Subgroups — C₂×C₁₉×#3567 #18068696

Order 4864.

6662 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3567	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#562	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₉×#553	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₉×#552	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₉×#540	C₂	1	6	yes	maximal, complemented
7	C₂×C₁₉×#539	C₂	1	6	yes	maximal, complemented
8	C₂×C₁₉×#529	C₂	1	3	yes	maximal, complemented
9	C₁₉×#564	C₂²	1	16	yes	complemented
10	C₁₉×#562	C₂²	1	48	yes	complemented
11	C₁₉×#553	C₂²	1	96	yes	complemented
12	C₁₉×#552	C₂²	1	96	yes	complemented
13	C₁₉×#540	C₂²	1	96	yes	complemented
14	C₁₉×#539	C₂²	1	96	yes	complemented
15	C₂×C₁₉×#127	C₂²	1	2	yes	—
16	C₁₉×#529	C₂²	1	48	yes	complemented
17	C₂×C₁₉×#126	C₂²	1	6	yes	—
18	C₂×C₁₉×#126	C₂²	1	2	yes	—
19	C₂×C₁₉×#126	C₂²	1	6	yes	—
20	C₂×C₁₉×#125	C₂²	1	3	yes	—
21	C₂×C₁₉×#125	C₂²	1	6	yes	—
22	C₂×C₁₉×#125	C₂²	1	6	yes	—
23	C₂×C₁₉×#125	C₂²	1	6	yes	—
24	C₂×C₁₉×#124	C₂²	1	3	yes	—
25	C₂×C₁₉×#123	C₂²	1	6	yes	—
26	C₂×C₁₉×#123	C₂²	1	6	yes	—
27	C₂×C₁₉×#123	C₂²	1	6	yes	—
28	C₂×C₁₉×#123	C₂²	1	6	yes	—
29	C₂×C₁₉×#123	C₂²	1	6	yes	—
30	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
31	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
32	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	—
33	C₂×C₁₉×#121	C₂²	1	3	yes	—
34	C₂×C₁₉×#121	C₂²	1	6	yes	—
35	C₂×C₁₉×#121	C₂²	1	6	yes	—
36	C₂×C₁₉×#121	C₂²	1	6	yes	—
37	C₂×C₁₉×#121	C₂²	1	6	yes	—
38	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
39	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
40	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
41	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
42	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
43	C₂×C₁₉×#117	C₂²	1	6	yes	—
44	C₂×C₁₉×#117	C₂²	1	6	yes	—
45	C₂²×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
46	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
48	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
49	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
56	C₁₉×#127	C₂³	1	16	yes	—
57	C₁₉×#126	C₂³	1	48	yes	—
58	C₁₉×#126	C₂³	1	16	yes	—
59	C₁₉×#126	C₂³	1	48	yes	—
60	C₁₉×#125	C₂³	1	24	yes	—
61	C₁₉×#125	C₂³	1	48	yes	—
62	C₁₉×#125	C₂³	1	48	yes	—
63	C₁₉×#125	C₂³	1	48	yes	—
64	C₁₉×#124	C₂³	1	24	yes	—
65	C₁₉×#123	C₂³	1	48	yes	—
66	C₁₉×#123	C₂³	1	48	yes	—
67	C₁₉×#123	C₂³	1	48	yes	—
68	C₁₉×#123	C₂³	1	48	yes	—
69	C₁₉×#123	C₂³	1	48	yes	—
70	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
71	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
72	C₁₉×C₂²⋊Q₈	C₂³	1	48	yes	—
73	C₁₉×#121	C₂³	1	24	yes	—
74	C₁₉×#121	C₂³	1	48	yes	—
75	C₁₉×#121	C₂³	1	48	yes	—
76	C₁₉×#121	C₂³	1	48	yes	—
77	C₁₉×#121	C₂³	1	48	yes	—
78	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
79	C₄×D₄×C₁₉	C₂³	1	48	yes	—
80	C₄×D₄×C₁₉	C₂³	1	24	yes	—
81	C₄×D₄×C₁₉	C₂³	1	48	yes	—
82	C₄×D₄×C₁₉	C₂³	1	48	yes	—
83	C₁₉×#117	C₂³	1	48	yes	—
84	C₁₉×#117	C₂³	1	48	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	48	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
96	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
97	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
99	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
100	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
103	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
106	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
110	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₁₉	—	4	6	no	—
112	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
113	C₂×D₄×C₁₉	—	4	12	no	—
114	C₂×D₄×C₁₉	—	4	12	no	—
115	C₂×D₄×C₁₉	—	4	12	no	—
116	C₂×D₄×C₁₉	—	4	6	no	—
