Subgroups — C₁₉×#32852 #18038811

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2864	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2859	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	2	yes	maximal
4	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2088	C₂	1	2	yes	maximal
7	C₁₉×#2087	C₂	1	2	yes	maximal
8	C₁₉×#2085	C₂	1	2	yes	maximal
9	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1831	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₉×#125	—	2	1	no	—
13	C₂×C₁₉×#107	C₂²	1	2	yes	—
14	C₂×C₁₉×#106	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
16	C₁₉×#389	—	2	1	no	—
17	C₁₉×#389	—	2	1	no	—
18	C₁₉×#389	C₂²	1	1	yes	characteristic
19	C₁₉×#389	C₂²	1	1	yes	characteristic
20	C₁₉×#389	C₂²	1	2	yes	—
21	C₁₉×#389	C₂²	1	1	yes	characteristic
22	C₁₉×#389	C₂²	1	2	yes	—
23	C₁₉×#389	C₂²	1	1	yes	characteristic
24	C₁₉×#387	—	2	1	no	—
25	C₁₉×#387	—	2	1	no	—
26	C₁₉×#387	—	2	1	no	—
27	C₁₉×#387	—	2	1	no	—
28	C₁₉×#384	C₂²	1	1	yes	characteristic
29	C₁₉×#384	C₂²	1	1	yes	characteristic
30	C₁₉×#382	—	2	1	no	—
31	C₁₉×#382	C₂²	1	1	yes	characteristic
32	C₁₉×#382	C₂²	1	1	yes	characteristic
33	C₄³×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₁₉×#125	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#107	—	4	2	no	—
70	C₁₉×#106	—	4	2	no	—
71	C₁₉×C₄⋊C₈	—	4	2	no	—
72	C₁₉×#95	—	2	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	1	no	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	—	2	1	no	—
79	C₁₉×#95	—	2	1	no	—
80	C₁₉×#95	—	2	1	no	—
81	C₁₉×#95	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	4	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₄⋊C₄×C₁₉	—	4	2	no	—
112	C₄⋊C₄×C₁₉	—	4	4	no	—
113	C₄⋊C₄×C₁₉	—	4	4	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	2	no	—
116	C₄⋊C₄×C₁₉	—	4	2	no	—
117	C₄⋊C₄×C₁₉	—	4	2	no	—
118	C₄⋊C₄×C₁₉	—	4	2	no	—
119	C₄⋊C₄×C₁₉	—	4	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	—	2	2	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	#32852	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	#135	1	2	yes	—
164	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₉	#137	1	2	yes	—
166	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
168	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
169	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₁₉	—	4	2	no	—
171	C₈×C₁₉	—	4	2	no	—
172	#2864	C₂×C₁₉	1	1	yes	characteristic
173	#2859	C₂×C₁₉	1	1	yes	characteristic
174	#2101	C₂×C₁₉	1	2	yes	—
175	#2099	C₂×C₁₉	1	1	yes	characteristic
176	#2099	C₂×C₁₉	1	1	yes	characteristic
177	#2088	C₂×C₁₉	1	2	yes	—
178	#2087	C₂×C₁₉	1	2	yes	—
179	#2085	C₂×C₁₉	1	2	yes	—
180	#2084	C₂×C₁₉	1	1	yes	characteristic
181	#2083	C₂×C₁₉	1	1	yes	characteristic
182	#1831	C₂×C₁₉	1	1	yes	characteristic
183	C₂²×C₁₉	#536	1	1	yes	characteristic
184	C₂²×C₁₉	#536	1	1	yes	characteristic
185	C₂²×C₁₉	#537	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
189	C₂²×C₁₉	#575	1	1	yes	characteristic
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	4	1	no	—
194	C₄×C₁₉	—	4	1	no	—
195	C₄×C₁₉	—	4	1	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	#563	1	2	yes	—
