Subgroups — #18072499

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572268	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926568	C₂	1	1	yes	maximal, characteristic
3	#14561510	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	—	2	1	no	—
6	#11926601	—	2	1	no	—
7	#11926601	C₄	1	2	yes	—
8	#11926597	—	2	1	no	—
9	#11926597	C₄	1	2	yes	—
10	#11926568	—	2	1	no	—
11	#11926568	—	2	1	no	—
12	#11926568	C₄	1	2	yes	—
13	#11926568	C₂²	1	2	yes	—
14	#11926568	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
17	#11926508	—	2	1	no	—
18	C₄×#64520	—	2	1	no	—
19	C₂²×M₁₆×C₁₉	C₄	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#423	—	2	1	no	—
22	C₁₉×#423	—	2	1	no	—
23	C₁₉×#423	—	2	1	no	—
24	C₁₉×#423	—	2	1	no	—
25	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂×M₁₆×C₁₉	—	4	4	no	—
33	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂×C₄	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	C₂³	1	1	yes	characteristic
46	C₂×#64520	—	2	2	no	—
47	C₂×#64520	—	2	2	no	—
48	C₂×#64520	—	2	2	no	—
49	C₂×#64520	—	4	4	no	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₁₉×C₄⋊C₈	—	2	2	no	—
52	C₁₉×C₄⋊C₈	—	2	2	no	—
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×C₄⋊C₈	—	2	2	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
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)	C₂×C₄	1	4	yes	—
62	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
63	#10597260	—	2	2	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
89	M₁₆×C₁₉	—	4	4	no	—
90	M₁₆×C₁₉	—	4	4	no	—
91	C₂×C₈×C₁₉	—	2	4	no	—
92	C₂×C₈×C₁₉	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	#64520	—	4	4	no	—
110	#64520	—	4	2	no	—
111	#64520	—	4	4	no	—
112	#64520	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	2	4	no	—
114	C₂×C₁₉⋊C₈	—	2	4	no	—
115	C₂×C₁₉⋊C₈	—	4	4	no	—
116	#8004	—	19	1	no	maximal, Sylow
117	C₂³×C₁₉	—	2	2	no	—
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	4	1	no	—
120	C₂³×C₁₉	#95	1	1	yes	characteristic
121	C₂³×C₁₉	#95	1	1	yes	characteristic
122	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	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	1	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	#95	1	1	yes	characteristic
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	#100	1	2	yes	—
150	C₂×C₄×C₁₉	#101	1	2	yes	—
151	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₁₉	#137	1	2	yes	—
159	C₈×C₁₉	—	4	4	no	—
160	C₁₉⋊C₈	—	4	4	no	—
161	C₁₉⋊C₈	—	4	4	no	—
162	#2920	—	19	1	no	—
163	C₂×#423	—	19	1	no	—
164	C₂×#423	D₁₉	1	1	yes	characteristic
165	#1292	—	19	4	no	—
166	C₂²×C₁₉	—	2	1	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	4	no	—
174	C₂²×C₁₉	#343	1	2	yes	—
175	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
176	C₂²×C₁₉	#428	1	2	yes	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
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	#338	1	2	yes	—
185	C₄×C₁₉	#343	1	2	yes	—
186	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
187	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
188	C₄×C₁₉	#417	1	2	yes	—
189	C₄×C₁₉	#418	1	1	yes	characteristic
190	C₄×C₁₉	#419	1	1	yes	characteristic
191	C₂²×M₁₆	—	38	1	no	—
192	C₂²×M₁₆	Dic₁₉	1	2	yes	—
193	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
194	#432	—	19	2	no	—
195	#432	—	38	1	no	—
196	#431	—	19	2	no	—
197	#431	—	38	1	no	—
198	#423	—	2	1	no	—
199	#423	—	2	1	no	—
200	#423	—	2	1	no	—
201	#423	—	2	1	no	—
202	#423	—	19	2	no	—
203	#423	—	19	2	no	—
204	#423	—	19	2	no	—
205	#423	—	38	1	no	—
206	#423	—	38	1	no	—
207	C₂×C₄⋊C₈	—	19	2	no	—
208	C₂×C₄⋊C₈	—	38	1	no	—
209	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	—