117	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
118	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
119	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
120	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
121	C₂²×C₄×C₁₉	—	4	12	no	—
122	C₂²×C₄×C₁₉	—	4	6	no	—
123	C₂²×C₄×C₁₉	—	4	12	no	—
124	C₂²×C₄×C₁₉	—	4	12	no	—
125	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
134	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
135	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
136	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
137	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
138	C₄⋊C₄×C₁₉	C₂⁴	1	24	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	12	yes	—
143	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
144	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
145	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
146	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
147	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
148	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
149	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
150	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
151	C₄²×C₁₉	C₂⁴	1	12	yes	—
152	C₄²×C₁₉	C₂⁴	1	4	yes	—
153	C₄²×C₁₉	C₂⁴	1	8	yes	—
154	C₄²×C₁₉	C₂⁴	1	24	yes	—
155	C₄²×C₁₉	C₂⁴	1	8	yes	—
156	C₂×#3567	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	12	no	—
158	C₂³×C₁₉	—	2	12	no	—
159	C₂³×C₁₉	—	2	6	no	—
160	C₂³×C₁₉	—	2	12	no	—
161	C₂³×C₁₉	C₂⁵	1	12	yes	—
162	C₂³×C₁₉	C₂⁵	1	2	yes	—
163	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
164	Q₈×C₁₉	—	4	12	no	—
165	D₄×C₁₉	—	4	24	no	—
166	D₄×C₁₉	—	4	24	no	—
167	D₄×C₁₉	—	4	24	no	—
168	D₄×C₁₉	—	4	12	no	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	2	12	no	—
171	C₂×C₄×C₁₉	—	2	12	no	—
172	C₂×C₄×C₁₉	—	2	12	no	—
173	C₂×C₄×C₁₉	—	2	6	no	—
174	C₂×C₄×C₁₉	—	4	24	no	—
175	C₂×C₄×C₁₉	—	4	12	no	—
176	C₂×C₄×C₁₉	—	4	24	no	—
177	C₂×C₄×C₁₉	—	4	24	no	—
178	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
179	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
180	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
181	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
182	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
183	#3567	C₂×C₁₉	1	32	yes	direct product factor
184	C₂×#564	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂×#562	C₂×C₁₉	1	3	yes	complemented
186	C₂×#553	C₂×C₁₉	1	6	yes	complemented
187	C₂×#552	C₂×C₁₉	1	6	yes	complemented
188	C₂×#540	C₂×C₁₉	1	6	yes	complemented
189	C₂×#539	C₂×C₁₉	1	6	yes	complemented
190	C₂×#529	C₂×C₁₉	1	3	yes	complemented
191	C₂²×C₁₉	—	2	12	no	—
192	C₂²×C₁₉	—	2	12	no	—
193	C₂²×C₁₉	—	2	6	no	—
194	C₂²×C₁₉	—	2	12	no	—
195	C₂²×C₁₉	—	4	24	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	#585	1	6	yes	—
198	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
199	C₄×C₁₉	—	2	6	no	—
200	C₄×C₁₉	—	2	12	no	—
201	C₄×C₁₉	—	2	12	no	—
202	C₄×C₁₉	—	2	12	no	—
203	C₄×C₁₉	—	2	6	no	—
204	#564	C₂²×C₁₉	1	16	yes	complemented
205	#562	C₂²×C₁₉	1	48	yes	complemented
206	#553	C₂²×C₁₉	1	96	yes	complemented
207	#552	C₂²×C₁₉	1	96	yes	complemented
208	#540	C₂²×C₁₉	1	96	yes	complemented
209	#539	C₂²×C₁₉	1	96	yes	complemented
210	C₂×#127	C₂²×C₁₉	1	2	yes	—
211	#529	C₂²×C₁₉	1	48	yes	complemented
212	C₂×#126	C₂²×C₁₉	1	6	yes	—
213	C₂×#126	C₂²×C₁₉	1	2	yes	—
214	C₂×#126	C₂²×C₁₉	1	6	yes	—
215	C₂×#125	C₂²×C₁₉	1	3	yes	—
216	C₂×#125	C₂²×C₁₉	1	6	yes	—
217	C₂×#125	C₂²×C₁₉	1	6	yes	—
218	C₂×#125	C₂²×C₁₉	1	6	yes	—
219	C₂×#124	C₂²×C₁₉	1	3	yes	—
220	C₂×#123	C₂²×C₁₉	1	6	yes	—
221	C₂×#123	C₂²×C₁₉	1	6	yes	—
222	C₂×#123	C₂²×C₁₉	1	6	yes	—
223	C₂×#123	C₂²×C₁₉	1	6	yes	—
