Subgroups — C₂×C₁₉×#3176 #18066639

Order 4864.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#540	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₁₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
12	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#540	—	2	8	no	—
16	C₁₉×#540	C₂²	1	16	yes	complemented
17	C₂×C₁₉×#127	C₂²	1	2	yes	—
18	C₂×C₁₉×#125	C₂²	1	2	yes	—
19	C₂×C₁₉×#123	—	2	4	no	—
20	C₂×C₁₉×#121	—	2	4	no	—
21	C₂×C₁₉×#121	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₁₉×#499	C₂²	1	8	yes	complemented
25	C₁₉×#493	C₂²	1	8	yes	complemented
26	C₁₉×#490	C₂²	1	16	yes	complemented
27	C₁₉×#469	C₂²	1	16	yes	complemented
28	C₁₉×#466	C₂²	1	16	yes	complemented
29	C₁₉×#442	C₂²	1	16	yes	complemented
30	C₄×D₈×C₁₉	C₂²	1	16	yes	complemented
31	C₂×C₁₉×#107	C₂²	1	2	yes	—
32	C₂×C₁₉×#106	C₂²	1	2	yes	—
33	C₂×C₁₉×#102	C₂²	1	4	yes	—
34	C₂×C₁₉×#102	C₂²	1	4	yes	—
35	C₁₉×#405	C₂²	1	8	yes	complemented
36	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	—	2	4	no	—
41	C₂²×D₄×C₁₉	—	2	4	no	—
42	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	—	2	4	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₁₉	—	2	8	no	—
46	C₂×D₈×C₁₉	—	2	8	no	—
47	C₂×D₈×C₁₉	C₂³	1	8	yes	—
48	C₂×D₈×C₁₉	C₂³	1	8	yes	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
51	C₂²×C₈×C₁₉	—	2	4	no	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×#127	—	2	4	no	—
58	C₁₉×#127	C₂³	1	8	yes	—
59	C₁₉×#125	—	2	4	no	—
60	C₁₉×#125	C₂³	1	8	yes	—
61	C₁₉×#123	—	2	32	no	—
62	C₁₉×#121	—	2	8	no	—
63	C₁₉×#121	—	2	32	no	—
64	C₁₉×#121	C₂³	1	16	yes	—
65	C₄×D₄×C₁₉	—	2	8	no	—
66	C₄×D₄×C₁₉	C₂³	1	16	yes	—
67	C₁₉×#117	D₄	1	4	yes	—
68	C₁₉×#117	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#107	C₂³	1	8	yes	—
78	C₁₉×#106	C₂³	1	8	yes	—
79	C₁₉×#102	C₂³	1	16	yes	—
80	C₁₉×#102	C₂³	1	16	yes	—
81	C₁₉×#97	C₂³	1	4	yes	—
82	C₁₉×#97	C₂³	1	4	yes	—
83	C₄×C₈×C₁₉	C₂³	1	4	yes	—
84	C₄×C₈×C₁₉	C₂³	1	4	yes	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₁₉	—	2	16	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	16	no	—
90	C₂×D₄×C₁₉	—	2	8	no	—
91	C₂×D₄×C₁₉	—	2	8	no	—
92	C₂×D₄×C₁₉	—	8	8	no	—
93	C₂×D₄×C₁₉	—	8	8	no	—
94	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	16	no	—
99	C₂²×C₄×C₁₉	—	8	8	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	D₈×C₁₉	—	2	16	no	—
107	D₈×C₁₉	—	2	16	no	—
108	M₁₆×C₁₉	—	2	8	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	8	no	—
112	C₂×C₈×C₁₉	#41	1	4	yes	—
113	C₂×C₈×C₁₉	#41	1	4	yes	—
114	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
115	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
116	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
117	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
118	C₄⋊C₄×C₁₉	—	2	16	no	—
119	C₄⋊C₄×C₁₉	—	2	4	no	—
120	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
122	C₂²⋊C₄×C₁₉	—	2	16	no	—
123	C₂²⋊C₄×C₁₉	—	2	16	no	—
124	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
125	C₄²×C₁₉	C₂×D₄	1	2	yes	—
126	C₄²×C₁₉	C₂×D₄	1	2	yes	—
127	C₄²×C₁₉	C₂⁴	1	2	yes	—
128	C₄²×C₁₉	C₂⁴	1	2	yes	—
129	C₂×#3176	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	8	no	—
133	C₂³×C₁₉	—	4	8	no	—
134	C₂³×C₁₉	—	4	8	no	—
135	C₂³×C₁₉	—	4	8	no	—
136	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
137	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
138	D₄×C₁₉	—	2	8	no	—
139	D₄×C₁₉	—	2	8	no	—
140	D₄×C₁₉	—	4	8	no	—
141	D₄×C₁₉	—	8	16	no	—
142	D₄×C₁₉	—	8	16	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	8	no	—
