Subgroups — C₁₉×#32795 #18038754

Order 4864.

584 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2629	C₂	1	2	yes	maximal
2	C₁₉×#2100	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2099	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2077	C₂	1	2	yes	maximal
5	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2059	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₉×#125	C₂²	1	2	yes	—
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#106	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#398	—	2	2	no	—
18	C₁₉×#398	—	2	2	no	—
19	C₁₉×#396	—	2	2	no	—
20	C₁₉×#396	—	2	2	no	—
21	C₁₉×#389	C₂²	1	2	yes	—
22	C₁₉×#389	C₂²	1	2	yes	—
23	C₁₉×#384	C₂²	1	2	yes	—
24	C₁₉×#380	C₂²	1	2	yes	—
25	C₁₉×#380	C₂²	1	2	yes	—
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	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
39	C₁₉×#125	—	4	2	no	—
40	C₁₉×#125	—	4	2	no	—
41	C₁₉×#117	—	4	1	no	—
42	C₁₉×#117	—	4	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
58	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
59	C₁₉×#107	—	4	1	no	—
60	C₁₉×#107	—	4	1	no	—
61	C₁₉×#106	—	4	2	no	—
62	C₁₉×C₂²⋊C₈	—	4	1	no	—
63	C₁₉×C₂²⋊C₈	—	4	1	no	—
64	C₁₉×#95	—	2	2	no	—
65	C₁₉×#95	—	2	2	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₁₉×#95	—	2	2	no	—
68	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	2	no	—
74	C₂²×C₄×C₁₉	—	2	2	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₁₉	—	2	2	no	—
82	C₂×C₈×C₁₉	—	2	1	no	—
83	C₂×C₈×C₁₉	—	2	1	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	2	2	no	—
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	4	4	no	—
99	C₄⋊C₄×C₁₉	—	4	4	no	—
100	C₄⋊C₄×C₁₉	—	8	2	no	—
101	C₄⋊C₄×C₁₉	—	8	2	no	—
102	C₄⋊C₄×C₁₉	—	8	2	no	—
103	C₄⋊C₄×C₁₉	—	8	2	no	—
104	C₂²⋊C₄×C₁₉	—	4	2	no	—
105	C₂²⋊C₄×C₁₉	—	8	2	no	—
106	C₂²⋊C₄×C₁₉	—	8	2	no	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	2	no	—
109	#32795	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	2	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	1	no	—
115	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	—	2	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	4	2	no	—
138	C₂×C₄×C₁₉	—	4	2	no	—
139	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
140	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
142	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
143	C₈×C₁₉	—	4	2	no	—
144	C₈×C₁₉	—	4	1	no	—
145	C₈×C₁₉	—	4	1	no	—
146	#2629	C₂×C₁₉	1	2	yes	—
147	#2100	C₂×C₁₉	1	2	yes	complemented
148	#2099	C₂×C₁₉	1	2	yes	complemented
149	#2077	C₂×C₁₉	1	2	yes	—
150	#2076	C₂×C₁₉	1	1	yes	characteristic
151	#2075	C₂×C₁₉	1	1	yes	characteristic
152	#2059	C₂×C₁₉	1	2	yes	complemented
153	#2059	C₂×C₁₉	1	2	yes	complemented
154	#1818	C₂×C₁₉	1	1	yes	characteristic
155	C₂²×C₁₉	—	4	1	no	—
156	C₂²×C₁₉	—	4	1	no	—
157	C₂²×C₁₉	—	4	1	no	—
158	C₂²×C₁₉	—	4	2	no	—
159	C₂²×C₁₉	—	4	2	no	—
160	C₂²×C₁₉	#534	1	1	yes	characteristic
161	C₂²×C₁₉	#536	1	2	yes	—
162	C₂²×C₁₉	#576	1	1	yes	characteristic
163	C₂²×C₁₉	#577	1	2	yes	—
164	C₂²×C₁₉	#578	1	1	yes	characteristic
165	C₄×C₁₉	—	4	1	no	—
166	C₄×C₁₉	—	4	2	no	—
167	C₄×C₁₉	—	4	2	no	—
168	C₄×C₁₉	—	8	2	no	—
169	C₄×C₁₉	—	8	2	no	—
170	C₄×C₁₉	—	8	2	no	—
171	C₄×C₁₉	—	8	2	no	—
172	C₄×C₁₉	#563	1	2	yes	—
173	C₄×C₁₉	#563	1	1	yes	characteristic
174	C₄×C₁₉	#563	1	1	yes	characteristic
175	C₂×#125	C₂²×C₁₉	1	2	yes	—
176	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
177	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
178	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
