Subgroups — #18072427

Order 4864.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566042	C₂	1	1	yes	maximal, characteristic
2	#14566033	C₂	1	1	yes	maximal, characteristic
3	#14561503	C₂	1	4	yes	maximal
4	C₂×C₁₉×#432	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597372	—	2	1	no	—
6	#11926414	—	2	1	no	—
7	#11926412	C₄	1	2	yes	complemented
8	#11926410	—	2	1	no	—
9	#11926410	C₄	1	2	yes	complemented
10	#11926407	—	2	1	no	—
11	#11926404	—	2	1	no	—
12	#11926404	C₂²	1	2	yes	—
13	#11926404	C₂²	1	2	yes	—
14	C₄×C₄⋊Dic₁₉	—	2	1	no	—
15	C₄×C₄⋊Dic₁₉	—	2	1	no	—
16	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	complemented
17	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
18	#11926390	C₄	1	2	yes	complemented
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#432	—	2	1	no	—
21	C₁₉×#432	—	2	1	no	—
22	C₁₉×#432	—	2	1	no	—
23	C₁₉×#432	—	2	1	no	—
24	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	complemented
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₉×#97	C₄	1	2	yes	complemented
27	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	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	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
43	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
44	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
45	#10597372	—	4	4	no	—
46	C₂×C₄⋊Dic₁₉	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	2	no	—
48	C₂×C₄⋊Dic₁₉	—	2	2	no	—
49	C₂×C₄⋊Dic₁₉	—	2	2	no	—
50	C₂×C₄×Dic₁₉	—	2	2	no	—
51	C₂×C₄×Dic₁₉	—	2	2	no	—
52	C₁₉×C₄⋊C₈	—	2	2	no	—
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×C₂²⋊C₈	—	2	2	no	—
55	C₁₉×C₂²⋊C₈	—	2	2	no	—
56	C₁₉×#97	—	2	2	no	—
57	C₁₉×#97	—	2	2	no	—
58	C₁₉⋊#95	—	2	2	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	—	2	2	no	—
61	C₁₉⋊#95	—	2	2	no	—
62	C₁₉⋊#95	C₂×C₄	1	4	yes	—
63	C₁₉⋊#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×Dic₁₉	—	2	4	no	—
88	C₂²×Dic₁₉	—	2	4	no	—
89	C₂×C₈×C₁₉	—	2	4	no	—
90	C₂×C₈×C₁₉	—	4	4	no	—
91	C₄²×C₁₉	C₄²	1	1	yes	characteristic
92	C₄²×C₁₉	C₄²	1	1	yes	characteristic
93	C₄²×C₁₉	C₄²	1	1	yes	characteristic
94	C₄²×C₁₉	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
107	C₂²⋊Dic₁₉	—	4	2	no	—
108	C₂²⋊Dic₁₉	—	4	4	no	—
109	C₂²⋊Dic₁₉	—	4	2	no	—
110	C₄⋊Dic₁₉	—	4	4	no	—
111	C₄⋊Dic₁₉	—	4	4	no	—
112	C₄⋊Dic₁₉	—	4	4	no	—
113	C₄⋊Dic₁₉	—	4	4	no	—
114	C₄×Dic₁₉	—	4	4	no	—
115	C₄×Dic₁₉	—	4	4	no	—
116	#7984	—	19	1	no	maximal, Sylow
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₁₉	#137	1	2	yes	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	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	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₉	—	4	4	no	—
157	C₂×Dic₁₉	—	4	4	no	—
158	C₂×Dic₁₉	—	4	4	no	—
159	C₂×Dic₁₉	—	4	4	no	—
160	C₂×Dic₁₉	—	4	4	no	—
161	C₂×Dic₁₉	—	4	4	no	—
162	C₈×C₁₉	—	4	4	no	—
163	C₂×#432	D₁₉	1	1	yes	characteristic
164	#2285	—	19	1	no	—
165	#2283	—	19	1	no	—
166	#1289	—	19	4	no	—
167	C₂²×C₁₉	—	2	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
176	C₂²×C₁₉	#417	1	2	yes	—
177	C₂²×C₁₉	#418	1	1	yes	characteristic
178	C₂²×C₁₉	#419	1	1	yes	characteristic
179	C₂²×C₁₉	#428	1	2	yes	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	H(3,ℤ/4)	1	2	yes	—
191	C₄×C₁₉	#410	1	2	yes	—
192	Dic₁₉	—	8	4	no	—
193	Dic₁₉	—	8	4	no	—
194	C₂×#117	—	38	1	no	—
195	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
196	#432	—	2	1	no	—
197	#432	—	2	1	no	—
198	#432	—	2	1	no	—
199	#432	—	2	1	no	—
200	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	complemented
201	C₂×C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
202	C₂×#97	Dic₁₉	1	2	yes	complemented
203	#384	—	38	1	no	—
204	#383	—	19	2	no	—
205	#382	—	19	2	no	—
206	#382	—	38	1	no	—
207	#381	—	38	1	no	—
208	#380	—	19	2	no	—
209	#380	—	19	2	no	—
210	#380	—	38	1	no	—
211	C₄×C₄⋊C₄	—	19	2	no	—
212	C₄×C₄⋊C₄	—	38	1	no	—
213	C₄×C₄⋊C₄	—	38	1	no	—
214	C₄×C₂²⋊C₄	—	38	1	no	—
215	#376	—	19	2	no	—
216	C₂×C₁₉	—	2	1	no	—
217	C₂×C₁₉	—	2	2	no	—
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	—	2	2	no	—
220	C₂×C₁₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
