Subgroups — C₁₉×#60070 #18066029

Order 4864.

4892 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3428	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2884	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2883	C₂	1	12	yes	maximal, complemented
5	C₂×C₁₉×#410	C₂	1	12	yes	maximal, complemented
6	C₁₉×#585	—	2	8	no	—
7	C₁₉×#585	—	2	8	no	—
8	C₂×C₁₉×2₋¹⁺⁴	C₄	1	4	yes	complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	2	yes	—
10	C₂×C₁₉×H(5,𝔽₂)	C₄	1	4	yes	complemented
11	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	6	yes	—
12	C₂²×#41×C₁₉	C₄	1	8	yes	complemented
13	C₂²×#41×C₁₉	C₂²	1	6	yes	—
14	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#520	—	2	8	no	—
16	C₁₉×#519	C₂²	1	4	yes	complemented
17	C₁₉×#518	C₂²	1	12	yes	complemented
18	C₄×#41×C₁₉	—	2	8	no	—
19	C₂×C₁₉×#117	C₂²	1	12	yes	complemented
20	C₁₉×#410	C₂²	1	16	yes	complemented
21	C₁₉×#410	C₂²	1	48	yes	complemented
22	C₂×C₁₉×#99	C₂²	1	48	yes	complemented
23	C₁₉×2₋¹⁺⁴	—	2	32	no	—
24	C₁₉×2₋¹⁺⁴	—	2	16	no	—
25	C₁₉×H(5,𝔽₂)	—	2	32	no	—
26	C₁₉×H(5,𝔽₂)	—	2	48	no	—
27	C₂×#41×C₁₉	—	2	32	no	—
28	C₂×#41×C₁₉	—	2	32	no	—
29	C₂×#41×C₁₉	—	2	24	no	—
30	C₂×#41×C₁₉	—	2	24	no	—
31	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
32	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
33	C₂×#41×C₁₉	C₂×C₄	1	12	yes	complemented
34	C₂×#41×C₁₉	C₂×C₄	1	8	yes	complemented
35	C₂×#41×C₁₉	C₂×C₄	1	24	yes	complemented
36	C₂×#41×C₁₉	C₂×C₄	1	12	yes	complemented
37	C₂×#41×C₁₉	D₄	1	8	yes	—
38	C₂×#41×C₁₉	D₄	1	8	yes	—
39	C₂×#41×C₁₉	C₂³	1	4	yes	—
40	C₂×#41×C₁₉	C₂³	1	12	yes	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
42	C₂²×Q₈×C₁₉	C₂×C₄	1	6	yes	complemented
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	C₂×C₄	1	24	yes	complemented
45	C₂²×D₄×C₁₉	C₂×C₄	1	6	yes	complemented
46	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
47	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	12	yes	complemented
49	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
50	C₄×Q₈×C₁₉	—	2	16	no	—
51	C₄×D₄×C₁₉	—	2	48	no	—
52	C₁₉×#117	—	2	12	no	—
53	C₁₉×#117	—	2	12	no	—
54	C₁₉×#117	C₂³	1	8	yes	—
55	C₁₉×#117	C₂³	1	24	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	12	no	—
57	C₂×C₂²⋊C₄×C₁₉	C₂³	1	24	yes	—
58	C₂×C₄²×C₁₉	—	2	12	no	—
59	C₁₉×#99	C₂³	1	64	yes	—
60	C₂⁴×C₁₉	C₂²×C₄	1	12	yes	—
61	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
62	#41×C₁₉	—	2	32	no	—
63	#41×C₁₉	—	2	96	no	—
64	#41×C₁₉	—	2	24	no	—
65	#41×C₁₉	—	2	24	no	—
66	#41×C₁₉	—	2	48	no	—
67	#41×C₁₉	—	2	8	no	—
68	#41×C₁₉	—	2	8	no	—
69	#41×C₁₉	—	2	48	no	—
70	#41×C₁₉	C₂²⋊C₄	1	16	yes	—
71	#41×C₁₉	C₂²⋊C₄	1	16	yes	—
72	#41×C₁₉	C₂²⋊C₄	1	32	yes	—
73	C₂×Q₈×C₁₉	—	2	32	no	—
74	C₂×Q₈×C₁₉	—	2	24	no	—
75	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
76	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
77	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
78	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
79	C₂×D₄×C₁₉	—	2	48	no	—
80	C₂×D₄×C₁₉	—	2	96	no	—
81	C₂×D₄×C₁₉	—	2	24	no	—
82	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
83	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₁₉	C₂²×C₄	1	24	yes	—
85	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
86	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	—
87	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₁₉	—	2	24	no	—