179	C₂×#106	C₂²×C₁₉	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
181	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
182	#398	—	2	2	no	—
183	#398	—	2	2	no	—
184	#396	—	2	2	no	—
185	#396	—	2	2	no	—
186	#389	C₂²×C₁₉	1	2	yes	—
187	#389	C₂²×C₁₉	1	2	yes	—
188	#384	C₂²×C₁₉	1	2	yes	—
189	#380	C₂²×C₁₉	1	2	yes	—
190	#380	C₂²×C₁₉	1	2	yes	—
191	#340	C₂²×C₁₉	1	2	yes	—
192	#340	C₂²×C₁₉	1	2	yes	—
193	#340	C₂²×C₁₉	1	2	yes	—
194	#340	C₂²×C₁₉	1	2	yes	—
195	#340	C₂²×C₁₉	1	1	yes	characteristic
196	#340	C₂²×C₁₉	1	1	yes	characteristic
197	#340	C₂²×C₁₉	1	2	yes	—
198	#336	C₂²×C₁₉	1	2	yes	—
199	#336	C₂²×C₁₉	1	2	yes	—
200	C₂×C₁₉	—	8	1	no	—
201	C₂×C₁₉	#2817	1	1	yes	characteristic
202	C₂×C₁₉	#3203	1	1	yes	characteristic
203	C₂×C₁₉	#3204	1	1	yes	characteristic
204	C₂×C₁₉	#3241	1	2	yes	—
205	C₂×C₁₉	#3242	1	2	yes	—
206	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
208	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
210	#125	—	4	2	no	—
211	#125	—	4	2	no	—
212	#117	—	4	1	no	—
213	#117	—	4	1	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
221	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
224	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
229	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
230	#107	—	4	1	no	—
231	#107	—	4	1	no	—
232	#106	—	4	2	no	—
233	C₂²⋊C₈	—	4	1	no	—
234	C₂²⋊C₈	—	4	1	no	—
235	#95	—	2	2	no	—
236	#95	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	C₁₉	#32795	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
241	C₂²×C₄	—	2	1	no	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
251	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
252	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	2	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	—	4	1	no	—
269	C₄⋊C₄	—	4	1	no	—
270	C₄⋊C₄	—	4	4	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₄⋊C₄	—	8	2	no	—
273	C₄⋊C₄	—	8	2	no	—
274	C₄⋊C₄	—	8	2	no	—
275	C₄⋊C₄	—	8	2	no	—
276	C₂²⋊C₄	—	4	2	no	—
277	C₂²⋊C₄	—	8	2	no	—
278	C₂²⋊C₄	—	8	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	1	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	1	no	—
286	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
313	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
314	C₈	—	4	2	no	—
315	C₈	—	4	1	no	—
316	C₈	—	4	1	no	—
317	C₂²	—	4	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	1	no	—
322	C₂²	C₁₉×#534	1	1	yes	characteristic
323	C₂²	C₁₉×#536	1	2	yes	—
324	C₂²	C₁₉×#576	1	1	yes	characteristic
325	C₂²	C₁₉×#577	1	2	yes	—
326	C₂²	C₁₉×#578	1	1	yes	characteristic
327	C₄	—	4	2	no	—
328	C₄	—	4	2	no	—
329	C₄	—	4	1	no	—
330	C₄	—	8	2	no	—
331	C₄	—	8	2	no	—
332	C₄	—	8	2	no	—
333	C₄	—	8	2	no	—
334	C₄	C₁₉×#563	1	2	yes	—
335	C₄	C₁₉×#563	1	1	yes	characteristic
336	C₄	C₁₉×#563	1	1	yes	characteristic
337	C₂	—	8	1	no	—
338	C₂	C₁₉×#2817	1	1	yes	characteristic
339	C₂	C₁₉×#3203	1	1	yes	characteristic
340	C₂	C₁₉×#3204	1	1	yes	characteristic
341	C₂	C₁₉×#3241	1	2	yes	—
342	C₂	C₁₉×#3242	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2100	C₂	semidirect
3. C₁₉×#2099	C₂	semidirect
7. C₁₉×#2059	C₂	semidirect
8. C₁₉×#2059	C₂	semidirect
109. #32795	C₁₉	direct (N × H)
147. #2100	C₂×C₁₉	semidirect
148. #2099	C₂×C₁₉	semidirect
152. #2059	C₂×C₁₉	semidirect
153. #2059	C₂×C₁₉	semidirect
239. C₁₉	#32795	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×#2629	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#2075	2
C₁₉×#2059	2
C₁₉×#1818	2
#32795	19

Subgroups — C19×#32795 #18038754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32795 #18038754