Subgroups — C₂×C₁₉×#3499 #18068761

Order 4864.

11126 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3499	C₂	1	32	yes	maximal, direct product factor
3	C₂×D₄×Q₈×C₁₉	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#547	C₂	1	12	yes	maximal, complemented
5	C₂×C₁₉×#536	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₉×#532	C₂	1	3	yes	maximal, complemented
7	C₂²×C₁₉×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	—	2	32	no	—
10	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	32	yes	complemented
11	C₂²×#41×C₁₉	C₂²	1	6	yes	—
12	C₂²×#41×C₁₉	C₂²	1	12	yes	—
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₉	C₂²	1	6	yes	—
15	C₂³×Q₈×C₁₉	C₂²	1	4	yes	—
16	D₄×Q₈×C₁₉	C₂²	1	64	yes	complemented
17	C₁₉×#547	C₂²	1	192	yes	complemented
18	C₁₉×#536	C₂²	1	96	yes	complemented
19	C₁₉×#532	C₂²	1	48	yes	complemented
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
21	C₂×C₁₉×C₄⋊Q₈	C₂²	1	6	yes	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	12	yes	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	48	yes	complemented
24	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#124	C₂²	1	6	yes	—
26	C₂×C₁₉×#123	C₂²	1	24	yes	—
27	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	24	yes	—
28	C₂×C₁₉×#121	C₂²	1	12	yes	—
29	C₄×#41×C₁₉	C₂²	1	16	yes	complemented
30	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	12	yes	—
33	C₂×C₁₉×#117	C₂²	1	3	yes	—
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	12	yes	—
35	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
36	C₁₉×2₋¹⁺⁴	—	2	256	no	—
37	C₂×#41×C₁₉	—	2	96	no	—
38	C₂×#41×C₁₉	—	2	48	no	—
39	C₂×#41×C₁₉	D₄	1	16	yes	complemented
40	C₂×#41×C₁₉	C₂³	1	48	yes	—
41	C₂×#41×C₁₉	C₂³	1	96	yes	—
42	C₂×#41×C₁₉	C₂³	1	8	yes	—
43	C₂²×Q₈×C₁₉	—	2	32	no	—
44	C₂²×Q₈×C₁₉	—	2	48	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	12	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	48	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	32	yes	—
49	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	12	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
58	C₁₉×C₄⋊Q₈	C₂³	1	24	yes	—
59	C₁₉×C₄⋊Q₈	C₂³	1	48	yes	—
60	C₁₉×C₄⋊Q₈	C₂³	1	96	yes	—
61	C₁₉×#127	C₂³	1	8	yes	—
62	C₁₉×#124	C₂³	1	48	yes	—
63	C₁₉×#123	C₂³	1	192	yes	—
64	C₁₉×C₂²⋊Q₈	C₂³	1	192	yes	—
65	C₁₉×#121	C₂³	1	96	yes	—
66	C₄×Q₈×C₁₉	C₂³	1	16	yes	—
67	C₄×D₄×C₁₉	C₂³	1	48	yes	—
68	C₄×D₄×C₁₉	C₂³	1	96	yes	—
69	C₁₉×#117	C₂³	1	24	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	96	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	24	yes	—
80	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
81	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
82	#41×C₁₉	—	2	384	no	—
83	#41×C₁₉	—	2	192	no	—
84	#41×C₁₉	C₂×D₄	1	64	yes	complemented
85	C₂×Q₈×C₁₉	—	2	128	no	—
86	C₂×Q₈×C₁₉	—	2	48	no	—
87	C₂×Q₈×C₁₉	—	2	24	no	—
88	C₂×Q₈×C₁₉	—	2	192	no	—
89	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
90	C₂×Q₈×C₁₉	C₂⁴	1	48	yes	—
91	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
92	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
93	C₂×D₄×C₁₉	—	2	48	no	—
94	C₂×D₄×C₁₉	—	2	8	no	—
95	C₂×D₄×C₁₉	—	2	16	no	—
96	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	—
97	C₂×D₄×C₁₉	C₂⁴	1	16	yes	—
98	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
99	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
100	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
101	C₂²×C₄×C₁₉	—	2	48	no	—
102	C₂²×C₄×C₁₉	—	2	48	no	—
