Subgroups — C₁₉×#34129 #18040088

Order 4864.

2610 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2354	C₂	1	6	yes	maximal, complemented
3	Q₈×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2346	C₂	1	6	yes	maximal, complemented
5	C₁₉×#2341	C₂	1	2	yes	maximal
6	C₁₉×#2293	C₂	1	6	yes	maximal, complemented
7	C₁₉×#2285	C₂	1	3	yes	maximal, complemented
8	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×#117	C₂	1	3	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₄×#41×C₁₉	C₄	1	16	yes	complemented
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
17	C₂×C₁₉×#117	C₂²	1	6	yes	—
18	C₂×C₁₉×#117	C₂²	1	6	yes	—
19	C₂×C₁₉×#117	C₂²	1	3	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
21	C₁₉×#390	C₂²	1	12	yes	—
22	C₁₉×#389	C₂²	1	12	yes	—
23	C₁₉×#388	C₂²	1	24	yes	—
24	C₁₉×#384	C₂²	1	6	yes	—
25	C₁₉×#382	C₂²	1	6	yes	—
26	C₁₉×#380	C₂²	1	6	yes	—
27	C₁₉×#380	C₂²	1	6	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	12	yes	—
33	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
35	C₁₉×#376	C₂²	1	6	yes	—
36	C₄³×C₁₉	C₂²	1	6	yes	—
37	C₂×#41×C₁₉	—	2	8	no	—
38	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
39	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
44	C₄×Q₈×C₁₉	—	2	16	no	—
45	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
46	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
47	C₄×D₄×C₁₉	C₂×C₄	1	24	yes	—
48	C₄×D₄×C₁₉	C₂×C₄	1	24	yes	—
49	C₁₉×#117	—	2	24	no	—
50	C₁₉×#117	—	4	12	no	—
51	C₁₉×#117	C₂×C₄	1	24	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
60	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
61	C₂×C₄²×C₁₉	C₂×C₄	1	24	yes	—
62	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
63	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
64	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×#95	C₂³	1	2	yes	—
71	C₁₉×#95	C₂³	1	6	yes	—
72	C₁₉×#95	C₂³	1	12	yes	—
73	C₁₉×#95	C₂³	1	12	yes	—
74	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
75	#41×C₁₉	—	2	32	no	—
76	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
77	C₂×Q₈×C₁₉	#41	1	8	yes	—
78	C₂×D₄×C₁₉	—	2	12	no	—
79	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
80	C₂²×C₄×C₁₉	—	2	12	no	—
81	C₂²×C₄×C₁₉	—	2	12	no	—
82	C₂²×C₄×C₁₉	—	2	6	no	—
83	C₂²×C₄×C₁₉	—	2	6	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
86	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
87	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
88	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
89	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
95	C₄⋊C₄×C₁₉	—	2	12	no	—
96	C₄⋊C₄×C₁₉	—	2	24	no	—
97	C₄⋊C₄×C₁₉	—	4	12	no	—
98	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
99	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
100	C₄⋊C₄×C₁₉	#41	1	8	yes	complemented
101	C₂²⋊C₄×C₁₉	—	2	24	no	—
102	C₂²⋊C₄×C₁₉	—	4	12	no	—
103	C₂²⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
104	C₄²×C₁₉	—	2	24	no	—
105	C₄²×C₁₉	—	2	24	no	—
106	C₄²×C₁₉	—	2	12	no	—
107	C₄²×C₁₉	—	2	4	no	—
108	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
109	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
110	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
111	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
112	#34129	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂³×C₁₉	—	2	6	no	—
114	C₂³×C₁₉	—	2	6	no	—
115	C₂³×C₁₉	—	2	3	no	—
116	C₂³×C₁₉	—	2	3	no	—
117	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
118	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
119	Q₈×C₁₉	#117	1	16	yes	complemented
120	D₄×C₁₉	—	2	24	no	—
121	C₂×C₄×C₁₉	—	2	4	no	—
122	C₂×C₄×C₁₉	—	2	6	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	3	no	—
125	C₂×C₄×C₁₉	—	2	4	no	—
126	C₂×C₄×C₁₉	—	2	3	no	—
127	C₂×C₄×C₁₉	—	2	24	no	—
128	C₂×C₄×C₁₉	—	2	24	no	—
129	C₂×C₄×C₁₉	—	2	24	no	—
130	C₂×C₄×C₁₉	—	2	12	no	—
131	C₂×C₄×C₁₉	—	2	12	no	—
132	C₂×C₄×C₁₉	—	2	12	no	—
133	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
134	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
135	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
136	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
137	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
