₈	—	2	2	no	—
130	C₂×C₃×C₈	—	2	4	no	—
131	C₂×C₃×C₈	—	2	4	no	—
132	C₂×C₃×C₈	—	4	2	no	—
133	C₂×C₃×C₈	—	4	2	no	—
134	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
135	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
136	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
137	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
138	C₂×C₃×C₈	C₄⋊C₄	1	4	yes	—
139	C₂×C₃×C₈	C₄⋊C₄	1	4	yes	—
140	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₈	C₂×Q₈	1	4	yes	—
144	C₃×C₄⋊C₄	—	2	2	no	—
145	C₃×C₄⋊C₄	—	2	2	no	—
146	C₃×C₂²⋊C₄	—	2	2	no	—
147	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
148	C₃×C₄²	—	2	2	no	—
149	C₃×C₄²	—	2	2	no	—
150	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	2	1	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	—	2	2	no	—
160	C₂×M₁₆	—	2	2	no	—
161	C₂×M₁₆	—	2	2	no	—
162	C₂×M₁₆	C₂×C₃×C₄	1	4	yes	—
163	C₂×M₁₆	C₂×C₃×C₄	1	4	yes	—
164	C₂×M₁₆	C₃×D₄	1	2	yes	—
165	C₂×M₁₆	C₃×D₄	1	2	yes	—
166	C₂×M₁₆	C₂³×C₃	1	4	yes	—
167	C₂×M₁₆	C₂³×C₃	1	4	yes	—
168	C₂×M₁₆	C₂³×C₃	1	2	yes	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	2	2	no	—
171	C₂²×C₈	—	2	2	no	—
172	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
173	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
174	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
175	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
176	C₂²×C₈	C₃×D₄	1	2	yes	—
177	C₂²×C₈	C₃×Q₈	1	2	yes	—
178	C₂²×C₈	C₃×Q₈	1	2	yes	—
179	C₂²×C₈	C₂³×C₃	1	2	yes	—
180	#117	—	2	1	no	—
181	#117	—	2	1	no	—
182	#117	C₃×Q₈	1	2	yes	—
183	#117	C₂³×C₃	1	2	yes	—
184	C₂×C₄⋊C₄	—	2	1	no	—
185	C₂×C₂²⋊C₄	C₃×Q₈	1	2	yes	—
186	C₂×C₄²	—	2	1	no	—
187	#108	—	2	16	no	—
188	#108	—	2	4	no	—
189	#108	—	2	4	no	—
190	#108	C₂×C₃×C₄	1	16	yes	complemented
191	#97	—	2	4	no	—
192	C₄×C₈	—	2	4	no	—
193	C₂³×C₃	—	4	2	no	—
194	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
195	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
196	C₂³×C₃	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂³×C₃	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂³×C₃	C₄⋊Q₈	1	1	yes	characteristic
199	C₂³×C₃	C₄⋊Q₈	1	1	yes	characteristic
200	C₂³×C₃	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₃×C₄	—	2	4	no	—
202	C₂×C₃×C₄	—	4	4	no	—
203	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
208	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
210	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
212	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
213	C₂×C₃×C₄	#121	1	1	yes	characteristic
214	C₂×C₃×C₄	#121	1	1	yes	characteristic
215	C₂×C₃×C₄	#121	1	1	yes	characteristic
216	C₂×C₃×C₄	#121	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂×C₃×C₄	#125	1	1	yes	characteristic
220	C₂×C₃×C₄	#125	1	1	yes	characteristic
221	C₂×C₃×C₄	#125	1	1	yes	characteristic
222	C₂×C₃×C₄	#125	1	1	yes	characteristic
223	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
224	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
231	C₃×C₈	—	2	8	no	—
232	C₃×C₈	—	2	4	no	—
233	C₃×C₈	—	4	4	no	—
234	C₃×C₈	C₂×C₄⋊C₄	1	4	yes	—
235	C₃×C₈	C₂×C₄⋊C₄	1	4	yes	—
236	C₂⁴	C₂×C₃×Q₈	1	1	yes	characteristic
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
247	C₂²×C₄	C₃×#41	1	1	yes	characteristic
248	C₂²×C₄	C₃×#41	1	1	yes	characteristic
249	C₂²×C₄	C₃×#41	1	1	yes	characteristic
250	C₂²×C₄	C₃×#41	1	1	yes	characteristic
251	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
252	M₁₆	—	2	4	no	—
253	M₁₆	—	2	4	no	—
254	M₁₆	—	2	2	no	—
255	M₁₆	—	2	2	no	—
256	M₁₆	—	2	4	no	—
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	4	no	—
259	M₁₆	—	2	4	no	—
260	M₁₆	—	4	2	no	—
261	M₁₆	—	4	2	no	—
262	M₁₆	C₂²×C₃×C₄	1	8	yes	—
263	M₁₆	C₂×C₃×D₄	1	4	yes	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
274	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
275	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
276	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
277	C₂×C₈	C₃×C₄⋊C₄	1	4	yes	—
278	C₂×C₈	C₃×C₄⋊C₄	1	4	yes	—
279	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
280	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
281	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₈	C₂×C₃×Q₈	1	4	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	2	2	no	—
286	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	4	1	no	—
