Subgroups — C₂×C₁₉×#2093 #18029684

Order 4864.

1454 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#107	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₉×#102	C₂	1	2	yes	maximal
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2093	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
13	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	—	2	8	no	—
15	C₂×C₁₉×#107	C₂²	1	8	yes	complemented
16	C₂×C₁₉×#102	—	2	8	no	—
17	C₂×C₁₉×#102	C₂²	1	8	yes	—
18	C₁₉×#390	—	2	2	no	—
19	C₁₉×#390	C₂²	1	4	yes	—
20	C₁₉×#384	—	2	2	no	—
21	C₁₉×#384	C₂²	1	4	yes	complemented
22	C₁₉×#336	C₂²	1	4	yes	complemented
23	C₂⁵×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	—	2	4	no	—
25	C₂²×D₄×C₁₉	—	2	1	no	—
26	C₂²×D₄×C₁₉	—	2	4	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
29	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	2	no	—
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₉	—	2	4	no	—
35	C₂²×C₈×C₁₉	—	2	4	no	—
36	C₂²×C₈×C₁₉	D₄	1	8	yes	—
37	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
38	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
49	C₂×C₄²×C₁₉	—	2	4	no	—
50	C₂×C₄²×C₁₉	D₄	1	2	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
52	C₁₉×#107	—	2	16	no	—
53	C₁₉×#102	—	2	16	no	—
54	C₂⁴×C₁₉	—	2	4	no	—
55	C₂⁴×C₁₉	—	2	2	no	—
56	C₂⁴×C₁₉	—	4	2	no	—
57	C₂⁴×C₁₉	—	4	2	no	—
58	C₂⁴×C₁₉	—	4	4	no	—
59	C₂⁴×C₁₉	—	4	4	no	—
60	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×D₄×C₁₉	—	2	16	no	—
62	C₂×D₄×C₁₉	—	2	4	no	—
63	C₂×D₄×C₁₉	—	2	4	no	—
64	C₂×D₄×C₁₉	—	2	4	no	—
65	C₂×D₄×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	—	4	8	no	—
67	C₂×D₄×C₁₉	—	4	2	no	—
68	C₂×D₄×C₁₉	—	4	2	no	—
69	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
70	C₂²×C₄×C₁₉	—	2	4	no	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	4	no	—
74	C₂²×C₄×C₁₉	—	4	4	no	—
75	C₂²×C₄×C₁₉	—	4	2	no	—
76	C₂²×C₄×C₁₉	—	4	4	no	—
77	C₂²×C₄×C₁₉	—	4	8	no	—
78	C₂²×C₄×C₁₉	D₈	1	8	yes	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
82	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₁₉	#41	1	4	yes	—
84	C₂²×C₄×C₁₉	#41	1	2	yes	—
85	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₉	—	2	16	no	—
87	C₂×C₈×C₁₉	—	2	4	no	—
88	C₂×C₈×C₁₉	—	2	4	no	—
89	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
90	C₄⋊C₄×C₁₉	—	2	4	no	—
91	C₄⋊C₄×C₁₉	—	2	4	no	—
92	C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₄⋊C₄×C₁₉	—	4	4	no	—
94	C₄⋊C₄×C₁₉	—	4	2	no	—
95	C₄⋊C₄×C₁₉	—	4	16	no	—
96	C₂²⋊C₄×C₁₉	—	4	16	no	—
97	C₄²×C₁₉	—	2	4	no	—
98	C₄²×C₁₉	—	2	4	no	—
99	C₂×#2093	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂³×C₁₉	—	2	4	no	—
101	C₂³×C₁₉	—	4	2	no	—
102	C₂³×C₁₉	—	4	2	no	—
103	C₂³×C₁₉	—	4	4	no	—
104	C₂³×C₁₉	—	4	4	no	—
105	C₂³×C₁₉	—	4	8	no	—
106	C₂³×C₁₉	—	4	16	no	—
107	C₂³×C₁₉	—	8	8	no	—
108	C₂³×C₁₉	—	8	4	no	—
109	C₂³×C₁₉	—	8	4	no	—
110	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
111	C₂³×C₁₉	#123	1	2	yes	—
112	C₂³×C₁₉	#127	1	2	yes	—
113	C₂³×C₁₉	C₂×D₈	1	4	yes	—
114	C₂³×C₁₉	#137	1	4	yes	—
115	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
116	D₄×C₁₉	—	2	8	no	—
117	D₄×C₁₉	—	4	4	no	—
118	D₄×C₁₉	—	4	8	no	—
119	C₂×C₄×C₁₉	—	2	4	no	—
120	C₂×C₄×C₁₉	—	2	4	no	—
121	C₂×C₄×C₁₉	—	2	16	no	—
122	C₂×C₄×C₁₉	—	4	4	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	4	no	—
125	C₂×C₄×C₁₉	—	4	8	no	—
126	C₂×C₄×C₁₉	—	8	4	no	—
127	C₂×C₄×C₁₉	—	8	8	no	—
128	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
129	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
