Subgroups — #18072093

Order 4864.

798 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926566	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#14566039	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64515	—	2	1	no	—
9	C₂²×C₈×D₁₉	—	2	1	no	—
10	C₂×#10597318	—	2	1	no	—
11	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
12	#11926566	—	2	2	no	—
13	#11926566	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₈	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₁₉	—	2	1	no	—
18	C₄×C₈×D₁₉	—	2	2	no	—
19	C₄×C₈×D₁₉	C₄	1	4	yes	complemented
20	#11926413	C₄	1	2	yes	—
21	#11926408	—	2	1	no	—
22	#11926403	—	2	1	no	—
23	#11926401	C₄	1	2	yes	—
24	C₄×Dic₁₉⋊C₄	—	2	1	no	—
25	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
38	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
39	C₂×Dic₁₉⋊C₄	—	2	2	no	—
40	C₂×Dic₁₉⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂×#64515	—	2	4	no	—
48	C₂×#64515	—	4	2	no	—
49	C₂×#64515	—	4	2	no	—
50	C₂×C₈×D₁₉	—	2	8	no	—
51	C₂×C₈×D₁₉	—	2	4	no	—
52	#10597318	—	4	2	no	—
53	#10597318	—	4	2	no	—
54	C₄²×D₁₉	C₂×C₄	1	2	yes	—
55	C₄²×D₁₉	C₂×C₄	1	2	yes	—
56	C₄²×D₁₉	D₄	1	2	yes	—
57	C₄²×D₁₉	Q₈	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₁₉×#95	—	2	1	no	—
63	C₁₉⋊#95	—	2	1	no	—
64	C₁₉⋊#95	—	2	2	no	—
65	Dic₁₉⋊C₈	—	2	4	no	—
66	C₈×Dic₁₉	—	2	4	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
71	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₁₉	—	2	2	no	—
77	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₉	—	2	2	no	—
81	C₂×C₄×D₁₉	—	2	2	no	—
82	C₂×C₄×D₁₉	—	2	4	no	—
83	C₂×C₄×D₁₉	C₄²	1	2	yes	—
84	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
85	C₂×C₄×D₁₉	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₁₉	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₁₉	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₁₉	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₁₉	D₈	1	2	yes	—
90	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
91	C₂×C₄×D₁₉	SD₁₆	1	2	yes	—
92	C₂×C₄×D₁₉	Q₁₆	1	2	yes	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	1	no	—
102	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	(C₂×D₁₉)⋊C₄	—	4	4	no	—
107	C₄⋊Dic₁₉	—	2	2	no	—
108	C₄⋊Dic₁₉	—	2	2	no	—
109	Dic₁₉⋊C₄	—	4	4	no	—
110	Dic₁₉⋊C₄	—	4	4	no	—
111	C₄×Dic₁₉	—	4	1	no	—
112	C₄×Dic₁₉	—	4	1	no	—
113	C₄×Dic₁₉	C₄²	1	2	yes	—
114	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
115	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
116	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
118	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
119	C₂×C₁₉⋊C₈	—	2	4	no	—
120	C₂×C₁₉⋊C₈	—	2	2	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	#64515	—	4	8	no	—
125	C₈×D₁₉	—	2	16	no	—
126	#7897	—	19	1	no	maximal, Sylow
127	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×D₁₉	—	2	2	no	—
129	C₂²×D₁₉	—	2	2	no	—
130	C₂²×D₁₉	#95	1	2	yes	—
131	C₂²×D₁₉	#102	1	2	yes	—
132	C₂²×D₁₉	#103	1	2	yes	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#131	1	2	yes	—
144	C₂×C₄×C₁₉	#131	1	2	yes	—
145	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
149	C₂×Dic₁₉	—	2	2	no	—
150	C₂×Dic₁₉	—	4	2	no	—
151	C₂×Dic₁₉	—	4	2	no	—
152	C₂×Dic₁₉	—	4	2	no	—
153	C₂×Dic₁₉	#95	1	2	yes	—
154	C₂×Dic₁₉	#95	1	2	yes	—
155	C₂×Dic₁₉	#95	1	2	yes	—
156	C₂×Dic₁₉	#102	1	2	yes	—
157	C₂×Dic₁₉	#103	1	2	yes	—
158	C₂×Dic₁₉	#104	1	4	yes	—
159	C₄×D₁₉	—	2	2	no	—
160	C₄×D₁₉	—	2	2	no	—
161	C₄×D₁₉	—	2	4	no	—
162	C₄×D₁₉	—	2	4	no	—
163	C₄×D₁₉	—	2	4	no	—
