Subgroups — C₂×Q₈×#41×C₁₉ #18068672

Order 4864.

7522 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₁₉	C₂	1	32	yes	maximal, direct product factor
2	C₂×Q₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#557	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₉×#554	C₂	1	9	yes	maximal, complemented
5	C₂×D₄×Q₈×C₁₉	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₉×#533	C₂	1	9	yes	maximal, complemented
7	C₂×C₄×#41×C₁₉	C₂	1	3	yes	maximal
8	C₂²×C₄×Q₈×C₁₉	C₂	1	3	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₉	C₂²	1	3	yes	—
11	Q₈²×C₁₉	C₂²	1	16	yes	complemented
12	C₁₉×#557	C₂²	1	48	yes	complemented
13	C₁₉×#554	C₂²	1	144	yes	complemented
14	D₄×Q₈×C₁₉	C₂²	1	48	yes	complemented
15	C₁₉×#533	C₂²	1	144	yes	complemented
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	9	yes	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	9	yes	—
18	C₂×C₁₉×#125	C₂²	1	18	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	18	yes	—
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	18	yes	—
21	C₄×#41×C₁₉	C₂²	1	48	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₉	C₂²	1	9	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	9	yes	—
26	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
28	C₂×C₄×Q₈×C₁₉	C₂²	1	6	yes	—
29	C₂×C₄×Q₈×C₁₉	C₂²	1	48	yes	complemented
30	C₂×C₄×D₄×C₁₉	C₂²	1	9	yes	—
31	C₂×C₄×D₄×C₁₉	C₂²	1	9	yes	—
32	C₂×C₁₉×#117	C₂²	1	9	yes	—
33	C₂²×C₄⋊C₄×C₁₉	C₂²	1	9	yes	—
34	C₂²×C₄²×C₁₉	C₂²	1	9	yes	—
35	C₂×#41×C₁₉	Q₈	1	16	yes	direct product factor
36	C₂×#41×C₁₉	C₂³	1	8	yes	—
37	C₂²×Q₈×C₁₉	—	2	24	no	—
38	C₂²×Q₈×C₁₉	C₂³	1	9	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	24	yes	—
40	C₂²×Q₈×C₁₉	C₂³	1	6	yes	—
41	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	9	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	9	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
47	C₁₉×C₄⋊Q₈	C₂³	1	72	yes	—
48	C₁₉×C₄⋊Q₈	C₂³	1	72	yes	—
49	C₁₉×#125	C₂³	1	144	yes	—
50	C₁₉×C₂²⋊Q₈	C₂³	1	144	yes	—
51	C₁₉×C₂²⋊Q₈	C₂³	1	144	yes	—
52	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
53	C₄×Q₈×C₁₉	C₂³	1	72	yes	—
54	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
55	C₄×Q₈×C₁₉	C₂³	1	72	yes	—
56	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
57	C₄×Q₈×C₁₉	C₂³	1	24	yes	—
58	C₄×Q₈×C₁₉	C₂³	1	48	yes	—
59	C₄×D₄×C₁₉	C₂³	1	72	yes	—
60	C₄×D₄×C₁₉	C₂³	1	72	yes	—
61	C₁₉×#117	C₂³	1	72	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	18	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	9	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	72	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	9	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	9	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	18	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	18	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	9	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	9	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	72	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	9	yes	—
