Subgroups — C₁₉×#20585 #18026544

Order 4864.

4098 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	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2308	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1782	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1781	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×H(5,𝔽₂)	—	2	16	no	—
7	C₂×C₁₉×H(5,𝔽₂)	—	2	8	no	—
8	C₂²×#41×C₁₉	C₄	1	4	yes	complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₉	C₄	1	4	yes	complemented
11	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#99	—	2	16	no	—
16	C₂×C₁₉×#99	C₂²	1	16	yes	complemented
17	C₁₉×#386	—	2	8	no	—
18	C₁₉×#381	C₂²	1	4	yes	complemented
19	C₁₉×#379	C₂²	1	4	yes	complemented
20	C₂⁵×C₁₉	C₂×C₄	1	2	yes	—
21	C₂⁵×C₁₉	C₂×C₄	1	2	yes	complemented
22	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
23	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×H(5,𝔽₂)	—	2	64	no	—
25	C₁₉×H(5,𝔽₂)	—	2	64	no	—
26	C₂×#41×C₁₉	—	2	16	no	—
27	C₂×#41×C₁₉	—	2	16	no	—
28	C₂×#41×C₁₉	—	2	16	no	—
29	C₂×#41×C₁₉	—	2	16	no	—
30	C₂×#41×C₁₉	—	2	8	no	—
31	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	complemented
32	C₂²×D₄×C₁₉	—	2	16	no	—
33	C₂²×D₄×C₁₉	—	2	8	no	—
34	C₂²×D₄×C₁₉	—	2	8	no	—
35	C₂²×D₄×C₁₉	—	2	8	no	—
36	C₂²×D₄×C₁₉	—	2	8	no	—
37	C₂²×D₄×C₁₉	—	2	16	no	—
38	C₂²×D₄×C₁₉	—	2	16	no	—
39	C₂²×D₄×C₁₉	—	2	16	no	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	complemented
43	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
44	C₂²×D₄×C₁₉	D₄	1	16	yes	—
45	C₂²×D₄×C₁₉	D₄	1	8	yes	—
46	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₉	—	2	4	no	—
48	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	complemented
50	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	complemented
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
56	C₁₉×#99	—	2	32	no	—
57	C₁₉×#95	—	2	8	no	—
58	C₂⁴×C₁₉	—	2	4	no	—
59	C₂⁴×C₁₉	—	2	4	no	—
60	C₂⁴×C₁₉	—	2	8	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	2	4	no	—
63	C₂⁴×C₁₉	—	8	2	no	—
64	C₂⁴×C₁₉	—	8	2	no	—
65	C₂⁴×C₁₉	—	8	4	no	—
66	C₂⁴×C₁₉	—	8	4	no	—
67	C₂⁴×C₁₉	C₂²⋊C₄	1	8	yes	complemented
68	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
69	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
71	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
72	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
74	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
75	#41×C₁₉	—	2	64	no	—
76	#41×C₁₉	—	2	128	no	—
77	C₂×Q₈×C₁₉	—	2	8	no	—
78	C₂×Q₈×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	64	no	—
80	C₂×D₄×C₁₉	—	2	128	no	—
81	C₂×D₄×C₁₉	—	2	8	no	—
82	C₂×D₄×C₁₉	—	2	8	no	—
83	C₂×D₄×C₁₉	—	2	8	no	—
84	C₂×D₄×C₁₉	—	2	8	no	—
85	C₂×D₄×C₁₉	—	2	8	no	—
86	C₂×D₄×C₁₉	—	2	8	no	—
87	C₂×D₄×C₁₉	—	2	8	no	—
88	C₂×D₄×C₁₉	—	2	16	no	—
89	C₂×D₄×C₁₉	—	2	16	no	—
90	C₂×D₄×C₁₉	—	2	32	no	—
91	C₂×D₄×C₁₉	—	2	32	no	—
92	C₂×D₄×C₁₉	—	2	8	no	—
93	C₂×D₄×C₁₉	—	2	8	no	—
94	C₂×D₄×C₁₉	—	2	8	no	—
95	C₂×D₄×C₁₉	—	2	4	no	—
96	C₂×D₄×C₁₉	C₂²⋊C₄	1	16	yes	—
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
98	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	8	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	2	8	no	—
106	C₂²×C₄×C₁₉	—	2	8	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	4	8	no	—
109	C₂²×C₄×C₁₉	—	8	8	no	—
110	C₂²×C₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
111	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
114	C₂²⋊C₄×C₁₉	—	2	16	no	—
115	C₂²⋊C₄×C₁₉	—	4	8	no	—
116	C₂²⋊C₄×C₁₉	—	8	8	no	—
117	#20585	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₉	—	2	16	no	—
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	4	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	8	no	—
123	C₂³×C₁₉	—	2	16	no	—
124	C₂³×C₁₉	—	4	8	no	—
125	C₂³×C₁₉	—	4	4	no	—
126	C₂³×C₁₉	—	4	4	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	8	no	—
129	C₂³×C₁₉	—	4	8	no	—
130	C₂³×C₁₉	—	8	8	no	—
131	C₂³×C₁₉	—	8	8	no	—
132	C₂³×C₁₉	—	8	8	no	—
133	C₂³×C₁₉	—	8	8	no	—
134	C₂³×C₁₉	—	8	8	no	—
135	C₂³×C₁₉	—	8	8	no	—
136	C₂³×C₁₉	—	8	16	no	—
137	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