221	C₂×C₁₉	#1736	1	1	yes	characteristic
222	C₂×C₁₉	#1740	1	1	yes	characteristic
223	C₂³×C₄	D₇₆	1	1	yes	characteristic
224	C₂³×C₄	D₇₆	1	1	yes	characteristic
225	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
226	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
227	#117	—	76	4	no	—
228	C₂×C₄⋊C₄	—	38	2	no	—
229	C₂×C₄⋊C₄	—	38	2	no	—
230	C₂×C₄⋊C₄	—	38	2	no	—
231	C₂×C₄⋊C₄	—	38	2	no	—
232	C₂×C₂²⋊C₄	—	38	2	no	—
233	C₂×C₂²⋊C₄	—	38	2	no	—
234	C₂×C₄²	—	38	2	no	—
235	C₂×C₄²	—	38	2	no	—
236	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
237	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
242	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	#95	—	19	4	no	—
255	#95	—	19	4	no	—
256	#95	—	38	2	no	—
257	#95	—	38	2	no	—
258	#95	—	38	2	no	—
259	#95	—	38	2	no	—
260	C₁₉	#7984	1	1	yes	characteristic, complemented, Sylow
261	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	38	4	no	—
267	C₂²×C₄	—	38	4	no	—
268	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₄⋊C₄	—	76	4	no	—
289	C₄⋊C₄	—	76	4	no	—
290	C₄⋊C₄	—	76	4	no	—
291	C₄⋊C₄	—	76	4	no	—
292	C₂²⋊C₄	—	76	2	no	—
293	C₂²⋊C₄	—	76	4	no	—
294	C₂²⋊C₄	—	76	2	no	—
295	C₄²	—	76	4	no	—
296	C₄²	—	76	4	no	—
297	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
298	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
299	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
300	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
301	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
302	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
303	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
304	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
305	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
306	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
307	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
308	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
309	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
310	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
311	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
312	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	#10597354	1	2	yes	—
316	C₂³	#10597355	1	2	yes	—
317	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
318	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
319	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	76	4	no	—
341	C₂×C₄	—	76	4	no	—
342	C₂×C₄	—	76	4	no	—
343	C₂×C₄	—	76	4	no	—
344	C₂×C₄	—	76	4	no	—
345	C₂×C₄	—	76	4	no	—
346	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
347	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
348	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
349	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
350	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
351	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
352	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
353	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
358	C₈	—	4	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
368	C₂²	#11926546	1	2	yes	—
369	C₂²	#11926550	1	1	yes	characteristic
370	C₂²	#11926554	1	1	yes	characteristic
371	C₂²	#11926586	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	152	4	no	—
383	C₄	—	152	4	no	—
384	C₄	#11926301	1	2	yes	—
385	C₄	#11926518	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×#11926301	1	1	yes	characteristic
391	C₂	#14563355	1	1	yes	characteristic
392	C₂	#14563368	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#432	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#432	D₁₉
hypocenter	C₁₉	#7984
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
7. #11926412	C₄	semidirect
9. #11926410	C₄	semidirect
16. C₄×C₄⋊Dic₁₉	C₄	semidirect
18. #11926390	C₄	semidirect
24. C₂×C₁₉×C₄⋊C₈	C₄	semidirect
26. C₂×C₁₉×#97	C₄	semidirect
200. C₂×C₄⋊C₈	Dic₁₉	semidirect
202. C₂×#97	Dic₁₉	semidirect
260. C₁₉	#7984	semidirect

Maximal subgroups

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

subgroup	index
#14566042	2
#14566033	2
#14561503	2
C₂×C₁₉×#432	2
#7984	19