Subgroups — C₂×C₁₉×#2095 #18029686

Order 4864.

1238 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#107	C₂	1	2	yes	maximal
2	C₂²×C₁₉×#103	C₂	1	2	yes	maximal
3	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2095	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#107	—	2	8	no	—
14	C₂×C₁₉×#107	C₂²	1	8	yes	—
15	C₂×C₁₉×#103	—	2	8	no	—
16	C₂×C₁₉×#103	C₂²	1	8	yes	—
17	C₁₉×#391	—	2	2	no	—
18	C₁₉×#391	C₂²	1	4	yes	—
19	C₁₉×#384	—	2	2	no	—
20	C₁₉×#384	C₂²	1	4	yes	—
21	C₂×C₁₉×#95	—	2	2	no	—
22	C₁₉×#336	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₉	—	2	1	no	—
24	C₂²×Q₈×C₁₉	—	2	2	no	—
25	C₂²×Q₈×C₁₉	—	2	4	no	—
26	C₂²×Q₈×C₁₉	—	2	4	no	—
27	C₂²×Q₈×C₁₉	Q₈	1	4	yes	—
28	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	4	no	—
35	C₂²×C₈×C₁₉	—	2	4	no	—
36	C₂²×C₈×C₁₉	D₄	1	8	yes	—
37	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
38	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂×C₄²×C₁₉	—	2	4	no	—
48	C₂×C₄²×C₁₉	D₄	1	2	yes	—
49	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
50	C₁₉×#107	—	2	16	no	—
51	C₁₉×#103	—	2	16	no	—
52	C₁₉×#95	—	2	8	no	—
53	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×Q₈×C₁₉	—	2	4	no	—
55	C₂×Q₈×C₁₉	—	2	2	no	—
56	C₂×Q₈×C₁₉	—	2	16	no	—
57	C₂×Q₈×C₁₉	—	2	4	no	—
58	C₂×Q₈×C₁₉	—	2	4	no	—
59	C₂×Q₈×C₁₉	—	4	2	no	—
60	C₂×Q₈×C₁₉	—	4	8	no	—
61	C₂×Q₈×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	2	4	no	—
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	4	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	—	4	4	no	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	8	no	—
74	C₂²×C₄×C₁₉	—	4	4	no	—
75	C₂²×C₄×C₁₉	Q₁₆	1	8	yes	—
76	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
79	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₉	#41	1	4	yes	—
81	C₂²×C₄×C₁₉	#41	1	2	yes	—
82	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₉	—	2	16	no	—
84	C₂×C₈×C₁₉	—	2	4	no	—
85	C₂×C₈×C₁₉	—	2	4	no	—
86	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
87	C₄⋊C₄×C₁₉	—	2	4	no	—
88	C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₄⋊C₄×C₁₉	—	2	4	no	—
90	C₄⋊C₄×C₁₉	—	4	16	no	—
91	C₄⋊C₄×C₁₉	—	4	4	no	—
92	C₄⋊C₄×C₁₉	—	4	2	no	—
93	C₄²×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	—	2	4	no	—
95	C₂×#2095	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
97	C₂³×C₁₉	#123	1	2	yes	—
98	C₂³×C₁₉	#127	1	2	yes	—
99	C₂³×C₁₉	C₂×Q₁₆	1	4	yes	—
100	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
101	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
102	Q₈×C₁₉	—	2	8	no	—
103	Q₈×C₁₉	—	4	4	no	—
104	Q₈×C₁₉	—	4	8	no	—
105	C₂×C₄×C₁₉	—	2	4	no	—
106	C₂×C₄×C₁₉	—	2	4	no	—
107	C₂×C₄×C₁₉	—	2	16	no	—
108	C₂×C₄×C₁₉	—	2	4	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	8	no	—
112	C₂×C₄×C₁₉	—	4	4	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	8	no	—
115	C₂×C₄×C₁₉	—	4	4	no	—
116	C₂×C₄×C₁₉	—	8	8	no	—
117	C₂×C₄×C₁₉	—	8	4	no	—
118	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
119	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
120	C₂×C₄×C₁₉	#123	1	8	yes	—
121	C₂×C₄×C₁₉	#123	1	2	yes	—
122	C₂×C₄×C₁₉	#127	1	2	yes	—
123	C₂×C₄×C₁₉	C₂×Q₁₆	1	8	yes	—
124	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
