Subgroups — C₂×C₁₉×#3459 #18068632

Order 4864.

8146 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3459	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#539	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₉×#538	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₉×#534	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₉×#529	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₉×#525	C₂	1	6	yes	maximal, complemented
8	C₂²×C₄×D₄×C₁₉	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	complemented
10	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	complemented
13	C₁₉×#543	C₂²	1	16	yes	complemented
14	C₁₉×#539	C₂²	1	96	yes	complemented
15	C₁₉×#538	C₂²	1	96	yes	complemented
16	C₁₉×#534	C₂²	1	48	yes	complemented
17	C₁₉×#529	C₂²	1	96	yes	complemented
18	C₂×C₁₉×#126	C₂²	1	12	yes	complemented
19	C₂×C₁₉×#125	C₂²	1	6	yes	complemented
20	C₂×C₁₉×#124	C₂²	1	6	yes	complemented
21	C₁₉×#525	C₂²	1	96	yes	complemented
22	C₂×C₁₉×#123	C₂²	1	12	yes	complemented
23	C₂×C₁₉×#123	C₂²	1	12	yes	complemented
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
26	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
27	C₂×C₁₉×#121	C₂²	1	6	yes	—
28	C₂×C₁₉×#121	C₂²	1	6	yes	—
29	C₂×C₁₉×#121	C₂²	1	6	yes	complemented
30	C₂×C₁₉×#120	C₂²	1	12	yes	complemented
31	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
32	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
33	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	complemented
34	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	complemented
35	C₂×C₄×D₄×C₁₉	C₂²	1	48	yes	complemented
36	C₂×C₁₉×#117	C₂²	1	6	yes	complemented
37	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
39	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
40	C₂²×C₄²×C₁₉	C₂²	1	3	yes	complemented
41	C₂⁵×C₁₉	C₂³	1	3	yes	—
42	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#41×C₁₉	—	4	8	no	—
44	C₂×#41×C₁₉	C₂³	1	16	yes	complemented
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₉	—	2	24	no	—
48	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
49	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
52	C₂³×C₄×C₁₉	—	4	4	no	—
53	C₂³×C₄×C₁₉	—	4	12	no	—
54	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	24	yes	complemented
63	C₁₉×#126	C₂³	1	96	yes	complemented
64	C₁₉×#125	C₂³	1	48	yes	complemented
65	C₁₉×#124	C₂³	1	48	yes	complemented
66	C₁₉×#123	C₂³	1	96	yes	complemented
67	C₁₉×#123	C₂³	1	96	yes	complemented
68	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	complemented
69	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	complemented
70	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	complemented
71	C₁₉×#121	C₂³	1	48	yes	—
72	C₁₉×#121	C₂³	1	48	yes	—
73	C₁₉×#121	C₂³	1	48	yes	complemented
74	C₁₉×#120	C₂³	1	96	yes	complemented
75	C₄×Q₈×C₁₉	C₂³	1	16	yes	complemented
76	C₄×D₄×C₁₉	C₂³	1	96	yes	complemented
77	C₄×D₄×C₁₉	C₂³	1	96	yes	complemented
78	C₄×D₄×C₁₉	C₂³	1	48	yes	complemented
79	C₁₉×#117	C₂³	1	48	yes	complemented
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	complemented
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	complemented
92	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	24	yes	complemented
95	C₂⁴×C₁₉	—	2	12	no	—
96	C₂⁴×C₁₉	—	4	2	no	—
97	C₂⁴×C₁₉	—	4	6	no	—
98	C₂⁴×C₁₉	—	4	2	no	—
99	C₂⁴×C₁₉	—	4	6	no	—
100	C₂⁴×C₁₉	#41	1	8	yes	complemented
101	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
102	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
103	C₂⁴×C₁₉	C₂⁴	1	12	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
105	#41×C₁₉	—	4	32	no	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
109	C₂×Q₈×C₁₉	C₂⁴	1	8	yes	—
110	C₂×D₄×C₁₉	—	2	48	no	—
111	C₂×D₄×C₁₉	—	2	96	no	—
112	C₂×D₄×C₁₉	—	4	12	no	—
113	C₂×D₄×C₁₉	—	4	12	no	—
114	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