293	C₂²×C₃	—	4	1	no	—
294	C₂²×C₃	—	4	1	no	—
295	C₂²×C₃	—	4	1	no	—
296	C₂²×C₃	#389	1	1	yes	characteristic
297	C₂²×C₃	#389	1	1	yes	characteristic
298	C₂²×C₃	#389	1	1	yes	characteristic
299	C₂²×C₃	#389	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₄×Q₈	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
302	C₂²×C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
303	C₃×C₄	—	4	4	no	—
304	C₃×C₄	#389	1	1	yes	characteristic
305	C₃×C₄	#389	1	1	yes	characteristic
306	C₃×C₄	#389	1	1	yes	characteristic
307	C₃×C₄	#389	1	1	yes	characteristic
308	C₃×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
309	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
310	C₃×C₄	C₂×#121	1	1	yes	characteristic
311	C₃×C₄	C₂×#125	1	1	yes	characteristic
312	C₂³	—	4	2	no	—
313	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
314	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
315	C₂³	C₃×C₂²⋊Q₈	1	1	yes	characteristic
316	C₂³	C₃×C₂²⋊Q₈	1	1	yes	characteristic
317	C₂³	C₃×C₄⋊Q₈	1	1	yes	characteristic
318	C₂³	C₃×C₄⋊Q₈	1	1	yes	characteristic
319	C₂³	C₂²×C₃×Q₈	1	1	yes	characteristic
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
327	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
328	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
329	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
330	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
331	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
332	C₂×C₄	C₃×#121	1	1	yes	characteristic
333	C₂×C₄	C₃×#121	1	1	yes	characteristic
334	C₂×C₄	C₃×#121	1	1	yes	characteristic
335	C₂×C₄	C₃×#121	1	1	yes	characteristic
336	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
337	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₄	C₃×#125	1	1	yes	characteristic
339	C₂×C₄	C₃×#125	1	1	yes	characteristic
340	C₂×C₄	C₃×#125	1	1	yes	characteristic
341	C₂×C₄	C₃×#125	1	1	yes	characteristic
342	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
343	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
344	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
346	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
348	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
349	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
350	C₈	—	2	8	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	4	no	—
353	C₈	C₂×C₃×C₄⋊C₄	1	4	yes	—
354	C₈	C₂×C₃×C₄⋊C₄	1	4	yes	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	#1953	1	2	yes	direct product factor
362	C₂×C₃	C₂×#389	1	1	yes	characteristic
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	C₃×#389	1	1	yes	characteristic
371	C₂²	C₃×#389	1	1	yes	characteristic
372	C₂²	C₃×#389	1	1	yes	characteristic
373	C₂²	C₃×#389	1	1	yes	characteristic
374	C₂²	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
375	C₂²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
376	C₂²	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
377	C₄	—	4	4	no	—
378	C₄	C₃×#389	1	1	yes	characteristic
379	C₄	C₃×#389	1	1	yes	characteristic
380	C₄	C₃×#389	1	1	yes	characteristic
381	C₄	C₃×#389	1	1	yes	characteristic
382	C₄	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
383	C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
384	C₄	C₂×C₃×#121	1	1	yes	characteristic
385	C₄	C₂×C₃×#125	1	1	yes	characteristic
386	C₃	C₂×#1953	1	1	yes	characteristic, direct product factor, Sylow
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	C₃×#1953	1	2	yes	direct product factor
394	C₂	C₂×C₃×#389	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#121
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂²×C₃	#389
prime radical	C₂⁴×C₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×#1953	C₂	direct (N × H)
7. C₂×#1953	C₃	direct (N × H)
19. C₂×C₃×#108	C₄	semidirect
20. C₂×C₃×#108	C₄	semidirect
32. #1953	C₂×C₃	direct (N × H)
74. C₃×#108	C₂×C₄	semidirect
88. C₂×#108	C₃×C₄	semidirect
89. C₂×#108	C₃×C₄	semidirect
190. #108	C₂×C₃×C₄	semidirect
361. C₂×C₃	#1953	direct (N × H)
386. C₃	C₂×#1953	direct (N × H)
393. C₂	C₃×#1953	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×#430	2
C₂²×C₃×#108	2
C₂×C₃×#405	2
C₃×#1953	2
C₂×C₃×#344	2
C₂×#1953	3

Subgroups — C2×C3×#1953 #10639790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#1953 #10639790