130	C₂×C₄×C₁₉	#123	1	8	yes	—
131	C₂×C₄×C₁₉	#123	1	2	yes	—
132	C₂×C₄×C₁₉	#127	1	2	yes	—
133	C₂×C₄×C₁₉	C₂×D₈	1	8	yes	—
134	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
135	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
137	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
138	C₈×C₁₉	—	2	8	no	—
139	C₂²×#107	C₂×C₁₉	1	2	yes	complemented
140	C₂²×#102	C₂×C₁₉	1	2	yes	—
141	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
142	C₂×#384	C₂×C₁₉	1	1	yes	characteristic, complemented
143	#2093	C₂×C₁₉	1	8	yes	direct product factor
144	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
145	C₂²×C₁₉	—	4	4	no	—
146	C₂²×C₁₉	—	4	8	no	—
147	C₂²×C₁₉	—	8	4	no	—
148	C₂²×C₁₉	—	8	16	no	—
149	C₂²×C₁₉	—	8	2	no	—
150	C₂²×C₁₉	—	8	2	no	—
151	C₂²×C₁₉	#399	1	4	yes	—
152	C₂²×C₁₉	#474	1	8	yes	—
153	C₂²×C₁₉	#480	1	8	yes	—
154	C₂²×C₁₉	#493	1	4	yes	—
155	C₂²×C₁₉	#497	1	4	yes	—
156	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
157	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
158	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
159	C₂²×C₁₉	C₂²×D₈	1	2	yes	—
160	C₂²×C₁₉	C₂×#137	1	2	yes	—
161	C₄×C₁₉	—	2	8	no	—
162	C₄×C₁₉	—	8	2	no	—
163	C₄×C₁₉	—	8	4	no	—
164	C₄×C₁₉	#399	1	4	yes	—
165	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
166	C₄×C₁₉	C₂×#123	1	2	yes	—
167	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
168	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
169	C₂²×C₄⋊C₄	—	2	2	no	—
170	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
172	C₂²×C₂²⋊C₄	—	2	2	no	—
173	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
174	C₂×#107	—	2	8	no	—
175	C₂×#107	C₂²×C₁₉	1	8	yes	complemented
176	C₂×#102	—	2	8	no	—
177	C₂×#102	C₂²×C₁₉	1	8	yes	—
178	#390	—	2	2	no	—
179	#390	C₂²×C₁₉	1	4	yes	—
180	#384	—	2	2	no	—
181	#384	C₂²×C₁₉	1	4	yes	complemented
182	#336	C₂²×C₁₉	1	4	yes	complemented
183	C₂×C₁₉	—	8	4	no	—
184	C₂×C₁₉	#2093	1	8	yes	direct product factor
185	C₂×C₁₉	C₂×#399	1	1	yes	characteristic
186	C₂×C₁₉	C₂×#474	1	2	yes	—
187	C₂×C₁₉	C₂×#480	1	2	yes	—
188	C₂×C₁₉	C₂×#493	1	1	yes	characteristic
189	C₂×C₁₉	C₂×#497	1	1	yes	characteristic
190	C₂⁵	—	2	1	no	—
191	C₂²×D₄	—	2	4	no	—
192	C₂²×D₄	—	2	1	no	—
193	C₂²×D₄	—	2	4	no	—
194	C₂²×D₄	—	2	2	no	—
195	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
196	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
197	C₂³×C₄	—	2	1	no	—
198	C₂³×C₄	—	2	2	no	—
199	C₂³×C₄	D₄×C₁₉	1	2	yes	—
200	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	D₄×C₁₉	1	8	yes	—
204	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	8	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	1	no	—
211	C₂×C₄⋊C₄	—	4	8	no	—
212	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
214	C₂×C₂²⋊C₄	—	2	8	no	—
215	C₂×C₂²⋊C₄	—	4	8	no	—
216	C₂×C₄²	—	2	4	no	—
217	C₂×C₄²	D₄×C₁₉	1	2	yes	—
218	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
219	#107	—	2	16	no	—
220	#102	—	2	16	no	—
221	C₁₉	C₂×#2093	1	1	yes	characteristic, direct product factor, Sylow
222	C₂⁴	—	2	4	no	—
223	C₂⁴	—	2	2	no	—
224	C₂⁴	—	4	2	no	—
225	C₂⁴	—	4	2	no	—
226	C₂⁴	—	4	4	no	—
227	C₂⁴	—	4	4	no	—
228	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
229	C₂×D₄	—	2	16	no	—
230	C₂×D₄	—	2	4	no	—
231	C₂×D₄	—	2	4	no	—
232	C₂×D₄	—	2	4	no	—
233	C₂×D₄	—	2	2	no	—
234	C₂×D₄	—	4	2	no	—
235	C₂×D₄	—	4	8	no	—
236	C₂×D₄	—	4	2	no	—
237	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	4	4	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	—	4	4	no	—
