Group #18080379 — subgroups

Subgroups — #18080379

Order 4864.

542 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572659	C₂	1	1	yes	maximal, characteristic
2	#14563627	C₂	1	1	yes	maximal, characteristic
3	#14562064	C₂	1	2	yes	maximal, complemented
4	#14561493	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2580	C₂	1	1	yes	maximal, characteristic
6	D₄×C₁₉⋊C₈	—	2	4	no	—
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	2	yes	—
9	C₂×#10597290	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
11	#11926313	—	2	1	no	—
12	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#399	C₄	1	2	yes	—
16	C₁₉×#393	C₄	1	2	yes	—
17	C₁₉×#390	—	2	1	no	—
18	C₁₉×#389	—	2	1	no	—
19	C₁₉×#385	—	2	2	no	—
20	C₁₉×#382	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	2	yes	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×#64520	—	2	2	no	—
39	C₂²×C₁₉⋊C₈	—	2	4	no	—
40	C₁₉×#95	—	2	2	no	—
41	C₁₉×#95	—	2	1	no	—
42	C₁₉×#95	C₂×C₄	1	2	yes	—
43	#10597290	—	4	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
50	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
56	C₂×D₄×C₁₉	Q₁₆	1	2	yes	—
57	C₂²×C₄×C₁₉	—	2	1	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	1	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	8	2	no	—
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	4	1	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄⋊C₄×C₁₉	—	8	2	no	—
73	C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂²⋊C₄×C₁₉	—	4	4	no	—
75	C₂²⋊C₄×C₁₉	—	8	2	no	—
76	C₄²×C₁₉	—	4	2	no	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	C₄²×C₁₉	#41	1	2	yes	—
79	#64520	—	4	2	no	—
80	#64520	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	4	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	C₂×C₁₉⋊C₈	—	8	4	no	—
84	#9483	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	—	2	2	no	—
86	C₂³×C₁₉	—	2	2	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	—	4	2	no	—
89	C₂³×C₁₉	#103	1	4	yes	—
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	Q₈×C₁₉	—	2	4	no	—
92	Q₈×C₁₉	—	4	2	no	—
93	D₄×C₁₉	—	2	4	no	—
94	D₄×C₁₉	—	2	4	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	4	1	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	4	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	1	no	—
107	C₂×C₄×C₁₉	—	4	1	no	—
108	C₂×C₄×C₁₉	—	4	2	no	—
109	C₂×C₄×C₁₉	—	8	2	no	—
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
112	C₂×C₄×C₁₉	#121	1	2	yes	—
113	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
114	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#135	1	2	yes	—
117	C₁₉⋊C₈	—	4	4	no	—
118	C₁₉⋊C₈	—	8	2	no	—
119	#2972	—	19	1	no	—
120	#2580	D₁₉	1	1	yes	characteristic
121	#1800	—	19	1	no	—
122	#1487	—	19	2	no	—
123	#1286	—	19	2	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	4	no	—
127	C₂²×C₁₉	—	4	4	no	—
128	C₂²×C₁₉	—	4	2	no	—
129	C₂²×C₁₉	—	4	2	no	—
130	C₂²×C₁₉	—	8	2	no	—
131	C₂²×C₁₉	#386	1	1	yes	characteristic
132	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
133	C₂²×C₁₉	#416	1	1	yes	characteristic
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	2	1	no	—
136	C₄×C₁₉	—	2	1	no	—
137	C₄×C₁₉	—	4	2	no	—
138	C₄×C₁₉	—	4	2	no	—
139	C₄×C₁₉	—	8	2	no	—
140	C₄×C₁₉	—	8	1	no	—
141	C₄×C₁₉	#465	1	2	yes	—
142	C₄×C₁₉	#467	1	2	yes	—
143	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
145	C₈×D₄	—	38	4	no	—
146	#431	—	19	2	no	—
147	#423	—	19	2	no	—
148	C₂×#100	—	38	1	no	—
149	C₂×C₂²⋊C₈	—	38	2	no	—
150	#399	Dic₁₉	1	2	yes	—
