Subgroups — C₁₉×#32855 #18038814

Order 4864.

510 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2647	C₂	1	2	yes	maximal
2	C₁₉×#2100	C₂	1	2	yes	maximal
3	C₁₉×#2099	C₂	1	2	yes	maximal
4	C₁₉×#2088	C₂	1	2	yes	maximal
5	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2086	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2085	C₂	1	2	yes	maximal
8	C₁₉×#2085	C₂	1	2	yes	maximal
9	C₁₉×#1832	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#106	C₂²	1	2	yes	—
13	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#400	—	2	2	no	—
16	C₁₉×#400	—	2	2	no	—
17	C₁₉×#398	—	2	2	no	—
18	C₁₉×#398	—	2	2	no	—
19	C₁₉×#389	C₂²	1	2	yes	—
20	C₁₉×#389	C₂²	1	2	yes	—
21	C₁₉×#389	C₂²	1	2	yes	—
22	C₁₉×#389	C₂²	1	2	yes	—
23	C₁₉×#384	C₂²	1	2	yes	—
24	C₁₉×#382	C₂²	1	2	yes	—
25	C₁₉×#376	C₂²	1	1	yes	characteristic
26	C₁₉×#340	C₂²	1	2	yes	—
27	C₁₉×#340	C₂²	1	2	yes	—
28	C₁₉×#340	C₂²	1	2	yes	—
29	C₁₉×#340	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#107	—	4	1	no	—
51	C₁₉×#107	—	4	1	no	—
52	C₁₉×#106	—	4	2	no	—
53	C₁₉×C₄⋊C₈	—	4	1	no	—
54	C₁₉×C₄⋊C₈	—	4	1	no	—
55	C₁₉×#95	—	2	2	no	—
56	C₁₉×#95	—	2	2	no	—
57	C₁₉×#95	—	2	2	no	—
58	C₁₉×#95	—	2	2	no	—
59	C₁₉×#95	—	2	2	no	—
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	D₄	1	1	yes	characteristic
62	C₁₉×#95	D₄	1	2	yes	—
63	C₁₉×#95	D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	2	1	no	—
75	C₂×C₈×C₁₉	—	2	1	no	—
76	C₂×C₈×C₁₉	—	2	4	no	—
77	C₂×C₈×C₁₉	—	2	2	no	—
78	C₂×C₈×C₁₉	—	2	2	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₄⋊C₄×C₁₉	—	8	2	no	—
88	C₄⋊C₄×C₁₉	—	8	2	no	—
89	C₄⋊C₄×C₁₉	—	8	2	no	—
90	C₄⋊C₄×C₁₉	—	8	2	no	—
91	C₄⋊C₄×C₁₉	—	8	2	no	—
92	C₄⋊C₄×C₁₉	—	8	2	no	—
93	C₄²×C₁₉	—	2	1	no	—
94	C₄²×C₁₉	—	2	2	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	#32855	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	2	no	—
106	C₂×C₄×C₁₉	—	2	2	no	—
107	C₂×C₄×C₁₉	—	2	2	no	—
108	C₂×C₄×C₁₉	—	2	2	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	—	4	2	no	—
113	C₂×C₄×C₁₉	—	4	2	no	—
114	C₂×C₄×C₁₉	—	4	2	no	—
115	C₂×C₄×C₁₉	—	4	2	no	—
116	C₂×C₄×C₁₉	—	4	2	no	—
117	C₂×C₄×C₁₉	—	4	2	no	—
118	C₂×C₄×C₁₉	—	4	2	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
123	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
124	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
125	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
126	C₈×C₁₉	—	4	2	no	—
127	C₈×C₁₉	—	4	1	no	—
128	C₈×C₁₉	—	4	1	no	—
129	#2647	C₂×C₁₉	1	2	yes	—
130	#2100	C₂×C₁₉	1	2	yes	—
131	#2099	C₂×C₁₉	1	2	yes	—
132	#2088	C₂×C₁₉	1	2	yes	—
133	#2087	C₂×C₁₉	1	1	yes	characteristic
134	#2086	C₂×C₁₉	1	1	yes	characteristic
135	#2085	C₂×C₁₉	1	2	yes	—
136	#2085	C₂×C₁₉	1	2	yes	—
137	#1832	C₂×C₁₉	1	1	yes	characteristic
138	C₂²×C₁₉	#536	1	2	yes	—
139	C₂²×C₁₉	#537	1	1	yes	characteristic
140	C₂²×C₁₉	#576	1	1	yes	characteristic
141	C₂²×C₁₉	#577	1	2	yes	—
142	C₂²×C₁₉	#578	1	1	yes	characteristic
143	C₄×C₁₉	—	4	2	no	—
144	C₄×C₁₉	—	4	2	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	—	4	1	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₄×C₁₉	—	8	2	no	—
149	C₄×C₁₉	—	8	2	no	—
150	C₄×C₁₉	—	8	2	no	—
151	C₄×C₁₉	#563	1	1	yes	characteristic
152	C₄×C₁₉	#563	1	1	yes	characteristic
153	C₄×C₁₉	#564	1	2	yes	—
154	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
155	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
156	C₂×#106	C₂²×C₁₉	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
159	#400	—	2	2	no	—
160	#400	—	2	2	no	—
161	#398	—	2	2	no	—
162	#398	—	2	2	no	—
163	#389	C₂²×C₁₉	1	2	yes	—
164	#389	C₂²×C₁₉	1	2	yes	—
