Subgroups — #18088333

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926299	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	complemented
10	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
11	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
12	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
13	#11926299	—	2	8	no	—
14	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₁₉×#95	C₄	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₉	C₈	1	8	yes	complemented
27	C₂×C₄²×C₁₉	—	2	4	no	—
28	C₂×C₄²×C₁₉	—	2	2	no	—
29	C₂×C₄²×C₁₉	—	2	2	no	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₂²×C₁₉⋊C₈	—	2	2	no	—
40	C₂²×C₁₉⋊C₈	—	2	2	no	—
41	C₂²×C₁₉⋊C₈	—	2	4	no	—
42	C₂²×C₁₉⋊C₈	—	2	2	no	—
43	C₂²×C₁₉⋊C₈	—	2	2	no	—
44	C₂²×C₁₉⋊C₈	—	2	4	no	—
45	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
46	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
47	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
48	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
49	C₁₉×#95	—	2	4	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
51	C₄×C₁₉⋊C₈	—	2	8	no	—
52	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	—	2	4	no	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	—	2	8	no	—
56	C₂²×C₄×C₁₉	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	2	8	no	—
58	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
59	C₂²×C₄×C₁₉	C₄²	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×C₈	1	8	yes	—
65	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	—
66	C₂²×C₄×C₁₉	M₁₆	1	4	yes	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₁₉	#41	1	2	yes	—
76	C₂²×C₄×C₁₉	#41	1	2	yes	—
77	C₄⋊C₄×C₁₉	—	2	16	no	—
78	C₄²×C₁₉	—	4	4	no	—
79	C₄²×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
82	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
83	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
84	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
85	C₂×C₁₉⋊C₈	—	2	4	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	2	4	no	—
88	C₂×C₁₉⋊C₈	—	2	4	no	—
89	C₂×C₁₉⋊C₈	—	2	4	no	—
90	C₂×C₁₉⋊C₈	—	2	4	no	—
91	C₂×C₁₉⋊C₈	—	2	4	no	—
92	C₂×C₁₉⋊C₈	—	2	8	no	—
93	C₂×C₁₉⋊C₈	—	4	4	no	—
94	C₂×C₁₉⋊C₈	—	4	2	no	—
95	C₂×C₁₉⋊C₈	—	4	2	no	—
96	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	complemented
97	#10834	—	19	1	no	maximal, Sylow
98	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
99	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₂³×C₁₉	C₄×D₄	1	2	yes	—
102	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
103	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
104	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
105	C₂³×C₁₉	#131	1	4	yes	—
106	C₂×C₄×C₁₉	—	2	4	no	—
107	C₂×C₄×C₁₉	—	2	4	no	—
108	C₂×C₄×C₁₉	—	2	4	no	—
109	C₂×C₄×C₁₉	—	2	8	no	—
110	C₂×C₄×C₁₉	—	2	16	no	—
111	C₂×C₄×C₁₉	—	4	4	no	—
112	C₂×C₄×C₁₉	—	4	4	no	—
113	C₂×C₄×C₁₉	—	4	8	no	—
114	C₂×C₄×C₁₉	#95	1	4	yes	—
115	C₂×C₄×C₁₉	#95	1	4	yes	—
116	C₂×C₄×C₁₉	C₄×C₈	1	4	yes	—
117	C₂×C₄×C₁₉	#97	1	4	yes	—
118	C₂×C₄×C₁₉	C₂²⋊C₈	1	8	yes	—
119	C₂×C₄×C₁₉	C₄⋊C₈	1	8	yes	—
120	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	#117	1	2	yes	—
126	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
127	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
128	C₂×C₄×C₁₉	#121	1	2	yes	—
129	C₂×C₄×C₁₉	#121	1	2	yes	—
130	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#125	1	2	yes	—
135	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
138	C₁₉⋊C₈	—	2	8	no	—
139	C₁₉⋊C₈	—	4	4	no	—
140	C₂²×C₄⋊C₈	—	19	1	no	—
141	C₂²×C₄×C₈	—	19	1	no	—
142	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
