Subgroups — C₂×C₁₉×#3491 #18068734

Order 4864.

7390 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#552	C₂	1	8	yes	maximal, complemented
3	C₂×C₁₉×#551	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#539	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#529	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₉×#123	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#518	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#552	C₂²	1	128	yes	complemented
14	C₁₉×#551	C₂²	1	128	yes	complemented
15	C₁₉×#543	C₂²	1	16	yes	complemented
16	C₁₉×#539	C₂²	1	64	yes	complemented
17	C₁₉×#534	C₂²	1	16	yes	—
18	C₁₉×#529	C₂²	1	64	yes	complemented
19	C₂×C₁₉×#126	C₂²	1	8	yes	complemented
20	C₂×C₁₉×#126	C₂²	1	8	yes	complemented
21	C₂×C₁₉×#125	C₂²	1	4	yes	complemented
22	C₂×C₁₉×#125	C₂²	1	8	yes	complemented
23	C₂×C₁₉×#124	C₂²	1	4	yes	complemented
24	C₂×C₁₉×#123	C₂²	1	8	yes	—
25	C₂×C₁₉×#123	C₂²	1	4	yes	—
26	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
27	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
28	C₂×C₁₉×#123	C₂²	1	8	yes	complemented
29	C₂×C₁₉×#123	C₂²	1	32	yes	complemented
30	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
31	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
32	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
33	C₂×C₁₉×#121	C₂²	1	4	yes	—
34	C₂×C₁₉×#120	C₂²	1	4	yes	—
35	C₁₉×#518	C₂²	1	32	yes	complemented
36	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
37	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
38	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
39	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	complemented
40	C₂×C₁₉×#117	C₂²	1	4	yes	complemented
41	C₂×C₁₉×#117	C₂²	1	8	yes	complemented
42	C₂×C₁₉×#117	C₂²	1	8	yes	complemented
43	C₂×C₁₉×#117	C₂²	1	16	yes	complemented
44	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
45	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
46	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
48	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
50	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
51	C₂²×C₄²×C₁₉	C₂²	1	2	yes	complemented
52	C₂⁵×C₁₉	C₂³	1	2	yes	—
53	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₉	—	2	16	no	—
56	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₉	—	2	8	no	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
70	C₁₉×#126	C₂³	1	64	yes	complemented
71	C₁₉×#126	C₂³	1	64	yes	complemented
72	C₁₉×#125	C₂³	1	32	yes	complemented
73	C₁₉×#125	C₂³	1	64	yes	complemented
74	C₁₉×#124	C₂³	1	32	yes	complemented
75	C₁₉×#123	C₂³	1	64	yes	—
76	C₁₉×#123	C₂³	1	32	yes	—
77	C₁₉×#123	C₂³	1	32	yes	complemented
78	C₁₉×#123	C₂³	1	32	yes	complemented
79	C₁₉×#123	C₂³	1	64	yes	complemented
80	C₁₉×C₂²⋊Q₈	C₂³	1	32	yes	complemented
81	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
82	C₁₉×C₂²⋊Q₈	C₂³	1	64	yes	complemented
83	C₁₉×#121	C₂³	1	32	yes	—
84	C₁₉×#120	C₂³	1	32	yes	—
85	C₄×Q₈×C₁₉	C₂³	1	32	yes	complemented
86	C₄×D₄×C₁₉	C₂³	1	64	yes	—
87	C₄×D₄×C₁₉	C₂³	1	64	yes	complemented
88	C₄×D₄×C₁₉	C₂³	1	32	yes	complemented
89	C₁₉×#117	C₂³	1	64	yes	complemented
90	C₁₉×#117	C₂³	1	32	yes	complemented
91	C₁₉×#117	C₂³	1	64	yes	complemented
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	complemented
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	32	yes	complemented
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
108	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	complemented
113	C₂×C₂²⋊C₄×C₁₉	C₂³	1	32	yes	complemented
114	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
117	C₂×C₄²×C₁₉	C₂³	1	16	yes	complemented
118	C₂⁴×C₁₉	—	2	8	no	—
119	C₂⁴×C₁₉	—	4	4	no	—
120	C₂⁴×C₁₉	—	4	8	no	—
121	C₂⁴×C₁₉	#41	1	8	yes	—
122	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
123	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₁₉	C₂⁴	1	8	yes	—
126	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
127	C₂×Q₈×C₁₉	—	4	8	no	—
128	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
129	C₂×D₄×C₁₉	—	2	16	no	—