89	C₂²×C₄×C₁₉	—	2	24	no	—
90	C₂²×C₄×C₁₉	—	2	24	no	—
91	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	24	yes	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
100	C₄⋊C₄×C₁₉	—	2	8	no	—
101	C₄⋊C₄×C₁₉	—	2	24	no	—
102	C₂²⋊C₄×C₁₉	—	2	24	no	—
103	C₂²⋊C₄×C₁₉	C₂⁴	1	16	yes	—
104	C₄²×C₁₉	—	2	8	no	—
105	C₄²×C₁₉	—	2	24	no	—
106	#60070	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₁₉	—	2	24	no	—
108	C₂³×C₁₉	—	8	3	no	—
109	C₂³×C₁₉	—	8	12	no	—
110	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
111	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
112	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
113	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
114	Q₈×C₁₉	—	2	24	no	—
115	Q₈×C₁₉	—	2	8	no	—
116	Q₈×C₁₉	C₂×C₂²⋊C₄	1	16	yes	—
117	D₄×C₁₉	—	2	48	no	—
118	D₄×C₁₉	—	2	16	no	—
119	D₄×C₁₉	—	2	24	no	—
120	D₄×C₁₉	—	2	8	no	—
121	D₄×C₁₉	C₂×C₂²⋊C₄	1	48	yes	—
122	C₂×C₄×C₁₉	—	2	24	no	—
123	C₂×C₄×C₁₉	—	2	8	no	—
124	C₂×C₄×C₁₉	—	2	48	no	—
125	C₂×C₄×C₁₉	—	2	8	no	—
126	C₂×C₄×C₁₉	—	2	16	no	—
127	C₂×C₄×C₁₉	—	8	24	no	—
128	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
129	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	24	yes	—
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	12	yes	—
131	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
132	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
133	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
136	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
137	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
138	C₂×#585	C₂×C₁₉	1	1	yes	characteristic
139	#3428	C₂×C₁₉	1	2	yes	complemented
140	#2884	C₂×C₁₉	1	4	yes	complemented
141	#2883	C₂×C₁₉	1	12	yes	complemented
142	C₂×#410	C₂×C₁₉	1	12	yes	complemented
143	C₂²×C₁₉	—	2	8	no	—
144	C₂²×C₁₉	—	4	12	no	—
145	C₂²×C₁₉	—	4	6	no	—
146	C₂²×C₁₉	—	4	1	no	—
147	C₂²×C₁₉	—	4	8	no	—
148	C₂²×C₁₉	—	8	24	no	—
149	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	12	yes	—
150	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
151	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
152	C₄×C₁₉	—	2	8	no	—
153	C₄×C₁₉	—	4	16	no	—
154	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₄×C₁₉	C₂²×C₂²⋊C₄	1	12	yes	—
156	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
157	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
158	#585	—	2	8	no	—
159	#585	—	2	8	no	—
160	C₂×2₋¹⁺⁴	C₄×C₁₉	1	4	yes	complemented
161	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	2	yes	—
162	C₂×H(5,𝔽₂)	C₄×C₁₉	1	4	yes	complemented
163	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	6	yes	—
164	C₂²×#41	C₄×C₁₉	1	8	yes	complemented
165	C₂²×#41	C₂²×C₁₉	1	6	yes	—
166	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
167	#520	—	2	8	no	—
168	#519	C₂²×C₁₉	1	4	yes	complemented
169	#518	C₂²×C₁₉	1	12	yes	complemented
170	C₄×#41	—	2	8	no	—
171	C₂×#117	C₂²×C₁₉	1	12	yes	complemented
172	#410	C₂²×C₁₉	1	16	yes	complemented
173	#410	C₂²×C₁₉	1	48	yes	complemented
174	C₂×#99	C₂²×C₁₉	1	48	yes	complemented
175	C₂×C₁₉	—	2	2	no	—
176	C₂×C₁₉	—	2	1	no	—
177	C₂×C₁₉	—	2	12	no	—
178	C₂×C₁₉	—	4	8	no	—
179	C₂×C₁₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
180	2₋¹⁺⁴	—	2	32	no	—
181	2₋¹⁺⁴	—	2	16	no	—
182	H(5,𝔽₂)	—	2	32	no	—
183	H(5,𝔽₂)	—	2	48	no	—
184	C₂×#41	—	2	32	no	—
