Subgroups — #18072856

Order 4864.

742 conjugacy classes of subgroups.

The subgroup lattice has 392 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	#14572268	C₂	1	1	yes	maximal, characteristic
3	#14561538	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926601	—	2	1	no	—
6	#11926601	—	2	1	no	—
7	#11926601	C₄	1	2	yes	complemented
8	#11926601	C₄	1	2	yes	complemented
9	#11926597	—	2	1	no	—
10	#11926597	—	2	1	no	—
11	#11926597	C₄	1	2	yes	complemented
12	#11926597	C₂²	1	2	yes	—
13	#11926568	C₄	1	2	yes	complemented
14	#11926568	C₂²	1	2	yes	—
15	#11926508	—	2	1	no	—
16	#11926508	—	2	1	no	—
17	C₄×#64520	—	2	1	no	—
18	C₄×#64520	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄²×C₁₉	—	2	1	no	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂×C₁₉×#95	C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	—	2	2	no	—
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	—	4	4	no	—
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	C₂×C₄	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	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×#64520	—	2	2	no	—
50	C₂×#64520	—	2	2	no	—
51	C₁₉×#95	—	2	2	no	—
52	C₁₉×#95	C₂×C₄	1	4	yes	—
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)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
60	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
61	#10597260	—	2	2	no	—
62	#10597260	—	2	2	no	—
63	C₄×C₁₉⋊C₈	—	2	2	no	—
64	C₄×C₁₉⋊C₈	—	2	2	no	—
65	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	—	2	4	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	8	no	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	4	2	no	—
72	C₂²×C₄×C₁₉	—	4	4	no	—
73	C₂²×C₄×C₁₉	—	4	4	no	—
74	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²⋊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	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	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₁₉	—	2	8	no	—
93	C₄⋊C₄×C₁₉	—	2	8	no	—
94	C₄²×C₁₉	—	4	4	no	—
95	C₄²×C₁₉	—	4	4	no	—
96	C₄²×C₁₉	C₄²	1	1	yes	characteristic
97	C₄²×C₁₉	C₄²	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	C₂²⋊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	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	#64520	—	4	4	no	—
113	#64520	—	4	2	no	—
114	#64520	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	2	4	no	—
116	C₂×C₁₉⋊C₈	—	2	4	no	—
117	#8098	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	—	2	2	no	—
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	#95	1	1	yes	characteristic
123	C₂³×C₁₉	#95	1	1	yes	characteristic
124	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	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	—	2	8	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	16	no	—
144	C₂×C₄×C₁₉	—	4	4	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
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	#104	1	4	yes	—
153	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₁₉	#137	1	2	yes	—
161	C₁₉⋊C₈	—	4	4	no	—
162	C₁₉⋊C₈	—	4	4	no	—
163	#2920	—	19	1	no	—
164	#2920	—	19	1	no	—
165	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
166	#1303	—	19	4	no	—
167	C₂²×C₁₉	—	2	4	no	—
168	C₂²×C₁₉	—	2	4	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	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	#339	1	2	yes	—
176	C₂²×C₁₉	#344	1	2	yes	—
177	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
178	C₂²×C₁₉	#418	1	1	yes	characteristic
179	C₂²×C₁₉	#419	1	1	yes	characteristic
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	—	4	8	no	—
189	C₄×C₁₉	#339	1	2	yes	—
190	C₄×C₁₉	#417	1	2	yes	—
191	C₄×C₁₉	C₂×#104	1	2	yes	—
192	C₄×C₁₉	#428	1	2	yes	—
193	C₂²×C₄⋊C₄	—	2	1	no	—
194	C₂²×C₄²	—	2	1	no	—
195	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
196	#432	—	19	2	no	—
197	#432	—	19	2	no	—
198	#432	—	38	1	no	—
199	#432	—	38	1	no	—
200	#431	—	19	2	no	—
201	#431	—	19	2	no	—
202	#431	—	38	1	no	—
203	#431	—	38	1	no	—
204	#423	—	19	2	no	—
205	#423	—	19	2	no	—
206	#407	—	38	1	no	—
207	#407	—	38	1	no	—
208	C₄×M₁₆	—	38	1	no	—
209	C₄×M₁₆	—	38	1	no	—
210	C₄×C₄⋊C₄	—	2	1	no	—
211	C₄×C₄⋊C₄	—	2	1	no	—
212	C₄×C₄⋊C₄	Dic₁₉	1	2	yes	—
213	C₄×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
214	C₂×#95	Dic₁₉	1	2	yes	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	2	2	no	—
217	C₂×C₁₉	—	2	2	no	—