125	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
127	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
128	C₈×C₁₉	—	2	8	no	—
129	C₂²×#107	C₂×C₁₉	1	2	yes	—
130	C₂²×#103	C₂×C₁₉	1	2	yes	—
131	C₂×#391	C₂×C₁₉	1	1	yes	characteristic
132	C₂×#384	C₂×C₁₉	1	1	yes	characteristic
133	#2095	C₂×C₁₉	1	8	yes	direct product factor
134	C₂×#336	C₂×C₁₉	1	1	yes	characteristic
135	C₂²×C₁₉	#399	1	4	yes	—
136	C₂²×C₁₉	#477	1	8	yes	—
137	C₂²×C₁₉	#484	1	8	yes	—
138	C₂²×C₁₉	#494	1	4	yes	—
139	C₂²×C₁₉	#496	1	4	yes	—
140	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
141	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
142	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
143	C₂²×C₁₉	C₂²×Q₁₆	1	2	yes	—
144	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
145	C₄×C₁₉	—	2	8	no	—
146	C₄×C₁₉	—	4	4	no	—
147	C₄×C₁₉	—	8	4	no	—
148	C₄×C₁₉	—	8	2	no	—
149	C₄×C₁₉	#399	1	4	yes	—
150	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
151	C₄×C₁₉	C₂×#123	1	2	yes	—
152	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
153	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
154	C₂²×C₄⋊C₄	—	2	2	no	—
155	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
156	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
157	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
158	C₂×#107	—	2	8	no	—
159	C₂×#107	C₂²×C₁₉	1	8	yes	—
160	C₂×#103	—	2	8	no	—
161	C₂×#103	C₂²×C₁₉	1	8	yes	—
162	#391	—	2	2	no	—
163	#391	C₂²×C₁₉	1	4	yes	—
164	#384	—	2	2	no	—
165	#384	C₂²×C₁₉	1	4	yes	—
166	C₂×#95	—	2	2	no	—
167	#336	C₂²×C₁₉	1	4	yes	—
168	C₂×C₁₉	#2095	1	8	yes	direct product factor
169	C₂×C₁₉	C₂×#399	1	1	yes	characteristic
170	C₂×C₁₉	C₂×#477	1	2	yes	—
171	C₂×C₁₉	C₂×#484	1	2	yes	—
172	C₂×C₁₉	C₂×#494	1	1	yes	characteristic
173	C₂×C₁₉	C₂×#496	1	1	yes	characteristic
174	C₂²×Q₈	—	2	1	no	—
175	C₂²×Q₈	—	2	2	no	—
176	C₂²×Q₈	—	2	4	no	—
177	C₂²×Q₈	—	2	4	no	—
178	C₂²×Q₈	Q₈×C₁₉	1	4	yes	—
179	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
180	C₂³×C₄	—	2	1	no	—
181	C₂³×C₄	—	2	2	no	—
182	C₂³×C₄	—	2	1	no	—
183	C₂³×C₄	D₄×C₁₉	1	2	yes	—
184	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
185	C₂²×C₈	—	2	4	no	—
186	C₂²×C₈	—	2	4	no	—
187	C₂²×C₈	D₄×C₁₉	1	8	yes	—
188	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
189	C₂×C₄⋊C₄	—	2	4	no	—
190	C₂×C₄⋊C₄	—	2	4	no	—
191	C₂×C₄⋊C₄	—	2	4	no	—
192	C₂×C₄⋊C₄	—	2	8	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	—	4	8	no	—
196	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
197	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
198	C₂×C₄²	—	2	4	no	—
199	C₂×C₄²	D₄×C₁₉	1	2	yes	—
200	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
201	#107	—	2	16	no	—
202	#103	—	2	16	no	—
203	#95	—	2	8	no	—
204	C₁₉	C₂×#2095	1	1	yes	characteristic, direct product factor, Sylow
205	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
206	C₂×Q₈	—	2	4	no	—
207	C₂×Q₈	—	2	2	no	—
208	C₂×Q₈	—	2	16	no	—
209	C₂×Q₈	—	2	4	no	—
210	C₂×Q₈	—	2	4	no	—
211	C₂×Q₈	—	4	8	no	—
212	C₂×Q₈	—	4	2	no	—
213	C₂×Q₈	—	4	2	no	—
214	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	4	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	2	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	4	2	no	—