164	C₄×D₁₉	#102	1	4	yes	—
165	C₄×D₁₉	#103	1	4	yes	—
166	C₄×D₁₉	#106	1	4	yes	—
167	C₄×D₁₉	#107	1	4	yes	—
168	C₈×C₁₉	—	2	4	no	—
169	C₈×C₁₉	—	4	2	no	—
170	C₁₉⋊C₈	—	2	4	no	—
171	C₁₉⋊C₈	—	4	2	no	—
172	C₂×#423	—	19	1	no	—
173	C₂²×C₄×C₈	—	19	1	no	—
174	#2285	—	19	1	no	—
175	#1279	—	19	1	no	—
176	#1279	—	19	1	no	—
177	#1279	—	19	1	no	—
178	#1279	D₁₉	1	1	yes	characteristic, complemented
179	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
180	C₂²×C₁₉	#408	1	2	yes	—
181	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
183	C₂²×C₁₉	C₂×#104	1	2	yes	—
184	C₂×D₁₉	—	2	2	no	—
185	C₂×D₁₉	—	2	2	no	—
186	C₂×D₁₉	—	2	4	no	—
187	C₂×D₁₉	—	2	4	no	—
188	C₂×D₁₉	#340	1	4	yes	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	8	2	no	—
192	C₄×C₁₉	#405	1	1	yes	characteristic
193	C₄×C₁₉	#405	1	1	yes	characteristic
194	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
195	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
196	C₄×C₁₉	#424	1	2	yes	—
197	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
198	C₄×C₁₉	C₂×#107	1	1	yes	characteristic
199	Dic₁₉	—	2	2	no	—
200	Dic₁₉	—	8	2	no	—
201	Dic₁₉	#339	1	4	yes	—
202	Dic₁₉	#340	1	4	yes	—
203	C₂²×M₁₆	—	38	1	no	—
204	C₂³×C₈	—	38	1	no	—
205	C₂×#117	—	38	1	no	—
206	C₂²×C₄²	—	19	1	no	—
207	#423	—	19	4	no	—
208	#423	—	38	2	no	—
209	C₂×C₄⋊C₈	—	19	1	no	—
210	C₂×C₄⋊C₈	—	38	1	no	—
211	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₄×C₈	—	19	1	no	—
213	C₂×C₄×C₈	—	19	4	no	—
214	C₂×C₄×C₈	—	38	2	no	—
215	C₂×C₄×C₈	—	38	1	no	—
216	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
217	#384	—	19	2	no	—
218	#382	—	38	1	no	—
219	#380	—	19	2	no	—
220	#380	—	38	1	no	—
221	C₄×C₄⋊C₄	—	19	1	no	—
222	C₄×C₄⋊C₄	—	38	1	no	—
223	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
224	C₂×C₁₉	#1492	1	2	yes	—
225	C₂×C₁₉	#1493	1	2	yes	—
226	C₂×C₁₉	#1729	1	1	yes	characteristic
227	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
228	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
229	D₁₉	—	2	4	no	—
230	C₂³×C₄	—	19	1	no	—
231	C₂³×C₄	—	19	1	no	—
232	C₂³×C₄	—	19	1	no	—
233	C₂×M₁₆	—	38	4	no	—
234	C₂×M₁₆	—	76	2	no	—
235	C₂×M₁₆	—	76	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	38	4	no	—
239	C₂²×C₈	—	38	8	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	#117	—	76	2	no	—
243	#117	—	76	2	no	—
244	C₂×C₄⋊C₄	—	19	2	no	—
245	C₂×C₄⋊C₄	—	38	2	no	—
246	C₂×C₄⋊C₄	—	38	2	no	—
247	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
248	C₂×C₂²⋊C₄	—	38	2	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	—	19	1	no	—
251	C₂×C₄²	—	19	1	no	—
252	C₂×C₄²	—	19	1	no	—
253	C₂×C₄²	—	19	2	no	—
254	C₂×C₄²	—	19	2	no	—
255	C₂×C₄²	—	19	2	no	—
256	C₂×C₄²	—	19	2	no	—
257	C₂×C₄²	—	38	1	no	—
258	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	19	2	no	—
261	C₄⋊C₈	—	38	4	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	19	2	no	—
266	C₄×C₈	—	38	4	no	—
267	C₄×C₈	—	38	1	no	—
268	C₄×C₈	C₄×D₁₉	1	2	yes	—
269	#95	—	2	1	no	—
270	#95	—	38	2	no	—
271	#95	—	38	1	no	—
272	C₁₉	#7897	1	1	yes	characteristic, complemented, Sylow
273	C₂⁴	—	19	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	19	1	no	—
276	C₂²×C₄	—	19	1	no	—
277	C₂²×C₄	—	19	2	no	—
278	C₂²×C₄	—	19	2	no	—
279	C₂²×C₄	—	19	2	no	—
280	C₂²×C₄	—	19	2	no	—
281	C₂²×C₄	—	19	2	no	—
282	C₂²×C₄	—	19	2	no	—
283	C₂²×C₄	—	19	1	no	—
284	C₂²×C₄	—	19	2	no	—
285	C₂²×C₄	—	19	2	no	—
286	C₂²×C₄	—	19	2	no	—
287	C₂²×C₄	—	19	2	no	—
288	C₂²×C₄	—	38	4	no	—
289	C₂²×C₄	—	38	2	no	—
290	C₂²×C₄	—	38	2	no	—
