Subgroups — C₁₉×#60399 #18066358

Order 4864.

5128 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3484	C₂	1	3	yes	maximal, complemented
3	C₁₉×#3027	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3026	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3025	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×B(4,𝔽₂)	C₂	1	8	yes	maximal, complemented
7	C₁₉×#2883	C₂	1	3	yes	maximal, complemented
8	C₁₉×#585	—	2	12	no	—
9	C₁₉×#585	C₂²	1	4	yes	complemented
10	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
11	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	3	yes	—
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	8	yes	complemented
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
14	C₁₉×#546	—	2	12	no	—
15	D₄²×C₁₉	—	2	12	no	—
16	C₁₉×#535	C₂²	1	6	yes	complemented
17	C₁₉×#534	C₂²	1	12	yes	complemented
18	C₁₉×#525	C₂²	1	6	yes	complemented
19	C₂×C₁₉×#120	C₂²	1	12	yes	complemented
20	C₁₉×#518	C₂²	1	3	yes	complemented
21	C₁₉×#458	C₂²	1	16	yes	complemented
22	C₁₉×B(4,𝔽₂)	C₂²	1	16	yes	complemented
23	C₁₉×B(4,𝔽₂)	C₂²	1	32	yes	complemented
24	C₁₉×#410	C₂²	1	12	yes	complemented
25	C₂×C₁₉×#99	C₂²	1	24	yes	complemented
26	C₂⁵×C₁₉	C₂³	1	2	yes	complemented
27	C₁₉×2₋¹⁺⁴	—	2	16	no	—
28	C₁₉×2₋¹⁺⁴	—	2	12	no	—
29	C₁₉×H(5,𝔽₂)	—	2	48	no	—
30	C₁₉×H(5,𝔽₂)	—	2	24	no	—
31	C₁₉×H(5,𝔽₂)	—	2	12	no	—
32	C₁₉×H(5,𝔽₂)	—	2	48	no	—
33	C₁₉×H(5,𝔽₂)	C₂³	1	16	yes	—
34	C₂×#41×C₁₉	—	2	48	no	—
35	C₂×#41×C₁₉	—	2	24	no	—
36	C₂×#41×C₁₉	—	2	24	no	—
37	C₂×#41×C₁₉	D₄	1	12	yes	complemented
38	C₂×#41×C₁₉	C₂³	1	6	yes	—
39	C₂²×D₄×C₁₉	—	2	16	no	—
40	C₂²×D₄×C₁₉	—	2	24	no	—
41	C₂²×D₄×C₁₉	—	2	12	no	—
42	C₂²×D₄×C₁₉	—	2	12	no	—
43	C₂²×D₄×C₁₉	D₄	1	12	yes	complemented
44	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	complemented
47	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
49	C₁₉×#127	—	2	6	no	—
50	C₁₉×#124	—	2	6	no	—
51	C₁₉×#123	—	2	12	no	—
52	C₁₉×#123	C₂³	1	12	yes	complemented
53	C₁₉×C₂²⋊Q₈	—	2	6	no	—
54	C₁₉×#121	—	2	6	no	—
55	C₁₉×#121	—	2	24	no	—
56	C₁₉×#121	—	2	12	no	—
57	C₁₉×#120	—	2	12	no	—
58	C₁₉×#120	—	2	24	no	—
59	C₁₉×#120	C₂³	1	12	yes	complemented
60	C₁₉×#120	C₂³	1	24	yes	complemented
61	C₄×D₄×C₁₉	—	2	12	no	—
62	C₄×D₄×C₁₉	—	2	12	no	—
63	C₁₉×#117	C₂³	1	6	yes	complemented
64	C₂×C₂²⋊C₄×C₁₉	—	2	12	no	—
65	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	complemented
66	C₁₉×#99	C₂³	1	48	yes	complemented
67	C₂⁴×C₁₉	—	2	8	no	—
68	C₂⁴×C₁₉	—	2	12	no	—
69	C₂⁴×C₁₉	—	8	4	no	—
70	C₂⁴×C₁₉	C₂×D₄	1	12	yes	complemented
71	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
72	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
73	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
74	#41×C₁₉	—	2	96	no	—
75	#41×C₁₉	—	2	48	no	—
76	#41×C₁₉	—	2	16	no	—
