Subgroups — C₄×#11926285 #18073458

Order 4864.

532 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	C₄×#10597316	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926285	C₂	1	2	yes	maximal
4	#14561517	C₂	1	2	yes	maximal
5	C₄×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597316	C₂²	1	1	yes	characteristic
7	C₂×#10597260	—	2	1	no	—
8	C₂×#10597260	C₂²	1	2	yes	—
9	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
10	#11926442	C₄	1	1	yes	characteristic
11	#11926442	C₄	1	1	yes	characteristic
12	#11926428	—	2	1	no	—
13	#11926428	—	2	1	no	—
14	#11926410	C₂²	1	1	yes	characteristic
15	C₄×Dic₁₉⋊C₄	—	2	1	no	—
16	C₄×Dic₁₉⋊C₄	—	2	1	no	—
17	C₄×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
18	C₄×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
19	#11926285	C₄	1	8	yes	direct product factor
20	C₂×C₁₉×#97	—	2	1	no	—
21	C₂×C₁₉×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₉	—	2	1	no	—
23	C₄³×C₁₉	C₂²	1	1	yes	characteristic
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×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×Dic₁₉⋊C₄	—	2	1	no	—
37	C₂×Dic₁₉⋊C₄	—	2	1	no	—
38	C₂×Dic₁₉⋊C₄	—	2	1	no	—
39	C₂×Dic₁₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂²×C₁₉⋊C₈	—	2	2	no	—
43	#10597316	—	2	2	no	—
44	#10597316	C₂×C₄	1	4	yes	—
45	C₁₉×#97	—	2	4	no	—
46	C₁₉×#97	—	2	2	no	—
47	C₁₉×#97	C₂×C₄	1	4	yes	—
48	C₄×C₈×C₁₉	—	2	4	no	—
49	C₁₉⋊#95	—	2	1	no	—
50	C₁₉⋊#95	—	2	1	no	—
51	C₁₉⋊#95	—	2	1	no	—
52	C₁₉⋊#95	—	2	1	no	—
53	C₁₉⋊#95	—	2	1	no	—
54	C₁₉⋊#95	—	2	1	no	—
55	#10597260	—	2	4	no	—
56	#10597260	—	2	2	no	—
57	#10597260	C₂×C₄	1	4	yes	—
58	C₄×C₁₉⋊C₈	—	2	4	no	—
59	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×Dic₁₉	—	2	1	no	—
67	C₂²×Dic₁₉	—	2	1	no	—
68	C₂²×Dic₁₉	—	2	1	no	—
69	C₂²×Dic₁₉	—	2	1	no	—
70	C₂×C₈×C₁₉	—	2	4	no	—
71	C₂×C₈×C₁₉	—	2	4	no	—
72	C₂×C₈×C₁₉	—	2	4	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	2	2	no	—
76	C₄²×C₁₉	—	2	2	no	—
77	C₄²×C₁₉	—	2	2	no	—
78	C₄²×C₁₉	—	4	1	no	—
79	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
80	C₄²×C₁₉	#41	1	2	yes	—
81	C₄⋊Dic₁₉	—	2	1	no	—
82	C₄⋊Dic₁₉	—	2	1	no	—
83	C₄⋊Dic₁₉	—	4	1	no	—
84	C₄⋊Dic₁₉	—	4	1	no	—
85	C₄⋊Dic₁₉	C₄²	1	2	yes	—
86	C₄⋊Dic₁₉	C₄²	1	2	yes	—
87	Dic₁₉⋊C₄	—	2	4	no	—
88	Dic₁₉⋊C₄	—	2	4	no	—
89	Dic₁₉⋊C₄	—	4	2	no	—
90	Dic₁₉⋊C₄	—	4	2	no	—
91	C₄×Dic₁₉	—	4	2	no	—
92	C₄×Dic₁₉	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	2	4	no	—
94	C₂×C₁₉⋊C₈	—	2	4	no	—
95	C₂×C₁₉⋊C₈	—	2	4	no	—
96	C₄×#330	—	19	1	no	maximal, Sylow
97	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	#101	1	2	yes	—
112	C₂×C₄×C₁₉	#104	1	2	yes	—
113	C₂×C₄×C₁₉	#104	1	2	yes	—
114	C₂×C₄×C₁₉	#104	1	2	yes	—
115	C₂×C₄×C₁₉	#104	1	2	yes	—
116	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
117	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
120	C₂×Dic₁₉	—	2	2	no	—
121	C₂×Dic₁₉	—	2	2	no	—
