Subgroups — C₁₉×#23498 #18029457

Order 4864.

1450 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2040	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2039	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#537	C₂²	1	4	yes	—
11	C₁₉×#536	—	2	2	no	—
12	C₁₉×#535	—	2	2	no	—
13	C₁₉×#534	—	2	2	no	—
14	C₁₉×#532	—	2	2	no	—
15	C₁₉×#525	—	2	4	no	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#104	—	2	8	no	—
20	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
21	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
22	C₁₉×#419	—	2	2	no	—
23	C₁₉×#418	—	2	2	no	—
24	C₁₉×#417	C₂²	1	8	yes	complemented
25	C₁₉×#416	—	2	4	no	—
26	C₁₉×#384	C₂²	1	2	yes	complemented
27	C₁₉×#382	C₂²	1	2	yes	complemented
28	C₁₉×#380	—	2	2	no	—
29	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₁₉×#343	C₂²	1	4	yes	complemented
31	C₂×#41×C₁₉	—	2	2	no	—
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	4	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	4	no	—
37	C₂×#41×C₁₉	D₄	1	4	yes	—
38	C₂×#41×C₁₉	C₂³	1	4	yes	—
39	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	D₄	1	2	yes	—
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₉	—	2	2	no	—
50	C₁₉×C₄⋊Q₈	—	2	2	no	—
51	C₁₉×#127	—	2	2	no	—
52	C₁₉×#124	—	2	4	no	—
53	C₁₉×#123	—	2	8	no	—
54	C₁₉×C₂²⋊Q₈	—	2	8	no	—
55	C₁₉×#121	—	2	8	no	—
56	C₁₉×#121	—	2	8	no	—
57	C₁₉×#120	—	2	8	no	—
58	C₄×D₄×C₁₉	—	2	8	no	—
59	C₁₉×#117	—	2	2	no	—
60	C₁₉×#117	—	2	2	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	2	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₉	D₄	1	4	yes	complemented
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#104	—	2	8	no	—
76	C₁₉×#104	—	2	8	no	—
77	C₁₉×#103	—	2	8	no	—
78	C₁₉×#102	—	2	8	no	—
79	C₁₉×#95	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
82	#41×C₁₉	—	2	8	no	—
83	#41×C₁₉	—	2	8	no	—
84	#41×C₁₉	—	2	4	no	—
85	#41×C₁₉	—	2	4	no	—
86	#41×C₁₉	—	2	4	no	—
87	#41×C₁₉	—	2	4	no	—
88	#41×C₁₉	—	4	4	no	—
89	#41×C₁₉	—	4	4	no	—
90	#41×C₁₉	—	4	4	no	—
91	#41×C₁₉	—	4	4	no	—
92	C₂×Q₈×C₁₉	—	2	2	no	—
93	C₂×Q₈×C₁₉	—	2	4	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	8	no	—
99	C₂×D₄×C₁₉	—	2	2	no	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	4	4	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	#41	1	4	yes	—
121	C₂²×C₄×C₁₉	#41	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₁₉	—	2	4	no	—
124	M₁₆×C₁₉	—	2	4	no	—
125	M₁₆×C₁₉	—	4	4	no	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	4	4	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	4	8	no	—
132	C₂²⋊C₄×C₁₉	—	2	16	no	—
133	C₂²⋊C₄×C₁₉	—	2	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	2	no	—
135	C₄²×C₁₉	—	2	2	no	—
136	C₄²×C₁₉	—	2	2	no	—
137	C₄²×C₁₉	—	2	4	no	—
138	C₄²×C₁₉	—	2	1	no	—
139	C₄²×C₁₉	—	2	1	no	—
140	C₄²×C₁₉	—	4	1	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	C₂×D₄	1	2	yes	—
143	C₄²×C₁₉	C₂×D₄	1	2	yes	—
144	#23498	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	—	8	4	no	—
149	C₂³×C₁₉	#120	1	2	yes	—
150	C₂³×C₁₉	#121	1	2	yes	—
151	C₂³×C₁₉	#124	1	2	yes	—
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₉	—	2	4	no	—
154	Q₈×C₁₉	—	2	4	no	—
155	Q₈×C₁₉	—	4	4	no	—
156	D₄×C₁₉	—	2	4	no	—
157	D₄×C₁₉	—	2	4	no	—
158	D₄×C₁₉	—	4	4	no	—
159	D₄×C₁₉	—	4	4	no	—
160	D₄×C₁₉	—	4	8	no	—
161	D₄×C₁₉	—	4	4	no	—
162	D₄×C₁₉	—	8	8	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	4	8	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	4	4	no	—
173	C₂×C₄×C₁₉	—	4	8	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	4	yes	—
180	C₂×C₄×C₁₉	#121	1	4	yes	—
181	C₂×C₄×C₁₉	#121	1	2	yes	—
182	C₂×C₄×C₁₉	#123	1	4	yes	—
183	C₂×C₄×C₁₉	#123	1	4	yes	—
184	C₂×C₄×C₁₉	#124	1	2	yes	—
185	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₉	—	4	4	no	—
190	#3449	C₂×C₁₉	1	1	yes	characteristic
191	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
192	#2896	C₂×C₁₉	1	2	yes	complemented
193	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#2040	C₂×C₁₉	1	4	yes	complemented
195	#2039	C₂×C₁₉	1	4	yes	complemented
196	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	8	no	—
203	C₂²×C₁₉	—	8	8	no	—
204	C₂²×C₁₉	#394	1	4	yes	—
205	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
206	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
207	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
208	C₄×C₁₉	—	2	4	no	—
209	C₄×C₁₉	—	4	2	no	—
210	C₄×C₁₉	—	4	4	no	—
211	C₄×C₁₉	—	4	4	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	#394	1	2	yes	—
214	C₄×C₁₉	#394	1	2	yes	—
215	C₄×C₁₉	C₂×#121	1	2	yes	—
216	C₄×C₁₉	C₂×#123	1	2	yes	—
217	C₂²×#41	C₂²×C₁₉	1	2	yes	—
218	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
