Subgroups — #18070988

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14571992	C₂	1	1	yes	maximal, characteristic
2	#14563381	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561455	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597315	C₄	1	1	yes	characteristic
6	C₂×#10597320	C₄	1	1	yes	characteristic
7	C₂×#10597321	—	2	1	no	—
8	C₂×#10597321	—	2	1	no	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926446	—	2	1	no	—
11	#11926446	—	2	1	no	—
12	#11926446	C₄	1	2	yes	—
13	#11926446	C₂²	1	2	yes	—
14	#11926299	—	2	1	no	—
15	#11926299	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
17	C₂×C₁₉×#97	—	2	1	no	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	C₂²	1	2	yes	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	C₂×C₄	1	2	yes	—
23	C₂²×Dic₃₈	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
33	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
34	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
35	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	#10597321	—	4	4	no	—
40	#10597321	—	4	2	no	—
41	#10597321	—	4	2	no	—
42	#10597320	—	4	2	no	—
43	#10597315	—	4	2	no	—
44	C₁₉×C₄⋊C₈	—	2	4	no	—
45	C₁₉×#97	—	4	2	no	—
46	C₄×C₁₉⋊C₈	—	2	4	no	—
47	C₂³×D₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×Dic₁₉	—	2	2	no	—
56	C₂×D₇₆	—	2	4	no	—
57	C₂×D₇₆	—	4	2	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×D₇₆	—	4	2	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	—	4	2	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	2	no	—
65	C₂×Dic₃₈	—	4	2	no	—
66	C₂×Dic₃₈	—	4	2	no	—
67	C₂×Dic₃₈	—	4	2	no	—
68	C₂×C₈×C₁₉	—	2	4	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	2	2	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	D₈	1	2	yes	—
78	C₄²×C₁₉	SD₁₆	1	2	yes	—
79	(C₂×D₁₉)⋊C₄	—	4	4	no	—
80	(C₂×D₁₉)⋊C₄	—	4	4	no	—
81	(C₂×D₁₉)⋊C₄	—	4	2	no	—
82	(C₂×D₁₉)⋊C₄	—	4	2	no	—
83	(C₂×D₁₉)⋊C₄	—	4	4	no	—
84	C₄⋊Dic₁₉	—	4	2	no	—
85	C₄⋊Dic₁₉	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#7679	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×D₁₉	—	4	2	no	—
92	C₂²×D₁₉	—	4	2	no	—
93	C₂²×D₁₉	—	4	2	no	—
94	C₂²×D₁₉	—	4	2	no	—
95	C₂²×D₁₉	—	4	2	no	—
96	C₂²×D₁₉	—	4	2	no	—
97	C₂²×D₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	#100	1	2	yes	—
112	C₂×C₄×C₁₉	#102	1	2	yes	—
113	C₂×C₄×C₁₉	#102	1	2	yes	—
114	C₂×C₄×C₁₉	#104	1	2	yes	—
115	C₂×C₄×C₁₉	#104	1	2	yes	—
116	C₂×C₄×C₁₉	#131	1	2	yes	—
117	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	D₇₆	—	8	4	no	—
124	D₇₆	—	8	4	no	—
125	D₇₆	—	8	4	no	—
126	Dic₃₈	—	8	4	no	—
127	C₈×C₁₉	—	4	4	no	—
128	C₁₉⋊C₈	—	4	4	no	—
129	#2858	—	19	1	no	—
130	#1767	D₁₉	1	1	yes	characteristic, complemented
131	#1744	—	19	1	no	—
132	#1270	—	19	4	no	—
133	C₂²×C₁₉	#408	1	1	yes	characteristic
