Subgroups — C₄×C₁₉×#408 #18026333

Order 4864.

1662 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#408	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1750	C₂	1	4	yes	maximal, complemented
6	C₄×C₁₉×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1729	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₄×#41×C₁₉	—	2	4	no	—
12	C₄×#41×C₁₉	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₄	1	4	yes	—
15	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#408	C₄	1	16	yes	direct product factor
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	8	yes	—
22	C₄×M₁₆×C₁₉	—	2	4	no	—
23	C₂×C₁₉×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	—	2	4	no	—
25	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#336	C₂²	1	8	yes	—
29	C₂×#41×C₁₉	—	2	2	no	—
30	C₂×#41×C₁₉	—	2	2	no	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₉	—	2	4	no	—
41	C₂×M₁₆×C₁₉	—	2	4	no	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	8	yes	complemented
43	C₂²×C₈×C₁₉	—	2	4	no	—
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₂²×C₈×C₁₉	C₂×C₄	1	8	yes	complemented
46	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
47	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
48	C₄×Q₈×C₁₉	—	2	8	no	—
49	C₄×D₄×C₁₉	—	2	16	no	—
50	C₄×D₄×C₁₉	—	2	8	no	—
51	C₁₉×#117	—	2	2	no	—
52	C₁₉×#117	—	2	2	no	—
53	C₁₉×#117	—	2	4	no	—
54	C₁₉×#117	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₁₉	—	2	4	no	—
60	C₂×C₄²×C₁₉	—	2	4	no	—
61	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₁₉	D₄	1	4	yes	—
64	C₂×C₄²×C₁₉	D₄	1	4	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×C₂²⋊C₈	C₂×C₄	1	32	yes	complemented
69	C₁₉×#97	—	2	4	no	—
70	C₄×C₈×C₁₉	—	2	4	no	—
71	C₄×C₈×C₁₉	—	2	4	no	—
72	C₄×C₈×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	#41×C₁₉	—	2	16	no	—
76	#41×C₁₉	—	2	16	no	—
77	C₂×Q₈×C₁₉	—	2	2	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	C₄²	1	4	yes	—
80	C₂×D₄×C₁₉	—	2	4	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	C₄²	1	8	yes	—
85	C₂×D₄×C₁₉	C₄²	1	4	yes	—
86	C₂²×C₄×C₁₉	—	2	8	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	2	16	no	—
92	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	#41	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₁₉	—	2	16	no	—
105	C₂×C₈×C₁₉	—	2	16	no	—
106	C₂×C₈×C₁₉	—	2	4	no	—
107	C₂×C₈×C₁₉	—	2	4	no	—
108	C₂×C₈×C₁₉	—	2	4	no	—
109	C₂×C₈×C₁₉	—	2	4	no	—
110	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
111	C₂×C₈×C₁₉	C₂²×C₄	1	8	yes	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₉	—	2	8	no	—
116	C₄²×C₁₉	—	2	8	no	—
117	C₄²×C₁₉	—	2	2	no	—
118	C₄²×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	C₂²⋊C₄	1	8	yes	—
120	C₄²×C₁₉	C₂×D₄	1	2	yes	—
121	C₄²×C₁₉	C₂×D₄	1	2	yes	—
122	C₄²×C₁₉	C₂×D₄	1	2	yes	—
123	C₄²×C₁₉	C₂×D₄	1	2	yes	—
124	C₄×#408	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	8	no	—
129	C₂³×C₁₉	C₂×C₄²	1	4	yes	—
130	C₂³×C₁₉	C₂×C₄²	1	2	yes	—
131	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂³×C₁₉	#117	1	2	yes	—
133	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
134	Q₈×C₁₉	—	2	8	no	—
135	D₄×C₁₉	—	2	16	no	—
136	D₄×C₁₉	—	2	8	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	8	no	—
141	C₂×C₄×C₁₉	—	2	8	no	—
142	C₂×C₄×C₁₉	—	2	16	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	8	no	—
145	C₂×C₄×C₁₉	—	4	16	no	—
146	C₂×C₄×C₁₉	C₂×C₄²	1	4	yes	—
147	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₉	#117	1	2	yes	—
152	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
