Subgroups — C₂×C₁₉×#3428 #18068607

Order 4864.

11534 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3428	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₁₉×#520	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₉×#519	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#518	C₂	1	6	yes	maximal, complemented
6	C₂×C₄×#41×C₁₉	C₂	1	8	yes	maximal, complemented
7	C₂²×C₁₉×#117	C₂	1	6	yes	maximal, complemented
8	C₂²×#41×C₁₉	C₄	1	32	yes	complemented
9	C₂²×#41×C₁₉	C₂²	1	4	yes	—
10	C₂²×#41×C₁₉	C₂²	1	4	yes	—
11	C₂²×#41×C₁₉	C₂²	1	16	yes	—
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₁₉	C₂²	1	3	yes	—
15	C₁₉×#520	C₂²	1	128	yes	complemented
16	C₁₉×#519	C₂²	1	32	yes	complemented
17	C₁₉×#518	C₂²	1	96	yes	complemented
18	C₄×#41×C₁₉	C₂²	1	128	yes	complemented
19	C₂×C₄×Q₈×C₁₉	C₂²	1	16	yes	complemented
20	C₂×C₄×D₄×C₁₉	C₂²	1	48	yes	complemented
21	C₂×C₁₉×#117	C₂²	1	12	yes	—
22	C₂×C₁₉×#117	C₂²	1	4	yes	—
23	C₂×C₁₉×#117	C₂²	1	12	yes	complemented
24	C₂×C₁₉×#117	C₂²	1	12	yes	complemented
25	C₂×C₁₉×#117	C₂²	1	96	yes	complemented
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	12	yes	complemented
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	12	yes	—
28	C₂²×C₄²×C₁₉	C₂²	1	12	yes	complemented
29	C₂⁵×C₁₉	C₂³	1	3	yes	—
30	C₂×#41×C₁₉	C₂×C₄	1	64	yes	complemented
31	C₂×#41×C₁₉	C₂×C₄	1	64	yes	complemented
32	C₂×#41×C₁₉	C₂×C₄	1	256	yes	complemented
33	C₂×#41×C₁₉	C₂³	1	32	yes	—
34	C₂×#41×C₁₉	C₂³	1	32	yes	—
35	C₂²×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
36	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
37	C₂²×Q₈×C₁₉	C₂³	1	8	yes	—
38	C₂²×D₄×C₁₉	C₂×C₄	1	48	yes	complemented
39	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
40	C₂²×D₄×C₁₉	C₂³	1	24	yes	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	48	yes	complemented
42	C₂³×C₄×C₁₉	C₂³	1	24	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	24	yes	—
48	C₄×Q₈×C₁₉	C₂³	1	128	yes	complemented
49	C₄×D₄×C₁₉	C₂³	1	384	yes	complemented
50	C₁₉×#117	C₂³	1	32	yes	—
51	C₁₉×#117	C₂³	1	96	yes	—
52	C₁₉×#117	C₂³	1	96	yes	complemented
53	C₁₉×#117	C₂³	1	96	yes	complemented
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	96	yes	complemented
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	96	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	24	yes	—
61	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
62	C₂×C₄²×C₁₉	C₂³	1	96	yes	complemented
63	C₂⁴×C₁₉	—	4	12	no	—
64	C₂⁴×C₁₉	C₂²×C₄	1	24	yes	—
65	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
66	C₂⁴×C₁₉	C₂⁴	1	6	yes	—
67	C₂⁴×C₁₉	C₂⁴	1	12	yes	—
68	#41×C₁₉	C₂²×C₄	1	256	yes	complemented
69	#41×C₁₉	C₂²×C₄	1	256	yes	complemented
70	C₂×Q₈×C₁₉	C₂²×C₄	1	32	yes	—
71	C₂×Q₈×C₁₉	C₂²×C₄	1	64	yes	complemented
72	C₂×Q₈×C₁₉	C₂⁴	1	16	yes	—
73	C₂×D₄×C₁₉	C₂²×C₄	1	96	yes	—