138	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
139	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
140	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
141	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
142	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
143	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
144	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
145	#2354	C₂×C₁₉	1	6	yes	complemented
146	Q₈×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
147	#2346	C₂×C₁₉	1	6	yes	complemented
148	#2341	C₂×C₁₉	1	2	yes	—
149	#2293	C₂×C₁₉	1	6	yes	complemented
150	#2285	C₂×C₁₉	1	3	yes	complemented
151	C₄²×Q₈	C₂×C₁₉	1	2	yes	complemented
152	C₄×#117	C₂×C₁₉	1	3	yes	complemented
153	C₂²×C₁₉	—	2	6	no	—
154	C₂²×C₁₉	—	2	6	no	—
155	C₂²×C₁₉	—	2	6	no	—
156	C₂²×C₁₉	—	4	6	no	—
157	C₂²×C₁₉	—	4	6	no	—
158	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
159	C₂²×C₁₉	C₂²×#41	1	2	yes	—
160	C₂²×C₁₉	C₂²×#41	1	2	yes	—
161	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
163	C₄×C₁₉	—	2	2	no	—
164	C₄×C₁₉	—	2	6	no	—
165	C₄×C₁₉	—	2	6	no	—
166	C₄×C₁₉	—	2	8	no	—
167	C₄×C₁₉	—	4	12	no	—
168	C₄×C₁₉	C₂×#117	1	12	yes	—
169	C₄×C₁₉	C₄×#41	1	4	yes	—
170	C₄×C₁₉	#520	1	4	yes	—
171	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
172	C₄×#41	C₄×C₁₉	1	16	yes	complemented
173	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
174	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
175	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
177	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
178	C₂×#117	C₂²×C₁₉	1	6	yes	—
179	C₂×#117	C₂²×C₁₉	1	6	yes	—
180	C₂×#117	C₂²×C₁₉	1	3	yes	—
181	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
182	#390	C₂²×C₁₉	1	12	yes	—
183	#389	C₂²×C₁₉	1	12	yes	—
184	#388	C₂²×C₁₉	1	24	yes	—
185	#384	C₂²×C₁₉	1	6	yes	—
186	#382	C₂²×C₁₉	1	6	yes	—
187	#380	C₂²×C₁₉	1	6	yes	—
188	#380	C₂²×C₁₉	1	6	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₉	1	12	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
191	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
193	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
194	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
195	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
196	#376	C₂²×C₁₉	1	6	yes	—
197	C₄³	C₂²×C₁₉	1	6	yes	—
198	C₂×C₁₉	—	4	6	no	—
199	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
200	C₂×C₁₉	C₂×C₄×#41	1	1	yes	characteristic
201	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
202	C₂×C₁₉	#3482	1	2	yes	—
203	C₂×C₁₉	#3483	1	2	yes	—
204	C₂×#41	—	2	8	no	—
205	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
206	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
208	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
209	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
210	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
211	C₄×Q₈	—	2	16	no	—
212	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
213	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
214	C₄×D₄	C₂×C₄×C₁₉	1	24	yes	—
215	C₄×D₄	C₂×C₄×C₁₉	1	24	yes	—
216	#117	—	2	24	no	—
217	#117	—	4	12	no	—
218	#117	C₂×C₄×C₁₉	1	24	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
226	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
228	C₂×C₄²	C₂×C₄×C₁₉	1	24	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
230	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
231	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
232	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
233	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
234	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
235	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
236	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
237	#95	C₂³×C₁₉	1	2	yes	—
238	#95	C₂³×C₁₉	1	6	yes	—
239	#95	C₂³×C₁₉	1	12	yes	—
240	#95	C₂³×C₁₉	1	12	yes	—
241	C₁₉	#34129	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
243	#41	—	2	32	no	—
244	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
245	C₂×Q₈	#41×C₁₉	1	8	yes	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
248	C₂²×C₄	—	2	12	no	—
249	C₂²×C₄	—	2	12	no	—
250	C₂²×C₄	—	2	6	no	—
251	C₂²×C₄	—	2	6	no	—