115	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
116	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
117	C₂²×C₄×C₁₉	—	2	12	no	—
118	C₂²×C₄×C₁₉	—	2	12	no	—
119	C₂²×C₄×C₁₉	—	2	24	no	—
120	C₂²×C₄×C₁₉	—	4	16	no	—
121	C₂²×C₄×C₁₉	—	4	48	no	—
122	C₂²×C₄×C₁₉	—	4	6	no	—
123	C₂²×C₄×C₁₉	—	4	12	no	—
124	C₂²×C₄×C₁₉	—	4	6	no	—
125	C₂²×C₄×C₁₉	—	4	6	no	—
126	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
139	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
140	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
141	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
142	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
143	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
144	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
145	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
146	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
147	C₄²×C₁₉	C₂⁴	1	24	yes	—
148	C₄²×C₁₉	C₂⁴	1	24	yes	—
149	C₂×#3459	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	6	no	—
151	C₂³×C₁₉	—	2	6	no	—
152	C₂³×C₁₉	—	2	24	no	—
153	C₂³×C₁₉	—	2	12	no	—
154	C₂³×C₁₉	—	2	12	no	—
155	C₂³×C₁₉	—	2	12	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	—	4	12	no	—
158	C₂³×C₁₉	—	4	16	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	12	no	—
161	C₂³×C₁₉	—	4	48	no	—
162	C₂³×C₁₉	C₂×#41	1	12	yes	—
163	C₂³×C₁₉	C₂×#41	1	16	yes	complemented
164	C₂³×C₁₉	C₂⁵	1	12	yes	—
165	C₂³×C₁₉	C₂⁵	1	6	yes	—
166	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
167	Q₈×C₁₉	—	4	8	no	—
168	Q₈×C₁₉	—	4	8	no	—
169	D₄×C₁₉	—	2	96	no	—
170	D₄×C₁₉	—	4	24	no	—
171	D₄×C₁₉	—	4	24	no	—
172	C₂×C₄×C₁₉	—	2	24	no	—
173	C₂×C₄×C₁₉	—	2	12	no	—
174	C₂×C₄×C₁₉	—	2	6	no	—
175	C₂×C₄×C₁₉	—	2	12	no	—
176	C₂×C₄×C₁₉	—	2	12	no	—
177	C₂×C₄×C₁₉	—	2	24	no	—
178	C₂×C₄×C₁₉	—	2	48	no	—
179	C₂×C₄×C₁₉	—	4	12	no	—
180	C₂×C₄×C₁₉	—	4	24	no	—
181	C₂×C₄×C₁₉	—	4	12	no	—
182	C₂×C₄×C₁₉	—	4	12	no	—
183	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
184	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
185	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
186	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
187	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
188	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
189	#3459	C₂×C₁₉	1	32	yes	direct product factor
190	C₂×#543	C₂×C₁₉	1	1	yes	characteristic, complemented
191	C₂×#539	C₂×C₁₉	1	6	yes	complemented
192	C₂×#538	C₂×C₁₉	1	6	yes	complemented
193	C₂×#534	C₂×C₁₉	1	3	yes	complemented
194	C₂×#529	C₂×C₁₉	1	6	yes	complemented
195	C₂×#525	C₂×C₁₉	1	6	yes	complemented
196	C₂²×C₄×D₄	C₂×C₁₉	1	3	yes	complemented
197	C₂²×C₁₉	—	2	6	no	—
198	C₂²×C₁₉	—	2	6	no	—
199	C₂²×C₁₉	—	2	24	no	—
200	C₂²×C₁₉	—	2	12	no	—
201	C₂²×C₁₉	—	2	12	no	—
202	C₂²×C₁₉	—	2	12	no	—
203	C₂²×C₁₉	—	4	16	no	—
204	C₂²×C₁₉	—	4	48	no	—
205	C₂²×C₁₉	—	4	24	no	—
206	C₂²×C₁₉	C₂²×#41	1	12	yes	—
207	C₂²×C₁₉	C₂²×#41	1	2	yes	—
208	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
209	C₂²×C₁₉	#585	1	2	yes	—
210	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
211	C₄×C₁₉	—	2	12	no	—
212	C₄×C₁₉	—	2	6	no	—
213	C₄×C₁₉	—	2	12	no	—
214	C₄×C₁₉	—	2	12	no	—
215	C₄×C₁₉	C₂×H(5,𝔽₂)	1	4	yes	—
216	C₂²×#41	C₂²×C₁₉	1	2	yes	complemented
217	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
218	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
219	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	complemented
220	#543	C₂²×C₁₉	1	16	yes	complemented
221	#539	C₂²×C₁₉	1	96	yes	complemented
222	#538	C₂²×C₁₉	1	96	yes	complemented
223	#534	C₂²×C₁₉	1	48	yes	complemented
224	#529	C₂²×C₁₉	1	96	yes	complemented
225	C₂×#126	C₂²×C₁₉	1	12	yes	complemented
226	C₂×#125	C₂²×C₁₉	1	6	yes	complemented
227	C₂×#124	C₂²×C₁₉	1	6	yes	complemented
228	#525	C₂²×C₁₉	1	96	yes	complemented
