Group #14575004 — subgroups

Subgroups — #14575004

Order 2432.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927076	C₂	1	1	yes	maximal, characteristic
3	#11926853	C₂	1	2	yes	maximal, complemented
4	#11926840	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926834	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926801	C₂	1	2	yes	maximal, complemented
7	#11926787	C₂	1	2	yes	maximal
8	#11926764	C₂	1	2	yes	maximal, complemented
9	#11926751	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926566	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	#10597392	C₂²	1	2	yes	—
16	Q₈×Dic₁₉	C₂²	1	2	yes	—
17	C₂×#64528	C₂²	1	2	yes	—
18	#10597384	C₂²	1	1	yes	characteristic
19	#10597382	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊D₁₉	—	2	1	no	—
21	#10597372	—	2	1	no	—
22	C₂×#64515	C₂²	1	2	yes	—
23	#10597343	—	2	1	no	—
24	#10597343	C₂²	1	1	yes	characteristic
25	#10597338	—	2	1	no	—
26	#10597336	—	2	1	no	—
27	#10597336	C₂²	1	1	yes	characteristic
28	#10597333	—	2	1	no	—
29	#10597329	—	2	1	no	—
30	#10597325	—	2	1	no	—
31	C₄²×D₁₉	C₂²	1	1	yes	characteristic
32	#10597315	C₂²	1	1	yes	characteristic
33	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₉×#103	C₂²	1	2	yes	—
36	#10597292	C₂²	1	2	yes	—
37	#10597289	C₂²	1	2	yes	—
38	#10597275	C₂²	1	2	yes	—
39	#10597273	C₂²	1	2	yes	—
40	Dic₁₉⋊C₈	C₂²	1	2	yes	—
41	#10597265	C₂²	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂×C₂²⋊D₁₉	—	2	1	no	—
47	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
50	C₂×Dic₃₈	—	2	1	no	—
51	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
52	SD₁₆×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	C₂³	1	2	yes	—
54	C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₄²×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²⋊Dic₁₉	—	2	1	no	—
60	C₂²⋊Dic₁₉	—	2	1	no	—
61	C₂²⋊Dic₁₉	—	2	1	no	—
62	#64528	—	4	2	no	—
63	(C₂×D₁₉)⋊C₄	—	2	2	no	—
64	(C₂×D₁₉)⋊C₄	—	2	1	no	—
65	C₄⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	—	2	2	no	—
67	C₄⋊Dic₁₉	—	2	1	no	—
68	C₄⋊Dic₁₉	—	2	1	no	—
69	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₁₉	C₂³	1	2	yes	—
71	Dic₁₉⋊C₄	—	2	1	no	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	Dic₁₉⋊C₄	—	2	1	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	—	2	2	no	—
76	C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₄×Dic₁₉	D₄	1	1	yes	characteristic
78	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
80	#64515	—	4	2	no	—
81	C₂³×C₁₉	—	2	1	no	—
82	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₁₉	—	2	2	no	—
84	Q₈×C₁₉	—	2	2	no	—
85	D₄×C₁₉	—	2	1	no	—
86	D₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
93	C₂²⋊D₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	2	1	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	C₂×Dic₁₉	—	2	1	no	—
97	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄×D₁₉	—	2	2	no	—
101	C₄×D₁₉	—	2	1	no	—
102	C₄×D₁₉	—	2	1	no	—
103	C₄×D₁₉	—	4	1	no	—
104	Dic₃₈	—	2	1	no	—
105	Dic₃₈	—	2	1	no	—
106	Dic₃₈	—	4	2	no	—
107	C₈×C₁₉	—	2	2	no	—
108	C₁₉⋊C₈	—	2	2	no	—
109	#3252	—	19	1	no	maximal, Sylow
110	C₂²×C₁₉	—	4	1	no	—
111	C₂²×C₁₉	—	4	1	no	—
112	C₂²×C₁₉	—	4	1	no	—
113	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
114	C₂×D₁₉	—	2	1	no	—
115	C₂×D₁₉	—	2	1	no	—
116	C₂×D₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	4	1	no	—
120	C₄×C₁₉	#137	1	2	yes	—
121	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
122	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
123	Dic₁₉	—	2	1	no	—
124	Dic₁₉	—	2	1	no	—
125	Dic₁₉	—	2	1	no	—
126	Dic₁₉	—	4	1	no	—
127	Dic₁₉	—	4	2	no	—
128	Dic₁₉	—	4	1	no	—