77	#41×C₁₉	—	2	48	no	—
78	#41×C₁₉	—	2	48	no	—
79	#41×C₁₉	—	2	24	no	—
80	C₂×Q₈×C₁₉	—	2	24	no	—
81	C₂×Q₈×C₁₉	—	2	8	no	—
82	C₂×Q₈×C₁₉	C₂×D₄	1	6	yes	complemented
83	C₂×D₄×C₁₉	—	2	96	no	—
84	C₂×D₄×C₁₉	—	2	24	no	—
85	C₂×D₄×C₁₉	—	2	24	no	—
86	C₂×D₄×C₁₉	—	2	48	no	—
87	C₂×D₄×C₁₉	—	2	48	no	—
88	C₂×D₄×C₁₉	—	2	48	no	—
89	C₂×D₄×C₁₉	—	2	12	no	—
90	C₂×D₄×C₁₉	—	2	12	no	—
91	C₂×D₄×C₁₉	—	2	24	no	—
92	C₂×D₄×C₁₉	—	2	6	no	—
93	C₂×D₄×C₁₉	—	4	16	no	—
94	C₂×D₄×C₁₉	—	8	24	no	—
95	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
96	C₂×D₄×C₁₉	C₂×D₄	1	24	yes	complemented
97	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	complemented
98	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
99	C₂²×C₄×C₁₉	—	2	24	no	—
100	C₂²×C₄×C₁₉	—	2	16	no	—
101	C₂²×C₄×C₁₉	—	2	12	no	—
102	C₂²×C₄×C₁₉	—	2	6	no	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	complemented
104	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	complemented
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₁₉	—	2	6	no	—
108	C₄⋊C₄×C₁₉	—	2	12	no	—
109	C₂²⋊C₄×C₁₉	—	2	12	no	—
110	C₂²⋊C₄×C₁₉	—	2	12	no	—
111	C₂²⋊C₄×C₁₉	—	2	12	no	—
112	C₂²⋊C₄×C₁₉	—	2	24	no	—
113	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
114	C₄²×C₁₉	—	2	6	no	—
115	#60399	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₁₉	—	2	16	no	—
117	C₂³×C₁₉	—	2	3	no	—
118	C₂³×C₁₉	—	2	24	no	—
119	C₂³×C₁₉	—	2	6	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	24	no	—
122	C₂³×C₁₉	—	4	8	no	—
123	C₂³×C₁₉	—	8	2	no	—
124	C₂³×C₁₉	—	8	2	no	—
125	C₂³×C₁₉	—	8	12	no	—
126	C₂³×C₁₉	—	8	12	no	—
127	C₂³×C₁₉	—	16	8	no	—
128	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
129	C₂³×C₁₉	C₂²×D₄	1	12	yes	—
130	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
131	Q₈×C₁₉	—	2	16	no	—
132	Q₈×C₁₉	—	2	12	no	—
133	D₄×C₁₉	—	2	48	no	—
134	D₄×C₁₉	—	2	48	no	—
135	D₄×C₁₉	—	2	24	no	—
136	D₄×C₁₉	—	2	12	no	—
137	D₄×C₁₉	—	4	24	no	—
138	D₄×C₁₉	—	4	8	no	—
139	D₄×C₁₉	—	4	4	no	—
140	D₄×C₁₉	—	8	24	no	—
141	D₄×C₁₉	#120	1	16	yes	—
142	C₂×C₄×C₁₉	—	2	48	no	—
143	C₂×C₄×C₁₉	—	2	24	no	—
144	C₂×C₄×C₁₉	—	2	24	no	—
145	C₂×C₄×C₁₉	—	2	12	no	—
146	C₂×C₄×C₁₉	—	2	3	no	—
147	C₂×C₄×C₁₉	—	4	4	no	—
148	C₂×C₄×C₁₉	—	8	12	no	—
149	C₂×C₄×C₁₉	C₂²×D₄	1	12	yes	—
150	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
151	H(7,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
152	#3484	C₂×C₁₉	1	3	yes	complemented
153	#3027	C₂×C₁₉	1	4	yes	complemented
154	#3026	C₂×C₁₉	1	8	yes	complemented
155	#3025	C₂×C₁₉	1	4	yes	complemented
156	C₂×B(4,𝔽₂)	C₂×C₁₉	1	8	yes	complemented
157	#2883	C₂×C₁₉	1	3	yes	complemented
158	C₂²×C₁₉	—	2	6	no	—
159	C₂²×C₁₉	—	2	12	no	—
160	C₂²×C₁₉	—	4	12	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	12	no	—
163	C₂²×C₁₉	—	4	3	no	—
