Group #18076920 — subgroups

Subgroups — #18076920

Order 4864.

468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14566809	C₂	1	1	yes	maximal, characteristic
2	#14564452	C₂	1	1	yes	maximal, characteristic
3	#14563769	C₂	1	2	yes	maximal, complemented
4	#14561517	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#329	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597292	—	2	1	no	—
7	C₂×#10597289	—	2	1	no	—
8	C₂×#10597260	C₂²	1	1	yes	characteristic
9	#11926451	—	2	1	no	—
10	#11926437	—	2	2	no	—
11	#11926424	—	2	1	no	—
12	#11926419	—	2	2	no	—
13	#11926414	C₂²	1	1	yes	characteristic
14	#11926410	C₂²	1	2	yes	—
15	#11926307	—	2	2	no	—
16	#11926307	—	2	2	no	—
17	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	C₂²	1	2	yes	—
19	C₁₉×#329	C₄	1	4	yes	complemented
20	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×Dic₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₁₉×#124	—	2	2	no	—
25	C₁₉×#124	C₂×C₄	1	2	yes	—
26	C₁₉×#124	Q₈	1	2	yes	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
30	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	—	2	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
35	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
36	C₂×C₄×Dic₁₉	—	2	1	no	—
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₁₉×#97	—	2	2	no	—
39	C₁₉×#97	C₂×C₄	1	4	yes	complemented
40	#10597292	—	4	2	no	—
41	#10597289	—	4	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₁₉⋊#95	—	2	2	no	—
45	#10597260	—	2	2	no	—
46	C₂⁴×C₁₉	—	2	1	no	—
47	C₂×Q₈×C₁₉	—	2	1	no	—
48	C₂×Q₈×C₁₉	—	4	1	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
51	C₂×D₄×C₁₉	—	2	1	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂×D₄×C₁₉	—	4	1	no	—
54	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₉	—	2	1	no	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂²×Dic₁₉	—	2	2	no	—
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂²×Dic₁₉	—	4	1	no	—
61	C₂²×Dic₁₉	—	8	1	no	—
62	C₂²×Dic₁₉	—	8	2	no	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	2	yes	—
71	C₂²⋊Dic₁₉	—	8	1	no	—
72	C₂²⋊Dic₁₉	—	8	2	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	C₄⋊Dic₁₉	—	4	4	no	—
78	C₄⋊Dic₁₉	—	8	1	no	—
79	C₄×Dic₁₉	—	8	1	no	—
80	C₂×C₁₉⋊C₈	—	2	2	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	C₂×C₁₉⋊C₈	—	4	1	no	—
83	#8914	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	—	2	2	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	—	4	2	no	—
87	C₂³×C₁₉	—	4	2	no	—
