Subgroups — #18072224

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
3	#14561486	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926597	—	2	1	no	—
6	#11926597	—	2	1	no	—
7	#11926597	—	2	1	no	—
8	#11926597	—	2	1	no	—
9	#11926597	—	2	1	no	—
10	#11926597	—	2	1	no	—
11	#11926597	C₄	1	2	yes	—
12	#11926597	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
16	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
17	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₄	1	2	yes	—
19	C₂²×M₁₆×C₁₉	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₁₉	—	2	1	no	—
22	C₄×M₁₆×C₁₉	—	2	1	no	—
23	C₄×M₁₆×C₁₉	C₄	1	2	yes	—
24	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
25	C₂×C₁₉×#97	—	2	1	no	—
26	C₂×C₄×C₈×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	4	no	—
32	C₂×M₁₆×C₁₉	C₈	1	8	yes	complemented
33	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
49	C₁₉×#97	—	2	2	no	—
50	C₁₉×#97	—	2	2	no	—
51	C₄×C₈×C₁₉	—	2	2	no	—
52	C₄×C₈×C₁₉	—	2	2	no	—
53	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₄×C₁₉⋊C₈	—	2	2	no	—
62	C₄×C₁₉⋊C₈	—	2	2	no	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₂⁴×C₁₉	C₄²	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	4	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	M₁₆×C₁₉	—	2	8	no	—
89	M₁₆×C₁₉	—	2	4	no	—
90	M₁₆×C₁₉	C₂×C₈	1	8	yes	complemented
91	C₂×C₈×C₁₉	—	2	8	no	—
92	C₂×C₈×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	4	4	no	—
112	C₂×C₁₉⋊C₈	—	4	4	no	—
113	#7932	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	—	4	1	no	—
115	C₂³×C₁₉	—	4	1	no	—
116	C₂³×C₁₉	#95	1	1	yes	characteristic
117	C₂³×C₁₉	#95	1	1	yes	characteristic
118	C₂³×C₁₉	C₄×C₈	1	2	yes	—
119	C₂³×C₁₉	#97	1	2	yes	—
120	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₁₉	#97	1	2	yes	—
141	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
142	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
143	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
153	C₈×C₁₉	—	2	8	no	—
154	C₁₉⋊C₈	—	4	4	no	—
155	C₁₉⋊C₈	—	4	4	no	—
156	C₂×#431	—	19	1	no	—
157	C₂×#431	—	19	1	no	—
158	C₂×C₄×M₁₆	D₁₉	1	1	yes	characteristic
159	#1283	—	19	4	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	4	2	no	—
167	C₂²×C₁₉	—	4	2	no	—
168	C₂²×C₁₉	#336	1	2	yes	—
169	C₂²×C₁₉	#336	1	2	yes	—
170	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
171	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
172	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	#336	1	2	yes	—
180	C₄×C₁₉	#336	1	2	yes	—
181	C₄×C₁₉	#344	1	2	yes	—
182	C₄×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
183	C₄×C₁₉	#413	1	2	yes	—
184	C₄×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
185	C₂²×M₁₆	Dic₁₉	1	2	yes	—
186	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
187	#431	—	19	2	no	—
188	#431	—	19	2	no	—
189	#431	—	38	1	no	—
190	#431	—	38	1	no	—
191	#431	—	38	1	no	—
192	#431	—	38	1	no	—
193	#431	—	38	1	no	—
194	#431	—	38	1	no	—
195	C₂×C₄⋊C₈	—	19	2	no	—
196	C₂×C₄⋊C₈	—	38	1	no	—
197	C₂×C₂²⋊C₈	—	19	2	no	—
198	C₂×C₂²⋊C₈	—	19	2	no	—
199	C₄×M₁₆	—	2	1	no	—
200	C₄×M₁₆	—	2	1	no	—
201	C₄×M₁₆	Dic₁₉	1	2	yes	—
202	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
203	C₂×#97	—	2	1	no	—
204	C₂×C₄×C₈	—	2	1	no	—
205	C₂×C₄×C₈	—	19	2	no	—
206	C₂×C₄×C₈	—	38	1	no	—
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	—	2	2	no	—
209	C₂×C₁₉	—	2	1	no	—
210	C₂×C₁₉	—	2	1	no	—
211	C₂×C₁₉	C₂×#336	1	1	yes	characteristic
212	C₂×C₁₉	#1742	1	1	yes	characteristic
213	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
214	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
215	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	C₁₉⋊C₈	1	8	yes	complemented