164	C₂²×C₁₉	—	4	12	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	—	4	2	no	—
167	C₂²×C₁₉	—	8	24	no	—
168	C₂²×C₁₉	—	8	16	no	—
169	C₂²×C₁₉	—	8	16	no	—
170	C₂²×C₁₉	C₂×#120	1	8	yes	—
171	C₂²×C₁₉	C₂³×D₄	1	3	yes	—
172	C₄×C₁₉	—	2	12	no	—
173	C₄×C₁₉	—	4	12	no	—
174	C₄×C₁₉	—	4	1	no	—
175	C₄×C₁₉	C₂×#120	1	4	yes	—
176	#585	—	2	12	no	—
177	#585	C₂²×C₁₉	1	4	yes	complemented
178	C₂×H(5,𝔽₂)	—	2	12	no	—
179	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	3	yes	—
180	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	8	yes	complemented
181	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
182	#546	—	2	12	no	—
183	D₄²	—	2	12	no	—
184	#535	C₂²×C₁₉	1	6	yes	complemented
185	#534	C₂²×C₁₉	1	12	yes	complemented
186	#525	C₂²×C₁₉	1	6	yes	complemented
187	C₂×#120	C₂²×C₁₉	1	12	yes	complemented
188	#518	C₂²×C₁₉	1	3	yes	complemented
189	#458	C₂²×C₁₉	1	16	yes	complemented
190	B(4,𝔽₂)	C₂²×C₁₉	1	16	yes	complemented
191	B(4,𝔽₂)	C₂²×C₁₉	1	32	yes	complemented
192	#410	C₂²×C₁₉	1	12	yes	complemented
193	C₂×#99	C₂²×C₁₉	1	24	yes	complemented
194	C₂×C₁₉	—	2	3	no	—
195	C₂×C₁₉	—	2	8	no	—
196	C₂×C₁₉	—	4	2	no	—
197	C₂×C₁₉	—	4	12	no	—
198	C₂×C₁₉	—	8	2	no	—
199	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
200	C₂⁵	C₂³×C₁₉	1	2	yes	complemented
201	2₋¹⁺⁴	—	2	16	no	—
202	2₋¹⁺⁴	—	2	12	no	—
203	H(5,𝔽₂)	—	2	48	no	—
204	H(5,𝔽₂)	—	2	24	no	—
205	H(5,𝔽₂)	—	2	12	no	—
206	H(5,𝔽₂)	—	2	48	no	—
207	H(5,𝔽₂)	C₂³×C₁₉	1	16	yes	—
208	C₂×#41	—	2	48	no	—
209	C₂×#41	—	2	24	no	—
210	C₂×#41	—	2	24	no	—
211	C₂×#41	D₄×C₁₉	1	12	yes	complemented
212	C₂×#41	C₂³×C₁₉	1	6	yes	—
213	C₂²×D₄	—	2	16	no	—
214	C₂²×D₄	—	2	24	no	—
215	C₂²×D₄	—	2	12	no	—
216	C₂²×D₄	—	2	12	no	—
217	C₂²×D₄	D₄×C₁₉	1	12	yes	complemented
218	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
219	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
220	C₂²×D₄	C₂³×C₁₉	1	2	yes	complemented
221	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
222	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic, complemented
223	#127	—	2	6	no	—
224	#124	—	2	6	no	—
225	#123	—	2	12	no	—
226	#123	C₂³×C₁₉	1	12	yes	complemented
227	C₂²⋊Q₈	—	2	6	no	—
228	#121	—	2	6	no	—
229	#121	—	2	24	no	—
230	#121	—	2	12	no	—
231	#120	—	2	12	no	—
232	#120	—	2	24	no	—
233	#120	C₂³×C₁₉	1	12	yes	complemented
234	#120	C₂³×C₁₉	1	24	yes	complemented
235	C₄×D₄	—	2	12	no	—
236	C₄×D₄	—	2	12	no	—
237	#117	C₂³×C₁₉	1	6	yes	complemented
238	C₂×C₂²⋊C₄	—	2	12	no	—
239	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	complemented
240	#99	C₂³×C₁₉	1	48	yes	complemented
241	C₁₉	#60399	1	1	yes	characteristic, direct product factor, Sylow
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	12	no	—
244	C₂⁴	—	8	4	no	—
245	C₂⁴	C₂×D₄×C₁₉	1	12	yes	complemented
246	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