252	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
255	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
256	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
257	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
258	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
259	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
260	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
261	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
262	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
263	C₄⋊C₄	—	2	12	no	—
264	C₄⋊C₄	—	2	24	no	—
265	C₄⋊C₄	—	4	12	no	—
266	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
267	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
268	C₄⋊C₄	#41×C₁₉	1	8	yes	complemented
269	C₂²⋊C₄	—	2	24	no	—
270	C₂²⋊C₄	—	4	12	no	—
271	C₂²⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
272	C₄²	—	2	24	no	—
273	C₄²	—	2	24	no	—
274	C₄²	—	2	12	no	—
275	C₄²	—	2	4	no	—
276	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
277	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
278	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
279	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
280	C₂³	—	2	6	no	—
281	C₂³	—	2	6	no	—
282	C₂³	—	2	3	no	—
283	C₂³	—	2	3	no	—
284	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
285	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
286	Q₈	C₁₉×#117	1	16	yes	complemented
287	D₄	—	2	24	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	6	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	3	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	3	no	—
294	C₂×C₄	—	2	24	no	—
295	C₂×C₄	—	2	24	no	—
296	C₂×C₄	—	2	24	no	—
297	C₂×C₄	—	2	12	no	—
298	C₂×C₄	—	2	12	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
301	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
302	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
303	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
304	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
305	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
306	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
307	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
308	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
309	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
310	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
311	C₂²	—	2	6	no	—
312	C₂²	—	2	6	no	—
313	C₂²	—	2	6	no	—
314	C₂²	—	4	6	no	—
315	C₂²	—	4	6	no	—
316	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
317	C₂²	C₂²×#41×C₁₉	1	2	yes	—
318	C₂²	C₂²×#41×C₁₉	1	2	yes	—
319	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
320	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
321	C₄	—	2	6	no	—
322	C₄	—	2	6	no	—
323	C₄	—	2	8	no	—
324	C₄	—	2	2	no	—
325	C₄	—	4	12	no	—
326	C₄	C₂×C₁₉×#117	1	12	yes	—
327	C₄	C₄×#41×C₁₉	1	4	yes	—
328	C₄	C₁₉×#520	1	4	yes	—
329	C₂	—	4	6	no	—
330	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
331	C₂	C₂×C₄×#41×C₁₉	1	1	yes	characteristic
332	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
333	C₂	C₁₉×#3482	1	2	yes	—
334	C₂	C₁₉×#3483	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×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
2. C₁₉×#2354	C₂	semidirect
3. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
4. C₁₉×#2346	C₂	semidirect
6. C₁₉×#2293	C₂	semidirect
7. C₁₉×#2285	C₂	semidirect
8. C₄²×Q₈×C₁₉	C₂	semidirect
9. C₄×C₁₉×#117	C₂	semidirect
11. C₄×#41×C₁₉	C₄	semidirect
100. C₄⋊C₄×C₁₉	#41	semidirect
112. #34129	C₁₉	direct (N × H)
119. Q₈×C₁₉	#117	semidirect
145. #2354	C₂×C₁₉	semidirect
146. Q₈×C₄⋊C₄	C₂×C₁₉	semidirect
147. #2346	C₂×C₁₉	semidirect
149. #2293	C₂×C₁₉	semidirect
150. #2285	C₂×C₁₉	semidirect
151. C₄²×Q₈	C₂×C₁₉	semidirect
152. C₄×#117	C₂×C₁₉	semidirect
172. C₄×#41	C₄×C₁₉	semidirect
241. C₁₉	#34129	direct (N × H)
268. C₄⋊C₄	#41×C₁₉	semidirect
286. Q₈	C₁₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₁₉×#2354	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2346	2
C₁₉×#2341	2
C₁₉×#2293	2
C₁₉×#2285	2
C₄²×Q₈×C₁₉	2
C₄×C₁₉×#117	2
#34129	19

Subgroups — C19×#34129 #18040088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34129 #18040088