Subgroups — C₁₉×#32977 #18038936

Order 4864.

1382 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2579	C₂	1	3	yes	maximal, complemented
3	C₁₉×#1867	C₂	1	3	yes	maximal, complemented
4	C₁₉×#1867	C₂	1	3	yes	maximal, complemented
5	C₁₉×#1799	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1790	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1790	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₁₉×#520	—	2	3	no	—
10	C₁₉×#518	—	2	3	no	—
11	C₁₉×#518	C₂²	1	3	yes	—
12	C₄×#41×C₁₉	—	2	3	no	—
13	C₂×C₄×D₄×C₁₉	—	2	3	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#99	C₂²	1	3	yes	—
17	C₂×C₁₉×#99	C₂²	1	3	yes	—
18	C₁₉×#398	—	2	3	no	—
19	C₁₉×#396	—	2	3	no	—
20	C₁₉×#387	—	2	3	no	—
21	C₁₉×#386	C₂²	1	3	yes	—
22	C₁₉×#386	C₂²	1	3	yes	—
23	C₁₉×#385	—	2	3	no	—
24	C₁₉×#385	C₂²	1	3	yes	complemented
25	C₁₉×#385	C₂²	1	3	yes	complemented
26	C₁₉×#380	C₂²	1	3	yes	complemented
27	C₁₉×#342	C₂²	1	6	yes	complemented
28	C₁₉×H(5,𝔽₂)	—	2	6	no	—
29	C₁₉×H(5,𝔽₂)	Q₈	1	4	yes	—
30	C₂×#41×C₁₉	—	2	3	no	—
31	C₂²×D₄×C₁₉	—	2	3	no	—
32	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂³×C₄×C₁₉	D₄	1	3	yes	—
35	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	3	no	—
40	C₄×D₄×C₁₉	—	2	3	no	—
41	C₄×D₄×C₁₉	—	2	6	no	—
42	C₄×D₄×C₁₉	—	2	3	no	—
43	C₄×D₄×C₁₉	—	2	6	no	—
44	C₄×D₄×C₁₉	—	2	6	no	—
45	C₄×D₄×C₁₉	—	2	6	no	—
46	C₄×D₄×C₁₉	—	2	6	no	—
47	C₁₉×#117	—	2	6	no	—
48	C₁₉×#117	—	2	3	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
60	C₂×C₂²⋊C₄×C₁₉	D₄	1	3	yes	—
61	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
62	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
64	C₂×C₄²×C₁₉	—	2	3	no	—
65	C₂×C₄²×C₁₉	D₄	1	3	yes	—
66	C₁₉×#99	—	2	6	no	—
67	C₁₉×#99	—	2	6	no	—
68	C₁₉×#95	—	2	3	no	—
69	C₁₉×#95	—	2	3	no	—
70	C₁₉×#95	—	2	3	no	—
71	C₁₉×#95	—	2	3	no	—
72	C₁₉×#95	—	2	3	no	—
73	C₂⁴×C₁₉	—	2	1	no	—
74	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
75	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
76	#41×C₁₉	—	2	12	no	—
77	#41×C₁₉	—	2	12	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×D₄×C₁₉	—	2	3	no	—
80	C₂×D₄×C₁₉	—	2	12	no	—
81	C₂×D₄×C₁₉	—	2	12	no	—
82	C₂×D₄×C₁₉	—	2	6	no	—
83	C₂×D₄×C₁₉	—	2	6	no	—
84	C₂×D₄×C₁₉	C₂×Q₈	1	6	yes	—
85	C₂×D₄×C₁₉	#41	1	6	yes	—
86	C₂²×C₄×C₁₉	—	2	3	no	—
87	C₂²×C₄×C₁₉	—	2	3	no	—
88	C₂²×C₄×C₁₉	—	2	3	no	—
89	C₂²×C₄×C₁₉	—	2	3	no	—
90	C₂²×C₄×C₁₉	—	2	3	no	—
91	C₂²×C₄×C₁₉	—	2	3	no	—
92	C₂²×C₄×C₁₉	—	2	3	no	—
93	C₂²×C₄×C₁₉	—	2	3	no	—
94	C₂²×C₄×C₁₉	—	2	3	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	8	1	no	—
97	C₂²×C₄×C₁₉	—	8	1	no	—
98	C₂²×C₄×C₁₉	—	8	3	no	—
99	C₂²×C₄×C₁₉	—	8	2	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
101	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
105	C₄⋊C₄×C₁₉	—	2	3	no	—
106	C₄⋊C₄×C₁₉	—	2	3	no	—
107	C₄⋊C₄×C₁₉	—	2	6	no	—