129	#533	—	19	1	no	—
130	#529	—	19	1	no	—
131	#479	—	19	2	no	—
132	#477	—	19	1	no	—
133	#476	—	19	1	no	—
134	#470	—	19	2	no	—
135	#468	—	19	2	no	—
136	#464	—	19	2	no	—
137	#462	—	19	1	no	—
138	#461	D₁₉	1	1	yes	characteristic, complemented
139	#423	—	19	1	no	—
140	C₂×C₁₉	—	8	1	no	—
141	C₂×C₁₉	#537	1	1	yes	characteristic
142	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
143	C₂×C₁₉	#575	1	1	yes	characteristic
144	D₁₉	—	4	1	no	—
145	C₂×Q₁₆	—	19	2	no	—
146	C₂×SD₁₆	C₂×D₁₉	1	2	yes	—
147	C₂×M₁₆	—	19	2	no	—
148	C₄⋊Q₈	—	19	1	no	—
149	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
150	#126	—	38	1	no	—
151	#125	—	19	1	no	—
152	#125	—	38	1	no	—
153	#124	—	19	1	no	—
154	#123	—	38	1	no	—
155	C₂²⋊Q₈	—	19	2	no	—
156	C₂²⋊Q₈	—	19	1	no	—
157	C₂²⋊Q₈	—	38	1	no	—
158	#121	—	19	1	no	—
159	C₄×Q₈	—	19	2	no	—
160	C₄×Q₈	—	19	1	no	—
161	C₄×Q₈	—	38	1	no	—
162	C₄×D₄	—	38	1	no	—
163	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
164	#117	—	38	1	no	—
165	#117	—	38	1	no	—
166	C₂×C₄²	—	19	1	no	—
167	#107	—	19	2	no	—
168	#106	—	19	2	no	—
169	C₄⋊C₈	—	19	2	no	—
170	C₄⋊C₈	—	19	1	no	—
171	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
172	#103	—	19	2	no	—
173	#103	—	19	2	no	—
174	#103	C₂×D₁₉	1	2	yes	—
175	#102	—	19	2	no	—
176	C₁₉	#3252	1	1	yes	characteristic, complemented, Sylow
177	C₂×Q₈	—	19	1	no	—
178	C₂×Q₈	—	38	1	no	—
179	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
180	C₂×D₄	—	38	1	no	—
181	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	19	1	no	—
184	C₂²×C₄	—	19	1	no	—
185	C₂²×C₄	—	19	1	no	—
186	Q₁₆	—	76	2	no	—
187	SD₁₆	—	4	2	no	—
188	M₁₆	—	76	2	no	—
189	C₂×C₈	—	19	2	no	—
190	C₂×C₈	C₂²×D₁₉	1	2	yes	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	2	1	no	—
193	C₄⋊C₄	—	19	2	no	—
194	C₄⋊C₄	—	19	1	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄⋊C₄	—	38	2	no	—
197	C₄⋊C₄	—	38	1	no	—
198	C₄⋊C₄	—	38	1	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₄⋊C₄	—	38	1	no	—
201	C₄⋊C₄	—	38	1	no	—
202	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	38	2	no	—
205	C₂²⋊C₄	—	38	1	no	—
206	C₂²⋊C₄	—	38	1	no	—
207	C₂²⋊C₄	—	38	1	no	—
208	C₂²⋊C₄	—	38	1	no	—
209	C₄²	—	19	1	no	—
210	C₄²	—	19	1	no	—
211	C₄²	—	19	1	no	—
212	C₄²	—	38	2	no	—
213	C₄²	—	38	1	no	—
214	C₄²	C₂²×D₁₉	1	1	yes	characteristic
215	C₂³	—	2	1	no	—
216	C₂³	—	19	1	no	—
217	Q₈	—	2	2	no	—
218	Q₈	—	2	2	no	—
219	Q₈	—	38	1	no	—
220	Q₈	—	38	1	no	—
221	Q₈	—	76	2	no	—
222	D₄	—	2	1	no	—
223	D₄	—	2	1	no	—
224	D₄	—	76	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	19	1	no	—
229	C₂×C₄	—	19	1	no	—
230	C₂×C₄	—	19	1	no	—
231	C₂×C₄	—	38	1	no	—
232	C₂×C₄	—	38	1	no	—
233	C₂×C₄	—	38	2	no	—
234	C₂×C₄	—	38	1	no	—
235	C₂×C₄	—	38	1	no	—
236	C₂×C₄	—	38	2	no	—
237	C₂×C₄	—	76	1	no	—
238	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
239	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
240	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
241	C₈	—	2	2	no	—
242	C₈	—	38	2	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	1	no	—
246	C₂²	—	38	1	no	—
247	C₂²	—	38	1	no	—
248	C₂²	—	38	1	no	—
249	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	4	1	no	—
252	C₄	—	4	2	no	—
253	C₄	—	38	1	no	—
254	C₄	—	38	1	no	—
255	C₄	—	38	1	no	—
256	C₄	—	76	1	no	—
257	C₄	—	76	2	no	—
258	C₄	—	76	1	no	—
259	C₄	#10597361	1	2	yes	—
260	C₄	#10597430	1	1	yes	characteristic
261	C₄	#10597436	1	1	yes	characteristic
262	C₂	—	8	1	no	—
263	C₂	—	76	1	no	—
264	C₂	#11927123	1	1	yes	characteristic
265	C₂	C₂×#10597361	1	1	yes	characteristic
266	C₂	#11927343	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal, characteristic, complemented