247	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
248	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
249	#41	—	2	96	no	—
250	#41	—	2	48	no	—
251	#41	—	2	16	no	—
252	#41	—	2	48	no	—
253	#41	—	2	48	no	—
254	#41	—	2	24	no	—
255	C₂×Q₈	—	2	24	no	—
256	C₂×Q₈	—	2	8	no	—
257	C₂×Q₈	C₂×D₄×C₁₉	1	6	yes	complemented
258	C₂×D₄	—	2	96	no	—
259	C₂×D₄	—	2	24	no	—
260	C₂×D₄	—	2	24	no	—
261	C₂×D₄	—	2	48	no	—
262	C₂×D₄	—	2	48	no	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	—	2	12	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	24	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	4	16	no	—
269	C₂×D₄	—	8	24	no	—
270	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
271	C₂×D₄	C₂×D₄×C₁₉	1	24	yes	complemented
272	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	complemented
273	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
274	C₂²×C₄	—	2	24	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	12	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	complemented
279	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	complemented
280	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
282	C₄⋊C₄	—	2	6	no	—
283	C₄⋊C₄	—	2	12	no	—
284	C₂²⋊C₄	—	2	12	no	—
285	C₂²⋊C₄	—	2	12	no	—
286	C₂²⋊C₄	—	2	12	no	—
287	C₂²⋊C₄	—	2	24	no	—
288	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
289	C₄²	—	2	6	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	3	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	2	6	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	24	no	—
296	C₂³	—	4	8	no	—
297	C₂³	—	8	2	no	—
298	C₂³	—	8	2	no	—
299	C₂³	—	8	12	no	—
300	C₂³	—	8	12	no	—
301	C₂³	—	16	8	no	—
302	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
303	C₂³	C₂²×D₄×C₁₉	1	12	yes	—
304	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
305	Q₈	—	2	16	no	—
306	Q₈	—	2	12	no	—
307	D₄	—	2	48	no	—
308	D₄	—	2	48	no	—
309	D₄	—	2	24	no	—
310	D₄	—	2	12	no	—
311	D₄	—	4	24	no	—
312	D₄	—	4	8	no	—
313	D₄	—	4	4	no	—
314	D₄	—	8	24	no	—
315	D₄	C₁₉×#120	1	16	yes	—
316	C₂×C₄	—	2	48	no	—
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	24	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	8	12	no	—
323	C₂×C₄	C₂²×D₄×C₁₉	1	12	yes	—
324	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
325	C₂²	—	2	6	no	—
326	C₂²	—	2	12	no	—
327	C₂²	—	4	12	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	12	no	—
330	C₂²	—	4	3	no	—
331	C₂²	—	4	12	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	8	24	no	—
335	C₂²	—	8	16	no	—
336	C₂²	—	8	16	no	—
337	C₂²	C₂×C₁₉×#120	1	8	yes	—
338	C₂²	C₂³×D₄×C₁₉	1	3	yes	—
339	C₄	—	2	12	no	—
340	C₄	—	4	12	no	—
341	C₄	—	4	1	no	—
342	C₄	C₂×C₁₉×#120	1	4	yes	—
343	C₂	—	2	3	no	—
344	C₂	—	2	8	no	—
345	C₂	—	4	2	no	—