150	C₂×C₄×C₁₉	—	4	8	no	—
151	C₂×C₄×C₁₉	—	8	16	no	—
152	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
155	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
157	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
158	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
159	C₈×C₁₉	—	2	2	no	—
160	C₈×C₁₉	—	2	2	no	—
161	C₈×C₁₉	C₂×#41	1	4	yes	—
162	C₈×C₁₉	C₂×#41	1	4	yes	—
163	C₂×#540	C₂×C₁₉	1	2	yes	complemented
164	#3176	C₂×C₁₉	1	16	yes	direct product factor
165	C₂×#499	C₂×C₁₉	1	1	yes	characteristic, complemented
166	C₂×#493	C₂×C₁₉	1	1	yes	characteristic, complemented
167	C₂×#490	C₂×C₁₉	1	2	yes	complemented
168	C₂×#469	C₂×C₁₉	1	2	yes	complemented
169	C₂×#466	C₂×C₁₉	1	2	yes	complemented
170	C₂×#442	C₂×C₁₉	1	2	yes	complemented
171	C₂×C₄×D₈	C₂×C₁₉	1	2	yes	complemented
172	C₂×#405	C₂×C₁₉	1	1	yes	characteristic, complemented
173	C₂²×C₁₉	—	2	2	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	4	4	no	—
176	C₂²×C₁₉	—	4	8	no	—
177	C₂²×C₁₉	—	4	8	no	—
178	C₂²×C₁₉	—	4	8	no	—
179	C₂²×C₁₉	—	8	16	no	—
180	C₂²×C₁₉	#532	1	2	yes	—
181	C₂²×C₁₉	#576	1	4	yes	—
182	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
183	C₄×C₁₉	—	2	2	no	—
184	C₄×C₁₉	—	2	4	no	—
185	C₄×C₁₉	—	2	4	no	—
186	C₄×C₁₉	—	4	8	no	—
187	C₄×C₁₉	#532	1	2	yes	—
188	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
189	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
190	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
191	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
192	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
194	#540	—	2	8	no	—
195	#540	C₂²×C₁₉	1	16	yes	complemented
196	C₂×#127	C₂²×C₁₉	1	2	yes	—
197	C₂×#125	C₂²×C₁₉	1	2	yes	—
198	C₂×#123	—	2	4	no	—
199	C₂×#121	—	2	4	no	—
200	C₂×#121	C₂²×C₁₉	1	4	yes	—
201	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
202	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
203	#499	C₂²×C₁₉	1	8	yes	complemented
204	#493	C₂²×C₁₉	1	8	yes	complemented
205	#490	C₂²×C₁₉	1	16	yes	complemented
206	#469	C₂²×C₁₉	1	16	yes	complemented
207	#466	C₂²×C₁₉	1	16	yes	complemented
208	#442	C₂²×C₁₉	1	16	yes	complemented
209	C₄×D₈	C₂²×C₁₉	1	16	yes	complemented
210	C₂×#107	C₂²×C₁₉	1	2	yes	—
211	C₂×#106	C₂²×C₁₉	1	2	yes	—
212	C₂×#102	C₂²×C₁₉	1	4	yes	—
213	C₂×#102	C₂²×C₁₉	1	4	yes	—
214	#405	C₂²×C₁₉	1	8	yes	complemented
215	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
219	C₂×C₁₉	—	4	2	no	—
220	C₂×C₁₉	—	8	8	no	—
221	C₂×C₁₉	#3176	1	4	yes	direct product factor
222	C₂×C₁₉	C₂×#532	1	1	yes	characteristic
223	C₂×C₁₉	C₂×#576	1	2	yes	—
224	C₂²×D₄	—	2	4	no	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
227	C₂³×C₄	—	2	4	no	—
228	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
229	C₂×D₈	—	2	8	no	—
230	C₂×D₈	—	2	8	no	—
231	C₂×D₈	C₂³×C₁₉	1	8	yes	—
232	C₂×D₈	C₂³×C₁₉	1	8	yes	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
238	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
241	#127	—	2	4	no	—
242	#127	C₂³×C₁₉	1	8	yes	—
243	#125	—	2	4	no	—
244	#125	C₂³×C₁₉	1	8	yes	—
245	#123	—	2	32	no	—
246	#121	—	2	8	no	—
247	#121	—	2	32	no	—
248	#121	C₂³×C₁₉	1	16	yes	—
249	C₄×D₄	—	2	8	no	—
250	C₄×D₄	C₂³×C₁₉	1	16	yes	—
251	#117	D₄×C₁₉	1	4	yes	—
252	#117	C₂³×C₁₉	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
259	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
261	#107	C₂³×C₁₉	1	8	yes	—
262	#106	C₂³×C₁₉	1	8	yes	—
263	#102	C₂³×C₁₉	1	16	yes	—
264	#102	C₂³×C₁₉	1	16	yes	—
