Subgroups — #18075895

Order 4864.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14561476	C₂	1	2	yes	maximal, complemented
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
10	#11926299	—	2	1	no	—
11	#11926299	—	2	1	no	—
12	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
21	C₁₉×#376	—	2	1	no	—
22	C₄³×C₁₉	—	2	1	no	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₁₉×#117	—	2	2	no	—
27	C₁₉×#117	—	2	2	no	—
28	C₁₉×#117	—	2	2	no	—
29	C₁₉×#117	C₈	1	4	yes	complemented
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	2	2	no	—
39	C₂×C₄²×C₁₉	—	2	2	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	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
55	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
56	C₄⋊(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	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	2	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
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×C₈	1	2	yes	—
80	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
89	C₄⋊C₄×C₁₉	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
91	C₄⋊C₄×C₁₉	M₁₆	1	2	yes	—
92	C₂²⋊C₄×C₁₉	—	2	4	no	—
93	C₂²⋊C₄×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	—	2	4	no	—
95	C₄²×C₁₉	—	2	4	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	C₄²×C₁₉	—	2	1	no	—
98	C₄²×C₁₉	—	2	2	no	—
99	C₄²×C₁₉	—	2	2	no	—
100	C₄²×C₁₉	—	4	2	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	#41	1	2	yes	—
106	C₄²×C₁₉	#41	1	2	yes	—
107	C₂×C₁₉⋊C₈	—	2	4	no	—
108	C₂×C₁₉⋊C₈	—	4	2	no	—
109	C₂×C₁₉⋊C₈	—	4	2	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	#8708	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	—	2	1	no	—
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	C₂²⋊C₈	1	2	yes	—
121	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	2	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	1	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	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	4	4	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	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
151	C₂×C₄×C₁₉	#104	1	2	yes	—
152	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#123	1	2	yes	—
155	C₂×C₄×C₁₉	#123	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×M₁₆	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	#135	1	2	yes	—
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
163	C₁₉⋊C₈	—	4	4	no	—
164	C₁₉⋊C₈	—	8	2	no	—
165	C₄×#117	D₁₉	1	1	yes	characteristic
166	#1797	—	19	1	no	—
167	C₄×C₂²⋊C₈	—	19	1	no	—
168	#1279	—	19	2	no	—
169	#1279	—	19	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	#381	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
179	C₂²×C₁₉	#407	1	1	yes	characteristic
180	C₂²×C₁₉	#416	1	1	yes	characteristic
181	C₂²×C₁₉	#417	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
183	C₂²×C₁₉	#421	1	1	yes	characteristic
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	4	1	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	#431	1	1	yes	characteristic
193	C₄×C₁₉	#431	1	1	yes	characteristic
194	C₄×C₁₉	#432	1	1	yes	characteristic
195	C₄×C₁₉	#432	1	1	yes	characteristic
196	C₄×C₁₉	#482	1	2	yes	—
197	C₄×C₁₉	#485	1	2	yes	—
198	C₂×#117	Dic₁₉	1	1	yes	characteristic
199	C₂×#117	Dic₁₉	1	1	yes	characteristic
200	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
201	C₂×C₄⋊C₈	—	19	2	no	—
202	C₂×C₂²⋊C₈	—	38	1	no	—
203	C₂×C₂²⋊C₈	—	38	1	no	—
204	C₂×C₄×C₈	—	19	2	no	—
205	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
209	C₄×C₂²⋊C₄	—	2	1	no	—
210	C₄×C₂²⋊C₄	—	2	1	no	—
211	#376	—	2	1	no	—
212	C₄³	—	2	1	no	—
213	#336	—	38	1	no	—
214	#336	—	38	1	no	—
215	C₂×C₁₉	—	4	2	no	—
216	C₂×C₁₉	#1476	1	1	yes	characteristic