74	C₂×D₄×C₁₉	C₂²×C₄	1	192	yes	complemented
75	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
76	C₂²×C₄×C₁₉	—	4	48	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
78	C₂²×C₄×C₁₉	C₂²×C₄	1	24	yes	—
79	C₂²×C₄×C₁₉	C₂²×C₄	1	48	yes	—
80	C₂²×C₄×C₁₉	C₂²×C₄	1	48	yes	—
81	C₂²×C₄×C₁₉	C₂²×C₄	1	192	yes	complemented
82	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
83	C₂²×C₄×C₁₉	C₂⁴	1	96	yes	—
84	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
85	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
86	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
88	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
89	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
90	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
91	C₄⋊C₄×C₁₉	C₂⁴	1	32	yes	—
92	C₄⋊C₄×C₁₉	C₂⁴	1	96	yes	—
93	C₂²⋊C₄×C₁₉	C₂⁴	1	32	yes	—
94	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
95	C₄²×C₁₉	C₂⁴	1	32	yes	—
96	C₄²×C₁₉	C₂⁴	1	96	yes	—
97	C₂×#3428	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂³×C₁₉	—	2	24	no	—
99	C₂³×C₁₉	—	2	4	no	—
100	C₂³×C₁₉	—	4	48	no	—
101	C₂³×C₁₉	—	4	24	no	—
102	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
103	C₂³×C₁₉	C₂³×C₄	1	24	yes	—
104	C₂³×C₁₉	C₂³×C₄	1	48	yes	—
105	C₂³×C₁₉	C₂⁵	1	2	yes	—
106	C₂³×C₁₉	C₂⁵	1	12	yes	—
107	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
108	Q₈×C₁₉	C₂³×C₄	1	64	yes	—
109	D₄×C₁₉	C₂³×C₄	1	192	yes	—
110	C₂×C₄×C₁₉	—	2	32	no	—
111	C₂×C₄×C₁₉	—	4	96	no	—
112	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
113	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
114	C₂×C₄×C₁₉	C₂³×C₄	1	24	yes	—
115	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
116	C₂×C₄×C₁₉	C₂³×C₄	1	48	yes	—
117	C₂×C₄×C₁₉	C₂³×C₄	1	96	yes	—
118	C₂×C₄×C₁₉	C₂³×C₄	1	96	yes	—
119	C₂×C₄×C₁₉	C₂⁵	1	32	yes	—
120	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
121	C₂×C₄×C₁₉	C₂⁵	1	12	yes	—
122	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
123	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic
124	#3428	C₂×C₁₉	1	32	yes	direct product factor
125	C₂×#520	C₂×C₁₉	1	8	yes	complemented
126	C₂×#519	C₂×C₁₉	1	2	yes	complemented
127	C₂×#518	C₂×C₁₉	1	6	yes	complemented
128	C₂×C₄×#41	C₂×C₁₉	1	8	yes	complemented
129	C₂²×#117	C₂×C₁₉	1	6	yes	complemented
130	C₂²×C₁₉	—	2	24	no	—
131	C₂²×C₁₉	—	2	4	no	—
132	C₂²×C₁₉	—	2	8	no	—
133	C₂²×C₁₉	—	2	48	no	—
134	C₂²×C₁₉	—	4	48	no	—
135	C₂²×C₁₉	C₂⁴×C₄	1	4	yes	—
136	C₂²×C₁₉	C₂⁴×C₄	1	24	yes	—
137	C₂²×C₁₉	C₂⁴×C₄	1	2	yes	—
138	C₂²×C₁₉	#585	1	4	yes	—
139	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
140	C₄×C₁₉	—	2	32	no	—
141	C₄×C₁₉	C₂⁴×C₄	1	4	yes	—
142	C₄×C₁₉	C₂⁴×C₄	1	4	yes	—
143	C₄×C₁₉	C₂⁴×C₄	1	24	yes	—
144	C₂²×#41	C₄×C₁₉	1	32	yes	complemented
145	C₂²×#41	C₂²×C₁₉	1	4	yes	—
146	C₂²×#41	C₂²×C₁₉	1	4	yes	—