88	C₂³×C₁₉	—	4	1	no	—
89	C₂³×C₁₉	#120	1	1	yes	characteristic
90	Q₈×C₁₉	—	4	2	no	—
91	Q₈×C₁₉	—	8	1	no	—
92	D₄×C₁₉	—	4	2	no	—
93	D₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	2	no	—
98	C₂×C₄×C₁₉	—	2	2	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
104	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	4	2	no	—
108	C₂×Dic₁₉	—	4	2	no	—
109	C₂×Dic₁₉	—	4	2	no	—
110	C₂×Dic₁₉	—	4	2	no	—
111	C₂×Dic₁₉	—	8	4	no	—
112	C₂×Dic₁₉	—	8	1	no	—
113	C₂×Dic₁₉	—	8	2	no	—
114	C₈×C₁₉	—	4	4	no	—
115	C₁₉⋊C₈	—	4	2	no	—
116	#2379	—	19	1	no	—
117	#1959	—	19	1	no	—
118	#1836	—	19	2	no	—
119	C₂×#329	D₁₉	1	1	yes	characteristic
120	#1295	—	19	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	4	no	—
123	C₂²×C₁₉	—	8	1	no	—
124	C₂²×C₁₉	—	8	1	no	—
125	C₂²×C₁₉	—	8	2	no	—
126	C₂²×C₁₉	#385	1	1	yes	characteristic
127	C₂²×C₁₉	#453	1	1	yes	characteristic
128	C₂²×C₁₉	#454	1	2	yes	—
129	C₂²×C₁₉	#455	1	2	yes	—
130	C₂²×C₁₉	#455	1	1	yes	characteristic
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	2	2	no	—
135	C₄×C₁₉	—	4	2	no	—
136	Dic₁₉	—	8	2	no	—
137	Dic₁₉	—	8	2	no	—
138	Dic₁₉	—	16	1	no	—
139	C₂×#124	C₂×D₁₉	1	1	yes	characteristic
140	C₂×#103	—	38	1	no	—
141	C₂×#102	—	38	1	no	—
142	C₂×#97	—	19	1	no	—
143	C₂×#97	C₂×D₁₉	1	2	yes	—
144	#391	—	38	1	no	—
145	#388	—	38	2	no	—
146	#386	—	38	1	no	—
147	#385	—	38	2	no	—
148	#384	—	19	1	no	—
149	#382	—	19	2	no	—
150	#340	—	38	2	no	—
151	#340	—	38	2	no	—
152	#329	Dic₁₉	1	4	yes	complemented
153	C₂×C₁₉	—	8	2	no	—
154	C₂×C₁₉	#1657	1	1	yes	characteristic
155	C₂×C₁₉	#1659	1	1	yes	characteristic
156	C₂×C₁₉	#1662	1	2	yes	—
157	C₂×C₁₉	#1856	1	1	yes	characteristic
158	C₂×C₁₉	#1860	1	2	yes	—
159	C₂²×Q₈	D₇₆	1	1	yes	characteristic
160	C₂²×D₄	D₇₆	1	1	yes	characteristic
161	C₂³×C₄	—	38	1	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	38	1	no	—
164	#124	—	2	2	no	—
165	#124	Dic₃₈	1	2	yes	—
166	#124	C₂×Dic₁₉	1	2	yes	—
167	C₂×C₄⋊C₄	—	19	2	no	—
168	C₂×C₄⋊C₄	—	19	2	no	—
169	C₂×C₄⋊C₄	—	38	1	no	—
170	C₂×C₄⋊C₄	—	38	2	no	—
171	C₂×C₄⋊C₄	—	38	1	no	—
172	C₂×C₂²⋊C₄	—	2	2	no	—
173	C₂×C₂²⋊C₄	—	38	2	no	—
174	C₂×C₂²⋊C₄	—	38	1	no	—
175	C₂×C₄²	—	38	1	no	—
176	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
177	#103	—	76	2	no	—
178	#102	—	76	2	no	—
179	#97	—	2	2	no	—
180	#97	—	38	2	no	—
181	#97	C₂×Dic₁₉	1	4	yes	complemented
182	#95	—	38	2	no	—
183	#95	—	38	2	no	—
184	#95	—	38	2	no	—
185	C₁₉	#8914	1	1	yes	characteristic, complemented, Sylow
