Subgroups — #18075227

Order 4864.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563787	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
4	#14561476	C₂	1	2	yes	maximal
5	C₄²×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
11	#11926299	—	2	1	no	—
12	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
18	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₄³×C₁₉	—	2	1	no	—
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	1	no	—
29	C₄×Q₈×C₁₉	—	2	1	no	—
30	C₄×Q₈×C₁₉	C₈	1	4	yes	complemented
31	C₄×Q₈×C₁₉	D₄	1	2	yes	—
32	C₄×Q₈×C₁₉	Q₈	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	2	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
62	C₄×C₁₉⋊C₈	—	2	2	no	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	1	no	—
66	C₂×Q₈×C₁₉	—	2	1	no	—
67	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
68	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
69	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	—	2	4	no	—
82	C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
89	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
91	C₄²×C₁₉	—	2	4	no	—
92	C₄²×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	—	2	2	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	C₄²×C₁₉	—	2	1	no	—
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	2	no	—
102	C₄²×C₁₉	—	4	2	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	C₂×C₈	1	2	yes	—
106	C₄²×C₁₉	M₁₆	1	2	yes	—
107	C₄²×C₁₉	SD₁₆	1	2	yes	—
108	C₄²×C₁₉	Q₁₆	1	2	yes	—
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₂×C₁₉⋊C₈	—	2	4	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	C₂×C₁₉⋊C₈	—	4	2	no	—
118	C₂×C₁₉⋊C₈	—	4	2	no	—
119	#8564	—	19	1	no	maximal, Sylow
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	Q₈×C₁₉	—	2	2	no	—
122	Q₈×C₁₉	—	2	2	no	—
123	Q₈×C₁₉	—	2	2	no	—
124	Q₈×C₁₉	C₄⋊C₈	1	4	yes	complemented
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₁₉	#103	1	2	yes	—
149	C₂×C₄×C₁₉	#103	1	2	yes	—
150	C₂×C₄×C₁₉	#104	1	2	yes	—
151	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
165	C₁₉⋊C₈	—	4	4	no	—
166	C₁₉⋊C₈	—	8	2	no	—
167	C₄²×Q₈	D₁₉	1	1	yes	characteristic
168	#1842	—	19	1	no	—
169	C₄×C₄⋊C₈	—	19	1	no	—
170	C₂×Q₈⋊C₈	—	19	2	no	—
171	#1279	—	19	2	no	—
172	C₂²×C₁₉	#380	1	1	yes	characteristic
173	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
174	C₂²×C₁₉	#407	1	1	yes	characteristic
175	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
176	C₂²×C₁₉	#417	1	1	yes	characteristic
177	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
178	C₂²×C₁₉	#421	1	1	yes	characteristic
179	C₄×C₁₉	—	2	4	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	4	2	no	—
185	C₄×C₁₉	—	4	2	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	2	no	—
188	C₄×C₁₉	Q₈⋊C₈	1	4	yes	complemented
189	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
190	C₄×C₁₉	#423	1	1	yes	characteristic
191	C₄×C₁₉	#431	1	1	yes	characteristic
192	C₄×C₁₉	#432	1	1	yes	characteristic
193	C₄×C₁₉	#460	1	1	yes	characteristic
194	C₄×C₁₉	#462	1	1	yes	characteristic
195	C₄×C₁₉	#475	1	1	yes	characteristic
196	C₄×C₁₉	#477	1	1	yes	characteristic
197	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
198	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
199	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
200	C₂×C₄⋊C₈	—	19	2	no	—
201	C₂×C₄⋊C₈	—	38	1	no	—
202	C₂×C₄⋊C₈	—	38	1	no	—
203	C₂×C₄⋊C₈	—	38	1	no	—
204	C₂×C₄×C₈	—	19	2	no	—
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	—	2	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
209	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
211	C₄³	—	2	1	no	—
212	C₄³	C₂×D₁₉	1	1	yes	characteristic
213	#336	—	38	1	no	—
214	Q₈⋊C₈	—	38	4	no	—
215	C₂×C₁₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
216	C₂×C₁₉	#1477	1	1	yes	characteristic
217	C₂×C₁₉	#1487	1	1	yes	characteristic
218	C₂×C₁₉	#1489	1	1	yes	characteristic
219	C₂×C₁₉	#1797	1	1	yes	characteristic
220	C₂×C₁₉	#1803	1	1	yes	characteristic