130	C₂×D₄×C₁₉	—	2	16	no	—
131	C₂×D₄×C₁₉	—	2	64	no	—
132	C₂×D₄×C₁₉	—	4	8	no	—
133	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
134	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
135	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
136	C₂²×C₄×C₁₉	—	2	16	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	4	no	—
139	C₂²×C₄×C₁₉	—	2	32	no	—
140	C₂²×C₄×C₁₉	—	2	8	no	—
141	C₂²×C₄×C₁₉	—	4	4	no	—
142	C₂²×C₄×C₁₉	—	4	16	no	—
143	C₂²×C₄×C₁₉	—	4	8	no	—
144	C₂²×C₄×C₁₉	—	4	4	no	—
145	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
158	C₂²×C₄×C₁₉	C₂⁴	1	32	yes	—
159	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
160	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
161	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
162	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
163	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
164	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
165	C₄⋊C₄×C₁₉	C₂⁴	1	16	yes	—
166	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
167	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
168	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
169	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
170	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
171	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
172	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
173	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
174	C₄²×C₁₉	C₂⁴	1	16	yes	—
175	C₄²×C₁₉	C₂⁴	1	16	yes	—
176	C₄²×C₁₉	C₂⁴	1	32	yes	—
177	C₂×#3491	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	2	8	no	—
180	C₂³×C₁₉	—	2	8	no	—
181	C₂³×C₁₉	—	2	16	no	—
182	C₂³×C₁₉	—	2	16	no	—
183	C₂³×C₁₉	—	4	16	no	—
184	C₂³×C₁₉	—	4	8	no	—
185	C₂³×C₁₉	—	4	16	no	—
186	C₂³×C₁₉	—	8	16	no	—
187	C₂³×C₁₉	C₂×#41	1	8	yes	—
188	C₂³×C₁₉	C₂×#41	1	4	yes	—
189	C₂³×C₁₉	C₂×#41	1	16	yes	—
190	C₂³×C₁₉	C₂⁵	1	8	yes	—
191	C₂³×C₁₉	C₂⁵	1	4	yes	—
192	C₂³×C₁₉	C₂⁵	1	2	yes	—
193	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
194	Q₈×C₁₉	—	4	16	no	—
195	D₄×C₁₉	—	2	32	no	—
196	D₄×C₁₉	—	2	32	no	—
197	D₄×C₁₉	—	4	16	no	—
198	C₂×C₄×C₁₉	—	2	32	no	—
199	C₂×C₄×C₁₉	—	2	8	no	—
200	C₂×C₄×C₁₉	—	2	8	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	16	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	2	8	no	—
206	C₂×C₄×C₁₉	—	2	16	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	4	8	no	—
209	C₂×C₄×C₁₉	—	4	32	no	—
210	C₂×C₄×C₁₉	—	4	16	no	—
211	C₂×C₄×C₁₉	—	4	8	no	—
212	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
213	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
214	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
215	C₂×C₄×C₁₉	C₂⁵	1	8	yes	—
216	C₂×C₄×C₁₉	C₂⁵	1	16	yes	—
217	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
218	#3491	C₂×C₁₉	1	32	yes	direct product factor
219	C₂×#552	C₂×C₁₉	1	8	yes	complemented
220	C₂×#551	C₂×C₁₉	1	8	yes	complemented
221	C₂×#543	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂×#539	C₂×C₁₉	1	4	yes	complemented
223	C₂×#534	C₂×C₁₉	1	1	yes	characteristic
224	C₂×#529	C₂×C₁₉	1	4	yes	complemented
225	C₂²×#123	C₂×C₁₉	1	2	yes	complemented
226	C₂×#518	C₂×C₁₉	1	2	yes	complemented
227	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂²×C₁₉	—	2	4	no	—
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	2	16	no	—
231	C₂²×C₁₉	—	2	8	no	—
232	C₂²×C₁₉	—	2	8	no	—
233	C₂²×C₁₉	—	2	16	no	—
234	C₂²×C₁₉	—	4	16	no	—
235	C₂²×C₁₉	—	4	16	no	—
236	C₂²×C₁₉	—	8	16	no	—
237	C₂²×C₁₉	C₂²×#41	1	8	yes	—
238	C₂²×C₁₉	C₂²×#41	1	4	yes	—
239	C₂²×C₁₉	C₂²×#41	1	2	yes	—
240	C₂²×C₁₉	#585	1	4	yes	—
241	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	4	no	—
244	C₄×C₁₉	—	2	8	no	—
245	C₄×C₁₉	—	2	8	no	—
246	C₄×C₁₉	—	2	16	no	—
247	C₄×C₁₉	—	2	8	no	—
248	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
249	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
250	#552	C₂²×C₁₉	1	128	yes	complemented
251	#551	C₂²×C₁₉	1	128	yes	complemented
252	#543	C₂²×C₁₉	1	16	yes	complemented
253	#539	C₂²×C₁₉	1	64	yes	complemented
254	#534	C₂²×C₁₉	1	16	yes	—