108	C₄⋊C₄×C₁₉	—	4	6	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	3	no	—
111	C₄⋊C₄×C₁₉	—	8	3	no	—
112	C₄⋊C₄×C₁₉	—	8	3	no	—
113	C₂²⋊C₄×C₁₉	—	2	6	no	—
114	C₂²⋊C₄×C₁₉	—	2	6	no	—
115	C₂²⋊C₄×C₁₉	—	2	6	no	—
116	C₂²⋊C₄×C₁₉	—	2	6	no	—
117	C₂²⋊C₄×C₁₉	—	2	6	no	—
118	C₂²⋊C₄×C₁₉	—	4	6	no	—
119	C₂²⋊C₄×C₁₉	—	8	3	no	—
120	C₄²×C₁₉	—	2	6	no	—
121	C₄²×C₁₉	—	2	3	no	—
122	C₄²×C₁₉	—	2	3	no	—
123	#32977	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₉	—	2	4	no	—
125	C₂³×C₁₉	—	2	3	no	—
126	C₂³×C₁₉	—	2	3	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	3	no	—
130	C₂³×C₁₉	—	4	3	no	—
131	C₂³×C₁₉	—	8	1	no	—
132	C₂³×C₁₉	—	8	1	no	—
133	C₂³×C₁₉	C₂²⋊Q₈	1	6	yes	—
134	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
135	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
136	C₂³×C₁₉	C₂×#41	1	3	yes	—
137	Q₈×C₁₉	—	2	4	no	—
138	D₄×C₁₉	—	2	12	no	—
139	D₄×C₁₉	—	2	12	no	—
140	D₄×C₁₉	—	2	12	no	—
141	C₂×C₄×C₁₉	—	2	12	no	—
142	C₂×C₄×C₁₉	—	2	3	no	—
143	C₂×C₄×C₁₉	—	2	3	no	—
144	C₂×C₄×C₁₉	—	2	6	no	—
145	C₂×C₄×C₁₉	—	2	3	no	—
146	C₂×C₄×C₁₉	—	2	3	no	—
147	C₂×C₄×C₁₉	—	4	3	no	—
148	C₂×C₄×C₁₉	—	4	3	no	—
149	C₂×C₄×C₁₉	—	4	6	no	—
150	C₂×C₄×C₁₉	—	4	3	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	3	no	—
153	C₂×C₄×C₁₉	—	4	3	no	—
154	C₂×C₄×C₁₉	—	4	3	no	—
155	C₂×C₄×C₁₉	—	4	3	no	—
156	C₂×C₄×C₁₉	—	4	3	no	—
157	C₂×C₄×C₁₉	—	4	3	no	—
158	C₂×C₄×C₁₉	—	4	3	no	—
159	C₂×C₄×C₁₉	—	4	3	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	3	no	—
162	C₂×C₄×C₁₉	—	4	3	no	—
163	C₂×C₄×C₁₉	—	8	3	no	—
164	C₂×C₄×C₁₉	—	8	3	no	—
165	C₂×C₄×C₁₉	—	8	3	no	—
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#120	1	3	yes	—
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	6	yes	—
169	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
170	#2579	C₂×C₁₉	1	3	yes	complemented
171	#1867	C₂×C₁₉	1	3	yes	complemented
172	#1867	C₂×C₁₉	1	3	yes	complemented
173	#1799	C₂×C₁₉	1	3	yes	complemented
174	#1790	C₂×C₁₉	1	1	yes	characteristic
175	#1790	C₂×C₁₉	1	1	yes	characteristic
176	C₂²×C₁₉	—	2	3	no	—
177	C₂²×C₁₉	—	2	3	no	—
178	C₂²×C₁₉	—	2	6	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	3	no	—
181	C₂²×C₁₉	—	4	6	no	—
182	C₂²×C₁₉	—	4	3	no	—
183	C₂²×C₁₉	—	4	3	no	—
184	C₂²×C₁₉	—	8	3	no	—
185	C₂²×C₁₉	—	8	4	no	—
186	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	3	yes	—
188	C₂²×C₁₉	#525	1	3	yes	—
189	C₄×C₁₉	—	2	6	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	3	no	—
192	C₄×C₁₉	—	4	2	no	—
193	C₄×C₁₉	—	4	3	no	—
194	C₄×C₁₉	—	4	3	no	—
195	C₄×C₁₉	—	8	3	no	—
196	C₄×C₁₉	—	8	3	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
199	#520	—	2	3	no	—
200	#518	—	2	3	no	—
201	#518	C₂²×C₁₉	1	3	yes	—
202	C₄×#41	—	2	3	no	—
203	C₂×C₄×D₄	—	2	3	no	—
204	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
206	C₂×#99	C₂²×C₁₉	1	3	yes	—
207	C₂×#99	C₂²×C₁₉	1	3	yes	—
208	#398	—	2	3	no	—
209	#396	—	2	3	no	—
