Subgroups — C₁₉×#34172 #18040131

Order 4864.

5430 conjugacy classes of subgroups.

The subgroup lattice has 326 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	C₂×C₁₉×#518	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2339	C₂	1	16	yes	maximal, complemented
4	C₁₉×#2310	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2308	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2280	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#381	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₉	—	2	16	no	—
9	C₂²×#41×C₁₉	C₄	1	16	yes	complemented
10	C₂²×#41×C₁₉	C₂²	1	8	yes	—
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#518	—	2	16	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	16	yes	complemented
18	C₂×C₁₉×#117	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
20	C₁₉×#391	C₂²	1	16	yes	complemented
21	C₁₉×#386	C₂²	1	32	yes	complemented
22	C₁₉×#381	C₂²	1	4	yes	—
23	C₁₉×#381	C₂²	1	8	yes	—
24	C₁₉×#381	C₂²	1	16	yes	complemented
25	C₁₉×#380	C₂²	1	8	yes	complemented
26	C₁₉×#379	C₂²	1	4	yes	—
27	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
28	C₂×C₁₉×#95	C₂²	1	16	yes	complemented
29	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
30	C₂⁵×C₁₉	C₂³	1	2	yes	—
31	C₂×#41×C₁₉	—	2	128	no	—
32	C₂×#41×C₁₉	—	2	64	no	—
33	C₂×#41×C₁₉	C₂×C₄	1	64	yes	complemented
34	C₂²×Q₈×C₁₉	—	2	8	no	—
35	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
36	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
37	C₂²×D₄×C₁₉	—	2	16	no	—
38	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	16	yes	complemented
40	C₂²×D₄×C₁₉	D₄	1	16	yes	—
41	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
42	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₉	—	2	16	no	—
44	C₂³×C₄×C₁₉	—	2	8	no	—
45	C₂³×C₄×C₁₉	C₂×C₄	1	16	yes	complemented
46	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	complemented
47	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	16	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₉	—	2	64	no	—
54	C₁₉×#117	—	2	16	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	32	no	—
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
58	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
59	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
60	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
61	C₁₉×#95	C₂³	1	16	yes	—
62	C₁₉×#95	C₂³	1	32	yes	—
63	C₂⁴×C₁₉	—	2	4	no	—
64	C₂⁴×C₁₉	—	4	8	no	—
65	C₂⁴×C₁₉	—	4	4	no	—
66	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
67	C₂⁴×C₁₉	C₂²×C₄	1	8	yes	—
68	C₂⁴×C₁₉	C₂×D₄	1	16	yes	—
69	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
70	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
71	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
72	#41×C₁₉	—	2	256	no	—
73	C₂×Q₈×C₁₉	—	2	32	no	—
74	C₂×Q₈×C₁₉	—	2	16	no	—
75	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
76	C₂×D₄×C₁₉	—	2	64	no	—
77	C₂×D₄×C₁₉	—	2	32	no	—
78	C₂×D₄×C₁₉	C₂²⋊C₄	1	64	yes	complemented
79	C₂×D₄×C₁₉	C₂²×C₄	1	32	yes	—
80	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
81	C₂×D₄×C₁₉	C₂×D₄	1	32	yes	—
82	C₂²×C₄×C₁₉	—	2	64	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	8	no	—
85	C₂²×C₄×C₁₉	—	2	32	no	—
86	C₂²×C₄×C₁₉	—	2	32	no	—
87	C₂²×C₄×C₁₉	—	2	16	no	—
88	C₂²×C₄×C₁₉	—	2	32	no	—
89	C₂²×C₄×C₁₉	—	4	32	no	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	32	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₉	C₂⁴	1	16	yes	—
97	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
100	C₄⋊C₄×C₁₉	—	2	16	no	—
101	C₂²⋊C₄×C₁₉	—	2	16	no	—
102	C₂²⋊C₄×C₁₉	—	2	32	no	—
103	C₂²⋊C₄×C₁₉	—	4	16	no	—
104	C₄²×C₁₉	—	2	16	no	—
105	#34172	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₉	—	2	16	no	—
107	C₂³×C₁₉	—	2	4	no	—
108	C₂³×C₁₉	—	2	8	no	—
109	C₂³×C₁₉	—	2	4	no	—
110	C₂³×C₁₉	—	2	8	no	—
111	C₂³×C₁₉	—	4	16	no	—
112	C₂³×C₁₉	—	4	8	no	—
113	C₂³×C₁₉	—	4	32	no	—
114	C₂³×C₁₉	—	4	16	no	—
115	C₂³×C₁₉	C₂×C₂²⋊C₄	1	32	yes	—
116	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
117	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
118	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
119	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
120	C₂³×C₁₉	C₂²×D₄	1	16	yes	—
121	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	32	no	—
123	D₄×C₁₉	—	2	64	no	—
124	D₄×C₁₉	C₂×C₂²⋊C₄	1	64	yes	—
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	2	16	no	—
127	C₂×C₄×C₁₉	—	2	64	no	—
128	C₂×C₄×C₁₉	—	2	4	no	—
129	C₂×C₄×C₁₉	—	2	8	no	—