255	#529	C₂²×C₁₉	1	64	yes	complemented
256	C₂×#126	C₂²×C₁₉	1	8	yes	complemented
257	C₂×#126	C₂²×C₁₉	1	8	yes	complemented
258	C₂×#125	C₂²×C₁₉	1	4	yes	complemented
259	C₂×#125	C₂²×C₁₉	1	8	yes	complemented
260	C₂×#124	C₂²×C₁₉	1	4	yes	complemented
261	C₂×#123	C₂²×C₁₉	1	8	yes	—
262	C₂×#123	C₂²×C₁₉	1	4	yes	—
263	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
264	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
265	C₂×#123	C₂²×C₁₉	1	8	yes	complemented
266	C₂×#123	C₂²×C₁₉	1	32	yes	complemented
267	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
268	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
269	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
270	C₂×#121	C₂²×C₁₉	1	4	yes	—
271	C₂×#120	C₂²×C₁₉	1	4	yes	—
272	#518	C₂²×C₁₉	1	32	yes	complemented
273	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
274	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
275	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
276	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	complemented
277	C₂×#117	C₂²×C₁₉	1	8	yes	complemented
278	C₂×#117	C₂²×C₁₉	1	4	yes	complemented
279	C₂×#117	C₂²×C₁₉	1	8	yes	complemented
280	C₂×#117	C₂²×C₁₉	1	16	yes	complemented
281	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
282	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
283	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
287	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
288	C₂²×C₄²	C₂²×C₁₉	1	2	yes	complemented
289	C₂×C₁₉	—	2	8	no	—
290	C₂×C₁₉	—	2	4	no	—
291	C₂×C₁₉	—	4	8	no	—
292	C₂×C₁₉	#3491	1	4	yes	direct product factor
293	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#585	1	2	yes	—
295	C₂⁵	C₂³×C₁₉	1	2	yes	—
296	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
298	C₂²×D₄	—	2	16	no	—
299	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
300	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
301	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
302	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
303	C₂³×C₄	—	2	8	no	—
304	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
305	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
310	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
311	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
313	#126	C₂³×C₁₉	1	64	yes	complemented
314	#126	C₂³×C₁₉	1	64	yes	complemented
315	#125	C₂³×C₁₉	1	32	yes	complemented
316	#125	C₂³×C₁₉	1	64	yes	complemented
317	#124	C₂³×C₁₉	1	32	yes	complemented
318	#123	C₂³×C₁₉	1	64	yes	—
319	#123	C₂³×C₁₉	1	32	yes	—
320	#123	C₂³×C₁₉	1	32	yes	complemented
321	#123	C₂³×C₁₉	1	32	yes	complemented
322	#123	C₂³×C₁₉	1	64	yes	complemented
323	C₂²⋊Q₈	C₂³×C₁₉	1	32	yes	complemented
324	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
325	C₂²⋊Q₈	C₂³×C₁₉	1	64	yes	complemented
326	#121	C₂³×C₁₉	1	32	yes	—
327	#120	C₂³×C₁₉	1	32	yes	—
328	C₄×Q₈	C₂³×C₁₉	1	32	yes	complemented
329	C₄×D₄	C₂³×C₁₉	1	64	yes	—
330	C₄×D₄	C₂³×C₁₉	1	64	yes	complemented
331	C₄×D₄	C₂³×C₁₉	1	32	yes	complemented
332	#117	C₂³×C₁₉	1	64	yes	complemented
333	#117	C₂³×C₁₉	1	32	yes	complemented
334	#117	C₂³×C₁₉	1	64	yes	complemented
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	complemented
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	32	yes	complemented
344	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	complemented
356	C₂×C₂²⋊C₄	C₂³×C₁₉	1	32	yes	complemented
357	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
358	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
359	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
360	C₂×C₄²	C₂³×C₁₉	1	16	yes	complemented
361	C₁₉	C₂×#3491	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	—	2	8	no	—
363	C₂⁴	—	4	4	no	—
364	C₂⁴	—	4	8	no	—
365	C₂⁴	#41×C₁₉	1	8	yes	—
366	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
367	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
368	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
369	C₂⁴	C₂⁴×C₁₉	1	8	yes	—
370	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