222	C₂²×C₄	—	4	2	no	—
223	C₂²×C₄	—	4	4	no	—
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	—	4	8	no	—
226	C₂²×C₄	—	4	4	no	—
227	C₂²×C₄	Q₁₆×C₁₉	1	8	yes	—
228	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
229	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
230	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
231	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
232	C₂²×C₄	#41×C₁₉	1	4	yes	—
233	C₂²×C₄	#41×C₁₉	1	2	yes	—
234	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
235	C₂×C₈	—	2	16	no	—
236	C₂×C₈	—	2	4	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
239	C₄⋊C₄	—	2	4	no	—
240	C₄⋊C₄	—	2	4	no	—
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	4	16	no	—
243	C₄⋊C₄	—	4	4	no	—
244	C₄⋊C₄	—	4	2	no	—
245	C₄²	—	2	4	no	—
246	C₄²	—	2	4	no	—
247	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
248	C₂³	C₁₉×#123	1	2	yes	—
249	C₂³	C₁₉×#127	1	2	yes	—
250	C₂³	C₂×Q₁₆×C₁₉	1	4	yes	—
251	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
252	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
253	Q₈	—	2	8	no	—
254	Q₈	—	4	8	no	—
255	Q₈	—	4	4	no	—
256	C₂×C₄	—	2	16	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	4	no	—
260	C₂×C₄	—	4	8	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	8	no	—
266	C₂×C₄	—	4	4	no	—
267	C₂×C₄	—	8	8	no	—
268	C₂×C₄	—	8	4	no	—
269	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
270	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
271	C₂×C₄	C₁₉×#123	1	2	yes	—
272	C₂×C₄	C₁₉×#123	1	8	yes	—
273	C₂×C₄	C₁₉×#127	1	2	yes	—
274	C₂×C₄	C₂×Q₁₆×C₁₉	1	8	yes	—
275	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
276	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
277	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
278	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
279	C₈	—	2	8	no	—
280	C₂²	C₁₉×#399	1	4	yes	—
281	C₂²	C₁₉×#477	1	8	yes	—
282	C₂²	C₁₉×#484	1	8	yes	—
283	C₂²	C₁₉×#494	1	4	yes	—
284	C₂²	C₁₉×#496	1	4	yes	—
285	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
286	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
287	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
288	C₂²	C₂²×Q₁₆×C₁₉	1	2	yes	—
289	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
290	C₄	—	2	8	no	—
291	C₄	—	4	4	no	—
292	C₄	—	8	4	no	—
293	C₄	—	8	2	no	—
294	C₄	C₁₉×#399	1	4	yes	—
295	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
296	C₄	C₂×C₁₉×#123	1	2	yes	—
297	C₂	C₁₉×#2095	1	8	yes	direct product factor
298	C₂	C₂×C₁₉×#399	1	1	yes	characteristic
299	C₂	C₂×C₁₉×#477	1	2	yes	—
300	C₂	C₂×C₁₉×#484	1	2	yes	—
301	C₂	C₂×C₁₉×#494	1	1	yes	characteristic
302	C₂	C₂×C₁₉×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₉×#2095	C₂	direct (N × H)
95. C₂×#2095	C₁₉	direct (N × H)
133. #2095	C₂×C₁₉	direct (N × H)
168. C₂×C₁₉	#2095	direct (N × H)
204. C₁₉	C₂×#2095	direct (N × H)
297. C₂	C₁₉×#2095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#107	2
C₂²×C₁₉×#103	2
C₂×C₁₉×#391	2
C₂×C₁₉×#384	2
C₁₉×#2095	2
C₂×C₁₉×#336	2
C₂×#2095	19

Subgroups — C2×C19×#2095 #18029686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2095 #18029686