224	C₂×#123	C₂²×C₁₉	1	6	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
227	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	—
228	C₂×#121	C₂²×C₁₉	1	3	yes	—
229	C₂×#121	C₂²×C₁₉	1	6	yes	—
230	C₂×#121	C₂²×C₁₉	1	6	yes	—
231	C₂×#121	C₂²×C₁₉	1	6	yes	—
232	C₂×#121	C₂²×C₁₉	1	6	yes	—
233	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
234	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
235	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
236	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
237	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
238	C₂×#117	C₂²×C₁₉	1	6	yes	—
239	C₂×#117	C₂²×C₁₉	1	6	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
241	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×C₁₉	—	4	12	no	—
243	C₂×C₁₉	—	4	2	no	—
244	C₂×C₁₉	#3567	1	4	yes	direct product factor
245	C₂×C₁₉	C₂×#585	1	3	yes	—
246	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
247	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
248	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
249	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
250	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
251	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
252	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
253	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
254	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
255	#127	C₂³×C₁₉	1	16	yes	—
256	#126	C₂³×C₁₉	1	48	yes	—
257	#126	C₂³×C₁₉	1	16	yes	—
258	#126	C₂³×C₁₉	1	48	yes	—
259	#125	C₂³×C₁₉	1	24	yes	—
260	#125	C₂³×C₁₉	1	48	yes	—
261	#125	C₂³×C₁₉	1	48	yes	—
262	#125	C₂³×C₁₉	1	48	yes	—
263	#124	C₂³×C₁₉	1	24	yes	—
264	#123	C₂³×C₁₉	1	48	yes	—
265	#123	C₂³×C₁₉	1	48	yes	—
266	#123	C₂³×C₁₉	1	48	yes	—
267	#123	C₂³×C₁₉	1	48	yes	—
268	#123	C₂³×C₁₉	1	48	yes	—
269	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
270	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
271	C₂²⋊Q₈	C₂³×C₁₉	1	48	yes	—
272	#121	C₂³×C₁₉	1	24	yes	—
273	#121	C₂³×C₁₉	1	48	yes	—
274	#121	C₂³×C₁₉	1	48	yes	—
275	#121	C₂³×C₁₉	1	48	yes	—
276	#121	C₂³×C₁₉	1	48	yes	—
277	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
278	C₄×D₄	C₂³×C₁₉	1	48	yes	—
279	C₄×D₄	C₂³×C₁₉	1	24	yes	—
280	C₄×D₄	C₂³×C₁₉	1	48	yes	—
281	C₄×D₄	C₂³×C₁₉	1	48	yes	—
282	#117	C₂³×C₁₉	1	48	yes	—
283	#117	C₂³×C₁₉	1	48	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	48	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
305	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
308	C₁₉	C₂×#3567	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
310	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
311	C₂×Q₈	—	4	6	no	—
312	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
313	C₂×D₄	—	4	12	no	—
314	C₂×D₄	—	4	12	no	—
315	C₂×D₄	—	4	12	no	—
316	C₂×D₄	—	4	6	no	—
317	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
318	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
319	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
320	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
321	C₂²×C₄	—	4	12	no	—
322	C₂²×C₄	—	4	6	no	—
323	C₂²×C₄	—	4	12	no	—
324	C₂²×C₄	—	4	12	no	—
325	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
326	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
327	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
328	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
329	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
331	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
332	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
333	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
334	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
335	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