229	C₂×#123	C₂²×C₁₉	1	12	yes	complemented
230	C₂×#123	C₂²×C₁₉	1	12	yes	complemented
231	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
232	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
233	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
234	C₂×#121	C₂²×C₁₉	1	6	yes	—
235	C₂×#121	C₂²×C₁₉	1	6	yes	—
236	C₂×#121	C₂²×C₁₉	1	6	yes	complemented
237	C₂×#120	C₂²×C₁₉	1	12	yes	complemented
238	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
239	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	complemented
240	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	complemented
241	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	complemented
242	C₂×C₄×D₄	C₂²×C₁₉	1	48	yes	complemented
243	C₂×#117	C₂²×C₁₉	1	6	yes	complemented
244	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	complemented
245	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
246	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
247	C₂²×C₄²	C₂²×C₁₉	1	3	yes	complemented
248	C₂×C₁₉	—	2	12	no	—
249	C₂×C₁₉	—	4	12	no	—
250	C₂×C₁₉	#3459	1	4	yes	direct product factor
251	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
252	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
254	C₂⁵	C₂³×C₁₉	1	3	yes	—
255	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×#41	—	4	8	no	—
257	C₂×#41	C₂³×C₁₉	1	16	yes	complemented
258	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
260	C₂²×D₄	—	2	24	no	—
261	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
262	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
263	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
264	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
265	C₂³×C₄	—	4	4	no	—
266	C₂³×C₄	—	4	12	no	—
267	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
268	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
269	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
270	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
272	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
274	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
275	C₂³×C₄	C₂³×C₁₉	1	24	yes	complemented
276	#126	C₂³×C₁₉	1	96	yes	complemented
277	#125	C₂³×C₁₉	1	48	yes	complemented
278	#124	C₂³×C₁₉	1	48	yes	complemented
279	#123	C₂³×C₁₉	1	96	yes	complemented
280	#123	C₂³×C₁₉	1	96	yes	complemented
281	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	complemented
282	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	complemented
283	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	complemented
284	#121	C₂³×C₁₉	1	48	yes	—
285	#121	C₂³×C₁₉	1	48	yes	—
286	#121	C₂³×C₁₉	1	48	yes	complemented
287	#120	C₂³×C₁₉	1	96	yes	complemented
288	C₄×Q₈	C₂³×C₁₉	1	16	yes	complemented
289	C₄×D₄	C₂³×C₁₉	1	96	yes	complemented
290	C₄×D₄	C₂³×C₁₉	1	96	yes	complemented
291	C₄×D₄	C₂³×C₁₉	1	48	yes	complemented
292	#117	C₂³×C₁₉	1	48	yes	complemented
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	complemented
299	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	complemented
305	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
306	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
307	C₂×C₄²	C₂³×C₁₉	1	24	yes	complemented
308	C₁₉	C₂×#3459	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	—	2	12	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	4	6	no	—
312	C₂⁴	—	4	2	no	—
313	C₂⁴	—	4	6	no	—
314	C₂⁴	#41×C₁₉	1	8	yes	complemented
315	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
316	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
317	C₂⁴	C₂⁴×C₁₉	1	12	yes	—
318	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
319	#41	—	4	32	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
323	C₂×Q₈	C₂⁴×C₁₉	1	8	yes	—
324	C₂×D₄	—	2	48	no	—
325	C₂×D₄	—	2	96	no	—
326	C₂×D₄	—	4	12	no	—
327	C₂×D₄	—	4	12	no	—