134	C₂²×C₁₉	#410	1	1	yes	characteristic
135	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
136	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
137	C₂²×C₁₉	#418	1	1	yes	characteristic
138	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
139	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
140	C₂×D₁₉	—	8	2	no	—
141	C₂×D₁₉	—	8	2	no	—
142	C₂×D₁₉	—	8	2	no	—
143	C₂×D₁₉	—	8	2	no	—
144	C₂×D₁₉	—	8	2	no	—
145	C₂×D₁₉	—	8	2	no	—
146	C₂×D₁₉	—	8	2	no	—
147	C₄×C₁₉	—	2	2	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	2	1	no	—
152	C₄×C₁₉	—	2	2	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	#329	1	4	yes	—
155	Dic₁₉	—	8	2	no	—
156	C₂×C₄⋊Q₈	—	19	1	no	—
157	C₂×#127	—	19	1	no	—
158	C₂×#124	—	38	1	no	—
159	C₂×#124	—	38	1	no	—
160	C₂×C₄⋊C₈	—	2	1	no	—
161	C₂×#97	—	2	1	no	—
162	C₂×C₄×C₈	—	38	1	no	—
163	#390	—	19	2	no	—
164	#390	—	19	2	no	—
165	#390	—	38	1	no	—
166	#390	—	38	1	no	—
167	C₄³	C₂×D₁₉	1	1	yes	characteristic
168	#336	—	19	2	no	—
169	#336	—	38	1	no	—
170	#336	C₂×D₁₉	1	2	yes	—
171	C₂×C₁₉	#1469	1	1	yes	characteristic
172	C₂×C₁₉	#1484	1	1	yes	characteristic
173	C₂×C₁₉	#1492	1	1	yes	characteristic
174	C₂×C₁₉	#1502	1	1	yes	characteristic
175	C₂×C₁₉	#1505	1	1	yes	characteristic
176	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
177	C₂×C₁₉	#1545	1	1	yes	characteristic
178	D₁₉	—	16	2	no	—
179	C₂²×Q₈	—	38	1	no	—
180	C₂²×D₄	—	19	2	no	—
181	C₂²×D₄	—	38	1	no	—
182	C₂²×D₄	—	38	1	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	—	38	2	no	—
185	C₄⋊Q₈	—	76	2	no	—
186	#127	—	76	2	no	—
187	#124	—	76	4	no	—
188	#124	—	76	2	no	—
189	#124	—	76	2	no	—
190	C₂×C₄⋊C₄	—	19	2	no	—
191	C₂×C₄⋊C₄	—	38	1	no	—
192	C₂×C₂²⋊C₄	—	38	2	no	—
193	C₂×C₂²⋊C₄	—	38	2	no	—
194	C₂×C₂²⋊C₄	—	38	2	no	—
195	C₂×C₂²⋊C₄	—	38	2	no	—
196	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
197	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
198	C₂×C₄²	D₇₆	1	1	yes	characteristic
199	C₂×C₄²	D₇₆	1	1	yes	characteristic
200	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
201	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
203	C₄⋊C₈	—	2	4	no	—
204	#97	—	4	2	no	—
205	C₄×C₈	—	38	4	no	—
206	C₁₉	#7679	1	1	yes	characteristic, complemented, Sylow
207	C₂⁴	—	38	2	no	—
208	C₂×Q₈	—	76	2	no	—
209	C₂×Q₈	—	76	2	no	—
210	C₂×Q₈	—	76	2	no	—
211	C₂×D₄	—	38	4	no	—
212	C₂×D₄	—	76	2	no	—
213	C₂×D₄	—	76	2	no	—
214	C₂×D₄	—	76	2	no	—
215	C₂×D₄	—	76	2	no	—
216	C₂×D₄	—	76	2	no	—
217	C₂×D₄	—	76	2	no	—
218	C₂×D₄	—	76	2	no	—
219	C₂×D₄	—	76	2	no	—
220	C₂²×C₄	—	38	2	no	—
221	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
222	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
223	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
224	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