336	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
337	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
338	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
339	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
340	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
341	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
342	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
343	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
344	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
345	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
346	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
347	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
348	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
349	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
350	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
351	C₄²	C₂⁴×C₁₉	1	12	yes	—
352	C₄²	C₂⁴×C₁₉	1	4	yes	—
353	C₄²	C₂⁴×C₁₉	1	8	yes	—
354	C₄²	C₂⁴×C₁₉	1	24	yes	—
355	C₄²	C₂⁴×C₁₉	1	8	yes	—
356	C₂³	—	2	12	no	—
357	C₂³	—	2	12	no	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	12	no	—
360	C₂³	C₂⁵×C₁₉	1	12	yes	—
361	C₂³	C₂⁵×C₁₉	1	2	yes	—
362	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
363	Q₈	—	4	12	no	—
364	D₄	—	4	24	no	—
365	D₄	—	4	24	no	—
366	D₄	—	4	24	no	—
367	D₄	—	4	12	no	—
368	C₂×C₄	—	2	6	no	—
369	C₂×C₄	—	2	12	no	—
370	C₂×C₄	—	2	12	no	—
371	C₂×C₄	—	2	12	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	4	24	no	—
374	C₂×C₄	—	4	12	no	—
375	C₂×C₄	—	4	24	no	—
376	C₂×C₄	—	4	24	no	—
377	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
378	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
379	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
380	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
381	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
382	C₂²	—	2	12	no	—
383	C₂²	—	2	12	no	—
384	C₂²	—	2	6	no	—
385	C₂²	—	2	12	no	—
386	C₂²	—	4	24	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₁₉×#585	1	6	yes	—
389	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
390	C₄	—	2	6	no	—
391	C₄	—	2	12	no	—
392	C₄	—	2	12	no	—
393	C₄	—	2	12	no	—
394	C₄	—	2	6	no	—
395	C₂	—	4	12	no	—
396	C₂	—	4	2	no	—
397	C₂	C₁₉×#3567	1	4	yes	direct product factor
398	C₂	C₂×C₁₉×#585	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
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×#3567	C₂	direct (N × H)
2. C₂×C₁₉×#564	C₂	semidirect
3. C₂×C₁₉×#562	C₂	semidirect
4. C₂×C₁₉×#553	C₂	semidirect
5. C₂×C₁₉×#552	C₂	semidirect
6. C₂×C₁₉×#540	C₂	semidirect
7. C₂×C₁₉×#539	C₂	semidirect
8. C₂×C₁₉×#529	C₂	semidirect
9. C₁₉×#564	C₂²	semidirect
10. C₁₉×#562	C₂²	semidirect
11. C₁₉×#553	C₂²	semidirect
12. C₁₉×#552	C₂²	semidirect
13. C₁₉×#540	C₂²	semidirect
14. C₁₉×#539	C₂²	semidirect
16. C₁₉×#529	C₂²	semidirect
156. C₂×#3567	C₁₉	direct (N × H)
183. #3567	C₂×C₁₉	direct (N × H)
184. C₂×#564	C₂×C₁₉	semidirect
185. C₂×#562	C₂×C₁₉	semidirect
186. C₂×#553	C₂×C₁₉	semidirect
187. C₂×#552	C₂×C₁₉	semidirect
188. C₂×#540	C₂×C₁₉	semidirect
189. C₂×#539	C₂×C₁₉	semidirect
190. C₂×#529	C₂×C₁₉	semidirect
204. #564	C₂²×C₁₉	semidirect
205. #562	C₂²×C₁₉	semidirect
206. #553	C₂²×C₁₉	semidirect
207. #552	C₂²×C₁₉	semidirect
208. #540	C₂²×C₁₉	semidirect
209. #539	C₂²×C₁₉	semidirect
211. #529	C₂²×C₁₉	semidirect
244. C₂×C₁₉	#3567	direct (N × H)
308. C₁₉	C₂×#3567	direct (N × H)
397. C₂	C₁₉×#3567	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×#3567	2
C₂×C₁₉×#564	2
C₂×C₁₉×#562	2
C₂×C₁₉×#553	2
C₂×C₁₉×#552	2
C₂×C₁₉×#540	2
C₂×C₁₉×#539	2
C₂×C₁₉×#529	2
C₂×#3567	19

Subgroups — C2×C19×#3567 #18068696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3567 #18068696