140	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂³×C₁₉	#120	1	8	yes	—
143	C₂³×C₁₉	#120	1	8	yes	—
144	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
147	Q₈×C₁₉	—	2	16	no	—
148	D₄×C₁₉	—	2	16	no	—
149	D₄×C₁₉	—	2	32	no	—
150	D₄×C₁₉	—	2	32	no	—
151	D₄×C₁₉	—	2	32	no	—
152	D₄×C₁₉	—	2	32	no	—
153	C₂×C₄×C₁₉	—	2	32	no	—
154	C₂×C₄×C₁₉	—	2	16	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	16	no	—
160	C₂×C₄×C₁₉	—	4	16	no	—
161	C₂×C₄×C₁₉	—	4	8	no	—
162	C₂×C₄×C₁₉	—	8	16	no	—
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
166	C₂²×#99	C₂×C₁₉	1	4	yes	complemented
167	#2308	C₂×C₁₉	1	2	yes	complemented
168	#1782	C₂×C₁₉	1	4	yes	complemented
169	#1781	C₂×C₁₉	1	4	yes	complemented
170	C₂²×C₁₉	—	2	4	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	8	no	—
173	C₂²×C₁₉	—	2	8	no	—
174	C₂²×C₁₉	—	2	4	no	—
175	C₂²×C₁₉	—	2	8	no	—
176	C₂²×C₁₉	—	4	8	no	—
177	C₂²×C₁₉	—	4	4	no	—
178	C₂²×C₁₉	—	4	4	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	4	8	no	—
181	C₂²×C₁₉	—	4	8	no	—
182	C₂²×C₁₉	—	4	8	no	—
183	C₂²×C₁₉	—	4	8	no	—
184	C₂²×C₁₉	—	4	8	no	—
185	C₂²×C₁₉	—	8	8	no	—
186	C₂²×C₁₉	—	8	16	no	—
187	C₂²×C₁₉	—	8	16	no	—
188	C₂²×C₁₉	#379	1	8	yes	—
189	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
190	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×#120	1	4	yes	—
192	C₄×C₁₉	—	2	4	no	—
193	C₄×C₁₉	—	2	8	no	—
194	C₄×C₁₉	—	8	8	no	—
195	C₂×H(5,𝔽₂)	—	2	16	no	—
196	C₂×H(5,𝔽₂)	—	2	8	no	—
197	C₂²×#41	C₄×C₁₉	1	4	yes	complemented
198	C₂²×#41	C₂²×C₁₉	1	2	yes	—
199	C₂³×D₄	C₄×C₁₉	1	4	yes	complemented
200	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
201	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
202	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
203	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
204	C₂×#99	—	2	16	no	—
205	C₂×#99	C₂²×C₁₉	1	16	yes	complemented
206	#386	—	2	8	no	—
207	#381	C₂²×C₁₉	1	4	yes	complemented
208	#379	C₂²×C₁₉	1	4	yes	complemented
209	C₂×C₁₉	—	2	4	no	—
210	C₂×C₁₉	—	2	2	no	—
211	C₂×C₁₉	—	2	8	no	—
212	C₂×C₁₉	—	4	4	no	—
213	C₂×C₁₉	—	4	8	no	—
214	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
215	C₂×C₁₉	#2883	1	2	yes	—
216	C₂⁵	C₂×C₄×C₁₉	1	2	yes	—
217	C₂⁵	C₂×C₄×C₁₉	1	2	yes	complemented
218	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
219	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
220	H(5,𝔽₂)	—	2	64	no	—
221	H(5,𝔽₂)	—	2	64	no	—
222	C₂×#41	—	2	16	no	—
223	C₂×#41	—	2	16	no	—
224	C₂×#41	—	2	16	no	—
225	C₂×#41	—	2	16	no	—
226	C₂×#41	—	2	8	no	—
227	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	complemented
228	C₂²×D₄	—	2	16	no	—
229	C₂²×D₄	—	2	8	no	—
230	C₂²×D₄	—	2	8	no	—
231	C₂²×D₄	—	2	8	no	—
232	C₂²×D₄	—	2	8	no	—
233	C₂²×D₄	—	2	16	no	—
234	C₂²×D₄	—	2	16	no	—
235	C₂²×D₄	—	2	16	no	—
236	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
237	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
238	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	complemented
239	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
240	C₂²×D₄	D₄×C₁₉	1	16	yes	—
241	C₂²×D₄	D₄×C₁₉	1	8	yes	—
242	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
245	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	complemented
246	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	complemented
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	16	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	2	8	no	—
251	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
252	#99	—	2	32	no	—
253	#95	—	2	8	no	—
254	C₁₉	#20585	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	—	8	2	no	—
261	C₂⁴	—	8	2	no	—
262	C₂⁴	—	8	4	no	—
263	C₂⁴	—	8	4	no	—
264	C₂⁴	C₂²⋊C₄×C₁₉	1	8	yes	complemented
265	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
266	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
267	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
268	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
269	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
270	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
