Subgroups — #18075242

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 408 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, complemented
2	C₄×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
4	#14561476	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2293	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	D₄⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#117	—	2	1	no	—
15	C₁₉×#390	C₄	1	1	yes	characteristic
16	C₁₉×#390	C₄	1	1	yes	characteristic
17	C₁₉×#389	C₄	1	1	yes	characteristic
18	C₁₉×#389	C₄	1	1	yes	characteristic
19	C₁₉×#388	—	2	1	no	—
20	C₁₉×#388	—	2	1	no	—
21	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₄×D₄×C₁₉	—	2	1	no	—
27	C₄×D₄×C₁₉	—	2	1	no	—
28	C₄×D₄×C₁₉	D₄	1	2	yes	—
29	C₄×D₄×C₁₉	Q₈	1	2	yes	—
30	C₁₉×#117	—	4	2	no	—
31	C₁₉×#117	—	4	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	C₂²×C₁₉⋊C₈	—	2	2	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
56	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
60	C₄×C₁₉⋊C₈	—	2	2	no	—
61	C₄×C₁₉⋊C₈	—	2	2	no	—
62	C₂⁴×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	2	no	—
65	C₂×D₄×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	4	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	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
87	C₄⋊C₄×C₁₉	—	4	2	no	—
88	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
89	C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂²⋊C₄×C₁₉	—	2	2	no	—
91	C₂²⋊C₄×C₁₉	—	4	2	no	—
92	C₂²⋊C₄×C₁₉	—	4	2	no	—
93	C₂²⋊C₄×C₁₉	—	4	2	no	—
94	C₂²⋊C₄×C₁₉	—	4	2	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	—	2	2	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	1	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	D₈	1	2	yes	—
104	C₄²×C₁₉	SD₁₆	1	2	yes	—
105	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	#8567	—	19	1	no	maximal, Sylow
116	C₂³×C₁₉	—	2	2	no	—
117	C₂³×C₁₉	—	4	1	no	—
118	C₂³×C₁₉	—	4	1	no	—
119	C₂³×C₁₉	—	4	1	no	—
120	C₂³×C₁₉	—	4	1	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	4	1	no	—
123	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	D₄×C₁₉	—	2	4	no	—
125	D₄×C₁₉	—	4	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	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	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	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	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	#102	1	2	yes	—
151	C₂×C₄×C₁₉	#102	1	2	yes	—
152	C₂×C₄×C₁₉	#104	1	2	yes	—
153	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#131	1	2	yes	—
160	C₂×C₄×C₁₉	#131	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×SD₁₆	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	#2293	D₁₉	1	1	yes	characteristic
168	#1842	—	19	1	no	—
169	C₄×C₄⋊C₈	—	19	1	no	—
170	C₂×D₄⋊C₈	—	19	2	no	—
171	#1279	—	19	2	no	—
172	C₂²×C₁₉	—	4	2	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	—	8	1	no	—
176	C₂²×C₁₉	—	8	1	no	—
177	C₂²×C₁₉	—	8	1	no	—
178	C₂²×C₁₉	—	8	1	no	—
179	C₂²×C₁₉	#380	1	1	yes	characteristic
180	C₂²×C₁₉	#408	1	1	yes	characteristic
181	C₂²×C₁₉	#408	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
183	C₂²×C₁₉	#417	1	1	yes	characteristic
184	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
185	C₂²×C₁₉	#421	1	1	yes	characteristic
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	4	1	no	—
193	C₄×C₁₉	—	8	1	no	—
194	C₄×C₁₉	—	8	1	no	—
195	C₄×C₁₉	#424	1	2	yes	—
196	C₄×C₁₉	#433	1	2	yes	—
197	C₄×C₁₉	#459	1	1	yes	characteristic
198	C₄×C₁₉	#461	1	1	yes	characteristic
199	C₄×C₁₉	#474	1	1	yes	characteristic
200	C₄×C₁₉	#476	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
202	C₂×#117	—	2	1	no	—
203	C₂×C₄⋊C₈	—	19	2	no	—
204	C₂×C₄⋊C₈	—	38	1	no	—
205	C₂×C₄⋊C₈	—	38	1	no	—
206	C₂×C₄⋊C₈	—	38	1	no	—
207	C₂×C₄×C₈	—	19	2	no	—
208	#390	Dic₁₉	1	1	yes	characteristic
209	#390	Dic₁₉	1	1	yes	characteristic
210	#389	Dic₁₉	1	1	yes	characteristic
211	#389	Dic₁₉	1	1	yes	characteristic