151	#393	Dic₁₉	1	2	yes	—
152	#390	—	2	1	no	—
153	#389	—	2	1	no	—
154	#385	—	2	2	no	—
155	#382	C₂×D₁₉	1	1	yes	characteristic
156	#343	—	38	1	no	—
157	Q₈⋊C₈	—	38	4	no	—
158	C₂×C₁₉	—	2	1	no	—
159	C₂×C₁₉	—	2	1	no	—
160	C₂×C₁₉	—	4	4	no	—
161	C₂×C₁₉	#1891	1	1	yes	characteristic
162	C₂×C₁₉	#1892	1	1	yes	characteristic
163	C₂×C₁₉	#1911	1	1	yes	characteristic
164	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
165	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
166	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
167	C₂×M₁₆	—	38	2	no	—
168	C₂²×C₈	—	38	4	no	—
169	C₄×Q₈	—	2	2	no	—
170	C₄×Q₈	—	2	2	no	—
171	C₄×D₄	—	2	2	no	—
172	C₄×D₄	—	2	2	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	2	no	—
176	C₂×C₄⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
177	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	—	2	2	no	—
179	C₂×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
181	C₂×C₄²	—	2	1	no	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	C₄⋊C₈	—	38	2	no	—
184	C₄⋊C₈	—	38	2	no	—
185	C₄⋊C₈	—	38	2	no	—
186	#100	—	76	2	no	—
187	C₂²⋊C₈	—	38	4	no	—
188	C₂²⋊C₈	—	38	2	no	—
189	C₄×C₈	—	19	4	no	—
190	#95	—	2	2	no	—
191	#95	—	2	1	no	—
192	#95	C₂×Dic₁₉	1	2	yes	—
193	C₁₉	#9483	1	1	yes	characteristic, complemented, Sylow
194	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	4	2	no	—
197	C₂×D₄	—	2	2	no	—
198	C₂×D₄	—	2	2	no	—
199	C₂×D₄	#64527	1	2	yes	—
200	C₂×D₄	#64528	1	2	yes	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	1	no	—
206	C₂²×C₄	—	8	2	no	—
207	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
208	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
211	M₁₆	—	76	2	no	—
212	M₁₆	—	76	2	no	—
213	C₂×C₈	—	38	4	no	—
214	C₂×C₈	—	76	2	no	—
215	C₂×C₈	—	152	4	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	4	1	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	2	no	—
221	C₄⋊C₄	—	8	2	no	—
222	C₂²⋊C₄	—	2	4	no	—
223	C₂²⋊C₄	—	4	4	no	—
224	C₂²⋊C₄	—	8	2	no	—
225	C₄²	—	4	2	no	—
226	C₄²	D₄×D₁₉	1	2	yes	—
227	C₄²	#64543	1	2	yes	—
228	C₂³	—	2	2	no	—
229	C₂³	—	2	2	no	—
230	C₂³	—	4	2	no	—
231	C₂³	—	4	2	no	—
232	C₂³	#10597292	1	4	yes	—
233	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
234	Q₈	—	2	4	no	—
235	Q₈	—	4	2	no	—
236	D₄	—	2	4	no	—
237	D₄	—	2	4	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	4	1	no	—
241	C₂×C₄	—	4	1	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	—	4	1	no	—
250	C₂×C₄	—	4	2	no	—
251	C₂×C₄	—	4	1	no	—
252	C₂×C₄	—	8	2	no	—
253	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
254	C₂×C₄	#10597381	1	1	yes	characteristic
255	C₂×C₄	#10597383	1	1	yes	characteristic
256	C₂×C₄	#10597385	1	2	yes	—
257	C₂×C₄	C₂×#64527	1	1	yes	characteristic
258	C₂×C₄	C₂×#64528	1	1	yes	characteristic
259	C₂×C₄	#10597396	1	2	yes	—
260	C₈	—	76	4	no	—
261	C₈	—	152	2	no	—
262	C₂²	—	2	1	no	—
263	C₂²	—	2	1	no	—
264	C₂²	—	2	4	no	—
265	C₂²	—	4	4	no	—
266	C₂²	—	4	2	no	—
267	C₂²	—	4	2	no	—
268	C₂²	—	8	2	no	—
269	C₂²	#11926424	1	1	yes	characteristic
270	C₂²	C₂×#10597292	1	1	yes	characteristic
271	C₂²	#11926540	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	2	2	no	—
275	C₄	—	4	2	no	—
276	C₄	—	4	2	no	—
277	C₄	—	8	2	no	—
278	C₄	—	8	1	no	—
279	C₄	#11926775	1	2	yes	—
280	C₄	#11926783	1	2	yes	—
281	C₂	—	2	1	no	—
282	C₂	—	2	1	no	—
283	C₂	—	4	4	no	—
284	C₂	#14564054	1	1	yes	characteristic
285	C₂	#14564059	1	1	yes	characteristic
286	C₂	#14564168	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572659