265	#97	C₂³×C₁₉	1	4	yes	—
266	#97	C₂³×C₁₉	1	4	yes	—
267	C₄×C₈	C₂³×C₁₉	1	4	yes	—
268	C₄×C₈	C₂³×C₁₉	1	4	yes	—
269	C₁₉	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	—	2	4	no	—
271	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	8	8	no	—
278	C₂×D₄	—	8	8	no	—
279	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	16	no	—
284	C₂²×C₄	—	8	8	no	—
285	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
291	D₈	—	2	16	no	—
292	D₈	—	2	16	no	—
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	#41×C₁₉	1	4	yes	—
298	C₂×C₈	#41×C₁₉	1	4	yes	—
299	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
300	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
301	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
302	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
310	C₄²	C₂×D₄×C₁₉	1	2	yes	—
311	C₄²	C₂×D₄×C₁₉	1	2	yes	—
312	C₄²	C₂⁴×C₁₉	1	2	yes	—
313	C₄²	C₂⁴×C₁₉	1	2	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
321	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
322	D₄	—	2	8	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	8	16	no	—
326	D₄	—	8	16	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	8	16	no	—
336	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
341	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
342	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₈	C₂×#41×C₁₉	1	4	yes	—
346	C₈	C₂×#41×C₁₉	1	4	yes	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₉×#532	1	2	yes	—
355	C₂²	C₁₉×#576	1	4	yes	—
356	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	4	no	—
360	C₄	—	4	8	no	—
361	C₄	C₁₉×#532	1	2	yes	—
362	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
363	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₁₉×#3176	1	4	yes	direct product factor
367	C₂	C₂×C₁₉×#532	1	1	yes	characteristic
368	C₂	C₂×C₁₉×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#540	C₂	semidirect
2. C₁₉×#3176	C₂	direct (N × H)
3. C₂×C₁₉×#499	C₂	semidirect
4. C₂×C₁₉×#493	C₂	semidirect
5. C₂×C₁₉×#490	C₂	semidirect
6. C₂×C₁₉×#469	C₂	semidirect
7. C₂×C₁₉×#466	C₂	semidirect
8. C₂×C₁₉×#442	C₂	semidirect
9. C₂×C₄×D₈×C₁₉	C₂	semidirect
10. C₂×C₁₉×#405	C₂	semidirect
16. C₁₉×#540	C₂²	semidirect
24. C₁₉×#499	C₂²	semidirect
25. C₁₉×#493	C₂²	semidirect
26. C₁₉×#490	C₂²	semidirect
27. C₁₉×#469	C₂²	semidirect
28. C₁₉×#466	C₂²	semidirect
29. C₁₉×#442	C₂²	semidirect
30. C₄×D₈×C₁₉	C₂²	semidirect
35. C₁₉×#405	C₂²	semidirect
129. C₂×#3176	C₁₉	direct (N × H)
163. C₂×#540	C₂×C₁₉	semidirect
164. #3176	C₂×C₁₉	direct (N × H)
165. C₂×#499	C₂×C₁₉	semidirect
166. C₂×#493	C₂×C₁₉	semidirect
167. C₂×#490	C₂×C₁₉	semidirect
168. C₂×#469	C₂×C₁₉	semidirect
169. C₂×#466	C₂×C₁₉	semidirect
170. C₂×#442	C₂×C₁₉	semidirect
171. C₂×C₄×D₈	C₂×C₁₉	semidirect
172. C₂×#405	C₂×C₁₉	semidirect
195. #540	C₂²×C₁₉	semidirect
203. #499	C₂²×C₁₉	semidirect
204. #493	C₂²×C₁₉	semidirect
205. #490	C₂²×C₁₉	semidirect
206. #469	C₂²×C₁₉	semidirect
207. #466	C₂²×C₁₉	semidirect
208. #442	C₂²×C₁₉	semidirect
209. C₄×D₈	C₂²×C₁₉	semidirect
214. #405	C₂²×C₁₉	semidirect
221. C₂×C₁₉	#3176	direct (N × H)
269. C₁₉	C₂×#3176	direct (N × H)
366. C₂	C₁₉×#3176	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×C₁₉×#540	2
C₁₉×#3176	2
C₂×C₁₉×#499	2
C₂×C₁₉×#493	2
C₂×C₁₉×#490	2
C₂×C₁₉×#469	2
C₂×C₁₉×#466	2
C₂×C₁₉×#442	2
C₂×C₄×D₈×C₁₉	2
C₂×C₁₉×#405	2
C₂×#3176	19

Subgroups — C2×C19×#3176 #18066639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3176 #18066639