218	C₂×C₁₉	—	2	1	no	—
219	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
220	C₂×C₁₉	#1736	1	1	yes	characteristic
221	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
224	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
226	C₂×M₁₆	—	38	2	no	—
227	C₂×M₁₆	—	38	2	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	4	4	no	—
234	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
235	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₁₉	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	D₇₆	1	1	yes	characteristic
241	C₂×C₄²	D₇₆	1	1	yes	characteristic
242	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
246	C₄⋊C₈	—	19	4	no	—
247	C₄⋊C₈	—	19	4	no	—
248	C₄⋊C₈	—	38	2	no	—
249	C₄⋊C₈	—	38	2	no	—
250	C₂²⋊C₈	—	38	2	no	—
251	C₂²⋊C₈	—	38	2	no	—
252	C₂²⋊C₈	—	38	2	no	—
253	C₂²⋊C₈	—	38	2	no	—
254	#97	—	38	2	no	—
255	#97	—	38	2	no	—
256	C₄×C₈	—	38	2	no	—
257	C₄×C₈	—	38	2	no	—
258	#95	—	2	2	no	—
259	#95	C₂×Dic₁₉	1	4	yes	—
260	C₁₉	#8098	1	1	yes	characteristic, complemented, Sylow
261	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
272	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊Dic₁₉	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×D₁₉)⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
288	M₁₆	—	76	2	no	—
289	M₁₆	—	76	2	no	—
290	M₁₆	—	76	4	no	—
291	C₂×C₈	—	38	4	no	—
292	C₂×C₈	—	38	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	4	4	no	—
297	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
298	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
299	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
300	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
301	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
302	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
303	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
304	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
305	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
306	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
307	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
308	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
309	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
310	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
312	C₄²	C₂×D₇₆	1	1	yes	characteristic
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	C₁₉⋊#95	1	1	yes	characteristic
318	C₂³	C₁₉⋊#95	1	1	yes	characteristic
319	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	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	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	8	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	16	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	#10597262	1	4	yes	—
342	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
346	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
347	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
352	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
354	C₂×C₄	#10597378	1	2	yes	—
355	C₂×C₄	#10597388	1	2	yes	—
356	C₈	—	76	4	no	—
357	C₈	—	76	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	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	—	2	1	no	—
366	C₂²	#11926304	1	2	yes	—
367	C₂²	#11926314	1	2	yes	—
368	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
369	C₂²	#11926549	1	1	yes	characteristic
370	C₂²	#11926553	1	1	yes	characteristic
371	C₄	—	2	1	no	—
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	—	4	8	no	—
380	C₄	#11926304	1	2	yes	—
381	C₄	#11926543	1	2	yes	—
382	C₄	C₂×#10597262	1	2	yes	—
383	C₄	#11926584	1	2	yes	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	2	no	—
387	C₂	—	2	2	no	—
388	C₂	C₂×#11926304	1	1	yes	characteristic
389	C₂	#14563354	1	1	yes	characteristic
390	C₂	C₂×#11926314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#8098
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #14561538	C₂	semidirect
7. #11926601	C₄	semidirect
8. #11926601	C₄	semidirect
11. #11926597	C₄	semidirect
13. #11926568	C₄	semidirect
59. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
60. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
260. C₁₉	#8098	semidirect

Maximal subgroups

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

subgroup	index
#14572268	2
#14561538	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#8098	19