Subgroups — C₁₉×#18682 #18024641

Order 4864.

1134 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3217	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1621	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1620	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1619	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×D₈×C₁₉	—	2	2	no	—
10	C₁₉×#560	—	2	2	no	—
11	C₁₉×#559	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#550	C₂²	1	2	yes	complemented
13	C₁₉×#546	—	2	2	no	—
14	D₄²×C₁₉	—	2	2	no	—
15	D₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#540	—	2	2	no	—
17	C₁₉×#535	—	2	2	no	—
18	C₁₉×#534	—	2	2	no	—
19	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#529	C₂²	1	2	yes	—
22	C₁₉×#496	—	2	2	no	—
23	C₁₉×#493	—	2	2	no	—
24	C₁₉×#493	C₂²	1	2	yes	—
25	C₁₉×#493	C₂²	1	2	yes	complemented
26	C₁₉×#490	—	2	2	no	—
27	C₁₉×#460	C₂²	1	4	yes	complemented
28	C₁₉×#459	C₂²	1	4	yes	complemented
29	C₁₉×#450	—	2	2	no	—
30	C₁₉×#447	—	2	2	no	—
31	C₁₉×#432	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#331	C₂²	1	2	yes	complemented
34	C₁₉×#331	C₂²	1	2	yes	complemented
35	C₁₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₁₉×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	D₄	1	2	yes	—
44	C₂×SD₁₆×C₁₉	—	2	4	no	—
45	C₂×D₈×C₁₉	—	2	4	no	—
46	C₂×D₈×C₁₉	—	2	4	no	—
47	C₂×D₈×C₁₉	—	2	4	no	—
48	C₂×D₈×C₁₉	—	4	8	no	—
49	C₂²×C₈×C₁₉	—	2	1	no	—
50	C₁₉×#127	—	2	2	no	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#127	—	2	2	no	—
53	C₁₉×#127	—	2	1	no	—
54	C₁₉×#127	D₄	1	2	yes	—
55	C₁₉×#127	C₂³	1	2	yes	—
56	C₁₉×#127	C₂³	1	1	yes	characteristic
57	C₁₉×#127	C₂³	1	1	yes	characteristic
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#125	D₄	1	2	yes	—
60	C₁₉×#124	—	2	2	no	—
61	C₁₉×#124	D₄	1	2	yes	—
62	C₁₉×#123	—	2	2	no	—
63	C₁₉×#123	—	2	4	no	—
64	C₁₉×#123	—	2	2	no	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
67	C₁₉×#121	—	2	4	no	—
68	C₁₉×#121	—	2	4	no	—
69	C₁₉×#121	—	2	4	no	—
70	C₁₉×#121	—	2	4	no	—
71	C₁₉×#121	—	2	2	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	D₄	1	2	yes	—
74	C₁₉×#120	—	2	2	no	—
75	C₁₉×#120	—	2	4	no	—
76	C₁₉×#120	—	2	4	no	—
77	C₁₉×#120	—	2	2	no	—
78	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
79	C₄×D₄×C₁₉	—	2	2	no	—
80	C₄×D₄×C₁₉	—	2	2	no	—
81	C₄×D₄×C₁₉	—	2	2	no	—
82	C₄×D₄×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#117	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	4	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×#97	—	2	2	no	—
91	C₄×C₈×C₁₉	—	2	1	no	—
92	C₄×C₈×C₁₉	C₂³	1	2	yes	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	4	1	no	—
96	#41×C₁₉	—	8	4	no	—
97	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₁₉	—	2	2	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	1	no	—
111	C₂×D₄×C₁₉	—	4	2	no	—
112	C₂×D₄×C₁₉	—	8	4	no	—
113	C₂×D₄×C₁₉	—	8	4	no	—
114	C₂×D₄×C₁₉	—	8	4	no	—
115	C₂×D₄×C₁₉	—	8	4	no	—
116	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	SD₁₆×C₁₉	—	8	4	no	—
125	D₈×C₁₉	—	4	8	no	—
126	D₈×C₁₉	—	4	8	no	—
127	D₈×C₁₉	—	8	4	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	2	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₁₉	—	2	2	no	—
138	C₂²⋊C₄×C₁₉	—	2	2	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	2	2	no	—
145	C₂²⋊C₄×C₁₉	—	2	2	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	C₂×D₄	1	2	yes	—
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