226	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
227	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	4	2	no	—
230	C₂×C₈	—	4	2	no	—
231	C₂×C₈	—	38	4	no	—
232	C₂×C₈	—	76	2	no	—
233	C₂×C₈	—	76	2	no	—
234	C₄⋊C₄	—	76	2	no	—
235	C₄⋊C₄	—	76	2	no	—
236	C₂²⋊C₄	—	76	4	no	—
237	C₂²⋊C₄	—	76	2	no	—
238	C₂²⋊C₄	—	76	2	no	—
239	C₂²⋊C₄	—	76	4	no	—
240	C₂²⋊C₄	—	76	4	no	—
241	C₄²	—	2	2	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	2	no	—
244	C₄²	—	2	2	no	—
245	C₄²	—	2	2	no	—
246	C₄²	—	4	1	no	—
247	C₄²	#64525	1	2	yes	—
248	C₄²	#64527	1	2	yes	—
249	C₂³	—	76	2	no	—
250	C₂³	—	76	2	no	—
251	C₂³	—	76	2	no	—
252	C₂³	—	76	2	no	—
253	C₂³	—	76	2	no	—
254	C₂³	—	76	2	no	—
255	C₂³	—	76	2	no	—
256	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
257	Q₈	—	152	4	no	—
258	D₄	—	152	4	no	—
259	D₄	—	152	4	no	—
260	D₄	—	152	4	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	76	2	no	—
275	C₂×C₄	—	76	2	no	—
276	C₂×C₄	—	76	2	no	—
277	C₂×C₄	#10597262	1	2	yes	—
278	C₂×C₄	#10597266	1	2	yes	—
279	C₂×C₄	#10597266	1	2	yes	—
280	C₂×C₄	#10597280	1	2	yes	—
281	C₂×C₄	#10597282	1	2	yes	—
282	C₂×C₄	#10597353	1	2	yes	—
283	C₂×C₄	#10597354	1	2	yes	—
284	C₂×C₄	C₂×#64525	1	1	yes	characteristic
285	C₂×C₄	C₂×#64527	1	1	yes	characteristic
286	C₈	—	4	4	no	—
287	C₈	—	76	4	no	—
288	C₂²	—	152	2	no	—
289	C₂²	—	152	2	no	—
290	C₂²	—	152	2	no	—
291	C₂²	—	152	2	no	—
292	C₂²	—	152	2	no	—
293	C₂²	—	152	2	no	—
294	C₂²	—	152	2	no	—
295	C₂²	#11926512	1	1	yes	characteristic
296	C₂²	#11926517	1	1	yes	characteristic
297	C₂²	C₂×#10597280	1	1	yes	characteristic
298	C₂²	C₂×#10597266	1	1	yes	characteristic
299	C₂²	#11926550	1	1	yes	characteristic
300	C₂²	C₂×#10597282	1	1	yes	characteristic
301	C₂²	C₂×#10597262	1	1	yes	characteristic
302	C₄	—	2	2	no	—
303	C₄	—	2	2	no	—
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	2	2	no	—
307	C₄	—	2	2	no	—
308	C₄	—	4	1	no	—
309	C₄	—	152	2	no	—
310	C₄	#11926283	1	4	yes	—
311	C₂	—	304	2	no	—
312	C₂	#14561988	1	1	yes	characteristic
313	C₂	#14562053	1	1	yes	characteristic
314	C₂	#14562085	1	1	yes	characteristic
315	C₂	#14562129	1	1	yes	characteristic
316	C₂	#14562144	1	1	yes	characteristic
317	C₂	C₂×#11926283	1	1	yes	characteristic
318	C₂	#14562304	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1767	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1767	D₁₉
hypocenter	C₁₉	#7679
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

Complements

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

N	H ≅ G/N	type
2. #14563381	C₂	semidirect
3. #14561455	C₂	semidirect
4. C₁₉×#1767	C₂	semidirect
130. #1767	D₁₉	semidirect
206. C₁₉	#7679	semidirect

Maximal subgroups

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

subgroup	index
#14571992	2
#14563381	2
#14561455	2
C₁₉×#1767	2
#7679	19