153	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
154	C₂×C₄×C₁₉	#131	1	8	yes	—
155	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
156	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
159	C₈×C₁₉	—	2	8	no	—
160	C₈×C₁₉	—	2	8	no	—
161	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
162	C₂×#408	C₂×C₁₉	1	2	yes	—
163	C₂×C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
164	C₂²×C₄×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
165	#1750	C₂×C₁₉	1	4	yes	complemented
166	C₄×C₂²⋊C₈	C₂×C₁₉	1	4	yes	complemented
167	#1729	C₂×C₁₉	1	2	yes	complemented
168	C₂²×C₁₉	—	2	4	no	—
169	C₂²×C₁₉	—	2	4	no	—
170	C₂²×C₁₉	—	2	4	no	—
171	C₂²×C₁₉	—	2	8	no	—
172	C₂²×C₁₉	—	2	4	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	4	no	—
175	C₂²×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
176	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
177	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₁₉	C₂×#117	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#131	1	4	yes	—
180	C₄×C₁₉	—	2	4	no	—
181	C₄×C₁₉	—	2	4	no	—
182	C₄×C₁₉	—	4	4	no	—
183	C₄×C₁₉	C₄×C₂²⋊C₄	1	4	yes	—
184	C₄×C₁₉	#408	1	8	yes	direct product factor
185	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
186	C₄×C₁₉	C₂×C₄×D₄	1	2	yes	—
187	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
188	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
189	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
190	C₄×#41	—	2	4	no	—
191	C₄×#41	—	2	4	no	—
192	C₂×C₄×Q₈	C₄×C₁₉	1	2	yes	—
193	C₂×C₄×D₄	C₄×C₁₉	1	4	yes	—
194	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
195	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×#117	C₂²×C₁₉	1	2	yes	—
197	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
198	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
199	#408	C₄×C₁₉	1	16	yes	direct product factor
200	C₂×C₂²⋊C₈	C₂²×C₁₉	1	8	yes	—
201	C₄×M₁₆	—	2	4	no	—
202	C₂×#97	C₂²×C₁₉	1	2	yes	—
203	C₂×C₄×C₈	—	2	4	no	—
204	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
207	#336	C₂²×C₁₉	1	8	yes	—
208	C₂×C₁₉	—	2	4	no	—
209	C₂×C₁₉	—	4	4	no	—
210	C₂×C₁₉	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₁₉	C₄×#131	1	2	yes	—
212	C₂×C₁₉	C₂×#408	1	2	yes	—
213	C₂×C₁₉	#2922	1	2	yes	—
214	C₂×#41	—	2	2	no	—
215	C₂×#41	—	2	2	no	—
216	C₂×#41	—	2	4	no	—
217	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
218	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
219	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
220	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
222	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	C₂×C₄×C₁₉	1	8	yes	complemented
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	C₂×C₄×C₁₉	1	8	yes	complemented
231	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
232	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
233	C₄×Q₈	—	2	8	no	—
234	C₄×D₄	—	2	16	no	—
235	C₄×D₄	—	2	8	no	—
236	#117	—	2	2	no	—
237	#117	—	2	2	no	—
238	#117	—	2	4	no	—
239	#117	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	C₂×C₄×C₁₉	1	4	yes	—
247	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
248	C₂×C₄²	D₄×C₁₉	1	4	yes	—
249	C₂×C₄²	D₄×C₁₉	1	4	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
253	C₂²⋊C₈	C₂×C₄×C₁₉	1	32	yes	complemented
254	#97	—	2	4	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	—	2	4	no	—
257	C₄×C₈	—	2	4	no	—
258	C₁₉	C₄×#408	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
