Subgroups — C₁₉×#32979 #18038938

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#481	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1874	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1853	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1824	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₁₉	—	2	1	no	—
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	C₂²	1	2	yes	—
12	C₂×C₁₉×#120	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#481	—	2	8	no	—
19	C₂×C₁₉×#106	C₂²	1	4	yes	complemented
20	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#386	—	2	2	no	—
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₁₉×#340	C₂²	1	8	yes	complemented
28	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	4	no	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	—	2	8	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	2	no	—
37	C₂³×C₄×C₁₉	—	4	8	no	—
38	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	D₄	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
43	C₁₉×#121	—	2	4	no	—
44	C₁₉×#121	—	2	8	no	—
45	C₁₉×#120	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
52	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₁₉×#106	—	2	8	no	—
61	C₁₉×#102	—	2	8	no	—
62	C₁₉×C₂²⋊C₈	—	2	4	no	—
63	C₁₉×C₂²⋊C₈	—	2	8	no	—
64	C₁₉×#95	—	2	1	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₂⁴×C₁₉	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	1	no	—
71	C₂⁴×C₁₉	SD₁₆	1	4	yes	—
72	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	4	no	—
76	C₂×D₄×C₁₉	—	4	2	no	—
77	C₂×D₄×C₁₉	—	4	4	no	—
78	C₂×D₄×C₁₉	—	4	2	no	—
79	C₂×D₄×C₁₉	—	4	4	no	—
80	C₂×D₄×C₁₉	—	4	4	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂²×C₄×C₁₉	—	2	32	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	4	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	16	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	32	no	—
97	C₂²×C₄×C₁₉	—	4	8	no	—
98	C₂²×C₄×C₁₉	—	4	8	no	—
99	C₂²×C₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	#41	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₁₉	—	2	4	no	—
106	C₂×C₈×C₁₉	—	2	8	no	—
107	C₄⋊C₄×C₁₉	—	2	16	no	—
108	C₄⋊C₄×C₁₉	—	2	8	no	—
109	C₄⋊C₄×C₁₉	—	2	4	no	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
113	C₂²⋊C₄×C₁₉	—	4	2	no	—
114	C₂²⋊C₄×C₁₉	—	4	4	no	—
115	C₂²⋊C₄×C₁₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	#32979	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₉	—	2	8	no	—
119	C₂³×C₁₉	—	2	8	no	—
120	C₂³×C₁₉	—	2	16	no	—
121	C₂³×C₁₉	—	2	2	no	—
122	C₂³×C₁₉	—	2	2	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	2	16	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	2	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	#120	1	2	yes	—
135	C₂³×C₁₉	#123	1	4	yes	—
136	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
137	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
138	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
139	C₂³×C₁₉	#137	1	2	yes	—
140	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₁₉	—	4	4	no	—
142	D₄×C₁₉	—	8	4	no	—
143	D₄×C₁₉	—	8	8	no	—
144	C₂×C₄×C₁₉	—	2	16	no	—
145	C₂×C₄×C₁₉	—	2	8	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	2	16	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	4	16	no	—
153	C₂×C₄×C₁₉	—	4	32	no	—
154	C₂×C₄×C₁₉	—	4	8	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	#120	1	2	yes	—
162	C₂×C₄×C₁₉	#123	1	4	yes	—
163	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
165	C₈×C₁₉	—	4	4	no	—
166	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
167	C₂×#481	C₂×C₁₉	1	2	yes	complemented
168	#2847	C₂×C₁₉	1	1	yes	characteristic
169	#1874	C₂×C₁₉	1	4	yes	complemented
170	#1853	C₂×C₁₉	1	4	yes	complemented
171	#1824	C₂×C₁₉	1	2	yes	complemented
172	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₂²×C₁₉	—	2	32	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	2	4	no	—
176	C₂²×C₁₉	—	2	4	no	—
177	C₂²×C₁₉	—	2	4	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	8	2	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	—	8	1	no	—
187	C₂²×C₁₉	—	8	1	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	#448	1	4	yes	—
190	C₂²×C₁₉	#481	1	8	yes	complemented
191	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#123	1	2	yes	—
193	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
194	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
195	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	4	no	—
198	C₄×C₁₉	—	4	8	no	—
199	C₄×C₁₉	—	8	2	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	#525	1	4	yes	—
202	C₂⁴×C₄	—	2	1	no	—
203	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×#121	C₂²×C₁₉	1	2	yes	—
206	C₂×#120	—	2	1	no	—