371	C₂×Q₈	—	4	8	no	—
372	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
373	C₂×D₄	—	2	16	no	—
374	C₂×D₄	—	2	16	no	—
375	C₂×D₄	—	2	64	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
378	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
379	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
380	C₂²×C₄	—	2	16	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	32	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	16	no	—
387	C₂²×C₄	—	4	8	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
394	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
397	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
398	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
400	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
401	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
402	C₂²×C₄	C₂⁴×C₁₉	1	32	yes	—
403	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
404	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
405	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
406	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
407	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
408	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
409	C₄⋊C₄	C₂⁴×C₁₉	1	16	yes	—
410	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
411	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
412	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
413	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
414	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
415	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
416	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
417	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
418	C₄²	C₂⁴×C₁₉	1	16	yes	—
419	C₄²	C₂⁴×C₁₉	1	16	yes	—
420	C₄²	C₂⁴×C₁₉	1	32	yes	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	16	no	—
426	C₂³	—	4	16	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	16	no	—
429	C₂³	—	8	16	no	—
430	C₂³	C₂×#41×C₁₉	1	8	yes	—
431	C₂³	C₂×#41×C₁₉	1	4	yes	—
432	C₂³	C₂×#41×C₁₉	1	16	yes	—
433	C₂³	C₂⁵×C₁₉	1	8	yes	—
434	C₂³	C₂⁵×C₁₉	1	4	yes	—
435	C₂³	C₂⁵×C₁₉	1	2	yes	—
436	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
437	Q₈	—	4	16	no	—
438	D₄	—	2	32	no	—
439	D₄	—	2	32	no	—
440	D₄	—	4	16	no	—
441	C₂×C₄	—	2	32	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	16	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	16	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	32	no	—
453	C₂×C₄	—	4	16	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
456	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
457	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
458	C₂×C₄	C₂⁵×C₁₉	1	8	yes	—
459	C₂×C₄	C₂⁵×C₁₉	1	16	yes	—
460	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
461	C₂²	—	2	16	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	16	no	—
467	C₂²	—	4	16	no	—
468	C₂²	—	4	16	no	—
469	C₂²	—	8	16	no	—
470	C₂²	C₂²×#41×C₁₉	1	8	yes	—
471	C₂²	C₂²×#41×C₁₉	1	4	yes	—
472	C₂²	C₂²×#41×C₁₉	1	2	yes	—
473	C₂²	C₁₉×#585	1	4	yes	—
474	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	8	no	—
478	C₄	—	2	8	no	—
479	C₄	—	2	16	no	—
480	C₄	—	2	8	no	—
481	C₂	—	2	8	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	8	no	—
484	C₂	C₁₉×#3491	1	4	yes	direct product factor
485	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
486	C₂	C₂×C₁₉×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
prime radical	C₂×C₁₉×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3491	C₂	direct (N × H)
2. C₂×C₁₉×#552	C₂	semidirect
3. C₂×C₁₉×#551	C₂	semidirect
4. C₂×C₁₉×#543	C₂	semidirect
5. C₂×C₁₉×#539	C₂	semidirect
7. C₂×C₁₉×#529	C₂	semidirect
8. C₂²×C₁₉×#123	C₂	semidirect
9. C₂×C₁₉×#518	C₂	semidirect
10. C₂²×C₁₉×#117	C₂	semidirect
13. C₁₉×#552	C₂²	semidirect
14. C₁₉×#551	C₂²	semidirect
15. C₁₉×#543	C₂²	semidirect
16. C₁₉×#539	C₂²	semidirect
18. C₁₉×#529	C₂²	semidirect
19. C₂×C₁₉×#126	C₂²	semidirect
20. C₂×C₁₉×#126	C₂²	semidirect
21. C₂×C₁₉×#125	C₂²	semidirect
22. C₂×C₁₉×#125	C₂²	semidirect