260	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
261	#41	—	2	16	no	—
262	#41	—	2	16	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	C₄²×C₁₉	1	4	yes	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₄²×C₁₉	1	8	yes	—
271	C₂×D₄	C₄²×C₁₉	1	4	yes	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
288	C₂²×C₄	#41×C₁₉	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
290	M₁₆	—	2	16	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
297	C₂×C₈	C₂²×C₄×C₁₉	1	8	yes	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₄²	—	2	8	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	C₂²⋊C₄×C₁₉	1	8	yes	—
306	C₄²	C₂×D₄×C₁₉	1	2	yes	—
307	C₄²	C₂×D₄×C₁₉	1	2	yes	—
308	C₄²	C₂×D₄×C₁₉	1	2	yes	—
309	C₄²	C₂×D₄×C₁₉	1	2	yes	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	8	no	—
314	C₂³	C₂×C₄²×C₁₉	1	4	yes	—
315	C₂³	C₂×C₄²×C₁₉	1	2	yes	—
316	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
317	C₂³	C₁₉×#117	1	2	yes	—
318	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
319	Q₈	—	2	8	no	—
320	D₄	—	2	16	no	—
321	D₄	—	2	8	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	16	no	—
331	C₂×C₄	C₂×C₄²×C₁₉	1	4	yes	—
332	C₂×C₄	C₂×C₄²×C₁₉	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
336	C₂×C₄	C₁₉×#117	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
338	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
339	C₂×C₄	C₁₉×#131	1	8	yes	—
340	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
343	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
344	C₈	—	2	8	no	—
345	C₈	—	2	8	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	8	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
354	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
355	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
356	C₂²	C₂×C₁₉×#117	1	1	yes	characteristic
357	C₂²	C₂×C₁₉×#131	1	4	yes	—
358	C₄	—	2	4	no	—
359	C₄	—	2	4	no	—
360	C₄	—	4	4	no	—
361	C₄	C₄×C₂²⋊C₄×C₁₉	1	4	yes	—
362	C₄	C₁₉×#408	1	8	yes	direct product factor
363	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
364	C₄	C₂×C₄×D₄×C₁₉	1	2	yes	—
365	C₂	—	2	4	no	—
366	C₂	—	4	4	no	—
367	C₂	C₂×C₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
368	C₂	C₄×C₁₉×#131	1	2	yes	—
369	C₂	C₂×C₁₉×#408	1	2	yes	—
370	C₂	C₁₉×#2922	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₉	C₂³
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×M₁₆×C₁₉	C₂	semidirect
4. C₂²×C₄×C₈×C₁₉	C₂	semidirect
5. C₁₉×#1750	C₂	semidirect
6. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
7. C₁₉×#1729	C₂	semidirect
20. C₁₉×#408	C₄	direct (N × H)
42. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
45. C₂²×C₈×C₁₉	C₂×C₄	semidirect
68. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
124. C₄×#408	C₁₉	direct (N × H)
163. C₂×C₄×M₁₆	C₂×C₁₉	semidirect
164. C₂²×C₄×C₈	C₂×C₁₉	semidirect
165. #1750	C₂×C₁₉	semidirect
166. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
167. #1729	C₂×C₁₉	semidirect
184. C₄×C₁₉	#408	direct (N × H)
199. #408	C₄×C₁₉	direct (N × H)
227. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
230. C₂²×C₈	C₂×C₄×C₁₉	semidirect
253. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
258. C₁₉	C₄×#408	direct (N × H)
362. C₄	C₁₉×#408	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₂×C₁₉×#408	2
C₂×C₄×M₁₆×C₁₉	2
C₂²×C₄×C₈×C₁₉	2
C₁₉×#1750	2
C₄×C₁₉×C₂²⋊C₈	2
C₁₉×#1729	2
C₄×#408	19

Subgroups — C4×C19×#408 #18026333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#408 #18026333