75	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
76	#41×C₁₉	C₂×Q₈	1	64	yes	direct product factor
77	C₂×Q₈×C₁₉	—	2	96	no	—
78	C₂×Q₈×C₁₉	—	2	36	no	—
79	C₂×Q₈×C₁₉	—	4	12	no	—
80	C₂×Q₈×C₁₉	C₂×Q₈	1	8	yes	complemented
81	C₂×Q₈×C₁₉	#41	1	8	yes	direct product factor
82	C₂×Q₈×C₁₉	C₂⁴	1	36	yes	—
83	C₂×Q₈×C₁₉	C₂⁴	1	24	yes	—
84	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
85	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
86	C₂×D₄×C₁₉	C₂×Q₈	1	24	yes	complemented
87	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
88	C₂²×C₄×C₁₉	—	2	36	no	—
89	C₂²×C₄×C₁₉	—	4	18	no	—
90	C₂²×C₄×C₁₉	C₂×Q₈	1	24	yes	complemented
91	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	9	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	9	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	36	yes	—
95	C₂²×C₄×C₁₉	C₂⁴	1	36	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
101	C₄⋊C₄×C₁₉	C₂⁴	1	72	yes	—
102	C₄⋊C₄×C₁₉	C₂⁴	1	36	yes	—
103	C₄⋊C₄×C₁₉	C₂⁴	1	36	yes	—
104	C₄⋊C₄×C₁₉	C₂⁴	1	36	yes	—
105	C₄⋊C₄×C₁₉	C₂⁴	1	72	yes	—
106	C₂²⋊C₄×C₁₉	C₂⁴	1	72	yes	—
107	C₄²×C₁₉	C₂⁴	1	12	yes	—
108	C₄²×C₁₉	C₂⁴	1	36	yes	—
109	C₄²×C₁₉	C₂⁴	1	36	yes	—
110	C₄²×C₁₉	C₂⁴	1	36	yes	—
111	C₂×Q₈×#41	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₁₉	—	2	6	no	—
113	C₂³×C₁₉	—	2	6	no	—
114	C₂³×C₁₉	C₂²×Q₈	1	12	yes	—
115	C₂³×C₁₉	C₂⁵	1	6	yes	—
116	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
117	Q₈×C₁₉	—	2	72	no	—
118	Q₈×C₁₉	—	4	24	no	—
119	Q₈×C₁₉	C₂²×Q₈	1	16	yes	complemented
120	Q₈×C₁₉	C₂×#41	1	16	yes	direct product factor
121	D₄×C₁₉	C₂²×Q₈	1	48	yes	complemented
122	C₂×C₄×C₁₉	—	2	18	no	—
123	C₂×C₄×C₁₉	—	2	6	no	—
124	C₂×C₄×C₁₉	—	2	18	no	—
125	C₂×C₄×C₁₉	—	2	72	no	—
126	C₂×C₄×C₁₉	—	4	36	no	—
127	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
128	C₂×C₄×C₁₉	C₂²×Q₈	1	12	yes	—
129	C₂×C₄×C₁₉	C₂²×Q₈	1	48	yes	complemented
130	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
131	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
132	C₂×C₄×C₁₉	C₂⁵	1	18	yes	—
133	C₂×C₄×C₁₉	C₂⁵	1	18	yes	—
134	C₂×C₄×C₁₉	C₂⁵	1	2	yes	—
135	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
136	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
137	Q₈×#41	C₂×C₁₉	1	32	yes	direct product factor
138	C₂×Q₈²	C₂×C₁₉	1	1	yes	characteristic, complemented
139	C₂×#557	C₂×C₁₉	1	3	yes	complemented
140	C₂×#554	C₂×C₁₉	1	9	yes	complemented
141	C₂×D₄×Q₈	C₂×C₁₉	1	3	yes	complemented
142	C₂×#533	C₂×C₁₉	1	9	yes	complemented
143	C₂×C₄×#41	C₂×C₁₉	1	3	yes	—