122	C₂×Dic₁₉	—	4	1	no	—
123	C₂×Dic₁₉	—	4	1	no	—
124	C₂×Dic₁₉	—	4	1	no	—
125	C₂×Dic₁₉	—	4	1	no	—
126	C₂×Dic₁₉	—	4	1	no	—
127	C₂×Dic₁₉	—	4	1	no	—
128	C₂×Dic₁₉	—	4	1	no	—
129	C₂×Dic₁₉	—	4	1	no	—
130	C₂×Dic₁₉	—	4	1	no	—
131	C₂×Dic₁₉	—	4	1	no	—
132	C₈×C₁₉	—	2	8	no	—
133	C₁₉⋊C₈	—	2	8	no	—
134	C₄×#125	—	19	1	no	—
135	C₄×#97	—	19	1	no	—
136	C₄×#97	D₁₉	1	1	yes	characteristic
137	C₂×#330	—	19	2	no	—
138	#1295	—	19	2	no	—
139	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
141	C₂²×C₁₉	#413	1	1	yes	characteristic
142	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
143	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
144	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
145	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	2	no	—
151	C₄×C₁₉	—	2	2	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	#330	1	4	yes	complemented
154	Dic₁₉	—	4	2	no	—
155	Dic₁₉	—	4	2	no	—
156	Dic₁₉	—	8	1	no	—
157	Dic₁₉	—	8	1	no	—
158	C₂×#125	—	19	1	no	—
159	C₂×#97	—	2	1	no	—
160	C₂×#97	—	19	2	no	—
161	C₂×#97	—	38	1	no	—
162	C₂×#97	C₂×D₁₉	1	2	yes	—
163	C₂×C₄×C₈	—	2	1	no	—
164	C₂×C₄×C₈	—	38	1	no	—
165	#389	—	19	1	no	—
166	#389	—	19	1	no	—
167	#387	—	38	1	no	—
168	#387	—	38	1	no	—
169	#382	—	19	1	no	—
170	C₄×C₄⋊C₄	—	19	1	no	—
171	C₄×C₄⋊C₄	—	19	1	no	—
172	C₄×C₄⋊C₄	—	38	1	no	—
173	C₄×C₄⋊C₄	—	38	1	no	—
174	C₄³	C₂×D₁₉	1	1	yes	characteristic
175	#330	—	19	8	no	—
176	C₂×C₁₉	C₂×#330	1	1	yes	characteristic
177	C₂×C₁₉	#1524	1	1	yes	characteristic
178	C₂×C₁₉	#1524	1	1	yes	characteristic
179	C₂×C₁₉	#1526	1	1	yes	characteristic
180	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
181	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
182	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	—	38	2	no	—
185	#125	—	19	4	no	—
186	#125	—	38	2	no	—
187	C₂×C₄⋊C₄	—	19	1	no	—
188	C₂×C₄⋊C₄	—	19	1	no	—
189	C₂×C₄⋊C₄	—	19	1	no	—
190	C₂×C₄⋊C₄	—	19	1	no	—
191	C₂×C₄⋊C₄	—	38	1	no	—
192	C₂×C₄⋊C₄	—	38	1	no	—
193	C₂×C₄⋊C₄	—	38	1	no	—
194	C₂×C₄⋊C₄	—	38	1	no	—
195	C₂×C₄²	—	38	1	no	—
196	C₂×C₄²	—	38	1	no	—
197	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
199	C₂×C₄²	D₇₆	1	1	yes	characteristic
200	C₂×C₄²	D₇₆	1	1	yes	characteristic
201	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
204	#97	—	2	4	no	—
205	#97	—	2	2	no	—
206	#97	—	19	4	no	—
207	#97	—	38	4	no	—
208	#97	—	38	2	no	—
209	#97	C₄×D₁₉	1	4	yes	—
210	C₄×C₈	—	2	4	no	—
211	C₄×C₈	—	38	4	no	—
212	#95	—	38	1	no	—
213	#95	—	38	1	no	—
214	#95	—	38	1	no	—
215	#95	—	38	1	no	—
216	#95	—	38	1	no	—
217	#95	—	38	1	no	—
218	C₁₉	C₄×#330	1	1	yes	characteristic, complemented, Sylow
219	C₂²×C₄	—	38	1	no	—
220	C₂²×C₄	—	38	1	no	—
221	C₂²×C₄	—	38	1	no	—
222	C₂²×C₄	—	38	1	no	—
223	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
224	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
225	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