217	C₂×C₁₉	#1477	1	1	yes	characteristic
218	C₂×C₁₉	#1488	1	1	yes	characteristic
219	C₂×C₁₉	#1489	1	1	yes	characteristic
220	C₂×C₁₉	#1817	1	1	yes	characteristic
221	C₂×C₁₉	#1825	1	1	yes	characteristic
222	C₂×C₁₉	#1826	1	1	yes	characteristic
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	C₂²×C₈	—	38	2	no	—
227	C₂²×C₈	—	38	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	—	2	2	no	—
231	#117	C₁₉⋊C₈	1	4	yes	complemented
232	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	2	1	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	1	no	—
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	C₄⋊C₈	—	38	2	no	—
251	C₄⋊C₈	—	38	2	no	—
252	C₂²⋊C₈	—	38	4	no	—
253	C₂²⋊C₈	—	76	2	no	—
254	C₄×C₈	—	38	2	no	—
255	C₄×C₈	—	38	2	no	—
256	#95	—	2	1	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	C₁₉	#8708	1	1	yes	characteristic, complemented, Sylow
261	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
278	C₂²×C₄	#64520	1	2	yes	—
279	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×C₈	—	38	4	no	—
286	C₂×C₈	—	76	2	no	—
287	C₂×C₈	—	76	2	no	—
288	C₂×C₈	—	76	2	no	—
289	C₂×C₈	—	76	2	no	—
290	C₂×C₈	—	76	2	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	—
296	C₄⋊C₄	C₂×C₁₉⋊C₈	1	2	yes	—
297	C₄⋊C₄	#64520	1	2	yes	—
298	C₄⋊C₄	#64520	1	2	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	2	no	—
310	C₄²	—	4	1	no	—
311	C₄²	—	4	2	no	—
312	C₄²	#64541	1	2	yes	—
313	C₄²	#64541	1	2	yes	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
321	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
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	1	no	—
327	C₂×C₄	—	2	1	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	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	4	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	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
351	C₂×C₄	#10597294	1	2	yes	—
352	C₂×C₄	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
353	C₂×C₄	C₂×#64520	1	1	yes	characteristic
354	C₂×C₄	C₂×#64520	1	1	yes	characteristic
355	C₂×C₄	C₂×#64520	1	1	yes	characteristic
356	C₂×C₄	#10597372	1	1	yes	characteristic
357	C₂×C₄	#10597372	1	1	yes	characteristic
358	C₂×C₄	#10597375	1	2	yes	—
359	C₂×C₄	#10597375	1	2	yes	—
360	C₂×C₄	#10597395	1	1	yes	characteristic
361	C₂×C₄	#10597396	1	2	yes	—
362	C₂×C₄	#10597397	1	1	yes	characteristic
363	C₈	—	76	4	no	—
364	C₈	—	152	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	#11926407	1	1	yes	characteristic
373	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
374	C₂²	#11926508	1	1	yes	characteristic
375	C₂²	#11926540	1	1	yes	characteristic
376	C₂²	#11926545	1	1	yes	characteristic
377	C₂²	C₂×#10597294	1	1	yes	characteristic
378	C₂²	#11926561	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	#11926597	1	1	yes	characteristic
388	C₄	#11926597	1	1	yes	characteristic
389	C₄	#11926601	1	1	yes	characteristic
390	C₄	#11926601	1	1	yes	characteristic
391	C₄	#11926868	1	2	yes	—
392	C₄	#11926885	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	#14562017	1	1	yes	characteristic
395	C₂	#14562022	1	1	yes	characteristic
396	C₂	#14562069	1	1	yes	characteristic
397	C₂	#14562074	1	1	yes	characteristic
398	C₂	#14563703	1	1	yes	characteristic
399	C₂	#14563730	1	1	yes	characteristic
400	C₂	#14563734	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	C₄×C₁₉×#117	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#117	D₁₉
hypocenter	C₁₉	#8708
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #14561476	C₂	semidirect
4. #14561476	C₂	semidirect
29. C₁₉×#117	C₈	semidirect
231. #117	C₁₉⋊C₈	semidirect
260. C₁₉	#8708	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₄×C₂²⋊(C₁₉⋊C₈)	2
#14561476	2
C₄×C₁₉×#117	2
#8708	19