150	#18682	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	8	4	no	—
157	C₂³×C₁₉	—	8	4	no	—
158	C₂³×C₁₉	—	8	4	no	—
159	C₂³×C₁₉	—	8	2	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	C₂³×C₁₉	#120	1	1	yes	characteristic
162	Q₈×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	2	4	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	4	4	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	4	4	no	—
171	D₄×C₁₉	—	4	4	no	—
172	D₄×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	8	4	no	—
174	D₄×C₁₉	—	8	2	no	—
175	D₄×C₁₉	—	8	4	no	—
176	D₄×C₁₉	—	8	4	no	—
177	D₄×C₁₉	—	8	4	no	—
178	D₄×C₁₉	—	8	4	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	#120	1	2	yes	—
188	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
191	C₈×C₁₉	—	2	4	no	—
192	C₈×C₁₉	—	4	4	no	—
193	#3543	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#3217	C₂×C₁₉	1	2	yes	complemented
195	C₂×#493	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#1621	C₂×C₁₉	1	4	yes	complemented
197	#1620	C₂×C₁₉	1	2	yes	complemented
198	#1619	C₂×C₁₉	1	2	yes	complemented
199	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#1494	C₂×C₁₉	1	2	yes	complemented
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	4	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	4	2	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	2	no	—
209	C₂²×C₁₉	—	8	4	no	—
210	C₂²×C₁₉	—	8	2	no	—
211	C₂²×C₁₉	—	16	4	no	—
212	C₂²×C₁₉	—	16	4	no	—
213	C₂²×C₁₉	—	16	4	no	—
214	C₂²×C₁₉	#453	1	2	yes	—
215	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	4	2	no	—
220	C₄×C₁₉	—	4	2	no	—
221	C₄×C₁₉	—	4	2	no	—
222	C₄×C₁₉	#576	1	4	yes	—
223	C₂²×D₈	—	2	2	no	—
224	#560	—	2	2	no	—
225	#559	C₂²×C₁₉	1	1	yes	characteristic, complemented
226	#550	C₂²×C₁₉	1	2	yes	complemented
227	#546	—	2	2	no	—
228	D₄²	—	2	2	no	—
229	D₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
230	#540	—	2	2	no	—
231	#535	—	2	2	no	—
232	#534	—	2	2	no	—
233	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic, complemented
235	#529	C₂²×C₁₉	1	2	yes	—
236	#496	—	2	2	no	—
237	#493	—	2	2	no	—
238	#493	C₂²×C₁₉	1	2	yes	—
239	#493	C₂²×C₁₉	1	2	yes	complemented
240	#490	—	2	2	no	—
241	#460	C₂²×C₁₉	1	4	yes	complemented
242	#459	C₂²×C₁₉	1	4	yes	complemented
243	#450	—	2	2	no	—
244	#447	—	2	2	no	—
245	#432	C₂²×C₁₉	1	2	yes	complemented
246	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
247	#331	C₂²×C₁₉	1	2	yes	complemented
248	#331	C₂²×C₁₉	1	2	yes	complemented
249	Q₈⋊C₈	C₂²×C₁₉	1	4	yes	complemented
250	D₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
251	C₂×C₁₉	—	2	2	no	—
252	C₂×C₁₉	—	8	2	no	—
253	C₂×C₁₉	—	8	2	no	—
254	C₂×C₁₉	—	8	2	no	—
255	C₂×C₁₉	—	16	2	no	—
256	C₂×C₁₉	#3008	1	2	yes	—
257	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
258	C₂×#41	—	2	2	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	D₄×C₁₉	1	2	yes	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	—	2	4	no	—
268	C₂×D₈	—	2	4	no	—
269	C₂×D₈	—	4	8	no	—
270	C₂²×C₈	—	2	1	no	—
271	#127	—	2	2	no	—
272	#127	—	2	2	no	—
273	#127	—	2	2	no	—
274	#127	—	2	1	no	—
275	#127	D₄×C₁₉	1	2	yes	—
276	#127	C₂³×C₁₉	1	2	yes	—
277	#127	C₂³×C₁₉	1	1	yes	characteristic
278	#127	C₂³×C₁₉	1	1	yes	characteristic
279	#126	—	2	2	no	—
280	#125	D₄×C₁₉	1	2	yes	—
281	#124	—	2	2	no	—
282	#124	D₄×C₁₉	1	2	yes	—
283	#123	—	2	2	no	—
284	#123	—	2	4	no	—
285	#123	—	2	2	no	—
286	#123	—	2	2	no	—
287	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	#121	—	2	4	no	—