212	#388	—	2	1	no	—
213	#388	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
215	C₄×C₂²⋊C₄	—	2	1	no	—
216	C₄³	C₂×D₁₉	1	1	yes	characteristic
217	#336	—	38	1	no	—
218	D₄⋊C₈	—	38	4	no	—
219	C₂×C₁₉	—	8	2	no	—
220	C₂×C₁₉	#1480	1	1	yes	characteristic
221	C₂×C₁₉	#1483	1	1	yes	characteristic
222	C₂×C₁₉	#1492	1	1	yes	characteristic
223	C₂×C₁₉	#1495	1	1	yes	characteristic
224	C₂×C₁₉	#1798	1	1	yes	characteristic
225	C₂×C₁₉	#1802	1	1	yes	characteristic
226	C₂×C₁₉	#1806	1	1	yes	characteristic
227	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂²×C₈	—	38	2	no	—
230	C₂²×C₈	—	38	2	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	Dic₃₈	1	2	yes	—
234	C₄×D₄	D₇₆	1	2	yes	—
235	#117	—	4	2	no	—
236	#117	—	4	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	1	no	—
246	C₂×C₂²⋊C₄	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
249	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
255	C₄⋊C₈	—	38	4	no	—
256	C₄⋊C₈	—	38	2	no	—
257	C₄⋊C₈	—	38	2	no	—
258	C₄⋊C₈	—	76	2	no	—
259	C₄⋊C₈	—	76	2	no	—
260	C₄×C₈	—	38	2	no	—
261	C₄×C₈	—	38	2	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	C₁₉	#8567	1	1	yes	characteristic, complemented, Sylow
266	C₂⁴	—	2	1	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
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	C₂²⋊Dic₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂×C₈	—	38	4	no	—
288	C₂×C₈	—	76	2	no	—
289	C₂×C₈	—	76	2	no	—
290	C₂×C₈	—	76	2	no	—
291	C₂×C₈	—	76	2	no	—
292	C₂×C₈	—	76	2	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	#64525	1	2	yes	—
314	C₄²	#64526	1	2	yes	—
315	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
316	C₄²	C₂×D₇₆	1	1	yes	characteristic
317	C₄²	#64541	1	1	yes	characteristic
318	C₄²	#64541	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
327	D₄	—	2	4	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	#10597289	1	2	yes	—
354	C₂×C₄	#10597289	1	2	yes	—
355	C₂×C₄	#10597294	1	2	yes	—
356	C₂×C₄	#10597370	1	1	yes	characteristic
357	C₂×C₄	#10597370	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
359	C₂×C₄	#10597372	1	1	yes	characteristic
360	C₂×C₄	#10597376	1	1	yes	characteristic
361	C₂×C₄	#10597376	1	1	yes	characteristic
362	C₂×C₄	C₂×#64525	1	1	yes	characteristic
363	C₂×C₄	C₂×#64526	1	1	yes	characteristic
364	C₂×C₄	#10597394	1	2	yes	—
365	C₂×C₄	#10597394	1	2	yes	—
366	C₂×C₄	#10597395	1	1	yes	characteristic
367	C₂×C₄	#10597397	1	1	yes	characteristic
368	C₈	—	76	4	no	—
369	C₈	—	152	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	1	no	—
377	C₂²	#11926404	1	1	yes	characteristic
378	C₂²	#11926511	1	1	yes	characteristic
379	C₂²	#11926511	1	1	yes	characteristic
380	C₂²	C₂×#10597289	1	1	yes	characteristic
381	C₂²	#11926545	1	1	yes	characteristic
382	C₂²	C₂×#10597294	1	1	yes	characteristic
383	C₂²	#11926561	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	8	1	no	—
392	C₄	—	8	1	no	—
393	C₄	#11926571	1	2	yes	—
394	C₄	#11926605	1	2	yes	—
395	C₄	#11926739	1	1	yes	characteristic
396	C₄	#11926749	1	1	yes	characteristic
397	C₄	#11926824	1	1	yes	characteristic
398	C₄	#11926834	1	1	yes	characteristic
399	C₂	—	8	2	no	—
400	C₂	#14562034	1	1	yes	characteristic
401	C₂	#14562048	1	1	yes	characteristic
402	C₂	#14562086	1	1	yes	characteristic
403	C₂	#14562100	1	1	yes	characteristic
404	C₂	#14563619	1	1	yes	characteristic
405	C₂	#14563635	1	1	yes	characteristic
406	C₂	#14563655	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2293	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2293	D₁₉
hypocenter	C₁₉	#8567
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #2293

Complements

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

N	H ≅ G/N	type
1. #14563787	C₂	semidirect
2. C₄×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561476	C₂	semidirect
265. C₁₉	#8567	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×D₄⋊(C₁₉⋊C₈)	2
#14561476	2
C₁₉×#2293	2
#8567	19