103	C₂²×C₄×C₁₉	—	2	24	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	24	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	48	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	48	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
114	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
115	C₄⋊C₄×C₁₉	C₂⁴	1	96	yes	—
116	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
117	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
118	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
119	C₄²×C₁₉	C₂⁴	1	4	yes	—
120	C₄²×C₁₉	C₂⁴	1	12	yes	—
121	C₄²×C₁₉	C₂⁴	1	24	yes	—
122	C₂×#3499	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₁₉	—	2	12	no	—
124	C₂³×C₁₉	—	2	8	no	—
125	C₂³×C₁₉	—	2	16	no	—
126	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
127	C₂³×C₁₉	C₂⁵	1	8	yes	—
128	C₂³×C₁₉	C₂⁵	1	6	yes	—
129	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
130	Q₈×C₁₉	—	2	96	no	—
131	Q₈×C₁₉	—	2	48	no	—
132	Q₈×C₁₉	C₂²×D₄	1	16	yes	—
133	D₄×C₁₉	—	2	96	no	—
134	D₄×C₁₉	—	2	16	no	—
135	D₄×C₁₉	—	2	32	no	—
136	D₄×C₁₉	C₂²×D₄	1	48	yes	—
137	C₂×C₄×C₁₉	—	2	24	no	—
138	C₂×C₄×C₁₉	—	2	96	no	—
139	C₂×C₄×C₁₉	—	2	12	no	—
140	C₂×C₄×C₁₉	—	2	96	no	—
141	C₂×C₄×C₁₉	—	2	48	no	—
142	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
143	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₁₉	C₂²×D₄	1	48	yes	—
145	C₂×C₄×C₁₉	2₋¹⁺⁴	1	8	yes	complemented
146	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
147	C₂×C₄×C₁₉	C₂⁵	1	24	yes	—
148	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
149	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
150	C₂×C₄×C₁₉	C₂⁵	1	4	yes	—
151	C₂²×2₋¹⁺⁴	C₂×C₁₉	1	2	yes	complemented
152	#3499	C₂×C₁₉	1	32	yes	direct product factor
153	C₂×D₄×Q₈	C₂×C₁₉	1	4	yes	complemented
154	C₂×#547	C₂×C₁₉	1	12	yes	complemented
155	C₂×#536	C₂×C₁₉	1	6	yes	complemented
156	C₂×#532	C₂×C₁₉	1	3	yes	complemented
157	C₂²×C₄⋊Q₈	C₂×C₁₉	1	3	yes	complemented
158	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
159	C₂²×C₁₉	—	2	12	no	—
160	C₂²×C₁₉	—	2	24	no	—
161	C₂²×C₁₉	—	2	8	no	—
162	C₂²×C₁₉	—	2	16	no	—
163	C₂²×C₁₉	—	4	16	no	—
164	C₂²×C₁₉	C₂³×D₄	1	12	yes	—
165	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
166	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	4	yes	—
167	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
168	C₄×C₁₉	—	2	24	no	—
169	C₄×C₁₉	—	2	12	no	—
170	C₄×C₁₉	C₂³×D₄	1	12	yes	—
171	C₄×C₁₉	C₂³×D₄	1	4	yes	—
172	C₄×C₁₉	C₂×2₋¹⁺⁴	1	8	yes	complemented
173	C₂×2₋¹⁺⁴	—	2	32	no	—
174	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	32	yes	complemented
175	C₂²×#41	C₂²×C₁₉	1	6	yes	—
176	C₂²×#41	C₂²×C₁₉	1	12	yes	—
177	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
178	C₂³×Q₈	C₂²×C₁₉	1	6	yes	—
179	C₂³×Q₈	C₂²×C₁₉	1	4	yes	—
180	D₄×Q₈	C₂²×C₁₉	1	64	yes	complemented
181	#547	C₂²×C₁₉	1	192	yes	complemented
182	#536	C₂²×C₁₉	1	96	yes	complemented
183	#532	C₂²×C₁₉	1	48	yes	complemented
184	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₁₉	1	6	yes	—
186	C₂×C₄⋊Q₈	C₂²×C₁₉	1	12	yes	—
187	C₂×C₄⋊Q₈	C₂²×C₁₉	1	48	yes	complemented
188	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
189	C₂×#124	C₂²×C₁₉	1	6	yes	—
190	C₂×#123	C₂²×C₁₉	1	24	yes	—
191	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	24	yes	—
192	C₂×#121	C₂²×C₁₉	1	12	yes	—
193	C₄×#41	C₂²×C₁₉	1	16	yes	complemented
194	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
195	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