245	C₂²×C₄	—	4	8	no	—
246	C₂²×C₄	D₈×C₁₉	1	8	yes	—
247	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
248	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
249	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
250	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
251	C₂²×C₄	#41×C₁₉	1	4	yes	—
252	C₂²×C₄	#41×C₁₉	1	2	yes	—
253	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
254	C₂×C₈	—	2	16	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	4	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	—	4	16	no	—
264	C₂²⋊C₄	—	4	16	no	—
265	C₄²	—	2	4	no	—
266	C₄²	—	2	4	no	—
267	C₂³	—	2	4	no	—
268	C₂³	—	4	8	no	—
269	C₂³	—	4	16	no	—
270	C₂³	—	4	2	no	—
271	C₂³	—	4	2	no	—
272	C₂³	—	4	4	no	—
273	C₂³	—	4	4	no	—
274	C₂³	—	8	8	no	—
275	C₂³	—	8	4	no	—
276	C₂³	—	8	4	no	—
277	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
278	C₂³	C₁₉×#123	1	2	yes	—
279	C₂³	C₁₉×#127	1	2	yes	—
280	C₂³	C₂×D₈×C₁₉	1	4	yes	—
281	C₂³	C₁₉×#137	1	4	yes	—
282	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
283	D₄	—	2	8	no	—
284	D₄	—	4	8	no	—
285	D₄	—	4	4	no	—
286	C₂×C₄	—	2	16	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	8	no	—
293	C₂×C₄	—	8	4	no	—
294	C₂×C₄	—	8	8	no	—
295	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
296	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
297	C₂×C₄	C₁₉×#123	1	2	yes	—
298	C₂×C₄	C₁₉×#123	1	8	yes	—
299	C₂×C₄	C₁₉×#127	1	2	yes	—
300	C₂×C₄	C₂×D₈×C₁₉	1	8	yes	—
301	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
302	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
303	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
304	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
305	C₈	—	2	8	no	—
306	C₂²	—	4	8	no	—
307	C₂²	—	4	4	no	—
308	C₂²	—	8	4	no	—
309	C₂²	—	8	16	no	—
310	C₂²	—	8	2	no	—
311	C₂²	—	8	2	no	—
312	C₂²	C₁₉×#399	1	4	yes	—
313	C₂²	C₁₉×#474	1	8	yes	—
314	C₂²	C₁₉×#480	1	8	yes	—
315	C₂²	C₁₉×#493	1	4	yes	—
316	C₂²	C₁₉×#497	1	4	yes	—
317	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
318	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
319	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
320	C₂²	C₂²×D₈×C₁₉	1	2	yes	—
321	C₂²	C₂×C₁₉×#137	1	2	yes	—
322	C₄	—	2	8	no	—
323	C₄	—	8	2	no	—
324	C₄	—	8	4	no	—
325	C₄	C₁₉×#399	1	4	yes	—
326	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
327	C₄	C₂×C₁₉×#123	1	2	yes	—
328	C₂	—	8	4	no	—
329	C₂	C₁₉×#2093	1	8	yes	direct product factor
330	C₂	C₂×C₁₉×#399	1	1	yes	characteristic
331	C₂	C₂×C₁₉×#474	1	2	yes	—
332	C₂	C₂×C₁₉×#480	1	2	yes	—
333	C₂	C₂×C₁₉×#493	1	1	yes	characteristic
334	C₂	C₂×C₁₉×#497	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#107	C₂	semidirect
4. C₂×C₁₉×#384	C₂	semidirect
5. C₁₉×#2093	C₂	direct (N × H)
6. C₂×C₁₉×#336	C₂	semidirect
15. C₂×C₁₉×#107	C₂²	semidirect
21. C₁₉×#384	C₂²	semidirect
22. C₁₉×#336	C₂²	semidirect
99. C₂×#2093	C₁₉	direct (N × H)
139. C₂²×#107	C₂×C₁₉	semidirect
142. C₂×#384	C₂×C₁₉	semidirect
143. #2093	C₂×C₁₉	direct (N × H)
144. C₂×#336	C₂×C₁₉	semidirect
175. C₂×#107	C₂²×C₁₉	semidirect
181. #384	C₂²×C₁₉	semidirect
182. #336	C₂²×C₁₉	semidirect
184. C₂×C₁₉	#2093	direct (N × H)
221. C₁₉	C₂×#2093	direct (N × H)
329. C₂	C₁₉×#2093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#107	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#384	2
C₁₉×#2093	2
C₂×C₁₉×#336	2
C₂×#2093	19

Subgroups — C2×C19×#2093 #18029684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2093 #18029684