291	C₂²×C₄	—	38	2	no	—
292	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
293	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
295	M₁₆	—	76	8	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	38	16	no	—
302	C₂×C₈	—	38	4	no	—
303	C₂×C₈	—	38	2	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	—	76	1	no	—
306	C₂×C₈	—	76	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	38	2	no	—
310	C₄⋊C₄	—	38	2	no	—
311	C₄⋊C₄	—	76	4	no	—
312	C₄⋊C₄	—	76	4	no	—
313	C₂²⋊C₄	—	76	4	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	19	2	no	—
317	C₄²	—	19	2	no	—
318	C₄²	—	19	2	no	—
319	C₄²	—	19	2	no	—
320	C₄²	—	19	2	no	—
321	C₄²	—	19	2	no	—
322	C₄²	—	76	1	no	—
323	C₄²	—	76	1	no	—
324	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
325	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
326	C₄²	D₄×D₁₉	1	1	yes	characteristic
327	C₄²	Q₈×D₁₉	1	1	yes	characteristic
328	C₂³	—	19	2	no	—
329	C₂³	—	19	2	no	—
330	C₂³	—	19	2	no	—
331	C₂³	—	38	2	no	—
332	C₂³	—	38	2	no	—
333	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	19	2	no	—
339	C₂×C₄	—	19	2	no	—
340	C₂×C₄	—	19	4	no	—
341	C₂×C₄	—	19	2	no	—
342	C₂×C₄	—	19	2	no	—
343	C₂×C₄	—	19	4	no	—
344	C₂×C₄	—	19	4	no	—
345	C₂×C₄	—	19	4	no	—
346	C₂×C₄	—	19	4	no	—
347	C₂×C₄	—	19	2	no	—
348	C₂×C₄	—	38	4	no	—
349	C₂×C₄	—	38	4	no	—
350	C₂×C₄	—	38	2	no	—
351	C₂×C₄	—	38	4	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	2	no	—
354	C₂×C₄	—	76	2	no	—
355	C₂×C₄	—	76	2	no	—
356	C₂×C₄	—	76	2	no	—
357	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
358	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
359	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
360	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
361	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
362	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
363	C₂×C₄	#10597347	1	2	yes	—
364	C₂×C₄	#10597353	1	2	yes	—
365	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
366	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
367	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
368	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₈	—	38	4	no	—
372	C₈	—	76	2	no	—
373	C₂²	—	19	4	no	—
374	C₂²	—	38	2	no	—
375	C₂²	—	38	2	no	—
376	C₂²	—	38	4	no	—
377	C₂²	—	38	4	no	—
378	C₂²	#95×D₁₉	1	1	yes	characteristic
379	C₂²	#11926509	1	2	yes	—
380	C₂²	#102×D₁₉	1	1	yes	characteristic
381	C₂²	#103×D₁₉	1	1	yes	characteristic
382	C₂²	#104×D₁₉	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	19	4	no	—
387	C₄	—	19	4	no	—
388	C₄	—	38	2	no	—
389	C₄	—	152	2	no	—
390	C₄	#11926498	1	1	yes	characteristic
391	C₄	#11926501	1	1	yes	characteristic
392	C₄	#102×D₁₉	1	1	yes	characteristic
393	C₄	#103×D₁₉	1	1	yes	characteristic
394	C₄	#11926569	1	2	yes	—
395	C₄	#106×D₁₉	1	1	yes	characteristic
396	C₄	#107×D₁₉	1	1	yes	characteristic
397	C₂	—	38	4	no	—
398	C₂	#14562084	1	2	yes	—
399	C₂	#14562088	1	2	yes	—
400	C₂	#14563330	1	1	yes	characteristic
401	C₂	D₁₉×#339	1	1	yes	characteristic
402	C₂	D₁₉×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#7897
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #14561476	C₂	semidirect
5. #14561475	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
13. #11926566	C₄	semidirect
19. C₄×C₈×D₁₉	C₄	semidirect
178. #1279	D₁₉	semidirect
272. C₁₉	#7897	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926566	2
C₂×C₄×C₈×D₁₉	2
#14566039	2
#14561476	2
#14561475	2
#14561474	2
C₁₉×#1279	2
#7897	19