196	C₂×C₄×D₄	C₂²×C₁₉	1	12	yes	—
197	C₂×#117	C₂²×C₁₉	1	3	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₉	1	12	yes	—
199	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
200	C₂×C₁₉	—	2	12	no	—
201	C₂×C₁₉	—	4	8	no	—
202	C₂×C₁₉	#3499	1	4	yes	direct product factor
203	C₂×C₁₉	C₂⁴×D₄	1	1	yes	characteristic
204	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	2	yes	—
205	2₋¹⁺⁴	—	2	256	no	—
206	C₂×#41	—	2	96	no	—
207	C₂×#41	—	2	48	no	—
208	C₂×#41	D₄×C₁₉	1	16	yes	complemented
209	C₂×#41	C₂³×C₁₉	1	48	yes	—
210	C₂×#41	C₂³×C₁₉	1	96	yes	—
211	C₂×#41	C₂³×C₁₉	1	8	yes	—
212	C₂²×Q₈	—	2	32	no	—
213	C₂²×Q₈	—	2	48	no	—
214	C₂²×Q₈	C₂³×C₁₉	1	12	yes	—
215	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
216	C₂²×Q₈	C₂³×C₁₉	1	48	yes	—
217	C₂²×Q₈	C₂³×C₁₉	1	32	yes	—
218	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
219	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
220	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
221	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
222	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
223	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
224	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
225	C₂³×C₄	C₂³×C₁₉	1	12	yes	—
226	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
227	C₄⋊Q₈	C₂³×C₁₉	1	24	yes	—
228	C₄⋊Q₈	C₂³×C₁₉	1	48	yes	—
229	C₄⋊Q₈	C₂³×C₁₉	1	96	yes	—
230	#127	C₂³×C₁₉	1	8	yes	—
231	#124	C₂³×C₁₉	1	48	yes	—
232	#123	C₂³×C₁₉	1	192	yes	—
233	C₂²⋊Q₈	C₂³×C₁₉	1	192	yes	—
234	#121	C₂³×C₁₉	1	96	yes	—
235	C₄×Q₈	C₂³×C₁₉	1	16	yes	—
236	C₄×D₄	C₂³×C₁₉	1	48	yes	—
237	C₄×D₄	C₂³×C₁₉	1	96	yes	—
238	#117	C₂³×C₁₉	1	24	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₉	1	96	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
245	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
246	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
247	C₂×C₄²	C₂³×C₁₉	1	24	yes	—
248	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
249	C₁₉	C₂×#3499	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
251	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
252	#41	—	2	384	no	—
253	#41	—	2	192	no	—
254	#41	C₂×D₄×C₁₉	1	64	yes	complemented
255	C₂×Q₈	—	2	128	no	—
256	C₂×Q₈	—	2	48	no	—
257	C₂×Q₈	—	2	24	no	—
258	C₂×Q₈	—	2	192	no	—
259	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
260	C₂×Q₈	C₂⁴×C₁₉	1	48	yes	—
261	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
262	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	—
267	C₂×D₄	C₂⁴×C₁₉	1	16	yes	—
268	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
269	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
270	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
271	C₂²×C₄	—	2	48	no	—
272	C₂²×C₄	—	2	48	no	—
273	C₂²×C₄	—	2	24	no	—
274	C₂²×C₄	C₂×D₄×C₁₉	1	24	yes	—
275	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
276	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
277	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
278	C₂²×C₄	C₂⁴×C₁₉	1	48	yes	—
279	C₂²×C₄	C₂⁴×C₁₉	1	48	yes	—
280	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
282	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
283	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
284	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
285	C₄⋊C₄	C₂⁴×C₁₉	1	96	yes	—
286	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
287	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
288	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