271	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
272	#41	—	2	128	no	—
273	#41	—	2	64	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×D₄	—	2	128	no	—
277	C₂×D₄	—	2	64	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	32	no	—
286	C₂×D₄	—	2	32	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	C₂²⋊C₄×C₁₉	1	16	yes	—
294	C₂×D₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
295	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	4	8	no	—
306	C₂²×C₄	—	8	8	no	—
307	C₂²×C₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
308	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₂²⋊C₄	—	4	8	no	—
313	C₂²⋊C₄	—	8	8	no	—
314	C₂³	—	2	16	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	16	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	4	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	8	8	no	—
327	C₂³	—	8	8	no	—
328	C₂³	—	8	8	no	—
329	C₂³	—	8	8	no	—
330	C₂³	—	8	8	no	—
331	C₂³	—	8	8	no	—
332	C₂³	—	8	16	no	—
333	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
334	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
335	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
336	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
337	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
338	C₂³	C₁₉×#120	1	8	yes	—
339	C₂³	C₁₉×#120	1	8	yes	—
340	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
341	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
342	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
343	Q₈	—	2	16	no	—
344	D₄	—	2	32	no	—
345	D₄	—	2	16	no	—
346	D₄	—	2	32	no	—
347	D₄	—	2	32	no	—
348	D₄	—	2	32	no	—
349	C₂×C₄	—	2	16	no	—
350	C₂×C₄	—	2	32	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	8	16	no	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	8	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	4	8	no	—
375	C₂²	—	4	8	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	16	no	—
378	C₂²	—	8	16	no	—
379	C₂²	C₁₉×#379	1	8	yes	—
380	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
381	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×#120	1	4	yes	—
383	C₄	—	2	8	no	—
384	C₄	—	2	4	no	—
385	C₄	—	8	8	no	—
386	C₂	—	2	4	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	8	no	—
389	C₂	—	4	4	no	—
390	C₂	—	4	8	no	—
391	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
392	C₂	C₁₉×#2883	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#99	C₂	semidirect
3. C₁₉×#2308	C₂	semidirect
4. C₁₉×#1782	C₂	semidirect
5. C₁₉×#1781	C₂	semidirect
8. C₂²×#41×C₁₉	C₄	semidirect
10. C₂³×D₄×C₁₉	C₄	semidirect
14. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
16. C₂×C₁₉×#99	C₂²	semidirect
18. C₁₉×#381	C₂²	semidirect
19. C₁₉×#379	C₂²	semidirect
21. C₂⁵×C₁₉	C₂×C₄	semidirect
31. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
42. C₂²×D₄×C₁₉	C₂×C₄	semidirect
43. C₂²×D₄×C₁₉	C₂×C₄	semidirect
49. C₂³×C₄×C₁₉	C₂×C₄	semidirect
50. C₂³×C₄×C₁₉	C₂×C₄	semidirect
67. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
97. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
110. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
117. #20585	C₁₉	direct (N × H)
166. C₂²×#99	C₂×C₁₉	semidirect
167. #2308	C₂×C₁₉	semidirect
168. #1782	C₂×C₁₉	semidirect
169. #1781	C₂×C₁₉	semidirect
197. C₂²×#41	C₄×C₁₉	semidirect
199. C₂³×D₄	C₄×C₁₉	semidirect
203. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
205. C₂×#99	C₂²×C₁₉	semidirect
207. #381	C₂²×C₁₉	semidirect
208. #379	C₂²×C₁₉	semidirect
217. C₂⁵	C₂×C₄×C₁₉	semidirect
227. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
238. C₂²×D₄	C₂×C₄×C₁₉	semidirect
239. C₂²×D₄	C₂×C₄×C₁₉	semidirect
245. C₂³×C₄	C₂×C₄×C₁₉	semidirect
246. C₂³×C₄	C₂×C₄×C₁₉	semidirect
254. C₁₉	#20585	direct (N × H)
264. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
294. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
307. C₂²×C₄	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
C₂²×C₁₉×H(5,𝔽₂)	2
C₂²×C₁₉×#99	2
C₁₉×#2308	2
C₁₉×#1782	2
C₁₉×#1781	2
#20585	19

Subgroups — C19×#20585 #18026544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20585 #18026544