147	C₂²×#41	C₂²×C₁₉	1	16	yes	—
148	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
149	C₂³×D₄	C₂²×C₁₉	1	3	yes	—
150	C₂⁴×C₄	C₂²×C₁₉	1	3	yes	—
151	#520	C₂²×C₁₉	1	128	yes	complemented
152	#519	C₂²×C₁₉	1	32	yes	complemented
153	#518	C₂²×C₁₉	1	96	yes	complemented
154	C₄×#41	C₂²×C₁₉	1	128	yes	complemented
155	C₂×C₄×Q₈	C₂²×C₁₉	1	16	yes	complemented
156	C₂×C₄×D₄	C₂²×C₁₉	1	48	yes	complemented
157	C₂×#117	C₂²×C₁₉	1	4	yes	—
158	C₂×#117	C₂²×C₁₉	1	12	yes	—
159	C₂×#117	C₂²×C₁₉	1	12	yes	complemented
160	C₂×#117	C₂²×C₁₉	1	12	yes	complemented
161	C₂×#117	C₂²×C₁₉	1	96	yes	complemented
162	C₂²×C₄⋊C₄	C₂²×C₁₉	1	12	yes	complemented
163	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	12	yes	—
164	C₂²×C₄²	C₂²×C₁₉	1	12	yes	complemented
165	C₂×C₁₉	—	2	4	no	—
166	C₂×C₁₉	—	2	24	no	—
167	C₂×C₁₉	#3428	1	4	yes	direct product factor
168	C₂×C₁₉	C₂⁵×C₄	1	1	yes	characteristic
169	C₂×C₁₉	C₂×#585	1	2	yes	—
170	C₂⁵	C₂³×C₁₉	1	3	yes	—
171	C₂×#41	C₂×C₄×C₁₉	1	64	yes	complemented
172	C₂×#41	C₂×C₄×C₁₉	1	64	yes	complemented
173	C₂×#41	C₂×C₄×C₁₉	1	256	yes	complemented
174	C₂×#41	C₂³×C₁₉	1	32	yes	—
175	C₂×#41	C₂³×C₁₉	1	32	yes	—
176	C₂²×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
177	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
178	C₂²×Q₈	C₂³×C₁₉	1	8	yes	—
179	C₂²×D₄	C₂×C₄×C₁₉	1	48	yes	complemented
180	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
181	C₂²×D₄	C₂³×C₁₉	1	24	yes	—
182	C₂³×C₄	C₂×C₄×C₁₉	1	48	yes	complemented
183	C₂³×C₄	C₂³×C₁₉	1	24	yes	—
184	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
185	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
187	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
188	C₂³×C₄	C₂³×C₁₉	1	24	yes	—
189	C₄×Q₈	C₂³×C₁₉	1	128	yes	complemented
190	C₄×D₄	C₂³×C₁₉	1	384	yes	complemented
191	#117	C₂³×C₁₉	1	32	yes	—
192	#117	C₂³×C₁₉	1	96	yes	—
193	#117	C₂³×C₁₉	1	96	yes	complemented
194	#117	C₂³×C₁₉	1	96	yes	complemented
195	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
196	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
197	C₂×C₄⋊C₄	C₂³×C₁₉	1	96	yes	complemented
198	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
199	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
200	C₂×C₂²⋊C₄	C₂³×C₁₉	1	96	yes	—
201	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
202	C₂×C₄²	C₂³×C₁₉	1	24	yes	—
203	C₂×C₄²	C₂³×C₁₉	1	96	yes	complemented
204	C₁₉	C₂×#3428	1	1	yes	characteristic, direct product factor, Sylow
205	C₂⁴	—	4	12	no	—
206	C₂⁴	C₂²×C₄×C₁₉	1	24	yes	—
207	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
208	C₂⁴	C₂⁴×C₁₉	1	6	yes	—
209	C₂⁴	C₂⁴×C₁₉	1	12	yes	—
210	#41	C₂²×C₄×C₁₉	1	256	yes	complemented
211	#41	C₂²×C₄×C₁₉	1	256	yes	complemented
212	C₂×Q₈	C₂²×C₄×C₁₉	1	32	yes	—
213	C₂×Q₈	C₂²×C₄×C₁₉	1	64	yes	complemented
214	C₂×Q₈	C₂⁴×C₁₉	1	16	yes	—