C₂

yes

maximal, characteristic

#14563627

C₂

yes

maximal, characteristic

#14562064

C₂

yes

maximal, complemented

#14561493

C₂

yes

maximal, complemented

C₁₉×#2580

C₂

yes

maximal, characteristic

D₄×C₁₉⋊C₈

—

#11926597

C₂²

yes

—

#11926568

C₂²

yes

—

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

#11926313

—

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#399

C₄

yes

—

C₁₉×#393

C₄

yes

—

C₁₉×#390

—

C₁₉×#389

—

C₁₉×#385

—

C₁₉×#382

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

C₂×C₄

yes

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

SD₁₆

yes

—

C₂×D₄×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9483

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#103

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

C₄×D₄

yes

—

111

C₂×C₄×C₁₉

#120

yes

characteristic

112

C₂×C₄×C₁₉

#121

yes

—

113

C₂×C₄×C₁₉

#123

yes

characteristic

114

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

115

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

116

C₂×C₄×C₁₉

#135

yes

—

117

C₁₉⋊C₈

—

118

C₁₉⋊C₈

—

119

#2972

—

120

#2580

D₁₉

yes

characteristic

121

#1800

—

122

#1487

—

123

#1286

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

#386

yes

characteristic

132

C₂²×C₁₉

C₂×#103

yes

characteristic

133

C₂²×C₁₉

#416

yes

characteristic

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

—

140

C₄×C₁₉

—

141

C₄×C₁₉

#465

yes

—

142

C₄×C₁₉

#467

yes

—

143

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

144

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

145

C₈×D₄

—

146

#431

—

147

#423

—

148

C₂×#100

—

149

C₂×C₂²⋊C₈

—

150

#399

Dic₁₉

yes

—

151

#393

Dic₁₉

yes

—

152

#390

—

153

#389

—

154

#385

—

155

#382

C₂×D₁₉

yes

characteristic

156

#343

—

157

Q₈⋊C₈

—

158

C₂×C₁₉

—

159

C₂×C₁₉

—

160

C₂×C₁₉

—

161

C₂×C₁₉

#1891

yes

characteristic

162

C₂×C₁₉

#1892

yes

characteristic

163

C₂×C₁₉

#1911

yes

characteristic

164

C₂²×Q₈

C₂×Dic₁₉

yes

characteristic

165

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

166

C₂³×C₄

C₂²⋊D₁₉

yes

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₄×Q₈

—

170

C₄×Q₈

—

171

C₄×D₄

—

172

C₄×D₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

characteristic

177

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

178

C₂×C₂²⋊C₄

—

179

C₂×C₂²⋊C₄

—

180

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

—

181

C₂×C₄²

—

182

C₂×C₄²

C₂²×D₁₉

yes

characteristic

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

#100

—

187

C₂²⋊C₈

—

188

C₂²⋊C₈

—

189

C₄×C₈

—

190

#95

—

191

#95

—

192

#95

C₂×Dic₁₉

yes

—

193

C₁₉

#9483

yes

characteristic, complemented, Sylow

194

C₂⁴

C₂²⋊Dic₁₉

yes

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

#64527

yes

—

200

C₂×D₄

#64528

yes

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

208

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

209

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

210

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

152

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₂²⋊C₄

—

223

C₂²⋊C₄

—

224

C₂²⋊C₄

—

225

C₄²

—

226

C₄²

D₄×D₁₉

yes

—

227

C₄²

#64543

yes

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

#10597292

yes

—

233

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

234

Q₈

—

235

Q₈

—

236

D₄

—

237

D₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

D₄×Dic₁₉

yes

—

254

C₂×C₄

#10597381

yes

characteristic

255

C₂×C₄

#10597383

yes

characteristic

256

C₂×C₄

#10597385

yes

—

257

C₂×C₄

C₂×#64527

yes

characteristic

258

C₂×C₄

C₂×#64528

yes

characteristic

259

C₂×C₄

#10597396

yes

—

260

C₈

—

261

C₈

—

152

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

#11926424

yes

characteristic

270

C₂²

C₂×#10597292

yes

characteristic

271

C₂²

#11926540

yes

characteristic

272

C₄

—

273

C₄

—

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

#11926775

yes

—

280

C₄

#11926783

yes

—

281

C₂

—

282

C₂

—

283

C₂

—

284

C₂

#14564054

yes

characteristic

285

C₂

#14564059

yes

characteristic

286

C₂

#14564168

yes

characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2580	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2580	D₁₉
hypocenter	C₁₉	#9483
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2580

subgroup

G/H

center

C₂²

#11926424

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2580

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2580

N	H ≅ G/N	type
3. #14562064	C₂	semidirect
4. #14561493	C₂	semidirect
193. C₁₉	#9483	semidirect

H ≅ G/N

type

3. #14562064

C₂

semidirect

4. #14561493

C₂

semidirect

193. C₁₉

#9483

semidirect

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

subgroup	index
#14572659	2
#14563627	2
#14562064	2
#14561493	2
C₁₉×#2580	2
#9483	19

subgroup

index

C₁₉×#2580

Subgroups — #18080379

Conjugacy classes of subgroups

Complements

Maximal subgroups