207	C₂²×C₄⋊C₄	—	2	1	no	—
208	C₂²×C₄⋊C₄	—	2	2	no	—
209	C₂²×C₄⋊C₄	—	2	8	no	—
210	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
212	#481	—	2	8	no	—
213	C₂×#106	C₂²×C₁₉	1	4	yes	complemented
214	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
215	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
217	#386	—	2	2	no	—
218	#386	—	2	1	no	—
219	#380	C₂²×C₁₉	1	1	yes	characteristic
220	#380	C₂²×C₁₉	1	2	yes	—
221	#340	C₂²×C₁₉	1	8	yes	complemented
222	C₂×C₁₉	—	2	4	no	—
223	C₂×C₁₉	—	2	8	no	—
224	C₂×C₁₉	—	16	1	no	—
225	C₂×C₁₉	#2849	1	1	yes	characteristic
226	C₂×C₁₉	C₂×#448	1	1	yes	characteristic
227	C₂×C₁₉	#3003	1	1	yes	characteristic
228	C₂×C₁₉	C₂×#481	1	2	yes	—
229	C₂×C₁₉	#3092	1	2	yes	—
230	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₂³×C₄	—	2	4	no	—
235	C₂³×C₄	—	2	8	no	—
236	C₂³×C₄	—	2	8	no	—
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	—	4	8	no	—
240	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₁₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
245	#121	—	2	4	no	—
246	#121	—	2	8	no	—
247	#120	—	4	4	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	16	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	16	no	—
254	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	#106	—	2	8	no	—
263	#102	—	2	8	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₂²⋊C₈	—	2	8	no	—
266	#95	—	2	1	no	—
267	#95	—	2	2	no	—
268	C₁₉	#32979	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	—	2	2	no	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	2	2	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	SD₁₆×C₁₉	1	4	yes	—
275	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
276	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂²×C₄	—	2	32	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	16	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	32	no	—
300	C₂²×C₄	—	4	8	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	#41×C₁₉	1	8	yes	—
307	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	8	no	—
310	C₄⋊C₄	—	2	16	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	16	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	16	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	C₁₉×#120	1	2	yes	—
337	C₂³	C₁₉×#123	1	4	yes	—
338	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
339	C₂³	C₂×SD₁₆×C₁₉	1	4	yes	—
340	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
341	C₂³	C₁₉×#137	1	2	yes	—
342	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
343	D₄	—	4	4	no	—
344	D₄	—	8	4	no	—
345	D₄	—	8	8	no	—
346	C₂×C₄	—	2	16	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	4	16	no	—
355	C₂×C₄	—	4	32	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	C₁₉×#120	1	2	yes	—
364	C₂×C₄	C₁₉×#123	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
366	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
367	C₈	—	4	4	no	—
368	C₂²	—	2	32	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	1	no	—
384	C₂²	C₁₉×#448	1	4	yes	—
385	C₂²	C₁₉×#481	1	8	yes	complemented
386	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
387	C₂²	C₂×C₁₉×#123	1	2	yes	—
388	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
389	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
390	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	8	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	2	no	—
396	C₄	C₁₉×#525	1	4	yes	—
397	C₂	—	2	4	no	—
398	C₂	—	2	8	no	—
399	C₂	—	16	1	no	—
400	C₂	C₁₉×#2849	1	1	yes	characteristic
401	C₂	C₂×C₁₉×#448	1	1	yes	characteristic
402	C₂	C₁₉×#3003	1	1	yes	characteristic
403	C₂	C₂×C₁₉×#481	1	2	yes	—
404	C₂	C₁₉×#3092	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄⋊C₄×C₁₉	C₂	semidirect
2. C₂×C₁₉×#481	C₂	semidirect
4. C₁₉×#1874	C₂	semidirect
5. C₁₉×#1853	C₂	semidirect
6. C₁₉×#1824	C₂	semidirect
7. C₁₉×#1779	C₂	semidirect
19. C₂×C₁₉×#106	C₂²	semidirect
20. C₂×C₁₉×#102	C₂²	semidirect
27. C₁₉×#340	C₂²	semidirect
52. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
117. #32979	C₁₉	direct (N × H)
166. C₂³×C₄⋊C₄	C₂×C₁₉	semidirect
167. C₂×#481	C₂×C₁₉	semidirect
169. #1874	C₂×C₁₉	semidirect
170. #1853	C₂×C₁₉	semidirect
171. #1824	C₂×C₁₉	semidirect
172. #1779	C₂×C₁₉	semidirect
190. C₂²×C₁₉	#481	semidirect
213. C₂×#106	C₂²×C₁₉	semidirect
214. C₂×#102	C₂²×C₁₉	semidirect
221. #340	C₂²×C₁₉	semidirect
254. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
268. C₁₉	#32979	direct (N × H)
385. C₂²	C₁₉×#481	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#481	2
C₁₉×#2847	2
C₁₉×#1874	2
C₁₉×#1853	2
C₁₉×#1824	2
C₁₉×#1779	2
#32979	19

Subgroups — C19×#32979 #18038938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32979 #18038938