291	#121	—	2	4	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	D₄×C₁₉	1	2	yes	—
295	#120	—	2	2	no	—
296	#120	—	2	4	no	—
297	#120	—	2	4	no	—
298	#120	—	2	2	no	—
299	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	C₂³×C₁₉	1	2	yes	—
304	#117	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	#97	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	C₂³×C₁₉	1	2	yes	—
314	C₁₉	#18682	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	4	1	no	—
318	#41	—	8	4	no	—
319	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	8	4	no	—
335	C₂×D₄	—	8	4	no	—
336	C₂×D₄	—	8	4	no	—
337	C₂×D₄	—	8	4	no	—
338	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
339	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
340	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	SD₁₆	—	8	4	no	—
347	D₈	—	4	8	no	—
348	D₈	—	4	8	no	—
349	D₈	—	8	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
358	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₁₉	1	2	yes	—
371	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	4	no	—
378	C₂³	—	8	4	no	—
379	C₂³	—	8	4	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	C₁₉×#120	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	4	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	D₄	—	8	4	no	—
399	D₄	—	8	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	C₁₉×#120	1	2	yes	—
409	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
412	C₈	—	2	4	no	—
413	C₈	—	4	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	16	4	no	—
425	C₂²	—	16	4	no	—
426	C₂²	—	16	4	no	—
427	C₂²	C₁₉×#453	1	2	yes	—
428	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	C₁₉×#576	1	4	yes	—
436	C₂	—	2	2	no	—
437	C₂	—	8	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	8	2	no	—
440	C₂	—	16	2	no	—
441	C₂	C₁₉×#3008	1	2	yes	—
442	C₂	C₂×C₁₉×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3543	C₂	semidirect
2. C₁₉×#3217	C₂	semidirect
3. C₂×C₁₉×#493	C₂	semidirect
4. C₁₉×#1621	C₂	semidirect
5. C₁₉×#1620	C₂	semidirect
6. C₁₉×#1619	C₂	semidirect
7. C₁₉×#1555	C₂	semidirect
8. C₁₉×#1494	C₂	semidirect
11. C₁₉×#559	C₂²	semidirect
12. C₁₉×#550	C₂²	semidirect
15. D₄²×C₁₉	C₂²	semidirect
20. C₂×C₁₉×#127	C₂²	semidirect
25. C₁₉×#493	C₂²	semidirect
27. C₁₉×#460	C₂²	semidirect
28. C₁₉×#459	C₂²	semidirect
31. C₁₉×#432	C₂²	semidirect
32. C₂×C₄×C₈×C₁₉	C₂²	semidirect
33. C₁₉×#331	C₂²	semidirect
34. C₁₉×#331	C₂²	semidirect
35. C₁₉×Q₈⋊C₈	C₂²	semidirect
36. C₁₉×D₄⋊C₈	C₂²	semidirect
150. #18682	C₁₉	direct (N × H)
193. #3543	C₂×C₁₉	semidirect
194. #3217	C₂×C₁₉	semidirect
195. C₂×#493	C₂×C₁₉	semidirect
196. #1621	C₂×C₁₉	semidirect
197. #1620	C₂×C₁₉	semidirect
198. #1619	C₂×C₁₉	semidirect
199. #1555	C₂×C₁₉	semidirect
200. #1494	C₂×C₁₉	semidirect
225. #559	C₂²×C₁₉	semidirect
226. #550	C₂²×C₁₉	semidirect
229. D₄²	C₂²×C₁₉	semidirect
234. C₂×#127	C₂²×C₁₉	semidirect
239. #493	C₂²×C₁₉	semidirect
241. #460	C₂²×C₁₉	semidirect
242. #459	C₂²×C₁₉	semidirect
245. #432	C₂²×C₁₉	semidirect
246. C₂×C₄×C₈	C₂²×C₁₉	semidirect
247. #331	C₂²×C₁₉	semidirect
248. #331	C₂²×C₁₉	semidirect
249. Q₈⋊C₈	C₂²×C₁₉	semidirect
250. D₄⋊C₈	C₂²×C₁₉	semidirect
314. C₁₉	#18682	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×#3543	2
C₁₉×#3217	2
C₂×C₁₉×#493	2
C₁₉×#1621	2
C₁₉×#1620	2
C₁₉×#1619	2
C₁₉×#1555	2
C₁₉×#1494	2
#18682	19

Subgroups — C19×#18682 #18024641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18682 #18024641