210	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
211	#407	—	38	1	no	—
212	C₄×M₁₆	—	38	1	no	—
213	C₂×C₁₉	—	2	2	no	—
214	C₂×C₁₉	—	2	2	no	—
215	C₂×C₁₉	—	4	1	no	—
216	C₂×C₁₉	C₂×#338	1	1	yes	characteristic
217	C₂×C₁₉	#1736	1	1	yes	characteristic
218	C₂×C₁₉	C₂×#343	1	1	yes	characteristic
219	C₂³×C₄	Dic₃₈	1	1	yes	characteristic
220	C₂³×C₄	D₇₆	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	4	4	no	—
225	C₂×M₁₆	—	38	2	no	—
226	C₂×M₁₆	—	38	2	no	—
227	C₂×M₁₆	—	38	2	no	—
228	C₂×M₁₆	—	76	4	no	—
229	C₂²×C₈	—	38	2	no	—
230	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
231	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
236	C₂×C₄²	D₇₆	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	19	4	no	—
248	C₄⋊C₈	—	19	4	no	—
249	C₄⋊C₈	—	38	2	no	—
250	C₄⋊C₈	—	38	2	no	—
251	C₄⋊C₈	—	38	2	no	—
252	C₄⋊C₈	—	38	2	no	—
253	C₂²⋊C₈	—	38	2	no	—
254	C₂²⋊C₈	—	38	2	no	—
255	#97	—	38	2	no	—
256	C₄×C₈	—	38	2	no	—
257	C₁₉	#8004	1	1	yes	characteristic, complemented, Sylow
258	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
265	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
266	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₁₉⋊C₄	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	C₄⋊Dic₁₉	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	C₂²⋊Dic₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
282	M₁₆	—	4	4	no	—
283	M₁₆	—	4	4	no	—
284	M₁₆	—	76	4	no	—
285	M₁₆	—	76	2	no	—
286	M₁₆	—	76	4	no	—
287	M₁₆	—	76	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₂×C₈	—	38	4	no	—
291	C₂×C₈	—	38	4	no	—
292	C₂×C₈	—	76	4	no	—
293	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
294	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
295	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
299	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
300	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
301	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
302	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
303	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
304	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
305	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
307	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
308	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	4	1	no	—
312	C₂³	C₁₉⋊#95	1	1	yes	characteristic
313	C₂³	C₁₉⋊#95	1	1	yes	characteristic
314	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
341	C₂×C₄	#10597290	1	2	yes	—
342	C₂×C₄	#10597293	1	2	yes	—
343	C₂×C₄	#10597354	1	2	yes	—
344	C₂×C₄	#10597355	1	2	yes	—
345	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₈	—	76	4	no	—
353	C₈	—	76	4	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	#11926313	1	2	yes	—
363	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
364	C₂²	#11926586	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	C₁₉⋊#338	1	2	yes	—
373	C₄	#11926313	1	2	yes	—
374	C₄	C₂×#10597290	1	1	yes	characteristic
375	C₄	C₂×#10597293	1	1	yes	characteristic
376	C₄	#11926546	1	2	yes	—
377	C₄	#11926550	1	1	yes	characteristic
378	C₄	#11926554	1	1	yes	characteristic
379	C₂	—	2	2	no	—
380	C₂	—	2	2	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×C₁₉⋊#338	1	1	yes	characteristic
383	C₂	#14563355	1	1	yes	characteristic
384	C₂	C₂×#11926313	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#423	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#423	D₁₉
hypocenter	C₁₉	#8004
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #14561510	C₂	semidirect
257. C₁₉	#8004	semidirect

Maximal subgroups

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

subgroup	index
#14572268	2
C₂×#11926568	2
#14561510	2
C₂×C₁₉×#423	2
#8004	19