289	C₄²	C₂⁴×C₁₉	1	4	yes	—
290	C₄²	C₂⁴×C₁₉	1	12	yes	—
291	C₄²	C₂⁴×C₁₉	1	24	yes	—
292	C₂³	—	2	12	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	2	16	no	—
295	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
296	C₂³	C₂⁵×C₁₉	1	8	yes	—
297	C₂³	C₂⁵×C₁₉	1	6	yes	—
298	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
299	Q₈	—	2	96	no	—
300	Q₈	—	2	48	no	—
301	Q₈	C₂²×D₄×C₁₉	1	16	yes	—
302	D₄	—	2	96	no	—
303	D₄	—	2	16	no	—
304	D₄	—	2	32	no	—
305	D₄	C₂²×D₄×C₁₉	1	48	yes	—
306	C₂×C₄	—	2	24	no	—
307	C₂×C₄	—	2	96	no	—
308	C₂×C₄	—	2	12	no	—
309	C₂×C₄	—	2	96	no	—
310	C₂×C₄	—	2	48	no	—
311	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
312	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
313	C₂×C₄	C₂²×D₄×C₁₉	1	48	yes	—
314	C₂×C₄	C₁₉×2₋¹⁺⁴	1	8	yes	complemented
315	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
316	C₂×C₄	C₂⁵×C₁₉	1	24	yes	—
317	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
318	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
319	C₂×C₄	C₂⁵×C₁₉	1	4	yes	—
320	C₂²	—	2	24	no	—
321	C₂²	—	2	12	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	4	16	no	—
325	C₂²	C₂³×D₄×C₁₉	1	12	yes	—
326	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
327	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	4	yes	—
328	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
329	C₄	—	2	24	no	—
330	C₄	—	2	12	no	—
331	C₄	C₂³×D₄×C₁₉	1	12	yes	—
332	C₄	C₂³×D₄×C₁₉	1	4	yes	—
333	C₄	C₂×C₁₉×2₋¹⁺⁴	1	8	yes	complemented
334	C₂	—	2	12	no	—
335	C₂	—	4	8	no	—
336	C₂	C₁₉×#3499	1	4	yes	direct product factor
337	C₂	C₂⁴×D₄×C₁₉	1	1	yes	characteristic
338	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	2	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. C₂²×C₁₉×2₋¹⁺⁴	C₂	semidirect
2. C₁₉×#3499	C₂	direct (N × H)
3. C₂×D₄×Q₈×C₁₉	C₂	semidirect
4. C₂×C₁₉×#547	C₂	semidirect
5. C₂×C₁₉×#536	C₂	semidirect
6. C₂×C₁₉×#532	C₂	semidirect
7. C₂²×C₁₉×C₄⋊Q₈	C₂	semidirect
8. C₂×C₄×#41×C₁₉	C₂	semidirect
10. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
16. D₄×Q₈×C₁₉	C₂²	semidirect
17. C₁₉×#547	C₂²	semidirect
18. C₁₉×#536	C₂²	semidirect
19. C₁₉×#532	C₂²	semidirect
23. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
29. C₄×#41×C₁₉	C₂²	semidirect
39. C₂×#41×C₁₉	D₄	semidirect
84. #41×C₁₉	C₂×D₄	semidirect
122. C₂×#3499	C₁₉	direct (N × H)
145. C₂×C₄×C₁₉	2₋¹⁺⁴	semidirect
151. C₂²×2₋¹⁺⁴	C₂×C₁₉	semidirect
152. #3499	C₂×C₁₉	direct (N × H)
153. C₂×D₄×Q₈	C₂×C₁₉	semidirect
154. C₂×#547	C₂×C₁₉	semidirect
155. C₂×#536	C₂×C₁₉	semidirect
156. C₂×#532	C₂×C₁₉	semidirect
157. C₂²×C₄⋊Q₈	C₂×C₁₉	semidirect
158. C₂×C₄×#41	C₂×C₁₉	semidirect
172. C₄×C₁₉	C₂×2₋¹⁺⁴	semidirect
174. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
180. D₄×Q₈	C₂²×C₁₉	semidirect
181. #547	C₂²×C₁₉	semidirect
182. #536	C₂²×C₁₉	semidirect
183. #532	C₂²×C₁₉	semidirect
187. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
193. C₄×#41	C₂²×C₁₉	semidirect
202. C₂×C₁₉	#3499	direct (N × H)
208. C₂×#41	D₄×C₁₉	semidirect
249. C₁₉	C₂×#3499	direct (N × H)
254. #41	C₂×D₄×C₁₉	semidirect
314. C₂×C₄	C₁₉×2₋¹⁺⁴	semidirect
333. C₄	C₂×C₁₉×2₋¹⁺⁴	semidirect
336. C₂	C₁₉×#3499	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×C₁₉×2₋¹⁺⁴	2
C₁₉×#3499	2
C₂×D₄×Q₈×C₁₉	2
C₂×C₁₉×#547	2
C₂×C₁₉×#536	2
C₂×C₁₉×#532	2
C₂²×C₁₉×C₄⋊Q₈	2
C₂×C₄×#41×C₁₉	2
C₂×#3499	19

Subgroups — C2×C19×#3499 #18068761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3499 #18068761