144	C₂²×C₄×Q₈	C₂×C₁₉	1	3	yes	complemented
145	C₂²×C₁₉	—	2	6	no	—
146	C₂²×C₁₉	—	2	6	no	—
147	C₂²×C₁₉	—	2	24	no	—
148	C₂²×C₁₉	C₂³×Q₈	1	12	yes	—
149	C₂²×C₁₉	C₂³×Q₈	1	2	yes	—
150	C₂²×C₁₉	C₂²×#41	1	2	yes	—
151	C₂²×C₁₉	#585	1	2	yes	—
152	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
153	C₄×C₁₉	—	2	18	no	—
154	C₄×C₁₉	—	2	6	no	—
155	C₄×C₁₉	—	2	18	no	—
156	C₄×C₁₉	C₂³×Q₈	1	4	yes	—
157	C₄×C₁₉	C₂³×Q₈	1	12	yes	—
158	C₄×C₁₉	C₂²×#41	1	12	yes	—
159	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
160	C₂³×Q₈	C₂²×C₁₉	1	3	yes	—
161	Q₈²	C₂²×C₁₉	1	16	yes	complemented
162	#557	C₂²×C₁₉	1	48	yes	complemented
163	#554	C₂²×C₁₉	1	144	yes	complemented
164	D₄×Q₈	C₂²×C₁₉	1	48	yes	complemented
165	#533	C₂²×C₁₉	1	144	yes	complemented
166	C₂×C₄⋊Q₈	C₂²×C₁₉	1	9	yes	—
167	C₂×C₄⋊Q₈	C₂²×C₁₉	1	9	yes	—
168	C₂×#125	C₂²×C₁₉	1	18	yes	—
169	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	18	yes	—
170	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	18	yes	—
171	C₄×#41	C₂²×C₁₉	1	48	yes	—
172	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
173	C₂×C₄×Q₈	C₂²×C₁₉	1	9	yes	—
174	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
175	C₂×C₄×Q₈	C₂²×C₁₉	1	9	yes	—
176	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
177	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
178	C₂×C₄×Q₈	C₂²×C₁₉	1	6	yes	—
179	C₂×C₄×Q₈	C₂²×C₁₉	1	48	yes	complemented
180	C₂×C₄×D₄	C₂²×C₁₉	1	9	yes	—
181	C₂×C₄×D₄	C₂²×C₁₉	1	9	yes	—
182	C₂×#117	C₂²×C₁₉	1	9	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₉	1	9	yes	—
184	C₂²×C₄²	C₂²×C₁₉	1	9	yes	—
185	C₂×C₁₉	—	2	12	no	—
186	C₂×C₁₉	Q₈×#41	1	4	yes	direct product factor
187	C₂×C₁₉	C₂⁴×Q₈	1	1	yes	characteristic
188	C₂×C₁₉	C₂³×#41	1	1	yes	characteristic
189	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
190	C₂×#41	Q₈×C₁₉	1	16	yes	direct product factor
191	C₂×#41	C₂³×C₁₉	1	8	yes	—
192	C₂²×Q₈	—	2	24	no	—
193	C₂²×Q₈	C₂³×C₁₉	1	9	yes	—
194	C₂²×Q₈	C₂³×C₁₉	1	24	yes	—
195	C₂²×Q₈	C₂³×C₁₉	1	6	yes	—
196	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
197	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
198	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
199	C₂³×C₄	C₂³×C₁₉	1	9	yes	—
200	C₂³×C₄	C₂³×C₁₉	1	9	yes	—
201	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
202	C₄⋊Q₈	C₂³×C₁₉	1	72	yes	—
203	C₄⋊Q₈	C₂³×C₁₉	1	72	yes	—
204	#125	C₂³×C₁₉	1	144	yes	—
205	C₂²⋊Q₈	C₂³×C₁₉	1	144	yes	—
206	C₂²⋊Q₈	C₂³×C₁₉	1	144	yes	—
207	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
208	C₄×Q₈	C₂³×C₁₉	1	72	yes	—
209	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
210	C₄×Q₈	C₂³×C₁₉	1	72	yes	—
211	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
212	C₄×Q₈	C₂³×C₁₉	1	24	yes	—
213	C₄×Q₈	C₂³×C₁₉	1	48	yes	—
214	C₄×D₄	C₂³×C₁₉	1	72	yes	—
215	C₄×D₄	C₂³×C₁₉	1	72	yes	—