186	C₂⁴	—	2	1	no	—
187	C₂×Q₈	—	2	1	no	—
188	C₂×Q₈	—	4	1	no	—
189	C₂×Q₈	—	4	1	no	—
190	C₂×Q₈	C₄⋊Dic₁₉	1	2	yes	—
191	C₂×D₄	—	2	1	no	—
192	C₂×D₄	—	4	1	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂×D₄	C₄⋊Dic₁₉	1	2	yes	—
195	C₂²×C₄	—	2	1	no	—
196	C₂²×C₄	—	38	2	no	—
197	C₂²×C₄	—	38	2	no	—
198	C₂²×C₄	—	76	1	no	—
199	C₂²×C₄	—	152	1	no	—
200	C₂²×C₄	—	152	2	no	—
201	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
202	C₂²×C₄	D₄×D₁₉	1	2	yes	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	4	2	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	38	2	no	—
207	C₂×C₈	—	76	1	no	—
208	C₂×C₈	—	76	1	no	—
209	C₄⋊C₄	—	76	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₄⋊C₄	—	76	1	no	—
212	C₄⋊C₄	—	76	1	no	—
213	C₄⋊C₄	—	76	4	no	—
214	C₄⋊C₄	—	152	1	no	—
215	C₂²⋊C₄	—	2	4	no	—
216	C₂²⋊C₄	—	2	4	no	—
217	C₂²⋊C₄	—	152	2	no	—
218	C₂²⋊C₄	—	152	1	no	—
219	C₄²	—	152	1	no	—
220	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
221	C₄²	#64543	1	2	yes	—
222	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
223	C₂³	—	2	2	no	—
224	C₂³	—	4	1	no	—
225	C₂³	—	4	2	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	1	no	—
228	C₂³	#10597328	1	1	yes	characteristic
229	Q₈	—	4	2	no	—
230	Q₈	—	8	1	no	—
231	D₄	—	4	2	no	—
232	D₄	—	8	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	—	76	2	no	—
241	C₂×C₄	—	76	2	no	—
242	C₂×C₄	—	76	2	no	—
243	C₂×C₄	—	76	2	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	76	2	no	—
246	C₂×C₄	—	152	1	no	—
247	C₂×C₄	—	152	2	no	—
248	C₂×C₄	—	152	4	no	—
249	C₂×C₄	#10597324	1	2	yes	—
250	C₂×C₄	#10597332	1	1	yes	characteristic
251	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
252	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
253	C₈	—	4	4	no	—
254	C₈	—	76	2	no	—
255	C₂²	—	4	2	no	—
256	C₂²	—	4	4	no	—
257	C₂²	—	8	1	no	—
258	C₂²	—	8	1	no	—
259	C₂²	—	8	2	no	—
260	C₂²	#11926419	1	1	yes	characteristic
261	C₂²	#11926714	1	1	yes	characteristic
262	C₂²	#11926718	1	2	yes	—
263	C₂²	#11926723	1	2	yes	—
264	C₂²	#11926724	1	1	yes	characteristic
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	2	2	no	—
268	C₄	—	2	2	no	—
269	C₄	—	4	2	no	—
270	C₄	—	304	1	no	—
271	C₄	—	152	2	no	—
272	C₄	—	152	2	no	—
273	C₂	—	8	2	no	—
274	C₂	#14562934	1	1	yes	characteristic
275	C₂	#14562942	1	1	yes	characteristic
276	C₂	#14562960	1	2	yes	—
277	C₂	#14563847	1	1	yes	characteristic
278	C₂	#14563870	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14566809

