Subgroups — C₁₉×#61935 #18067894

Order 4864.

1746 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3397	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3392	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3372	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3360	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3221	C₂	1	4	yes	maximal, complemented
8	C₁₉×#3206	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3126	C₂	1	4	yes	maximal, complemented
10	C₁₉×#3106	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	—	2	2	no	—
13	C₁₉×#557	C₂²	1	4	yes	—
14	C₁₉×#556	C₂²	1	4	yes	—
15	C₁₉×#554	C₂²	1	4	yes	—
16	C₁₉×#552	—	2	4	no	—
17	C₁₉×#550	C₂²	1	4	yes	—
18	C₁₉×#547	—	2	2	no	—
19	C₁₉×#541	—	2	2	no	—
20	C₁₉×#540	C₂²	1	4	yes	—
21	C₁₉×#537	—	2	4	no	—
22	C₁₉×#536	C₂²	1	2	yes	—
23	C₁₉×#533	—	2	2	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#532	C₂²	1	2	yes	—
26	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₉×#519	C₂²	1	2	yes	—
28	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#496	C₂²	1	4	yes	—
30	C₁₉×#492	C₂²	1	4	yes	—
31	C₁₉×#492	C₂²	1	4	yes	—
32	C₁₉×#491	C₂²	1	4	yes	—
33	C₁₉×#488	C₂²	1	4	yes	—
34	C₁₉×#487	C₂²	1	4	yes	—
35	C₁₉×#482	C₂²	1	4	yes	—
36	C₁₉×#479	C₂²	1	8	yes	—
37	C₁₉×#477	C₂²	1	2	yes	—
38	C₁₉×#476	C₂²	1	2	yes	—
39	C₁₉×#463	C₂²	1	8	yes	—
40	C₁₉×#461	C₂²	1	4	yes	—
41	C₁₉×#461	C₂²	1	4	yes	—
42	C₁₉×#461	C₂²	1	8	yes	—
43	C₁₉×#460	C₂²	1	2	yes	—
44	C₁₉×#460	C₂²	1	8	yes	—
45	C₁₉×#459	C₂²	1	2	yes	—
46	C₁₉×#449	C₂²	1	4	yes	—
47	C₁₉×#448	C₂²	1	8	yes	—
48	C₁₉×#446	C₂²	1	4	yes	—
49	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
50	C₁₉×#440	C₂²	1	8	yes	—
51	C₄×SD₁₆×C₁₉	C₂²	1	8	yes	—
52	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	—
53	C₄×D₈×C₁₉	C₂²	1	4	yes	—
54	C₁₉×#433	C₂²	1	4	yes	—
55	C₁₉×#431	C₂²	1	2	yes	—
56	C₂×#41×C₁₉	—	2	4	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
60	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
61	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
62	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
63	C₂×D₈×C₁₉	C₂³	1	4	yes	—
64	C₁₉×C₄⋊Q₈	—	2	1	no	—
65	C₁₉×C₄⋊Q₈	—	2	1	no	—
66	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
67	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₉×#127	C₂³	1	2	yes	—
71	C₁₉×#127	C₂³	1	4	yes	—
72	C₁₉×#126	—	2	8	no	—
73	C₁₉×#125	—	2	4	no	—
74	C₁₉×#125	—	2	8	no	—
75	C₁₉×#125	D₄	1	2	yes	—
76	C₁₉×#125	C₂³	1	4	yes	—
77	C₁₉×#124	—	2	2	no	—
78	C₁₉×#124	C₂³	1	4	yes	—
79	C₁₉×#123	—	2	8	no	—
80	C₁₉×#123	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	2	4	no	—
82	C₁₉×C₂²⋊Q₈	—	2	4	no	—
83	C₁₉×C₂²⋊Q₈	—	2	4	no	—
84	C₁₉×C₂²⋊Q₈	—	2	8	no	—
85	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	8	no	—
89	C₁₉×#121	—	2	8	no	—
90	C₁₉×#121	C₂³	1	4	yes	—
91	C₄×Q₈×C₁₉	—	2	4	no	—
92	C₄×Q₈×C₁₉	—	2	4	no	—
93	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
94	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	C₂³	1	2	yes	—
99	C₄×D₄×C₁₉	C₂³	1	4	yes	—
100	C₄×D₄×C₁₉	C₂³	1	8	yes	—
101	C₁₉×#117	—	2	4	no	—
102	C₁₉×#117	—	2	4	no	—