346	C₂	—	4	12	no	—
347	C₂	—	8	2	no	—
348	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×H(7,𝔽₂)	C₂	semidirect
2. C₁₉×#3484	C₂	semidirect
3. C₁₉×#3027	C₂	semidirect
4. C₁₉×#3026	C₂	semidirect
5. C₁₉×#3025	C₂	semidirect
6. C₂×C₁₉×B(4,𝔽₂)	C₂	semidirect
7. C₁₉×#2883	C₂	semidirect
9. C₁₉×#585	C₂²	semidirect
12. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
13. C₂³×D₄×C₁₉	C₂²	semidirect
16. C₁₉×#535	C₂²	semidirect
17. C₁₉×#534	C₂²	semidirect
18. C₁₉×#525	C₂²	semidirect
19. C₂×C₁₉×#120	C₂²	semidirect
20. C₁₉×#518	C₂²	semidirect
21. C₁₉×#458	C₂²	semidirect
22. C₁₉×B(4,𝔽₂)	C₂²	semidirect
23. C₁₉×B(4,𝔽₂)	C₂²	semidirect
24. C₁₉×#410	C₂²	semidirect
25. C₂×C₁₉×#99	C₂²	semidirect
26. C₂⁵×C₁₉	C₂³	semidirect
37. C₂×#41×C₁₉	D₄	semidirect
43. C₂²×D₄×C₁₉	D₄	semidirect
46. C₂²×D₄×C₁₉	C₂³	semidirect
47. C₂²×D₄×C₁₉	C₂³	semidirect
48. C₂³×C₄×C₁₉	C₂³	semidirect
52. C₁₉×#123	C₂³	semidirect
59. C₁₉×#120	C₂³	semidirect
60. C₁₉×#120	C₂³	semidirect
63. C₁₉×#117	C₂³	semidirect
65. C₂×C₂²⋊C₄×C₁₉	C₂³	semidirect
66. C₁₉×#99	C₂³	semidirect
70. C₂⁴×C₁₉	C₂×D₄	semidirect
82. C₂×Q₈×C₁₉	C₂×D₄	semidirect
96. C₂×D₄×C₁₉	C₂×D₄	semidirect
97. C₂×D₄×C₁₉	C₂×D₄	semidirect
103. C₂²×C₄×C₁₉	C₂×D₄	semidirect
104. C₂²×C₄×C₁₉	C₂×D₄	semidirect
115. #60399	C₁₉	direct (N × H)
151. H(7,𝔽₂)	C₂×C₁₉	semidirect
152. #3484	C₂×C₁₉	semidirect
153. #3027	C₂×C₁₉	semidirect
154. #3026	C₂×C₁₉	semidirect
155. #3025	C₂×C₁₉	semidirect
156. C₂×B(4,𝔽₂)	C₂×C₁₉	semidirect
157. #2883	C₂×C₁₉	semidirect
177. #585	C₂²×C₁₉	semidirect
180. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
181. C₂³×D₄	C₂²×C₁₉	semidirect
184. #535	C₂²×C₁₉	semidirect
185. #534	C₂²×C₁₉	semidirect
186. #525	C₂²×C₁₉	semidirect
187. C₂×#120	C₂²×C₁₉	semidirect
188. #518	C₂²×C₁₉	semidirect
189. #458	C₂²×C₁₉	semidirect
190. B(4,𝔽₂)	C₂²×C₁₉	semidirect
191. B(4,𝔽₂)	C₂²×C₁₉	semidirect
192. #410	C₂²×C₁₉	semidirect
193. C₂×#99	C₂²×C₁₉	semidirect
200. C₂⁵	C₂³×C₁₉	semidirect
211. C₂×#41	D₄×C₁₉	semidirect
217. C₂²×D₄	D₄×C₁₉	semidirect
220. C₂²×D₄	C₂³×C₁₉	semidirect
221. C₂²×D₄	C₂³×C₁₉	semidirect
222. C₂³×C₄	C₂³×C₁₉	semidirect
226. #123	C₂³×C₁₉	semidirect
233. #120	C₂³×C₁₉	semidirect
234. #120	C₂³×C₁₉	semidirect
237. #117	C₂³×C₁₉	semidirect
239. C₂×C₂²⋊C₄	C₂³×C₁₉	semidirect
240. #99	C₂³×C₁₉	semidirect
241. C₁₉	#60399	direct (N × H)
245. C₂⁴	C₂×D₄×C₁₉	semidirect
257. C₂×Q₈	C₂×D₄×C₁₉	semidirect
271. C₂×D₄	C₂×D₄×C₁₉	semidirect
272. C₂×D₄	C₂×D₄×C₁₉	semidirect
278. C₂²×C₄	C₂×D₄×C₁₉	semidirect
279. C₂²×C₄	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×H(7,𝔽₂)	2
C₁₉×#3484	2
C₁₉×#3027	2
C₁₉×#3026	2
C₁₉×#3025	2
C₂×C₁₉×B(4,𝔽₂)	2
C₁₉×#2883	2
#60399	19

Subgroups — C19×#60399 #18066358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60399 #18066358