130	C₂×C₄×C₁₉	—	2	32	no	—
131	C₂×C₄×C₁₉	—	2	16	no	—
132	C₂×C₄×C₁₉	—	2	32	no	—
133	C₂×C₄×C₁₉	—	8	32	no	—
134	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	16	yes	—
135	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
136	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
137	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
138	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
139	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic
140	C₂×#518	C₂×C₁₉	1	2	yes	complemented
141	#2339	C₂×C₁₉	1	16	yes	complemented
142	#2310	C₂×C₁₉	1	2	yes	complemented
143	#2308	C₂×C₁₉	1	4	yes	complemented
144	#2280	C₂×C₁₉	1	2	yes	complemented
145	C₂×#381	C₂×C₁₉	1	4	yes	complemented
146	C₂²×C₁₉	—	2	4	no	—
147	C₂²×C₁₉	—	2	16	no	—
148	C₂²×C₁₉	—	2	32	no	—
149	C₂²×C₁₉	—	2	8	no	—
150	C₂²×C₁₉	—	2	4	no	—
151	C₂²×C₁₉	—	2	8	no	—
152	C₂²×C₁₉	—	4	32	no	—
153	C₂²×C₁₉	—	4	16	no	—
154	C₂²×C₁₉	—	4	8	no	—
155	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	4	yes	—
156	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	16	yes	—
157	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
158	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
159	C₂²×C₁₉	#585	1	4	yes	—
160	C₄×C₁₉	—	2	4	no	—
161	C₄×C₁₉	—	2	8	no	—
162	C₄×C₁₉	—	4	16	no	—
163	C₄×C₁₉	C₂²×C₂²⋊C₄	1	8	yes	—
164	C₂²×#41	—	2	16	no	—
165	C₂²×#41	C₄×C₁₉	1	16	yes	complemented
166	C₂²×#41	C₂²×C₁₉	1	8	yes	—
167	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
168	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
169	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
170	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
171	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
172	#518	—	2	16	no	—
173	C₂×C₄×D₄	C₂²×C₁₉	1	16	yes	complemented
174	C₂×#117	C₂²×C₁₉	1	4	yes	—
175	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
176	#391	C₂²×C₁₉	1	16	yes	complemented
177	#386	C₂²×C₁₉	1	32	yes	complemented
178	#381	C₂²×C₁₉	1	8	yes	—
179	#381	C₂²×C₁₉	1	4	yes	—
180	#381	C₂²×C₁₉	1	16	yes	complemented
181	#380	C₂²×C₁₉	1	8	yes	complemented
182	#379	C₂²×C₁₉	1	4	yes	—
183	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
184	C₂×#95	C₂²×C₁₉	1	16	yes	complemented
185	C₂×C₁₉	—	2	4	no	—
186	C₂×C₁₉	—	2	16	no	—
187	C₂×C₁₉	—	4	4	no	—
188	C₂×C₁₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₁₉	#3428	1	2	yes	—
190	C₂×C₁₉	#3485	1	4	yes	—
191	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
192	C₂⁵	C₂³×C₁₉	1	2	yes	—
193	C₂×#41	—	2	128	no	—
194	C₂×#41	—	2	64	no	—
195	C₂×#41	C₂×C₄×C₁₉	1	64	yes	complemented
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
198	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
199	C₂²×D₄	—	2	16	no	—
200	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
201	C₂²×D₄	C₂×C₄×C₁₉	1	16	yes	complemented
202	C₂²×D₄	D₄×C₁₉	1	16	yes	—
203	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
204	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
205	C₂³×C₄	—	2	16	no	—
206	C₂³×C₄	—	2	8	no	—
207	C₂³×C₄	C₂×C₄×C₁₉	1	16	yes	complemented
208	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	complemented
209	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
211	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
212	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
213	C₂³×C₄	C₂³×C₁₉	1	16	yes	—
214	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
215	C₄×D₄	—	2	64	no	—
216	#117	—	2	16	no	—
217	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
218	C₂×C₂²⋊C₄	—	2	32	no	—
219	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
221	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
222	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
223	#95	C₂³×C₁₉	1	16	yes	—
224	#95	C₂³×C₁₉	1	32	yes	—
225	C₁₉	#34172	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁴	—	2	4	no	—
227	C₂⁴	—	4	8	no	—
228	C₂⁴	—	4	4	no	—
229	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
230	C₂⁴	C₂²×C₄×C₁₉	1	8	yes	—
231	C₂⁴	C₂×D₄×C₁₉	1	16	yes	—
232	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
233	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
234	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
235	#41	—	2	256	no	—
236	C₂×Q₈	—	2	32	no	—
237	C₂×Q₈	—	2	16	no	—
238	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
239	C₂×D₄	—	2	64	no	—
240	C₂×D₄	—	2	32	no	—
241	C₂×D₄	C₂²⋊C₄×C₁₉	1	64	yes	complemented
242	C₂×D₄	C₂²×C₄×C₁₉	1	32	yes	—
243	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