216	#117	C₂³×C₁₉	1	72	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₉	1	18	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₉	1	9	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₉	1	72	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₉	1	9	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	9	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₉	1	18	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₁₉	1	18	yes	—
225	C₂×C₄²	C₂³×C₁₉	1	9	yes	—
226	C₂×C₄²	C₂³×C₁₉	1	9	yes	—
227	C₂×C₄²	C₂³×C₁₉	1	9	yes	—
228	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	72	yes	—
230	C₁₉	C₂×Q₈×#41	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
232	#41	C₂×Q₈×C₁₉	1	64	yes	direct product factor
233	C₂×Q₈	—	2	96	no	—
234	C₂×Q₈	—	2	36	no	—
235	C₂×Q₈	—	4	12	no	—
236	C₂×Q₈	C₂×Q₈×C₁₉	1	8	yes	complemented
237	C₂×Q₈	#41×C₁₉	1	8	yes	direct product factor
238	C₂×Q₈	C₂⁴×C₁₉	1	36	yes	—
239	C₂×Q₈	C₂⁴×C₁₉	1	24	yes	—
240	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
241	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
242	C₂×D₄	C₂×Q₈×C₁₉	1	24	yes	complemented
243	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
244	C₂²×C₄	—	2	36	no	—
245	C₂²×C₄	—	4	18	no	—
246	C₂²×C₄	C₂×Q₈×C₁₉	1	24	yes	complemented
247	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
248	C₂²×C₄	C₂⁴×C₁₉	1	9	yes	—
249	C₂²×C₄	C₂⁴×C₁₉	1	9	yes	—
250	C₂²×C₄	C₂⁴×C₁₉	1	36	yes	—
251	C₂²×C₄	C₂⁴×C₁₉	1	36	yes	—
252	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
253	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
254	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
255	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
256	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
257	C₄⋊C₄	C₂⁴×C₁₉	1	72	yes	—
258	C₄⋊C₄	C₂⁴×C₁₉	1	36	yes	—
259	C₄⋊C₄	C₂⁴×C₁₉	1	36	yes	—
260	C₄⋊C₄	C₂⁴×C₁₉	1	36	yes	—
261	C₄⋊C₄	C₂⁴×C₁₉	1	72	yes	—
262	C₂²⋊C₄	C₂⁴×C₁₉	1	72	yes	—
263	C₄²	C₂⁴×C₁₉	1	12	yes	—
264	C₄²	C₂⁴×C₁₉	1	36	yes	—
265	C₄²	C₂⁴×C₁₉	1	36	yes	—
266	C₄²	C₂⁴×C₁₉	1	36	yes	—
267	C₂³	—	2	6	no	—
268	C₂³	—	2	6	no	—
269	C₂³	C₂²×Q₈×C₁₉	1	12	yes	—
270	C₂³	C₂⁵×C₁₉	1	6	yes	—
271	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
272	Q₈	—	2	72	no	—
273	Q₈	—	4	24	no	—
274	Q₈	C₂²×Q₈×C₁₉	1	16	yes	complemented
275	Q₈	C₂×#41×C₁₉	1	16	yes	direct product factor
276	D₄	C₂²×Q₈×C₁₉	1	48	yes	complemented
277	C₂×C₄	—	2	18	no	—
278	C₂×C₄	—	2	6	no	—
279	C₂×C₄	—	2	18	no	—
280	C₂×C₄	—	2	72	no	—
281	C₂×C₄	—	4	36	no	—
282	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
283	C₂×C₄	C₂²×Q₈×C₁₉	1	12	yes	—
284	C₂×C₄	C₂²×Q₈×C₁₉	1	48	yes	complemented
285	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
286	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
287	C₂×C₄	C₂⁵×C₁₉	1	18	yes	—