328	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
329	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
330	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
331	C₂²×C₄	—	2	12	no	—
332	C₂²×C₄	—	2	12	no	—
333	C₂²×C₄	—	2	24	no	—
334	C₂²×C₄	—	4	16	no	—
335	C₂²×C₄	—	4	48	no	—
336	C₂²×C₄	—	4	6	no	—
337	C₂²×C₄	—	4	12	no	—
338	C₂²×C₄	—	4	6	no	—
339	C₂²×C₄	—	4	6	no	—
340	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
342	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
344	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
345	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
346	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
347	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
348	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
349	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
350	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
351	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
353	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
354	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
355	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
356	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
357	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
358	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
359	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
360	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
361	C₄²	C₂⁴×C₁₉	1	24	yes	—
362	C₄²	C₂⁴×C₁₉	1	24	yes	—
363	C₂³	—	2	6	no	—
364	C₂³	—	2	6	no	—
365	C₂³	—	2	24	no	—
366	C₂³	—	2	12	no	—
367	C₂³	—	2	12	no	—
368	C₂³	—	2	12	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	12	no	—
371	C₂³	—	4	16	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	12	no	—
374	C₂³	—	4	48	no	—
375	C₂³	C₂×#41×C₁₉	1	12	yes	—
376	C₂³	C₂×#41×C₁₉	1	16	yes	complemented
377	C₂³	C₂⁵×C₁₉	1	12	yes	—
378	C₂³	C₂⁵×C₁₉	1	6	yes	—
379	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
380	Q₈	—	4	8	no	—
381	Q₈	—	4	8	no	—
382	D₄	—	2	96	no	—
383	D₄	—	4	24	no	—
384	D₄	—	4	24	no	—
385	C₂×C₄	—	2	24	no	—
386	C₂×C₄	—	2	12	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	2	12	no	—
389	C₂×C₄	—	2	12	no	—
390	C₂×C₄	—	2	24	no	—
391	C₂×C₄	—	2	48	no	—
392	C₂×C₄	—	4	12	no	—
393	C₂×C₄	—	4	24	no	—
394	C₂×C₄	—	4	12	no	—
395	C₂×C₄	—	4	12	no	—
396	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
397	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
398	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
399	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
400	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
401	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
402	C₂²	—	2	24	no	—
403	C₂²	—	2	6	no	—
404	C₂²	—	2	6	no	—
405	C₂²	—	2	12	no	—
406	C₂²	—	2	12	no	—
407	C₂²	—	2	12	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	48	no	—
410	C₂²	—	4	24	no	—
411	C₂²	C₂²×#41×C₁₉	1	12	yes	—
412	C₂²	C₂²×#41×C₁₉	1	2	yes	—
413	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
414	C₂²	C₁₉×#585	1	2	yes	—
415	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
416	C₄	—	2	12	no	—
417	C₄	—	2	6	no	—
418	C₄	—	2	12	no	—
419	C₄	—	2	12	no	—
420	C₄	C₂×C₁₉×H(5,𝔽₂)	1	4	yes	—
421	C₂	—	2	12	no	—
422	C₂	—	4	12	no	—
423	C₂	C₁₉×#3459	1	4	yes	direct product factor
424	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
425	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂	C₂×C₁₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
socle	C₂³×C₁₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3459	C₂	direct (N × H)
2. C₂×C₁₉×#543	C₂	semidirect
3. C₂×C₁₉×#539	C₂	semidirect
4. C₂×C₁₉×#538	C₂	semidirect
5. C₂×C₁₉×#534	C₂	semidirect
6. C₂×C₁₉×#529	C₂	semidirect
7. C₂×C₁₉×#525	C₂	semidirect
8. C₂²×C₄×D₄×C₁₉	C₂	semidirect
9. C₂²×#41×C₁₉	C₂²	semidirect
12. C₂⁴×C₄×C₁₉	C₂²	semidirect