C₂

yes

maximal, characteristic

#14564452

C₂

yes

maximal, characteristic

#14563769

C₂

yes

maximal, complemented

#14561517

C₂

yes

maximal, complemented

C₂×C₁₉×#329

C₂

yes

maximal, characteristic

C₂×#10597292

—

C₂×#10597289

—

C₂×#10597260

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#11926410

C₂²

yes

—

#11926307

—

#11926307

—

C₂×C₁₉×#124

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

—

C₁₉×#329

C₄

yes

complemented

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×Dic₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×#124

—

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#124

Q₈

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×#97

—

C₁₉×#97

C₂×C₄

yes

complemented

#10597292

—

#10597289

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597260

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8914

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

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

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

102

C₂×C₄×C₁₉

C₄×D₄

yes

—

103

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

104

C₂×C₄×C₁₉

#123

yes

characteristic

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₂×Dic₁₉

—

111

C₂×Dic₁₉

—

112

C₂×Dic₁₉

—

113

C₂×Dic₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

#2379

—

117

#1959

—

118

#1836

—

119

C₂×#329

D₁₉

yes

characteristic

120

#1295

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

#385

yes

characteristic

127

C₂²×C₁₉

#453

yes

characteristic

128

C₂²×C₁₉

#454

yes

—

129

C₂²×C₁₉

#455

yes

—

130

C₂²×C₁₉

#455

yes

characteristic

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

Dic₁₉

—

137

Dic₁₉

—

138

Dic₁₉

—

139

C₂×#124

C₂×D₁₉

yes

characteristic

140

C₂×#103

—

141

C₂×#102

—

142

C₂×#97

—

143

C₂×#97

C₂×D₁₉

yes

—

144

#391

—

145

#388

—

146

#386

—

147

#385

—

148

#384

—

149

#382

—

150

#340

—

151

#340

—

152

#329

Dic₁₉

yes

complemented

153

C₂×C₁₉

—

154

C₂×C₁₉

#1657

yes

characteristic

155

C₂×C₁₉

#1659

yes

characteristic

156

C₂×C₁₉

#1662

yes

—

157

C₂×C₁₉

#1856

yes

characteristic

158

C₂×C₁₉

#1860

yes

—

159

C₂²×Q₈

D₇₆

yes

characteristic

160

C₂²×D₄

D₇₆

yes

characteristic

161

C₂³×C₄

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

#124

—

165

#124

Dic₃₈

yes

—

166

#124

C₂×Dic₁₉

yes

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

—

172

C₂×C₂²⋊C₄

—

173

C₂×C₂²⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₄²

—

176

C₂×C₄²

C₂²×D₁₉

yes

characteristic

177

#103

—

178

#102

—

179

#97

—

180

#97

—

181

#97

C₂×Dic₁₉

yes

complemented

182

#95

—

183

#95

—

184

#95

—

185

C₁₉

#8914

yes

characteristic, complemented, Sylow

186

C₂⁴

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

C₄⋊Dic₁₉

yes

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

C₄⋊Dic₁₉

yes

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

152

—

200

C₂²×C₄

—

152

—

201

C₂²×C₄

C₂×D₇₆

yes

characteristic

202

C₂²×C₄

D₄×D₁₉

yes

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

152

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₂²⋊C₄

—

152

—

218

C₂²⋊C₄

—

152

—

219

C₄²

—

152

—

220

C₄²

C₂×Dic₃₈

yes

characteristic

221

C₄²

#64543

yes

—

222

C₄²

C₂²×Dic₁₉

yes

characteristic

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

#10597328

yes

characteristic

229

Q₈

—

230

Q₈

—

231

D₄

—

232

D₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

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

—

152

—

247

C₂×C₄

—

152

—

248

C₂×C₄

—

152

—

249

C₂×C₄

#10597324

yes

—

250

C₂×C₄

#10597332

yes

characteristic

251

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

252

C₂×C₄

D₄×Dic₁₉

yes

—

253

C₈

—

254

C₈

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

#11926419

yes

characteristic

261

C₂²

#11926714

yes

characteristic

262

C₂²

#11926718

yes

—

263

C₂²

#11926723

yes

—

264

C₂²

#11926724

yes

characteristic

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

304

—

271

C₄

—

152

—

272

C₄

—

152

—

273

C₂

—

274

C₂

#14562934

yes

characteristic

275

C₂

#14562942

yes

characteristic

276

C₂

#14562960

yes

—

277

C₂

#14563847

yes

characteristic

278

C₂

#14563870

yes

—

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#329	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#329	D₁₉
hypocenter	C₁₉	#8914
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#329

subgroup

G/H

center

C₂³

#10597328

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#329

C₂

socle

C₂³×C₁₉

#120

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#329

N	H ≅ G/N	type
3. #14563769	C₂	semidirect
4. #14561517	C₂	semidirect
19. C₁₉×#329	C₄	semidirect
39. C₁₉×#97	C₂×C₄	semidirect
152. #329	Dic₁₉	semidirect
181. #97	C₂×Dic₁₉	semidirect
185. C₁₉	#8914	semidirect

H ≅ G/N

type

3. #14563769

C₂

semidirect

4. #14561517

C₂

semidirect

19. C₁₉×#329

C₄

semidirect

39. C₁₉×#97

C₂×C₄

semidirect

152. #329

Dic₁₉

semidirect

181. #97

C₂×Dic₁₉

semidirect

185. C₁₉

#8914

semidirect

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

subgroup	index
#14566809	2
#14564452	2
#14563769	2
#14561517	2
C₂×C₁₉×#329	2
#8914	19

subgroup

index

C₂×C₁₉×#329

Subgroups — #18076920

Conjugacy classes of subgroups

Complements

Maximal subgroups