288	C₂×C₄	C₂⁵×C₁₉	1	18	yes	—
289	C₂×C₄	C₂⁵×C₁₉	1	2	yes	—
290	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
291	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
292	C₂²	—	2	24	no	—
293	C₂²	—	2	6	no	—
294	C₂²	—	2	6	no	—
295	C₂²	C₂³×Q₈×C₁₉	1	12	yes	—
296	C₂²	C₂³×Q₈×C₁₉	1	2	yes	—
297	C₂²	C₂²×#41×C₁₉	1	2	yes	—
298	C₂²	C₁₉×#585	1	2	yes	—
299	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
300	C₄	—	2	18	no	—
301	C₄	—	2	6	no	—
302	C₄	—	2	18	no	—
303	C₄	C₂³×Q₈×C₁₉	1	4	yes	—
304	C₄	C₂³×Q₈×C₁₉	1	12	yes	—
305	C₄	C₂²×#41×C₁₉	1	12	yes	—
306	C₂	—	2	12	no	—
307	C₂	Q₈×#41×C₁₉	1	4	yes	direct product factor
308	C₂	C₂⁴×Q₈×C₁₉	1	1	yes	characteristic
309	C₂	C₂³×#41×C₁₉	1	1	yes	characteristic
310	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
prime radical	C₂²×#41×C₁₉	C₂²
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. Q₈×#41×C₁₉	C₂	direct (N × H)
2. C₂×Q₈²×C₁₉	C₂	semidirect
3. C₂×C₁₉×#557	C₂	semidirect
4. C₂×C₁₉×#554	C₂	semidirect
5. C₂×D₄×Q₈×C₁₉	C₂	semidirect
6. C₂×C₁₉×#533	C₂	semidirect
8. C₂²×C₄×Q₈×C₁₉	C₂	semidirect
11. Q₈²×C₁₉	C₂²	semidirect
12. C₁₉×#557	C₂²	semidirect
13. C₁₉×#554	C₂²	semidirect
14. D₄×Q₈×C₁₉	C₂²	semidirect
15. C₁₉×#533	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
35. C₂×#41×C₁₉	Q₈	direct (N × H)
76. #41×C₁₉	C₂×Q₈	direct (N × H)
80. C₂×Q₈×C₁₉	C₂×Q₈	semidirect
81. C₂×Q₈×C₁₉	#41	direct (N × H)
86. C₂×D₄×C₁₉	C₂×Q₈	semidirect
90. C₂²×C₄×C₁₉	C₂×Q₈	semidirect
111. C₂×Q₈×#41	C₁₉	direct (N × H)
119. Q₈×C₁₉	C₂²×Q₈	semidirect
120. Q₈×C₁₉	C₂×#41	direct (N × H)
121. D₄×C₁₉	C₂²×Q₈	semidirect
129. C₂×C₄×C₁₉	C₂²×Q₈	semidirect
137. Q₈×#41	C₂×C₁₉	direct (N × H)
138. C₂×Q₈²	C₂×C₁₉	semidirect
139. C₂×#557	C₂×C₁₉	semidirect
140. C₂×#554	C₂×C₁₉	semidirect
141. C₂×D₄×Q₈	C₂×C₁₉	semidirect
142. C₂×#533	C₂×C₁₉	semidirect
144. C₂²×C₄×Q₈	C₂×C₁₉	semidirect
161. Q₈²	C₂²×C₁₉	semidirect
162. #557	C₂²×C₁₉	semidirect
163. #554	C₂²×C₁₉	semidirect
164. D₄×Q₈	C₂²×C₁₉	semidirect
165. #533	C₂²×C₁₉	semidirect
179. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
186. C₂×C₁₉	Q₈×#41	direct (N × H)
190. C₂×#41	Q₈×C₁₉	direct (N × H)
230. C₁₉	C₂×Q₈×#41	direct (N × H)
232. #41	C₂×Q₈×C₁₉	direct (N × H)
236. C₂×Q₈	C₂×Q₈×C₁₉	semidirect
237. C₂×Q₈	#41×C₁₉	direct (N × H)
242. C₂×D₄	C₂×Q₈×C₁₉	semidirect
246. C₂²×C₄	C₂×Q₈×C₁₉	semidirect
274. Q₈	C₂²×Q₈×C₁₉	semidirect
275. Q₈	C₂×#41×C₁₉	direct (N × H)
276. D₄	C₂²×Q₈×C₁₉	semidirect
284. C₂×C₄	C₂²×Q₈×C₁₉	semidirect
307. C₂	Q₈×#41×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×#41×C₁₉	2
C₂×Q₈²×C₁₉	2
C₂×C₁₉×#557	2
C₂×C₁₉×#554	2
C₂×D₄×Q₈×C₁₉	2
C₂×C₁₉×#533	2
C₂×C₄×#41×C₁₉	2
C₂²×C₄×Q₈×C₁₉	2
C₂×Q₈×#41	19

Subgroups — C2×Q8×#41×C19 #18068672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#41×C₁₉ #18068672