221	C₂×C₁₉	#1806	1	1	yes	characteristic
222	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
223	C₂²×C₈	—	38	2	no	—
224	C₂²×C₈	—	38	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	2	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	C₁₉⋊C₈	1	4	yes	complemented
231	C₄×Q₈	Dic₃₈	1	2	yes	—
232	C₄×Q₈	D₇₆	1	2	yes	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
252	C₄⋊C₈	—	38	4	no	—
253	C₄⋊C₈	—	38	2	no	—
254	C₄⋊C₈	—	38	2	no	—
255	C₄⋊C₈	—	76	2	no	—
256	C₄⋊C₈	—	76	2	no	—
257	C₄×C₈	—	38	2	no	—
258	C₄×C₈	—	38	2	no	—
259	#95	—	2	1	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	C₁₉	#8564	1	1	yes	characteristic, complemented, Sylow
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	C₂×C₁₉⋊C₈	1	2	yes	—
267	C₂×Q₈	#64520	1	2	yes	—
268	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂×C₈	—	38	4	no	—
281	C₂×C₈	—	76	2	no	—
282	C₂×C₈	—	76	2	no	—
283	C₂×C₈	—	76	2	no	—
284	C₂×C₈	—	76	2	no	—
285	C₂×C₈	—	76	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	—
294	C₄⋊C₄	#64520	1	2	yes	—
295	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	2	no	—
310	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
311	C₄²	#64520	1	2	yes	—
312	C₄²	#64527	1	2	yes	—
313	C₄²	#64528	1	2	yes	—
314	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
315	C₄²	C₂×D₇₆	1	1	yes	characteristic
316	C₄²	#64541	1	1	yes	characteristic
317	C₄²	#64541	1	1	yes	characteristic
318	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
319	Q₈	—	2	2	no	—
320	Q₈	—	2	2	no	—
321	Q₈	—	2	2	no	—
322	Q₈	C₄⋊(C₁₉⋊C₈)	1	4	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
345	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
346	C₂×C₄	#10597292	1	2	yes	—
347	C₂×C₄	#10597292	1	2	yes	—
348	C₂×C₄	#10597294	1	2	yes	—
349	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
350	C₂×C₄	C₂×#64520	1	1	yes	characteristic
351	C₂×C₄	C₂×#64520	1	1	yes	characteristic
352	C₂×C₄	C₂×#64520	1	1	yes	characteristic
353	C₂×C₄	#10597370	1	1	yes	characteristic
354	C₂×C₄	#10597370	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
356	C₂×C₄	#10597372	1	1	yes	characteristic
357	C₂×C₄	#10597376	1	1	yes	characteristic
358	C₂×C₄	#10597376	1	1	yes	characteristic
359	C₂×C₄	C₂×#64527	1	1	yes	characteristic
360	C₂×C₄	C₂×#64528	1	1	yes	characteristic
361	C₂×C₄	#10597395	1	1	yes	characteristic
362	C₂×C₄	#10597397	1	1	yes	characteristic
363	C₈	—	76	4	no	—
364	C₈	—	152	2	no	—
365	C₂²	#11926404	1	1	yes	characteristic
366	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
367	C₂²	#11926508	1	1	yes	characteristic
368	C₂²	C₂×#10597292	1	1	yes	characteristic
369	C₂²	#11926545	1	1	yes	characteristic
370	C₂²	C₂×#10597294	1	1	yes	characteristic
371	C₂²	#11926561	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	Q₈⋊(C₁₉⋊C₈)	1	4	yes	complemented
382	C₄	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
383	C₄	#11926568	1	1	yes	characteristic
384	C₄	#11926597	1	1	yes	characteristic
385	C₄	#11926601	1	1	yes	characteristic
386	C₄	#11926744	1	1	yes	characteristic
387	C₄	#11926754	1	1	yes	characteristic
388	C₄	#11926829	1	1	yes	characteristic
389	C₄	#11926839	1	1	yes	characteristic
390	C₂	C₂×Q₈⋊(C₁₉⋊C₈)	1	1	yes	characteristic
391	C₂	#14562022	1	1	yes	characteristic
392	C₂	#14562064	1	1	yes	characteristic
393	C₂	#14562074	1	1	yes	characteristic
394	C₂	#14563615	1	1	yes	characteristic
395	C₂	#14563640	1	1	yes	characteristic
396	C₂	#14563655	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×Q₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×Q₈	D₁₉
hypocenter	C₁₉	#8564
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
30. C₄×Q₈×C₁₉	C₈	semidirect
124. Q₈×C₁₉	C₄⋊C₈	semidirect
188. C₄×C₁₉	Q₈⋊C₈	semidirect
230. C₄×Q₈	C₁₉⋊C₈	semidirect
262. C₁₉	#8564	semidirect
322. Q₈	C₄⋊(C₁₉⋊C₈)	semidirect
381. C₄	Q₈⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#14563787	2
C₄×C₄⋊(C₁₉⋊C₈)	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561476	2
C₄²×Q₈×C₁₉	2
#8564	19