13. C₁₉×#543	C₂²	semidirect
14. C₁₉×#539	C₂²	semidirect
15. C₁₉×#538	C₂²	semidirect
16. C₁₉×#534	C₂²	semidirect
17. C₁₉×#529	C₂²	semidirect
18. C₂×C₁₉×#126	C₂²	semidirect
19. C₂×C₁₉×#125	C₂²	semidirect
20. C₂×C₁₉×#124	C₂²	semidirect
21. C₁₉×#525	C₂²	semidirect
22. C₂×C₁₉×#123	C₂²	semidirect
23. C₂×C₁₉×#123	C₂²	semidirect
24. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₁₉×#121	C₂²	semidirect
30. C₂×C₁₉×#120	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₉	C₂²	semidirect
33. C₂×C₄×D₄×C₁₉	C₂²	semidirect
34. C₂×C₄×D₄×C₁₉	C₂²	semidirect
35. C₂×C₄×D₄×C₁₉	C₂²	semidirect
36. C₂×C₁₉×#117	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
40. C₂²×C₄²×C₁₉	C₂²	semidirect
44. C₂×#41×C₁₉	C₂³	semidirect
62. C₂³×C₄×C₁₉	C₂³	semidirect
63. C₁₉×#126	C₂³	semidirect
64. C₁₉×#125	C₂³	semidirect
65. C₁₉×#124	C₂³	semidirect
66. C₁₉×#123	C₂³	semidirect
67. C₁₉×#123	C₂³	semidirect
68. C₁₉×C₂²⋊Q₈	C₂³	semidirect
69. C₁₉×C₂²⋊Q₈	C₂³	semidirect
70. C₁₉×C₂²⋊Q₈	C₂³	semidirect
73. C₁₉×#121	C₂³	semidirect
74. C₁₉×#120	C₂³	semidirect
75. C₄×Q₈×C₁₉	C₂³	semidirect
76. C₄×D₄×C₁₉	C₂³	semidirect
77. C₄×D₄×C₁₉	C₂³	semidirect
78. C₄×D₄×C₁₉	C₂³	semidirect
79. C₁₉×#117	C₂³	semidirect
85. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
91. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
94. C₂×C₄²×C₁₉	C₂³	semidirect
100. C₂⁴×C₁₉	#41	semidirect
149. C₂×#3459	C₁₉	direct (N × H)
163. C₂³×C₁₉	C₂×#41	semidirect
189. #3459	C₂×C₁₉	direct (N × H)
190. C₂×#543	C₂×C₁₉	semidirect
191. C₂×#539	C₂×C₁₉	semidirect
192. C₂×#538	C₂×C₁₉	semidirect
193. C₂×#534	C₂×C₁₉	semidirect
194. C₂×#529	C₂×C₁₉	semidirect
195. C₂×#525	C₂×C₁₉	semidirect
196. C₂²×C₄×D₄	C₂×C₁₉	semidirect
216. C₂²×#41	C₂²×C₁₉	semidirect
219. C₂⁴×C₄	C₂²×C₁₉	semidirect
220. #543	C₂²×C₁₉	semidirect
221. #539	C₂²×C₁₉	semidirect
222. #538	C₂²×C₁₉	semidirect
223. #534	C₂²×C₁₉	semidirect
224. #529	C₂²×C₁₉	semidirect
225. C₂×#126	C₂²×C₁₉	semidirect
226. C₂×#125	C₂²×C₁₉	semidirect
227. C₂×#124	C₂²×C₁₉	semidirect
228. #525	C₂²×C₁₉	semidirect
229. C₂×#123	C₂²×C₁₉	semidirect
230. C₂×#123	C₂²×C₁₉	semidirect
231. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
232. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
233. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
236. C₂×#121	C₂²×C₁₉	semidirect
237. C₂×#120	C₂²×C₁₉	semidirect
238. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
239. C₂×C₄×D₄	C₂²×C₁₉	semidirect
240. C₂×C₄×D₄	C₂²×C₁₉	semidirect
241. C₂×C₄×D₄	C₂²×C₁₉	semidirect
242. C₂×C₄×D₄	C₂²×C₁₉	semidirect
243. C₂×#117	C₂²×C₁₉	semidirect
244. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
246. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
247. C₂²×C₄²	C₂²×C₁₉	semidirect
250. C₂×C₁₉	#3459	direct (N × H)
257. C₂×#41	C₂³×C₁₉	semidirect
275. C₂³×C₄	C₂³×C₁₉	semidirect
276. #126	C₂³×C₁₉	semidirect
277. #125	C₂³×C₁₉	semidirect
278. #124	C₂³×C₁₉	semidirect
279. #123	C₂³×C₁₉	semidirect
280. #123	C₂³×C₁₉	semidirect
281. C₂²⋊Q₈	C₂³×C₁₉	semidirect
282. C₂²⋊Q₈	C₂³×C₁₉	semidirect
283. C₂²⋊Q₈	C₂³×C₁₉	semidirect
286. #121	C₂³×C₁₉	semidirect
287. #120	C₂³×C₁₉	semidirect
288. C₄×Q₈	C₂³×C₁₉	semidirect
289. C₄×D₄	C₂³×C₁₉	semidirect
290. C₄×D₄	C₂³×C₁₉	semidirect
291. C₄×D₄	C₂³×C₁₉	semidirect
292. #117	C₂³×C₁₉	semidirect
298. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
304. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
307. C₂×C₄²	C₂³×C₁₉	semidirect
308. C₁₉	C₂×#3459	direct (N × H)
314. C₂⁴	#41×C₁₉	semidirect
376. C₂³	C₂×#41×C₁₉	semidirect
423. C₂	C₁₉×#3459	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×#3459	2
C₂×C₁₉×#543	2
C₂×C₁₉×#539	2
C₂×C₁₉×#538	2
C₂×C₁₉×#534	2
C₂×C₁₉×#529	2
C₂×C₁₉×#525	2
C₂²×C₄×D₄×C₁₉	2
C₂×#3459	19

Subgroups — C2×C19×#3459 #18068632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3459 #18068632