226	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
227	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
228	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
229	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂×C₈	—	2	4	no	—
231	C₂×C₈	—	2	4	no	—
232	C₂×C₈	—	2	4	no	—
233	C₂×C₈	—	38	4	no	—
234	C₂×C₈	—	38	4	no	—
235	C₂×C₈	—	38	4	no	—
236	C₄⋊C₄	—	19	2	no	—
237	C₄⋊C₄	—	19	2	no	—
238	C₄⋊C₄	—	38	1	no	—
239	C₄⋊C₄	—	38	1	no	—
240	C₄⋊C₄	—	38	4	no	—
241	C₄⋊C₄	—	38	4	no	—
242	C₄⋊C₄	—	76	1	no	—
243	C₄⋊C₄	—	76	1	no	—
244	C₄⋊C₄	—	76	2	no	—
245	C₄⋊C₄	—	76	2	no	—
246	C₄²	—	2	2	no	—
247	C₄²	—	2	2	no	—
248	C₄²	—	2	2	no	—
249	C₄²	—	2	2	no	—
250	C₄²	—	2	2	no	—
251	C₄²	—	4	1	no	—
252	C₄²	—	76	2	no	—
253	C₄²	—	76	2	no	—
254	C₄²	C₂×C₄×D₁₉	1	2	yes	—
255	C₄²	#64541	1	2	yes	—
256	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	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	—	38	2	no	—
271	C₂×C₄	—	38	2	no	—
272	C₂×C₄	—	76	1	no	—
273	C₂×C₄	—	76	1	no	—
274	C₂×C₄	—	76	1	no	—
275	C₂×C₄	—	76	1	no	—
276	C₂×C₄	—	76	1	no	—
277	C₂×C₄	—	76	1	no	—
278	C₂×C₄	—	76	1	no	—
279	C₂×C₄	—	76	1	no	—
280	C₂×C₄	—	76	1	no	—
281	C₂×C₄	—	76	1	no	—
282	C₂×C₄	#10597262	1	2	yes	—
283	C₂×C₄	#10597262	1	2	yes	—
284	C₂×C₄	#10597281	1	2	yes	—
285	C₂×C₄	#10597282	1	2	yes	—
286	C₂×C₄	#10597282	1	2	yes	—
287	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
288	C₂×C₄	#10597318	1	1	yes	characteristic
289	C₂×C₄	C₄×D₇₆	1	2	yes	—
290	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
291	C₈	—	2	8	no	—
292	C₈	—	38	8	no	—
293	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
294	C₂²	C₂×#10597281	1	1	yes	characteristic
295	C₂²	#11926526	1	1	yes	characteristic
296	C₂²	C₂×#10597282	1	1	yes	characteristic
297	C₂²	C₂×#10597282	1	1	yes	characteristic
298	C₂²	C₂×#10597262	1	1	yes	characteristic
299	C₂²	C₂×#10597262	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	2	no	—
303	C₄	—	2	2	no	—
304	C₄	—	2	2	no	—
305	C₄	—	2	2	no	—
306	C₄	—	4	1	no	—
307	C₄	—	76	2	no	—
308	C₄	—	76	2	no	—
309	C₄	—	152	1	no	—
310	C₄	—	152	1	no	—
311	C₄	#11926285	1	4	yes	direct product factor
312	C₂	C₂×#11926285	1	1	yes	characteristic
313	C₂	#14562221	1	1	yes	characteristic
314	C₂	#14562224	1	1	yes	characteristic
315	C₂	#14562229	1	1	yes	characteristic
316	C₂	C₄×#10597281	1	1	yes	characteristic
317	C₂	C₄×#10597262	1	1	yes	characteristic
318	C₂	C₄×#10597282	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#97	D₁₉
hypocenter	C₁₉	C₄×#330
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
19. #11926285	C₄	direct (N × H)
153. C₄×C₁₉	#330	semidirect
218. C₁₉	C₄×#330	semidirect
311. C₄	#11926285	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10597316	2
C₄×#10597260	2
C₂×#11926285	2
#14561517	2
C₄×C₁₉×#97	2
C₄×#330	19

Subgroups — C4×#11926285 #18073458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926285 #18073458