210	#387	—	2	3	no	—
211	#386	C₂²×C₁₉	1	3	yes	—
212	#386	C₂²×C₁₉	1	3	yes	—
213	#385	—	2	3	no	—
214	#385	C₂²×C₁₉	1	3	yes	complemented
215	#385	C₂²×C₁₉	1	3	yes	complemented
216	#380	C₂²×C₁₉	1	3	yes	complemented
217	#342	C₂²×C₁₉	1	6	yes	complemented
218	C₂×C₁₉	—	2	3	no	—
219	C₂×C₁₉	—	2	3	no	—
220	C₂×C₁₉	—	4	6	no	—
221	C₂×C₁₉	#2848	1	1	yes	characteristic
222	C₂×C₁₉	#3025	1	1	yes	characteristic
223	C₂×C₁₉	#3026	1	1	yes	characteristic
224	H(5,𝔽₂)	—	2	6	no	—
225	H(5,𝔽₂)	Q₈×C₁₉	1	4	yes	—
226	C₂×#41	—	2	3	no	—
227	C₂²×D₄	—	2	3	no	—
228	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	D₄×C₁₉	1	3	yes	—
231	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	3	no	—
236	C₄×D₄	—	2	3	no	—
237	C₄×D₄	—	2	6	no	—
238	C₄×D₄	—	2	3	no	—
239	C₄×D₄	—	2	6	no	—
240	C₄×D₄	—	2	6	no	—
241	C₄×D₄	—	2	6	no	—
242	C₄×D₄	—	2	6	no	—
243	#117	—	2	6	no	—
244	#117	—	2	3	no	—
245	C₂×C₄⋊C₄	—	2	3	no	—
246	C₂×C₄⋊C₄	—	2	3	no	—
247	C₂×C₄⋊C₄	—	2	3	no	—
248	C₂×C₄⋊C₄	—	2	3	no	—
249	C₂×C₄⋊C₄	—	2	3	no	—
250	C₂×C₄⋊C₄	—	2	3	no	—
251	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	—
252	C₂×C₂²⋊C₄	—	2	3	no	—
253	C₂×C₂²⋊C₄	—	2	3	no	—
254	C₂×C₂²⋊C₄	—	2	3	no	—
255	C₂×C₂²⋊C₄	—	2	3	no	—
256	C₂×C₂²⋊C₄	D₄×C₁₉	1	3	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
260	C₂×C₄²	—	2	3	no	—
261	C₂×C₄²	D₄×C₁₉	1	3	yes	—
262	#99	—	2	6	no	—
263	#99	—	2	6	no	—
264	#95	—	2	3	no	—
265	#95	—	2	3	no	—
266	#95	—	2	3	no	—
267	#95	—	2	3	no	—
268	#95	—	2	3	no	—
269	C₁₉	#32977	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁴	—	2	1	no	—
271	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
272	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
273	#41	—	2	12	no	—
274	#41	—	2	12	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×D₄	—	2	3	no	—
277	C₂×D₄	—	2	12	no	—
278	C₂×D₄	—	2	12	no	—
279	C₂×D₄	—	2	6	no	—
280	C₂×D₄	—	2	6	no	—
281	C₂×D₄	C₂×Q₈×C₁₉	1	6	yes	—
282	C₂×D₄	#41×C₁₉	1	6	yes	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	3	no	—
287	C₂²×C₄	—	2	3	no	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	—	2	3	no	—
290	C₂²×C₄	—	2	3	no	—
291	C₂²×C₄	—	2	3	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	8	1	no	—
294	C₂²×C₄	—	8	1	no	—
295	C₂²×C₄	—	8	3	no	—
296	C₂²×C₄	—	8	2	no	—
297	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
298	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
299	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
300	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
301	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
302	C₄⋊C₄	—	2	3	no	—
303	C₄⋊C₄	—	2	3	no	—
304	C₄⋊C₄	—	2	6	no	—
305	C₄⋊C₄	—	4	6	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	3	no	—
308	C₄⋊C₄	—	8	3	no	—
309	C₄⋊C₄	—	8	3	no	—
310	C₂²⋊C₄	—	2	6	no	—
311	C₂²⋊C₄	—	2	6	no	—
312	C₂²⋊C₄	—	2	6	no	—
313	C₂²⋊C₄	—	2	6	no	—
314	C₂²⋊C₄	—	2	6	no	—