103	C₁₉×#117	—	2	1	no	—
104	C₁₉×#117	C₂³	1	1	yes	characteristic
105	C₁₉×#117	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
108	C₂×C₄²×C₁₉	—	2	1	no	—
109	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₁₉×#107	C₂³	1	4	yes	—
111	C₁₉×#106	C₂³	1	4	yes	—
112	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
113	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
114	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
115	C₁₉×#103	C₂³	1	8	yes	—
116	C₁₉×#103	C₂³	1	4	yes	—
117	C₁₉×#103	C₂³	1	8	yes	—
118	C₁₉×#102	C₂³	1	4	yes	—
119	C₁₉×#102	C₂³	1	4	yes	—
120	C₁₉×#102	C₂³	1	4	yes	—
121	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
122	C₁₉×#97	C₂³	1	4	yes	—
123	C₄×C₈×C₁₉	C₂³	1	4	yes	—
124	C₄×C₈×C₁₉	C₂³	1	4	yes	—
125	#41×C₁₉	—	4	2	no	—
126	#41×C₁₉	—	8	4	no	—
127	#41×C₁₉	—	8	8	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	4	4	no	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
132	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
133	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	8	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	8	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	SD₁₆×C₁₉	—	4	8	no	—
149	SD₁₆×C₁₉	—	4	8	no	—
150	SD₁₆×C₁₉	—	4	4	no	—
151	D₈×C₁₉	—	4	4	no	—
152	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
153	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	8	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	8	no	—
160	C₄⋊C₄×C₁₉	—	2	8	no	—
161	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
164	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
165	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
166	C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₂²⋊C₄×C₁₉	—	2	2	no	—
168	C₂²⋊C₄×C₁₉	—	2	8	no	—
169	C₂²⋊C₄×C₁₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₉	—	2	8	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
173	C₄²×C₁₉	—	2	1	no	—
174	C₄²×C₁₉	—	2	2	no	—
175	C₄²×C₁₉	—	2	8	no	—
176	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₉	C₂⁴	1	2	yes	—
179	C₄²×C₁₉	C₂⁴	1	4	yes	—
180	#61935	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	1	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₉	—	2	8	no	—
185	Q₈×C₁₉	—	2	8	no	—
186	Q₈×C₁₉	—	2	2	no	—
187	Q₈×C₁₉	—	4	4	no	—
188	Q₈×C₁₉	—	8	2	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	4	no	—
194	D₄×C₁₉	—	8	2	no	—
195	D₄×C₁₉	—	8	8	no	—
196	D₄×C₁₉	—	8	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	8	no	—
207	C₂×C₄×C₁₉	—	8	8	no	—
208	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
210	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
213	C₈×C₁₉	—	2	4	no	—
214	C₈×C₁₉	—	2	4	no	—
215	#3548	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#3509	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#3397	C₂×C₁₉	1	4	yes	complemented
218	#3392	C₂×C₁₉	1	4	yes	complemented
219	#3372	C₂×C₁₉	1	4	yes	complemented
220	#3360	C₂×C₁₉	1	4	yes	complemented
221	#3221	C₂×C₁₉	1	4	yes	complemented
222	#3206	C₂×C₁₉	1	2	yes	complemented
223	#3126	C₂×C₁₉	1	4	yes	complemented