203	C₄×C₁₉	#564	1	2	yes	—
204	C₂×#125	—	2	1	no	—
205	C₂×#107	C₂²×C₁₉	1	2	yes	—
206	C₂×#106	C₂²×C₁₉	1	2	yes	—
207	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
208	#389	—	2	1	no	—
209	#389	—	2	1	no	—
210	#389	C₂²×C₁₉	1	1	yes	characteristic
211	#389	C₂²×C₁₉	1	1	yes	characteristic
212	#389	C₂²×C₁₉	1	2	yes	—
213	#389	C₂²×C₁₉	1	1	yes	characteristic
214	#389	C₂²×C₁₉	1	2	yes	—
215	#389	C₂²×C₁₉	1	1	yes	characteristic
216	#387	—	2	1	no	—
217	#387	—	2	1	no	—
218	#387	—	2	1	no	—
219	#387	—	2	1	no	—
220	#384	C₂²×C₁₉	1	1	yes	characteristic
221	#384	C₂²×C₁₉	1	1	yes	characteristic
222	#382	—	2	1	no	—
223	#382	C₂²×C₁₉	1	1	yes	characteristic
224	#382	C₂²×C₁₉	1	1	yes	characteristic
225	C₄³	C₂²×C₁₉	1	1	yes	characteristic
226	#340	C₂²×C₁₉	1	2	yes	—
227	#340	C₂²×C₁₉	1	2	yes	—
228	#340	C₂²×C₁₉	1	2	yes	—
229	#340	C₂²×C₁₉	1	2	yes	—
230	#340	C₂²×C₁₉	1	2	yes	—
231	#340	C₂²×C₁₉	1	2	yes	—
232	#336	C₂²×C₁₉	1	1	yes	characteristic
233	#336	C₂²×C₁₉	1	1	yes	characteristic
234	#336	C₂²×C₁₉	1	2	yes	—
235	C₂×C₁₉	#2822	1	1	yes	characteristic
236	C₂×C₁₉	#3228	1	1	yes	characteristic
237	C₂×C₁₉	#3232	1	1	yes	characteristic
238	C₂×C₁₉	#3237	1	1	yes	characteristic
239	C₂×C₁₉	#3238	1	1	yes	characteristic
240	C₂×C₁₉	#3248	1	1	yes	characteristic
241	C₂×C₁₉	#3251	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
244	#125	—	4	4	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
261	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
268	#107	—	4	2	no	—
269	#106	—	4	2	no	—
270	C₄⋊C₈	—	4	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	C₁₉	#32852	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	4	1	no	—
328	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	C₁₉×#135	1	2	yes	—
363	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
364	C₂×C₄	C₁₉×#137	1	2	yes	—
365	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
367	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
368	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₂²	C₁₉×#536	1	1	yes	characteristic
372	C₂²	C₁₉×#536	1	1	yes	characteristic
373	C₂²	C₁₉×#537	1	1	yes	characteristic
374	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
375	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
376	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
377	C₂²	C₁₉×#575	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	C₁₉×#563	1	2	yes	—
391	C₄	C₁₉×#564	1	2	yes	—
392	C₂	C₁₉×#2822	1	1	yes	characteristic
393	C₂	C₁₉×#3228	1	1	yes	characteristic
394	C₂	C₁₉×#3232	1	1	yes	characteristic
395	C₂	C₁₉×#3237	1	1	yes	characteristic
396	C₂	C₁₉×#3238	1	1	yes	characteristic
397	C₂	C₁₉×#3248	1	1	yes	characteristic
398	C₂	C₁₉×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
128. #32852	C₁₉	direct (N × H)
281. C₁₉	#32852	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2864	2
C₁₉×#2859	2
C₁₉×#2101	2
C₁₉×#2099	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2085	2
C₁₉×#2084	2
C₁₉×#2083	2
C₁₉×#1831	2
#32852	19

Subgroups — C19×#32852 #18038811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32852 #18038811