220	C₂×M₁₆	C₂×Dic₁₉	1	4	yes	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	19	4	no	—
223	C₂²×C₈	—	38	2	no	—
224	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
225	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
228	C₂×C₄²	D₇₆	1	1	yes	characteristic
229	C₂×C₄²	D₇₆	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
236	C₄⋊C₈	—	38	2	no	—
237	C₄⋊C₈	—	38	2	no	—
238	C₄⋊C₈	—	38	2	no	—
239	C₄⋊C₈	—	38	2	no	—
240	C₂²⋊C₈	—	19	4	no	—
241	C₂²⋊C₈	—	38	2	no	—
242	C₂²⋊C₈	—	38	2	no	—
243	C₂²⋊C₈	—	38	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	38	2	no	—
249	C₄×C₈	—	38	2	no	—
250	C₄×C₈	—	38	2	no	—
251	C₄×C₈	—	38	2	no	—
252	C₁₉	#7932	1	1	yes	characteristic, complemented, Sylow
253	C₂⁴	C₄×Dic₁₉	1	1	yes	characteristic
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
257	C₂²×C₄	#64520	1	4	yes	—
258	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
259	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
260	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
276	M₁₆	—	2	8	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	C₂×C₁₉⋊C₈	1	8	yes	complemented
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	38	4	no	—
282	C₂×C₈	—	38	4	no	—
283	C₂×C₈	—	76	4	no	—
284	C₂×C₈	—	76	4	no	—
285	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
288	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
291	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
292	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
293	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
295	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
296	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
297	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
298	C₄²	C₂×D₇₆	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₄×C₁₉⋊C₈	1	2	yes	—
304	C₂³	#10597260	1	2	yes	—
305	C₂³	C₁₉⋊#95	1	1	yes	characteristic
306	C₂³	C₁₉⋊#95	1	1	yes	characteristic
307	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	C₄×C₁₉⋊C₈	1	2	yes	—
321	C₂×C₄	#10597260	1	2	yes	—
322	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
323	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
324	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
325	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
326	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
327	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
328	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₁₉⋊C₈	1	2	yes	—
333	C₂×C₄	C₂×#64520	1	2	yes	—
334	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
337	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
340	C₈	—	2	8	no	—
341	C₈	—	76	4	no	—
342	C₈	—	76	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	#11926299	1	2	yes	—
352	C₂²	#11926299	1	2	yes	—
353	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
354	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
355	C₂²	C₂×#10597260	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#11926299	1	2	yes	—
363	C₄	#11926299	1	2	yes	—
364	C₄	#11926316	1	2	yes	—
365	C₄	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
366	C₄	#11926526	1	2	yes	—
367	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	C₂×#11926299	1	1	yes	characteristic
373	C₂	#14563373	1	1	yes	characteristic
374	C₂	C₂×#11926316	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	(C₂×D₁₉)⋊C₄
commutator	C₂²×C₁₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₉
hypocenter	C₁₉	#7932
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14561486	C₂	semidirect
32. C₂×M₁₆×C₁₉	C₈	semidirect
90. M₁₆×C₁₉	C₂×C₈	semidirect
219. C₂×M₁₆	C₁₉⋊C₈	semidirect
252. C₁₉	#7932	semidirect
278. M₁₆	C₂×C₁₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926597	2
#14561486	2
C₂×C₄×M₁₆×C₁₉	2
#7932	19