224	#3106	C₂×C₁₉	1	2	yes	complemented
225	#2986	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	—	4	4	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	2	8	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	4	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	#577	1	4	yes	—
242	C₄×C₁₉	#585	1	2	yes	—
243	#562	—	2	2	no	—
244	#557	C₂²×C₁₉	1	4	yes	—
245	#556	C₂²×C₁₉	1	4	yes	—
246	#554	C₂²×C₁₉	1	4	yes	—
247	#552	—	2	4	no	—
248	#550	C₂²×C₁₉	1	4	yes	—
249	#547	—	2	2	no	—
250	#541	—	2	2	no	—
251	#540	C₂²×C₁₉	1	4	yes	—
252	#537	—	2	4	no	—
253	#536	C₂²×C₁₉	1	2	yes	—
254	#533	—	2	2	no	—
255	#533	C₂²×C₁₉	1	1	yes	characteristic
256	#532	C₂²×C₁₉	1	2	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
258	#519	C₂²×C₁₉	1	2	yes	—
259	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
260	#496	C₂²×C₁₉	1	4	yes	—
261	#492	C₂²×C₁₉	1	4	yes	—
262	#492	C₂²×C₁₉	1	4	yes	—
263	#491	C₂²×C₁₉	1	4	yes	—
264	#488	C₂²×C₁₉	1	4	yes	—
265	#487	C₂²×C₁₉	1	4	yes	—
266	#482	C₂²×C₁₉	1	4	yes	—
267	#479	C₂²×C₁₉	1	8	yes	—
268	#477	C₂²×C₁₉	1	2	yes	—
269	#476	C₂²×C₁₉	1	2	yes	—
270	#463	C₂²×C₁₉	1	8	yes	—
271	#461	C₂²×C₁₉	1	4	yes	—
272	#461	C₂²×C₁₉	1	8	yes	—
273	#461	C₂²×C₁₉	1	4	yes	—
274	#460	C₂²×C₁₉	1	2	yes	—
275	#460	C₂²×C₁₉	1	8	yes	—
276	#459	C₂²×C₁₉	1	2	yes	—
277	#449	C₂²×C₁₉	1	4	yes	—
278	#448	C₂²×C₁₉	1	8	yes	—
279	#446	C₂²×C₁₉	1	4	yes	—
280	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
281	#440	C₂²×C₁₉	1	8	yes	—
282	C₄×SD₁₆	C₂²×C₁₉	1	8	yes	—
283	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	—
284	C₄×D₈	C₂²×C₁₉	1	4	yes	—
285	#433	C₂²×C₁₉	1	4	yes	—
286	#431	C₂²×C₁₉	1	2	yes	—
287	C₂×C₁₉	—	4	1	no	—
288	C₂×C₁₉	—	8	1	no	—
289	C₂×C₁₉	—	8	4	no	—
290	C₂×C₁₉	#3487	1	1	yes	characteristic
291	C₂×C₁₉	C₂×#577	1	2	yes	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
296	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
297	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
298	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
299	C₂×D₈	C₂³×C₁₉	1	4	yes	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
304	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
305	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
306	#127	C₂³×C₁₉	1	2	yes	—
307	#127	C₂³×C₁₉	1	4	yes	—
308	#126	—	2	8	no	—
309	#125	—	2	4	no	—
310	#125	—	2	8	no	—
311	#125	D₄×C₁₉	1	2	yes	—
312	#125	C₂³×C₁₉	1	4	yes	—
313	#124	—	2	2	no	—
314	#124	C₂³×C₁₉	1	4	yes	—
315	#123	—	2	8	no	—
316	#123	—	2	4	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	8	no	—
321	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
322	#121	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	—	2	8	no	—
325	#121	—	2	8	no	—
326	#121	C₂³×C₁₉	1	4	yes	—
327	C₄×Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
330	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
331	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	C₂³×C₁₉	1	2	yes	—
335	C₄×D₄	C₂³×C₁₉	1	4	yes	—
336	C₄×D₄	C₂³×C₁₉	1	8	yes	—
337	#117	—	2	4	no	—
338	#117	—	2	4	no	—
339	#117	—	2	1	no	—
340	#117	C₂³×C₁₉	1	1	yes	characteristic