165	#389	C₂²×C₁₉	1	2	yes	—
166	#389	C₂²×C₁₉	1	2	yes	—
167	#384	C₂²×C₁₉	1	2	yes	—
168	#382	C₂²×C₁₉	1	2	yes	—
169	#376	C₂²×C₁₉	1	1	yes	characteristic
170	#340	C₂²×C₁₉	1	2	yes	—
171	#340	C₂²×C₁₉	1	2	yes	—
172	#340	C₂²×C₁₉	1	2	yes	—
173	#340	C₂²×C₁₉	1	2	yes	—
174	#340	C₂²×C₁₉	1	1	yes	characteristic
175	#340	C₂²×C₁₉	1	1	yes	characteristic
176	#340	C₂²×C₁₉	1	2	yes	—
177	#336	C₂²×C₁₉	1	2	yes	—
178	#336	C₂²×C₁₉	1	2	yes	—
179	C₂×C₁₉	#2822	1	1	yes	characteristic
180	C₂×C₁₉	#3241	1	2	yes	—
181	C₂×C₁₉	#3242	1	2	yes	—
182	C₂×C₁₉	#3262	1	1	yes	characteristic
183	C₂×C₁₉	#3263	1	1	yes	characteristic
184	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
185	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
186	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
194	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
195	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
197	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
198	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
199	#107	—	4	1	no	—
200	#107	—	4	1	no	—
201	#106	—	4	2	no	—
202	C₄⋊C₈	—	4	1	no	—
203	C₄⋊C₈	—	4	1	no	—
204	#95	—	2	2	no	—
205	#95	—	2	2	no	—
206	#95	—	2	2	no	—
207	#95	—	2	2	no	—
208	#95	—	2	2	no	—
209	#95	—	2	2	no	—
210	#95	D₄×C₁₉	1	1	yes	characteristic
211	#95	D₄×C₁₉	1	2	yes	—
212	#95	D₄×C₁₉	1	1	yes	characteristic
213	C₁₉	#32855	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²×C₄	—	2	2	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	2	2	no	—
218	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
219	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
220	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
221	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
222	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
223	C₂×C₈	—	2	2	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	2	4	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	2	no	—
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	2	2	no	—
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	2	2	no	—
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	8	2	no	—
238	C₄⋊C₄	—	8	2	no	—
239	C₄⋊C₄	—	8	2	no	—
240	C₄⋊C₄	—	8	2	no	—
241	C₄⋊C₄	—	8	2	no	—
242	C₄⋊C₄	—	8	2	no	—
243	C₄²	—	2	1	no	—
244	C₄²	—	2	2	no	—
245	C₄²	—	2	2	no	—
246	C₄²	—	2	1	no	—
247	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
273	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
274	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
275	C₈	—	4	2	no	—
276	C₈	—	4	1	no	—
277	C₈	—	4	1	no	—
278	C₂²	C₁₉×#536	1	2	yes	—
279	C₂²	C₁₉×#537	1	1	yes	characteristic
280	C₂²	C₁₉×#576	1	1	yes	characteristic
281	C₂²	C₁₉×#577	1	2	yes	—
282	C₂²	C₁₉×#578	1	1	yes	characteristic
283	C₄	—	4	2	no	—
284	C₄	—	4	2	no	—
285	C₄	—	4	1	no	—
286	C₄	—	4	1	no	—
287	C₄	—	8	2	no	—
288	C₄	—	8	2	no	—
289	C₄	—	8	2	no	—
290	C₄	—	8	2	no	—
291	C₄	C₁₉×#563	1	1	yes	characteristic
292	C₄	C₁₉×#563	1	1	yes	characteristic
293	C₄	C₁₉×#564	1	2	yes	—
294	C₂	C₁₉×#2822	1	1	yes	characteristic
295	C₂	C₁₉×#3241	1	2	yes	—
296	C₂	C₁₉×#3242	1	2	yes	—
297	C₂	C₁₉×#3262	1	1	yes	characteristic
298	C₂	C₁₉×#3263	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 ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
97. #32855	C₁₉	direct (N × H)
213. C₁₉	#32855	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×#2647	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2086	2
C₁₉×#2085	2
C₁₉×#1832	2
#32855	19

Subgroups — C19×#32855 #18038814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32855 #18038814