219	#537	C₂²×C₁₉	1	4	yes	—
220	#536	—	2	2	no	—
221	#535	—	2	2	no	—
222	#534	—	2	2	no	—
223	#532	—	2	2	no	—
224	#525	—	2	4	no	—
225	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
227	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#104	—	2	8	no	—
229	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
230	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
231	#419	—	2	2	no	—
232	#418	—	2	2	no	—
233	#417	C₂²×C₁₉	1	8	yes	complemented
234	#416	—	2	4	no	—
235	#384	C₂²×C₁₉	1	2	yes	complemented
236	#382	C₂²×C₁₉	1	2	yes	complemented
237	#380	—	2	2	no	—
238	C₄×C₄⋊C₄	—	2	2	no	—
239	#343	C₂²×C₁₉	1	4	yes	complemented
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	4	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	8	4	no	—
244	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
245	C₂×C₁₉	#3018	1	2	yes	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	4	no	—
252	C₂×#41	D₄×C₁₉	1	4	yes	—
253	C₂×#41	C₂³×C₁₉	1	4	yes	—
254	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	D₄×C₁₉	1	2	yes	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
264	C₂²×C₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	#127	—	2	2	no	—
267	#124	—	2	4	no	—
268	#123	—	2	8	no	—
269	C₂²⋊Q₈	—	2	8	no	—
270	#121	—	2	8	no	—
271	#121	—	2	8	no	—
272	#120	—	2	8	no	—
273	C₄×D₄	—	2	8	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	D₄×C₁₉	1	2	yes	—
287	C₂×C₄²	D₄×C₁₉	1	4	yes	complemented
288	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
290	#104	—	2	8	no	—
291	#104	—	2	8	no	—
292	#103	—	2	8	no	—
293	#102	—	2	8	no	—
294	#95	—	2	4	no	—
295	C₁₉	#23498	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	—	2	2	no	—
297	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
298	#41	—	2	8	no	—
299	#41	—	2	8	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	4	4	no	—
305	#41	—	4	4	no	—
306	#41	—	4	4	no	—
307	#41	—	4	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
336	C₂²×C₄	#41×C₁₉	1	4	yes	—
337	C₂²×C₄	#41×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	4	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	4	8	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₁₉	1	2	yes	—
359	C₄²	C₂×D₄×C₁₉	1	2	yes	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	8	4	no	—
364	C₂³	C₁₉×#120	1	2	yes	—
365	C₂³	C₁₉×#121	1	2	yes	—
366	C₂³	C₁₉×#124	1	2	yes	—
367	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	Q₈	—	4	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	4	no	—
377	D₄	—	8	8	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
393	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
394	C₂×C₄	C₁₉×#121	1	2	yes	—
395	C₂×C₄	C₁₉×#121	1	4	yes	—
396	C₂×C₄	C₁₉×#121	1	4	yes	—
397	C₂×C₄	C₁₉×#123	1	4	yes	—
398	C₂×C₄	C₁₉×#123	1	4	yes	—
399	C₂×C₄	C₁₉×#124	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
402	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
403	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
404	C₈	—	4	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	8	no	—
412	C₂²	C₁₉×#394	1	4	yes	—
413	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
414	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
415	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	8	2	no	—
421	C₄	C₁₉×#394	1	2	yes	—
422	C₄	C₁₉×#394	1	2	yes	—
423	C₄	C₂×C₁₉×#121	1	2	yes	—
424	C₄	C₂×C₁₉×#123	1	2	yes	—
425	C₂	—	2	1	no	—
426	C₂	—	2	4	no	—
427	C₂	—	2	1	no	—
428	C₂	—	8	4	no	—
429	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
430	C₂	C₁₉×#3018	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#104	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₁₉×#2285	C₂	semidirect
5. C₁₉×#2040	C₂	semidirect
6. C₁₉×#2039	C₂	semidirect
7. C₁₉×#1742	C₂	semidirect
20. C₂×C₁₉×#104	C₂²	semidirect
21. C₂×C₁₉×#104	C₂²	semidirect
24. C₁₉×#417	C₂²	semidirect
26. C₁₉×#384	C₂²	semidirect
27. C₁₉×#382	C₂²	semidirect
30. C₁₉×#343	C₂²	semidirect
72. C₂×C₄²×C₁₉	D₄	semidirect
144. #23498	C₁₉	direct (N × H)
191. C₂²×#104	C₂×C₁₉	semidirect
192. #2896	C₂×C₁₉	semidirect
193. #2285	C₂×C₁₉	semidirect
194. #2040	C₂×C₁₉	semidirect
195. #2039	C₂×C₁₉	semidirect
196. #1742	C₂×C₁₉	semidirect
229. C₂×#104	C₂²×C₁₉	semidirect
230. C₂×#104	C₂²×C₁₉	semidirect
233. #417	C₂²×C₁₉	semidirect
235. #384	C₂²×C₁₉	semidirect
236. #382	C₂²×C₁₉	semidirect
239. #343	C₂²×C₁₉	semidirect
287. C₂×C₄²	D₄×C₁₉	semidirect
295. C₁₉	#23498	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×#3449	2
C₂²×C₁₉×#104	2
C₁₉×#2896	2
C₁₉×#2285	2
C₁₉×#2040	2
C₁₉×#2039	2
C₁₉×#1742	2
#23498	19

Subgroups — C19×#23498 #18029457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23498 #18029457