244	C₂×D₄	C₂×D₄×C₁₉	1	32	yes	—
245	C₂²×C₄	—	2	64	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	32	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	32	no	—
252	C₂²×C₄	—	4	32	no	—
253	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₉	1	32	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
257	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
258	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
259	C₂²×C₄	C₂⁴×C₁₉	1	16	yes	—
260	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
261	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
262	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
263	C₄⋊C₄	—	2	16	no	—
264	C₂²⋊C₄	—	2	16	no	—
265	C₂²⋊C₄	—	2	32	no	—
266	C₂²⋊C₄	—	4	16	no	—
267	C₄²	—	2	16	no	—
268	C₂³	—	2	16	no	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	2	4	no	—
272	C₂³	—	2	8	no	—
273	C₂³	—	4	16	no	—
274	C₂³	—	4	8	no	—
275	C₂³	—	4	32	no	—
276	C₂³	—	4	16	no	—
277	C₂³	C₂×C₂²⋊C₄×C₁₉	1	32	yes	—
278	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
279	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
280	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
281	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
282	C₂³	C₂²×D₄×C₁₉	1	16	yes	—
283	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
284	Q₈	—	2	32	no	—
285	D₄	—	2	64	no	—
286	D₄	C₂×C₂²⋊C₄×C₁₉	1	64	yes	—
287	C₂×C₄	—	2	8	no	—
288	C₂×C₄	—	2	16	no	—
289	C₂×C₄	—	2	64	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	32	no	—
293	C₂×C₄	—	2	16	no	—
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	8	32	no	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	16	yes	—
297	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
298	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
299	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
300	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	16	no	—
303	C₂²	—	2	32	no	—
304	C₂²	—	2	8	no	—
305	C₂²	—	2	8	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	4	32	no	—
308	C₂²	—	4	16	no	—
309	C₂²	—	4	8	no	—
310	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	4	yes	—
311	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	16	yes	—
312	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
313	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
314	C₂²	C₁₉×#585	1	4	yes	—
315	C₄	—	2	4	no	—
316	C₄	—	2	8	no	—
317	C₄	—	4	16	no	—
318	C₄	C₂²×C₂²⋊C₄×C₁₉	1	8	yes	—
319	C₂	—	2	4	no	—
320	C₂	—	2	16	no	—
321	C₂	—	4	4	no	—
322	C₂	C₂³×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
323	C₂	C₁₉×#3428	1	2	yes	—
324	C₂	C₁₉×#3485	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×#41×C₁₉	C₂
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
2. C₂×C₁₉×#518	C₂	semidirect
3. C₁₉×#2339	C₂	semidirect
4. C₁₉×#2310	C₂	semidirect
5. C₁₉×#2308	C₂	semidirect
6. C₁₉×#2280	C₂	semidirect
7. C₂×C₁₉×#381	C₂	semidirect
9. C₂²×#41×C₁₉	C₄	semidirect
17. C₂×C₄×D₄×C₁₉	C₂²	semidirect
20. C₁₉×#391	C₂²	semidirect
21. C₁₉×#386	C₂²	semidirect
24. C₁₉×#381	C₂²	semidirect
25. C₁₉×#380	C₂²	semidirect
27. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
28. C₂×C₁₉×#95	C₂²	semidirect
33. C₂×#41×C₁₉	C₂×C₄	semidirect
35. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
39. C₂²×D₄×C₁₉	C₂×C₄	semidirect
45. C₂³×C₄×C₁₉	C₂×C₄	semidirect
46. C₂³×C₄×C₁₉	C₂×C₄	semidirect
78. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
105. #34172	C₁₉	direct (N × H)
140. C₂×#518	C₂×C₁₉	semidirect
141. #2339	C₂×C₁₉	semidirect
142. #2310	C₂×C₁₉	semidirect
143. #2308	C₂×C₁₉	semidirect
144. #2280	C₂×C₁₉	semidirect
145. C₂×#381	C₂×C₁₉	semidirect
165. C₂²×#41	C₄×C₁₉	semidirect
173. C₂×C₄×D₄	C₂²×C₁₉	semidirect
176. #391	C₂²×C₁₉	semidirect
177. #386	C₂²×C₁₉	semidirect
180. #381	C₂²×C₁₉	semidirect
181. #380	C₂²×C₁₉	semidirect
183. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
184. C₂×#95	C₂²×C₁₉	semidirect
195. C₂×#41	C₂×C₄×C₁₉	semidirect
197. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
201. C₂²×D₄	C₂×C₄×C₁₉	semidirect
207. C₂³×C₄	C₂×C₄×C₁₉	semidirect
208. C₂³×C₄	C₂×C₄×C₁₉	semidirect
225. C₁₉	#34172	direct (N × H)
241. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect

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
C₂×C₁₉×#518	2
C₁₉×#2339	2
C₁₉×#2310	2
C₁₉×#2308	2
C₁₉×#2280	2
C₂×C₁₉×#381	2
#34172	19

Subgroups — C19×#34172 #18040131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34172 #18040131