215	C₂×D₄	C₂²×C₄×C₁₉	1	96	yes	—
216	C₂×D₄	C₂²×C₄×C₁₉	1	192	yes	complemented
217	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
218	C₂²×C₄	—	4	48	no	—
219	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
220	C₂²×C₄	C₂²×C₄×C₁₉	1	24	yes	—
221	C₂²×C₄	C₂²×C₄×C₁₉	1	48	yes	—
222	C₂²×C₄	C₂²×C₄×C₁₉	1	48	yes	—
223	C₂²×C₄	C₂²×C₄×C₁₉	1	192	yes	complemented
224	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
225	C₂²×C₄	C₂⁴×C₁₉	1	96	yes	—
226	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
227	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
228	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
229	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
230	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
231	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
232	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
233	C₄⋊C₄	C₂⁴×C₁₉	1	32	yes	—
234	C₄⋊C₄	C₂⁴×C₁₉	1	96	yes	—
235	C₂²⋊C₄	C₂⁴×C₁₉	1	32	yes	—
236	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
237	C₄²	C₂⁴×C₁₉	1	32	yes	—
238	C₄²	C₂⁴×C₁₉	1	96	yes	—
239	C₂³	—	2	24	no	—
240	C₂³	—	2	4	no	—
241	C₂³	—	4	48	no	—
242	C₂³	—	4	24	no	—
243	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
244	C₂³	C₂³×C₄×C₁₉	1	24	yes	—
245	C₂³	C₂³×C₄×C₁₉	1	48	yes	—
246	C₂³	C₂⁵×C₁₉	1	2	yes	—
247	C₂³	C₂⁵×C₁₉	1	12	yes	—
248	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
249	Q₈	C₂³×C₄×C₁₉	1	64	yes	—
250	D₄	C₂³×C₄×C₁₉	1	192	yes	—
251	C₂×C₄	—	2	32	no	—
252	C₂×C₄	—	4	96	no	—
253	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
254	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
255	C₂×C₄	C₂³×C₄×C₁₉	1	24	yes	—
256	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
257	C₂×C₄	C₂³×C₄×C₁₉	1	48	yes	—
258	C₂×C₄	C₂³×C₄×C₁₉	1	96	yes	—
259	C₂×C₄	C₂³×C₄×C₁₉	1	96	yes	—
260	C₂×C₄	C₂⁵×C₁₉	1	32	yes	—
261	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
262	C₂×C₄	C₂⁵×C₁₉	1	12	yes	—
263	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
264	C₂²	—	2	8	no	—
265	C₂²	—	2	48	no	—
266	C₂²	—	2	24	no	—
267	C₂²	—	2	4	no	—
268	C₂²	—	4	48	no	—
269	C₂²	C₂⁴×C₄×C₁₉	1	4	yes	—
270	C₂²	C₂⁴×C₄×C₁₉	1	24	yes	—
271	C₂²	C₂⁴×C₄×C₁₉	1	2	yes	—
272	C₂²	C₁₉×#585	1	4	yes	—
273	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
274	C₄	—	2	32	no	—
275	C₄	C₂⁴×C₄×C₁₉	1	4	yes	—
276	C₄	C₂⁴×C₄×C₁₉	1	4	yes	—
277	C₄	C₂⁴×C₄×C₁₉	1	24	yes	—
278	C₂	—	2	4	no	—
279	C₂	—	2	24	no	—
280	C₂	C₁₉×#3428	1	4	yes	direct product factor
281	C₂	C₂⁵×C₄×C₁₉	1	1	yes	characteristic
282	C₂	C₂×C₁₉×#585	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂	C₂⁵×C₄×C₁₉
Frattini, cosocle	C₂²	C₂⁶×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂³×#41×C₁₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3428	C₂	direct (N × H)
3. C₂×C₁₉×#520	C₂	semidirect