143	C₂×#336	—	19	4	no	—
144	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
145	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
146	C₂²×C₁₉	#389	1	2	yes	—
147	C₂²×C₁₉	#390	1	1	yes	characteristic
148	C₂²×C₁₉	#391	1	1	yes	characteristic
149	C₂²×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
150	C₂²×C₁₉	C₂×#97	1	1	yes	characteristic
151	C₂²×C₁₉	#405	1	2	yes	—
152	C₂²×C₁₉	C₂×C₂²⋊C₈	1	2	yes	—
153	C₂²×C₁₉	#408	1	2	yes	—
154	C₂²×C₁₉	C₂×C₄⋊C₈	1	2	yes	—
155	C₂²×C₁₉	#424	1	2	yes	—
156	C₂²×C₁₉	C₈×D₄	1	4	yes	—
157	C₂²×C₁₉	#436	1	4	yes	—
158	C₂²×C₁₉	C₈×Q₈	1	4	yes	—
159	C₂²×C₁₉	#446	1	4	yes	—
160	C₄×C₁₉	—	2	4	no	—
161	C₄×C₁₉	—	4	8	no	—
162	C₄×C₁₉	#336	1	8	yes	complemented
163	C₄×C₁₉	#380	1	2	yes	—
164	C₄×C₁₉	#382	1	1	yes	characteristic
165	C₄×C₁₉	#384	1	1	yes	characteristic
166	C₄×C₁₉	#389	1	2	yes	—
167	C₄×C₁₉	#390	1	1	yes	characteristic
168	C₄×C₁₉	#391	1	1	yes	characteristic
169	C₂³×C₈	—	19	2	no	—
170	C₂³×C₈	—	19	2	no	—
171	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
172	C₂²×C₄²	C₂×D₁₉	1	2	yes	—
173	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
174	C₂×C₄⋊C₈	—	19	4	no	—
175	C₂×C₄⋊C₈	—	38	2	no	—
176	C₂×C₄⋊C₈	—	38	2	no	—
177	C₂×C₄×C₈	—	19	4	no	—
178	C₂×C₄×C₈	—	38	2	no	—
179	C₂×C₄×C₈	—	38	2	no	—
180	C₄×C₄⋊C₄	—	2	2	no	—
181	C₄×C₄⋊C₄	—	2	2	no	—
182	C₂×#95	Dic₁₉	1	2	yes	—
183	#336	—	38	8	no	—
184	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
185	C₂×C₁₉	C₂×#336	1	1	yes	characteristic
186	C₂×C₁₉	#1729	1	1	yes	characteristic
187	C₂×C₁₉	C₈×C₄⋊C₄	1	2	yes	—
188	C₂×C₁₉	#1770	1	2	yes	—
189	C₂×C₁₉	#1939	1	4	yes	—
190	C₂×C₁₉	#1954	1	2	yes	—
191	C₂×C₁₉	#1984	1	2	yes	—
192	C₂³×C₄	C₂×Dic₁₉	1	4	yes	—
193	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
194	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
195	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
196	C₂²×C₈	—	19	4	no	—
197	C₂²×C₈	—	19	4	no	—
198	C₂²×C₈	—	19	4	no	—
199	C₂²×C₈	—	19	4	no	—
200	C₂²×C₈	—	38	2	no	—
201	C₂²×C₈	—	38	2	no	—
202	C₂²×C₈	—	38	2	no	—
203	C₂²×C₈	—	38	2	no	—
204	C₂²×C₈	—	38	2	no	—
205	C₂²×C₈	—	38	4	no	—
206	C₂²×C₈	—	38	4	no	—
207	C₂²×C₈	—	38	2	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	C₁₉⋊C₈	1	8	yes	complemented
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	—	2	4	no	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	Dic₃₈	1	2	yes	—
216	C₂×C₄²	C₄×D₁₉	1	2	yes	—
217	C₂×C₄²	C₄×D₁₉	1	2	yes	—
218	C₂×C₄²	D₇₆	1	2	yes	—
219	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
220	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
221	C₄⋊C₈	—	38	8	no	—
222	C₄×C₈	—	38	8	no	—
223	#95	—	2	4	no	—
224	C₁₉	#10834	1	1	yes	characteristic, complemented, Sylow
225	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	2	8	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	C₂×C₁₉⋊C₈	1	8	yes	—
232	C₂²×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
233	C₂²×C₄	#64520	1	4	yes	—
234	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
235	C₂²×C₄	C₄×Dic₁₉	1	2	yes	—
236	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
237	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
238	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
239	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
240	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
244	C₂²×C₄	D₄×D₁₉	1	2	yes	—
245	C₂²×C₄	#64543	1	2	yes	—
246	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
247	C₂²×C₄	#64545	1	2	yes	—
248	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂×C₈	—	19	8	no	—
251	C₂×C₈	—	38	4	no	—
252	C₂×C₈	—	38	4	no	—
253	C₂×C₈	—	38	4	no	—
