Subgroups — #18075208

Order 4864.

682 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563615	C₂	1	2	yes	maximal
2	C₂×#11926270	C₂	1	2	yes	maximal
3	#14561478	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
7	#11926299	—	2	2	no	—
8	#11926270	—	2	4	no	—
9	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
12	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
17	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	C₈	1	4	yes	complemented
30	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	4	2	no	—
39	C₂×C₄²×C₁₉	—	4	2	no	—
40	C₂×C₄²×C₁₉	D₄	1	2	yes	—
41	C₂×C₄²×C₁₉	D₄	1	2	yes	—
42	C₂²×C₁₉⋊C₈	—	2	4	no	—
43	C₁₉×#95	—	2	2	no	—
44	C₁₉×#95	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
48	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	—	2	1	no	—
51	C₂²×C₄×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	—	2	1	no	—
53	C₂²×C₄×C₁₉	—	2	1	no	—
54	C₂²×C₄×C₁₉	—	2	1	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	1	no	—
59	C₂²×C₄×C₁₉	—	2	1	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	—	4	1	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	—	4	1	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
82	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
83	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	2	yes	—
88	C₄⋊C₄×C₁₉	—	2	8	no	—
89	C₄⋊C₄×C₁₉	—	2	4	no	—
90	C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₄²×C₁₉	—	2	4	no	—
92	C₄²×C₁₉	—	2	4	no	—
93	C₄²×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	—	4	2	no	—
95	C₄²×C₁₉	—	4	2	no	—
96	C₄²×C₁₉	—	4	2	no	—
97	C₂×C₁₉⋊C₈	—	4	4	no	—
98	C₂×C₁₉⋊C₈	—	4	4	no	—
99	C₂×C₁₉⋊C₈	—	4	4	no	—
100	#8560	—	19	1	no	maximal, Sylow
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂³×C₁₉	#117	1	1	yes	characteristic
108	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
109	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
110	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
111	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₉	—	2	4	no	—
113	C₂×C₄×C₁₉	—	2	4	no	—
114	C₂×C₄×C₁₉	—	2	2	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	1	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	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	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	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
149	C₂×C₄×C₁₉	#99	1	2	yes	—
150	C₂×C₄×C₁₉	#101	1	2	yes	—
151	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	complemented
152	C₂×C₄×C₁₉	#121	1	2	yes	—
153	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
154	C₁₉⋊C₈	—	8	4	no	—
155	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
156	#1797	—	19	2	no	—
157	C₂×#324	—	19	2	no	—
158	#1280	—	19	2	no	—
159	C₂²×C₁₉	—	2	1	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	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	#380	1	1	yes	characteristic
172	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
173	C₂²×C₁₉	#407	1	1	yes	characteristic
174	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
175	C₂²×C₁₉	#410	1	1	yes	characteristic
176	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
177	C₂²×C₁₉	#413	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
179	C₂²×C₁₉	#423	1	1	yes	characteristic
180	C₂²×C₁₉	#431	1	1	yes	characteristic
181	C₂²×C₁₉	#432	1	1	yes	characteristic
182	C₄×C₁₉	—	2	4	no	—
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	2	no	—
185	C₄×C₁₉	—	2	4	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	—	4	2	no	—
190	C₄×C₁₉	—	4	2	no	—
191	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
192	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
193	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
194	C₂²×C₄²	Dic₁₉	1	1	yes	characteristic
195	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
196	C₂×C₄⋊C₈	—	38	2	no	—
197	C₂×C₂²⋊C₈	—	19	4	no	—
198	C₄×C₄⋊C₄	—	2	2	no	—
199	C₄×C₄⋊C₄	—	2	2	no	—
200	C₂×#95	Dic₁₉	1	1	yes	characteristic
201	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
202	#336	—	38	2	no	—
203	#324	—	38	4	no	—
204	C₂×C₁₉	—	2	1	no	—
205	C₂×C₁₉	—	2	1	no	—
206	C₂×C₁₉	—	2	1	no	—
207	C₂×C₁₉	—	2	1	no	—
208	C₂×C₁₉	#1459	1	1	yes	characteristic
209	C₂×C₁₉	#1461	1	1	yes	characteristic
210	C₂×C₁₉	#1463	1	1	yes	characteristic
211	C₂×C₁₉	#1464	1	1	yes	characteristic
212	C₂×C₁₉	#1797	1	1	yes	characteristic
213	C₂×C₁₉	#1799	1	1	yes	characteristic
214	C₂×C₁₉	#1801	1	1	yes	characteristic
215	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
217	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
219	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
221	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
222	C₂²×C₈	—	38	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
228	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
229	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	4	2	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
239	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
240	C₄⋊C₈	—	76	4	no	—
241	C₂²⋊C₈	—	38	4	no	—
242	C₂²⋊C₈	—	38	4	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	C₁₉	#8560	1	1	yes	characteristic, complemented, Sylow
246	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
272	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
273	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
274	C₂²×C₄	#64520	1	2	yes	—
275	C₂²×C₄	#64520	1	2	yes	—
276	C₂²×C₄	#64520	1	2	yes	—
277	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
278	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
279	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
280	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
284	C₂²×C₄	#64541	1	2	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
286	C₂×C₈	—	76	4	no	—
287	C₂×C₈	—	76	4	no	—
288	C₂×C₈	—	76	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
303	C₂³	C₂×#64520	1	1	yes	characteristic
304	C₂³	C₂×#64520	1	1	yes	characteristic
305	C₂³	C₂×#64520	1	1	yes	characteristic
306	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
307	C₂³	#10597372	1	1	yes	characteristic
308	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	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	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	complemented
346	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	4	yes	—
347	C₂×C₄	#10597291	1	2	yes	—
348	C₂×C₄	#10597293	1	2	yes	—
349	C₂×C₄	#10597370	1	2	yes	—
350	C₂×C₄	#10597376	1	2	yes	—
351	C₈	—	152	4	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	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	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	#11926404	1	1	yes	characteristic
365	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
366	C₂²	#11926508	1	1	yes	characteristic
367	C₂²	C₂×#10597291	1	1	yes	characteristic
368	C₂²	#11926518	1	1	yes	characteristic
369	C₂²	C₂×#10597293	1	1	yes	characteristic
370	C₂²	#11926528	1	1	yes	characteristic
371	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
372	C₂²	#11926568	1	1	yes	characteristic
373	C₂²	#11926597	1	1	yes	characteristic
374	C₂²	#11926601	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	#14561953	1	1	yes	characteristic
389	C₂	#14561959	1	1	yes	characteristic
390	C₂	#14561965	1	1	yes	characteristic
391	C₂	#14561969	1	1	yes	characteristic
392	C₂	#14563615	1	1	yes	characteristic
393	C₂	#14563623	1	1	yes	characteristic
394	C₂	#14563631	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#8560
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
29. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
151. C₂×C₄×C₁₉	C₄⋊C₈	semidirect
227. C₂×C₄⋊C₄	C₁₉⋊C₈	semidirect
245. C₁₉	#8560	semidirect
345. C₂×C₄	C₄⋊(C₁₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#14563615	2
C₂×#11926270	2
#14561478	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#8560	19