185	C₂×#41	—	2	32	no	—
186	C₂×#41	—	2	24	no	—
187	C₂×#41	—	2	24	no	—
188	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
189	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
190	C₂×#41	C₂×C₄×C₁₉	1	12	yes	complemented
191	C₂×#41	C₂×C₄×C₁₉	1	8	yes	complemented
192	C₂×#41	C₂×C₄×C₁₉	1	24	yes	complemented
193	C₂×#41	C₂×C₄×C₁₉	1	12	yes	complemented
194	C₂×#41	D₄×C₁₉	1	8	yes	—
195	C₂×#41	D₄×C₁₉	1	8	yes	—
196	C₂×#41	C₂³×C₁₉	1	4	yes	—
197	C₂×#41	C₂³×C₁₉	1	12	yes	—
198	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
199	C₂²×Q₈	C₂×C₄×C₁₉	1	6	yes	complemented
200	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
201	C₂²×D₄	C₂×C₄×C₁₉	1	24	yes	complemented
202	C₂²×D₄	C₂×C₄×C₁₉	1	6	yes	complemented
203	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
204	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
205	C₂³×C₄	C₂×C₄×C₁₉	1	12	yes	complemented
206	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
207	C₄×Q₈	—	2	16	no	—
208	C₄×D₄	—	2	48	no	—
209	#117	—	2	12	no	—
210	#117	—	2	12	no	—
211	#117	C₂³×C₁₉	1	8	yes	—
212	#117	C₂³×C₁₉	1	24	yes	—
213	C₂×C₄⋊C₄	—	2	12	no	—
214	C₂×C₂²⋊C₄	C₂³×C₁₉	1	24	yes	—
215	C₂×C₄²	—	2	12	no	—
216	#99	C₂³×C₁₉	1	64	yes	—
217	C₁₉	#60070	1	1	yes	characteristic, direct product factor, Sylow
218	C₂⁴	C₂²×C₄×C₁₉	1	12	yes	—
219	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
220	#41	—	2	32	no	—
221	#41	—	2	96	no	—
222	#41	—	2	24	no	—
223	#41	—	2	24	no	—
224	#41	—	2	48	no	—
225	#41	—	2	8	no	—
226	#41	—	2	8	no	—
227	#41	—	2	48	no	—
228	#41	C₂²⋊C₄×C₁₉	1	16	yes	—
229	#41	C₂²⋊C₄×C₁₉	1	16	yes	—
230	#41	C₂²⋊C₄×C₁₉	1	32	yes	—
231	C₂×Q₈	—	2	32	no	—
232	C₂×Q₈	—	2	24	no	—
233	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
234	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
235	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
236	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
237	C₂×D₄	—	2	48	no	—
238	C₂×D₄	—	2	96	no	—
239	C₂×D₄	—	2	24	no	—
240	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
241	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
242	C₂×D₄	C₂²×C₄×C₁₉	1	24	yes	—
243	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
244	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	—
245	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
246	C₂²×C₄	—	2	24	no	—
247	C₂²×C₄	—	2	24	no	—
248	C₂²×C₄	—	2	24	no	—
249	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₉	1	24	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
254	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
255	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
256	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
257	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
258	C₄⋊C₄	—	2	8	no	—
259	C₄⋊C₄	—	2	24	no	—
260	C₂²⋊C₄	—	2	24	no	—
261	C₂²⋊C₄	C₂⁴×C₁₉	1	16	yes	—
262	C₄²	—	2	8	no	—
263	C₄²	—	2	24	no	—
264	C₂³	—	2	24	no	—
265	C₂³	—	8	3	no	—
266	C₂³	—	8	12	no	—
267	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
268	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
269	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
270	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
271	Q₈	—	2	24	no	—
272	Q₈	—	2	8	no	—
273	Q₈	C₂×C₂²⋊C₄×C₁₉	1	16	yes	—
274	D₄	—	2	48	no	—
275	D₄	—	2	16	no	—
276	D₄	—	2	24	no	—
277	D₄	—	2	8	no	—