23. C₂×C₁₉×#124	C₂²	semidirect
26. C₂×C₁₉×#123	C₂²	semidirect
27. C₂×C₁₉×#123	C₂²	semidirect
28. C₂×C₁₉×#123	C₂²	semidirect
29. C₂×C₁₉×#123	C₂²	semidirect
30. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₁₉×#518	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
38. C₂×C₄×D₄×C₁₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₉	C₂²	semidirect
40. C₂×C₁₉×#117	C₂²	semidirect
41. C₂×C₁₉×#117	C₂²	semidirect
42. C₂×C₁₉×#117	C₂²	semidirect
43. C₂×C₁₉×#117	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
51. C₂²×C₄²×C₁₉	C₂²	semidirect
70. C₁₉×#126	C₂³	semidirect
71. C₁₉×#126	C₂³	semidirect
72. C₁₉×#125	C₂³	semidirect
73. C₁₉×#125	C₂³	semidirect
74. C₁₉×#124	C₂³	semidirect
77. C₁₉×#123	C₂³	semidirect
78. C₁₉×#123	C₂³	semidirect
79. C₁₉×#123	C₂³	semidirect
80. C₁₉×C₂²⋊Q₈	C₂³	semidirect
81. C₁₉×C₂²⋊Q₈	C₂³	semidirect
82. C₁₉×C₂²⋊Q₈	C₂³	semidirect
85. C₄×Q₈×C₁₉	C₂³	semidirect
87. C₄×D₄×C₁₉	C₂³	semidirect
88. C₄×D₄×C₁₉	C₂³	semidirect
89. C₁₉×#117	C₂³	semidirect
90. C₁₉×#117	C₂³	semidirect
91. C₁₉×#117	C₂³	semidirect
99. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
100. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
112. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
113. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
117. C₂×C₄²×C₁₉	C₂³	semidirect
177. C₂×#3491	C₁₉	direct (N × H)
218. #3491	C₂×C₁₉	direct (N × H)
219. C₂×#552	C₂×C₁₉	semidirect
220. C₂×#551	C₂×C₁₉	semidirect
221. C₂×#543	C₂×C₁₉	semidirect
222. C₂×#539	C₂×C₁₉	semidirect
224. C₂×#529	C₂×C₁₉	semidirect
225. C₂²×#123	C₂×C₁₉	semidirect
226. C₂×#518	C₂×C₁₉	semidirect
227. C₂²×#117	C₂×C₁₉	semidirect
250. #552	C₂²×C₁₉	semidirect
251. #551	C₂²×C₁₉	semidirect
252. #543	C₂²×C₁₉	semidirect
253. #539	C₂²×C₁₉	semidirect
255. #529	C₂²×C₁₉	semidirect
256. C₂×#126	C₂²×C₁₉	semidirect
257. C₂×#126	C₂²×C₁₉	semidirect
258. C₂×#125	C₂²×C₁₉	semidirect
259. C₂×#125	C₂²×C₁₉	semidirect
260. C₂×#124	C₂²×C₁₉	semidirect
263. C₂×#123	C₂²×C₁₉	semidirect
264. C₂×#123	C₂²×C₁₉	semidirect
265. C₂×#123	C₂²×C₁₉	semidirect
266. C₂×#123	C₂²×C₁₉	semidirect
267. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
268. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
269. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
272. #518	C₂²×C₁₉	semidirect
273. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
275. C₂×C₄×D₄	C₂²×C₁₉	semidirect
276. C₂×C₄×D₄	C₂²×C₁₉	semidirect
277. C₂×#117	C₂²×C₁₉	semidirect
278. C₂×#117	C₂²×C₁₉	semidirect
279. C₂×#117	C₂²×C₁₉	semidirect
280. C₂×#117	C₂²×C₁₉	semidirect
281. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
282. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
286. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
287. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
288. C₂²×C₄²	C₂²×C₁₉	semidirect
292. C₂×C₁₉	#3491	direct (N × H)
313. #126	C₂³×C₁₉	semidirect
314. #126	C₂³×C₁₉	semidirect
315. #125	C₂³×C₁₉	semidirect
316. #125	C₂³×C₁₉	semidirect
317. #124	C₂³×C₁₉	semidirect
320. #123	C₂³×C₁₉	semidirect
321. #123	C₂³×C₁₉	semidirect
322. #123	C₂³×C₁₉	semidirect
323. C₂²⋊Q₈	C₂³×C₁₉	semidirect
324. C₂²⋊Q₈	C₂³×C₁₉	semidirect
325. C₂²⋊Q₈	C₂³×C₁₉	semidirect
328. C₄×Q₈	C₂³×C₁₉	semidirect
330. C₄×D₄	C₂³×C₁₉	semidirect
331. C₄×D₄	C₂³×C₁₉	semidirect
332. #117	C₂³×C₁₉	semidirect
333. #117	C₂³×C₁₉	semidirect
334. #117	C₂³×C₁₉	semidirect
342. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
343. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
355. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
356. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
360. C₂×C₄²	C₂³×C₁₉	semidirect
361. C₁₉	C₂×#3491	direct (N × H)
484. C₂	C₁₉×#3491	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×#3491	2
C₂×C₁₉×#552	2
C₂×C₁₉×#551	2
C₂×C₁₉×#543	2
C₂×C₁₉×#539	2
C₂×C₁₉×#534	2
C₂×C₁₉×#529	2
C₂²×C₁₉×#123	2
C₂×C₁₉×#518	2
C₂²×C₁₉×#117	2
C₂×#3491	19

Subgroups — C2×C19×#3491 #18068734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3491 #18068734