315	C₂²⋊C₄	—	4	6	no	—
316	C₂²⋊C₄	—	8	3	no	—
317	C₄²	—	2	6	no	—
318	C₄²	—	2	3	no	—
319	C₄²	—	2	3	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	3	no	—
322	C₂³	—	2	3	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	3	no	—
326	C₂³	—	4	3	no	—
327	C₂³	—	8	1	no	—
328	C₂³	—	8	1	no	—
329	C₂³	C₁₉×C₂²⋊Q₈	1	6	yes	—
330	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
331	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
332	C₂³	C₂×#41×C₁₉	1	3	yes	—
333	Q₈	—	2	4	no	—
334	D₄	—	2	12	no	—
335	D₄	—	2	12	no	—
336	D₄	—	2	12	no	—
337	C₂×C₄	—	2	12	no	—
338	C₂×C₄	—	2	3	no	—
339	C₂×C₄	—	2	3	no	—
340	C₂×C₄	—	2	6	no	—
341	C₂×C₄	—	2	3	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	4	3	no	—
344	C₂×C₄	—	4	3	no	—
345	C₂×C₄	—	4	6	no	—
346	C₂×C₄	—	4	3	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	3	no	—
349	C₂×C₄	—	4	3	no	—
350	C₂×C₄	—	4	3	no	—
351	C₂×C₄	—	4	3	no	—
352	C₂×C₄	—	4	3	no	—
353	C₂×C₄	—	4	3	no	—
354	C₂×C₄	—	4	3	no	—
355	C₂×C₄	—	4	3	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	3	no	—
358	C₂×C₄	—	4	3	no	—
359	C₂×C₄	—	8	3	no	—
360	C₂×C₄	—	8	3	no	—
361	C₂×C₄	—	8	3	no	—
362	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
363	C₂×C₄	C₁₉×#120	1	3	yes	—
364	C₂×C₄	C₁₉×C₂²⋊Q₈	1	6	yes	—
365	C₂²	—	2	3	no	—
366	C₂²	—	2	3	no	—
367	C₂²	—	2	6	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	3	no	—
370	C₂²	—	4	6	no	—
371	C₂²	—	4	3	no	—
372	C₂²	—	4	3	no	—
373	C₂²	—	8	3	no	—
374	C₂²	—	8	4	no	—
375	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
376	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	3	yes	—
377	C₂²	C₁₉×#525	1	3	yes	—
378	C₄	—	2	1	no	—
379	C₄	—	2	3	no	—
380	C₄	—	2	6	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	3	no	—
383	C₄	—	4	3	no	—
384	C₄	—	8	3	no	—
385	C₄	—	8	3	no	—
386	C₄	—	8	1	no	—
387	C₂	—	2	3	no	—
388	C₂	—	2	3	no	—
389	C₂	—	4	6	no	—
390	C₂	C₁₉×#2848	1	1	yes	characteristic
391	C₂	C₁₉×#3025	1	1	yes	characteristic
392	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2579	C₂	semidirect
3. C₁₉×#1867	C₂	semidirect
4. C₁₉×#1867	C₂	semidirect
5. C₁₉×#1799	C₂	semidirect
15. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
24. C₁₉×#385	C₂²	semidirect
25. C₁₉×#385	C₂²	semidirect
26. C₁₉×#380	C₂²	semidirect
27. C₁₉×#342	C₂²	semidirect
123. #32977	C₁₉	direct (N × H)
170. #2579	C₂×C₁₉	semidirect
171. #1867	C₂×C₁₉	semidirect
172. #1867	C₂×C₁₉	semidirect
173. #1799	C₂×C₁₉	semidirect
205. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
214. #385	C₂²×C₁₉	semidirect
215. #385	C₂²×C₁₉	semidirect
216. #380	C₂²×C₁₉	semidirect
217. #342	C₂²×C₁₉	semidirect
269. C₁₉	#32977	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#2579	2
C₁₉×#1867	2
C₁₉×#1799	2
C₁₉×#1790	2
#32977	19

Subgroups — C19×#32977 #18038936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32977 #18038936