278	D₄	C₂×C₂²⋊C₄×C₁₉	1	48	yes	—
279	C₂×C₄	—	2	24	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	48	no	—
283	C₂×C₄	—	2	16	no	—
284	C₂×C₄	—	8	24	no	—
285	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
286	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	12	yes	—
287	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	24	yes	—
288	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
289	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
290	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
291	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
292	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
294	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
295	C₂²	—	2	8	no	—
296	C₂²	—	4	12	no	—
297	C₂²	—	4	6	no	—
298	C₂²	—	4	1	no	—
299	C₂²	—	4	8	no	—
300	C₂²	—	8	24	no	—
301	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	12	yes	—
302	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
303	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
304	C₄	—	2	8	no	—
305	C₄	—	4	16	no	—
306	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
307	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
308	C₄	C₂²×C₂²⋊C₄×C₁₉	1	12	yes	—
309	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
310	C₂	—	2	2	no	—
311	C₂	—	2	1	no	—
312	C₂	—	2	12	no	—
313	C₂	—	4	8	no	—
314	C₂	C₂³×C₂²⋊C₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂×C₁₉	C₂³×C₂²⋊C₄
prime radical	C₂×C₁₉×#585	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3428	C₂	semidirect
3. C₁₉×#2884	C₂	semidirect
4. C₁₉×#2883	C₂	semidirect
5. C₂×C₁₉×#410	C₂	semidirect
8. C₂×C₁₉×2₋¹⁺⁴	C₄	semidirect
10. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
12. C₂²×#41×C₁₉	C₄	semidirect
16. C₁₉×#519	C₂²	semidirect
17. C₁₉×#518	C₂²	semidirect
19. C₂×C₁₉×#117	C₂²	semidirect
20. C₁₉×#410	C₂²	semidirect
21. C₁₉×#410	C₂²	semidirect
22. C₂×C₁₉×#99	C₂²	semidirect
33. C₂×#41×C₁₉	C₂×C₄	semidirect
34. C₂×#41×C₁₉	C₂×C₄	semidirect
35. C₂×#41×C₁₉	C₂×C₄	semidirect
36. C₂×#41×C₁₉	C₂×C₄	semidirect
41. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
42. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
44. C₂²×D₄×C₁₉	C₂×C₄	semidirect
45. C₂²×D₄×C₁₉	C₂×C₄	semidirect
48. C₂³×C₄×C₁₉	C₂×C₄	semidirect
106. #60070	C₁₉	direct (N × H)
139. #3428	C₂×C₁₉	semidirect
140. #2884	C₂×C₁₉	semidirect
141. #2883	C₂×C₁₉	semidirect
142. C₂×#410	C₂×C₁₉	semidirect
160. C₂×2₋¹⁺⁴	C₄×C₁₉	semidirect
162. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
164. C₂²×#41	C₄×C₁₉	semidirect
168. #519	C₂²×C₁₉	semidirect
169. #518	C₂²×C₁₉	semidirect
171. C₂×#117	C₂²×C₁₉	semidirect
172. #410	C₂²×C₁₉	semidirect
173. #410	C₂²×C₁₉	semidirect
174. C₂×#99	C₂²×C₁₉	semidirect
190. C₂×#41	C₂×C₄×C₁₉	semidirect
191. C₂×#41	C₂×C₄×C₁₉	semidirect
192. C₂×#41	C₂×C₄×C₁₉	semidirect
193. C₂×#41	C₂×C₄×C₁₉	semidirect
198. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
199. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
201. C₂²×D₄	C₂×C₄×C₁₉	semidirect
202. C₂²×D₄	C₂×C₄×C₁₉	semidirect
205. C₂³×C₄	C₂×C₄×C₁₉	semidirect
217. C₁₉	#60070	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#585	2
C₁₉×#3428	2
C₁₉×#2884	2
C₁₉×#2883	2
C₂×C₁₉×#410	2
#60070	19

Subgroups — C19×#60070 #18066029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60070 #18066029