4. C₂×C₁₉×#519	C₂	semidirect
5. C₂×C₁₉×#518	C₂	semidirect
6. C₂×C₄×#41×C₁₉	C₂	semidirect
7. C₂²×C₁₉×#117	C₂	semidirect
8. C₂²×#41×C₁₉	C₄	semidirect
15. C₁₉×#520	C₂²	semidirect
16. C₁₉×#519	C₂²	semidirect
17. C₁₉×#518	C₂²	semidirect
18. C₄×#41×C₁₉	C₂²	semidirect
19. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
20. C₂×C₄×D₄×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#117	C₂²	semidirect
24. C₂×C₁₉×#117	C₂²	semidirect
25. C₂×C₁₉×#117	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
28. C₂²×C₄²×C₁₉	C₂²	semidirect
30. C₂×#41×C₁₉	C₂×C₄	semidirect
31. C₂×#41×C₁₉	C₂×C₄	semidirect
32. C₂×#41×C₁₉	C₂×C₄	semidirect
35. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
38. C₂²×D₄×C₁₉	C₂×C₄	semidirect
41. C₂³×C₄×C₁₉	C₂×C₄	semidirect
48. C₄×Q₈×C₁₉	C₂³	semidirect
49. C₄×D₄×C₁₉	C₂³	semidirect
52. C₁₉×#117	C₂³	semidirect
53. C₁₉×#117	C₂³	semidirect
56. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
62. C₂×C₄²×C₁₉	C₂³	semidirect
68. #41×C₁₉	C₂²×C₄	semidirect
69. #41×C₁₉	C₂²×C₄	semidirect
71. C₂×Q₈×C₁₉	C₂²×C₄	semidirect
74. C₂×D₄×C₁₉	C₂²×C₄	semidirect
81. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
97. C₂×#3428	C₁₉	direct (N × H)
124. #3428	C₂×C₁₉	direct (N × H)
125. C₂×#520	C₂×C₁₉	semidirect
126. C₂×#519	C₂×C₁₉	semidirect
127. C₂×#518	C₂×C₁₉	semidirect
128. C₂×C₄×#41	C₂×C₁₉	semidirect
129. C₂²×#117	C₂×C₁₉	semidirect
144. C₂²×#41	C₄×C₁₉	semidirect
151. #520	C₂²×C₁₉	semidirect
152. #519	C₂²×C₁₉	semidirect
153. #518	C₂²×C₁₉	semidirect
154. C₄×#41	C₂²×C₁₉	semidirect
155. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
156. C₂×C₄×D₄	C₂²×C₁₉	semidirect
159. C₂×#117	C₂²×C₁₉	semidirect
160. C₂×#117	C₂²×C₁₉	semidirect
161. C₂×#117	C₂²×C₁₉	semidirect
162. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
164. C₂²×C₄²	C₂²×C₁₉	semidirect
167. C₂×C₁₉	#3428	direct (N × H)
171. C₂×#41	C₂×C₄×C₁₉	semidirect
172. C₂×#41	C₂×C₄×C₁₉	semidirect
173. C₂×#41	C₂×C₄×C₁₉	semidirect
176. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
179. C₂²×D₄	C₂×C₄×C₁₉	semidirect
182. C₂³×C₄	C₂×C₄×C₁₉	semidirect
189. C₄×Q₈	C₂³×C₁₉	semidirect
190. C₄×D₄	C₂³×C₁₉	semidirect
193. #117	C₂³×C₁₉	semidirect
194. #117	C₂³×C₁₉	semidirect
197. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
203. C₂×C₄²	C₂³×C₁₉	semidirect
204. C₁₉	C₂×#3428	direct (N × H)
210. #41	C₂²×C₄×C₁₉	semidirect
211. #41	C₂²×C₄×C₁₉	semidirect
213. C₂×Q₈	C₂²×C₄×C₁₉	semidirect
216. C₂×D₄	C₂²×C₄×C₁₉	semidirect
223. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
280. C₂	C₁₉×#3428	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₁₉×#3428	2
C₂×C₁₉×#520	2
C₂×C₁₉×#519	2
C₂×C₁₉×#518	2
C₂×C₄×#41×C₁₉	2
C₂²×C₁₉×#117	2
C₂×#3428	19

Subgroups — C2×C19×#3428 #18068607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3428 #18068607