341	#117	C₂³×C₁₉	1	2	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
346	#107	C₂³×C₁₉	1	4	yes	—
347	#106	C₂³×C₁₉	1	4	yes	—
348	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
349	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
350	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
351	#103	C₂³×C₁₉	1	8	yes	—
352	#103	C₂³×C₁₉	1	4	yes	—
353	#103	C₂³×C₁₉	1	8	yes	—
354	#102	C₂³×C₁₉	1	4	yes	—
355	#102	C₂³×C₁₉	1	4	yes	—
356	#102	C₂³×C₁₉	1	4	yes	—
357	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
358	#97	C₂³×C₁₉	1	4	yes	—
359	C₄×C₈	C₂³×C₁₉	1	4	yes	—
360	C₄×C₈	C₂³×C₁₉	1	4	yes	—
361	C₁₉	#61935	1	1	yes	characteristic, direct product factor, Sylow
362	#41	—	4	2	no	—
363	#41	—	8	4	no	—
364	#41	—	8	8	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
369	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
370	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	SD₁₆	—	4	8	no	—
386	SD₁₆	—	4	8	no	—
387	SD₁₆	—	4	4	no	—
388	D₈	—	4	4	no	—
389	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
390	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
400	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
401	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
402	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	8	no	—
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₄²	C₂⁴×C₁₉	1	2	yes	—
416	C₄²	C₂⁴×C₁₉	1	4	yes	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	4	no	—
419	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
420	Q₈	—	2	8	no	—
421	Q₈	—	2	8	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	8	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
446	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
448	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₈	—	2	4	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	8	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	2	no	—
466	C₄	C₁₉×#577	1	4	yes	—
467	C₄	C₁₉×#585	1	2	yes	—
468	C₂	—	4	1	no	—
469	C₂	—	8	1	no	—
470	C₂	—	8	4	no	—
471	C₂	C₁₉×#3487	1	1	yes	characteristic
472	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3548	C₂	semidirect
2. C₁₉×#3509	C₂	semidirect
3. C₁₉×#3397	C₂	semidirect
4. C₁₉×#3392	C₂	semidirect
5. C₁₉×#3372	C₂	semidirect
6. C₁₉×#3360	C₂	semidirect
7. C₁₉×#3221	C₂	semidirect
8. C₁₉×#3206	C₂	semidirect
9. C₁₉×#3126	C₂	semidirect
10. C₁₉×#3106	C₂	semidirect
11. C₁₉×#2986	C₂	semidirect
180. #61935	C₁₉	direct (N × H)
215. #3548	C₂×C₁₉	semidirect
216. #3509	C₂×C₁₉	semidirect
217. #3397	C₂×C₁₉	semidirect
218. #3392	C₂×C₁₉	semidirect
219. #3372	C₂×C₁₉	semidirect
220. #3360	C₂×C₁₉	semidirect
221. #3221	C₂×C₁₉	semidirect
222. #3206	C₂×C₁₉	semidirect
223. #3126	C₂×C₁₉	semidirect
224. #3106	C₂×C₁₉	semidirect
225. #2986	C₂×C₁₉	semidirect
361. C₁₉	#61935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3548	2
C₁₉×#3509	2
C₁₉×#3397	2
C₁₉×#3392	2
C₁₉×#3372	2
C₁₉×#3360	2
C₁₉×#3221	2
C₁₉×#3206	2
C₁₉×#3126	2
C₁₉×#3106	2
C₁₉×#2986	2
#61935	19

Subgroups — C19×#61935 #18067894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61935 #18067894