254	C₂×C₈	—	38	4	no	—
255	C₂×C₈	—	38	4	no	—
256	C₂×C₈	—	38	4	no	—
257	C₂×C₈	—	38	8	no	—
258	C₂×C₈	—	38	4	no	—
259	C₂×C₈	—	76	2	no	—
260	C₂×C₈	—	76	2	no	—
261	C₂×C₈	—	76	4	no	—
262	C₄⋊C₄	—	2	16	no	—
263	C₄²	—	4	2	no	—
264	C₄²	—	4	4	no	—
265	C₄²	—	4	2	no	—
266	C₄²	Dic₁₉⋊C₄	1	4	yes	—
267	C₄²	Dic₁₉⋊C₄	1	4	yes	—
268	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
269	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
270	C₂³	C₂²×C₁₉⋊C₈	1	2	yes	—
271	C₂³	C₂×#64520	1	2	yes	—
272	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
273	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
274	C₂³	D₄×Dic₁₉	1	2	yes	—
275	C₂³	Q₈×Dic₁₉	1	2	yes	—
276	C₂³	#10597394	1	4	yes	—
277	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	16	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	4	8	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	C₄×C₁₉⋊C₈	1	4	yes	—
287	C₂×C₄	#10597260	1	4	yes	—
288	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	8	yes	—
289	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	8	yes	—
290	C₂×C₄	C₁₉⋊#95	1	4	yes	—
291	C₂×C₄	C₁₉⋊#95	1	4	yes	—
292	C₂×C₄	#10597333	1	2	yes	—
293	C₂×C₄	#10597334	1	2	yes	—
294	C₂×C₄	#10597336	1	2	yes	—
295	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
296	C₂×C₄	#10597338	1	2	yes	—
297	C₂×C₄	#10597339	1	2	yes	—
298	C₂×C₄	#10597341	1	2	yes	—
299	C₂×C₄	#10597343	1	2	yes	—
300	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
301	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
302	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
303	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
304	C₂×C₄	#10597382	1	1	yes	characteristic
305	C₂×C₄	#10597384	1	2	yes	—
306	C₂×C₄	#10597386	1	1	yes	characteristic
307	C₂×C₄	#10597390	1	1	yes	characteristic
308	C₂×C₄	#10597392	1	2	yes	—
309	C₂×C₄	#10597393	1	1	yes	characteristic
310	C₈	—	38	8	no	—
311	C₈	—	76	4	no	—
312	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
313	C₂²	C₄⋊C₄×Dic₁₉	1	2	yes	—
314	C₂²	#11926443	1	2	yes	—
315	C₂²	#11926447	1	1	yes	characteristic
316	C₂²	#11926451	1	1	yes	characteristic
317	C₂²	C₂×C₄×C₁₉⋊C₈	1	1	yes	characteristic
318	C₂²	C₂×#10597260	1	1	yes	characteristic
319	C₂²	#11926500	1	2	yes	—
320	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
321	C₂²	#11926511	1	2	yes	—
322	C₂²	C₂×C₄⋊(C₁₉⋊C₈)	1	2	yes	—
323	C₂²	#11926571	1	2	yes	—
324	C₂²	D₄×C₁₉⋊C₈	1	4	yes	—
325	C₂²	#11926622	1	4	yes	—
326	C₂²	Q₈×C₁₉⋊C₈	1	4	yes	—
327	C₂²	#11926675	1	4	yes	—
328	C₄	—	2	4	no	—
329	C₄	—	4	8	no	—
330	C₄	#11926299	1	8	yes	complemented
331	C₄	#11926401	1	2	yes	—
332	C₄	#11926409	1	1	yes	characteristic
333	C₄	#11926413	1	1	yes	characteristic
334	C₄	#11926440	1	2	yes	—
335	C₄	#11926445	1	1	yes	characteristic
336	C₄	#11926449	1	1	yes	characteristic
337	C₂	#14561864	1	1	yes	characteristic
338	C₂	C₂×#11926299	1	1	yes	characteristic
339	C₂	#14563332	1	1	yes	characteristic
340	C₂	C₄⋊C₄×C₁₉⋊C₈	1	2	yes	—
341	C₂	#14563504	1	2	yes	—
342	C₂	#14564354	1	4	yes	—
343	C₂	#14564430	1	2	yes	—
344	C₂	#14564572	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄×C₈
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#10834
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
12. C₂×C₄×C₁₉⋊C₈	C₄	semidirect
26. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
96. C₂×C₁₉⋊C₈	C₄⋊C₄	semidirect
162. C₄×C₁₉	#336	semidirect
210. C₂×C₄⋊C₄	C₁₉⋊C₈	semidirect
224. C₁₉	#10834	semidirect
330. C₄	#11926299	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₁₉⋊C₈)	2
C₂²×C₄×C₁₉⋊C₈	2
C₂×#11926299	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#10834	19