#11927076

C₂

yes

maximal, characteristic

#11926853

C₂

yes

maximal, complemented

#11926840

C₂

yes

maximal, characteristic, complemented

#11926834

C₂

yes

maximal, characteristic, complemented

#11926801

C₂

yes

maximal, complemented

#11926787

C₂

yes

maximal

#11926764

C₂

yes

maximal, complemented

#11926751

C₂

yes

maximal, characteristic, complemented

#11926566

C₂

yes

maximal, characteristic, complemented

C₁₉×#461

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₂²

yes

characteristic

#10597392

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

—

C₂×#64528

C₂²

yes

—

#10597384

C₂²

yes

characteristic

#10597382

C₂²

yes

characteristic

C₄×C₂²⋊D₁₉

—

#10597372

—

C₂×#64515

C₂²

yes

—

#10597343

—

#10597343

C₂²

yes

—

—

C₂²

yes

—

—

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#103

C₂²

yes

—

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

#10597275

C₂²

yes

—

#10597273

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597265

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂×C₂²⋊D₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

characteristic

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64528

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

#64515

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

100

C₄×D₁₉

—

101

C₄×D₁₉

—

102

C₄×D₁₉

—

103

C₄×D₁₉

—

104

Dic₃₈

—

105

Dic₃₈

—

106

Dic₃₈

—

107

C₈×C₁₉

—

108

C₁₉⋊C₈

—

109

#3252

—

maximal, Sylow

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

C₂²×D₄

yes

characteristic

114

C₂×D₁₉

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#137

yes

—

121

C₄×C₁₉

H(5,𝔽₂)

yes

characteristic

122

C₄×C₁₉

2₋¹⁺⁴

yes

characteristic

123

Dic₁₉

—

124

Dic₁₉

—

125

Dic₁₉

—

126

Dic₁₉

—

127

Dic₁₉

—

128

Dic₁₉

—

129

#533

—

130

#529

—

131

#479

—

132

#477

—

133

#476

—

134

#470

—

135

#468

—

136

#464

—

137

#462

—

138

#461

D₁₉

yes

characteristic, complemented

139

#423

—

140

C₂×C₁₉

—

141

C₂×C₁₉

#537

yes

characteristic

142

C₂×C₁₉

C₂×#137

yes

characteristic

143

C₂×C₁₉

#575

yes

characteristic

144

D₁₉

—

145

C₂×Q₁₆

—

146

C₂×SD₁₆

C₂×D₁₉

yes

—

147

C₂×M₁₆

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

150

#126

—

151

#125

—

152

#125

—

153

#124

—

154

#123

—

155

C₂²⋊Q₈

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

#121

—

159

C₄×Q₈

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×D₄

—

163

C₄×D₄

C₂×D₁₉

yes

characteristic

164

#117

—

165

#117

—

166

C₂×C₄²

—

167

#107

—

168

#106

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

C₂×D₁₉

yes

characteristic

172

#103

—

173

#103

—

174

#103

C₂×D₁₉

yes

—

175

#102

—

176

C₁₉

#3252

yes

characteristic, complemented, Sylow

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

C₂²×D₁₉

yes

—

180

C₂×D₄

—

181

C₂×D₄

C₂²×D₁₉

yes

characteristic

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

Q₁₆

—

187

SD₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

C₂²×D₁₉

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

C₂²×D₁₉

yes

characteristic

215

C₂³

—

216

C₂³

—

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

Q₈

—

222

D₄

—

223

D₄

—

224

D₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

D₄×D₁₉

yes

characteristic

239

C₂×C₄

D₄×D₁₉

yes

characteristic

240

C₂×C₄

C₂³×D₁₉

yes

characteristic

241

C₈

—

242

C₈

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

C₂×D₄×D₁₉

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

#10597361

yes

—

260

C₄

#10597430

yes

characteristic

261

C₄

#10597436

yes

characteristic

262

C₂

—

263

C₂

—

264

C₂

#11927123

yes

characteristic

265

C₂

C₂×#10597361

yes

characteristic

266

C₂

#11927343

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#461	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597384	C₂²
hypercenter	#461	D₁₉
hypocenter	C₁₉	#3252
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #461

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#461

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #461

N	H ≅ G/N	type
1. #11927099	C₂	semidirect
3. #11926853	C₂	semidirect
4. #11926840	C₂	semidirect
5. #11926834	C₂	semidirect
6. #11926801	C₂	semidirect
8. #11926764	C₂	semidirect
9. #11926751	C₂	semidirect
10. #11926566	C₂	semidirect
11. C₁₉×#461	C₂	semidirect
138. #461	D₁₉	semidirect
176. C₁₉	#3252	semidirect

H ≅ G/N

type

1. #11927099

C₂

semidirect

3. #11926853

C₂

semidirect

4. #11926840

C₂

semidirect

5. #11926834

C₂

semidirect

6. #11926801

C₂

semidirect

8. #11926764

C₂

semidirect

9. #11926751

C₂

semidirect

10. #11926566

C₂

semidirect

11. C₁₉×#461

C₂

semidirect

138. #461

D₁₉

semidirect

176. C₁₉

#3252

semidirect

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

subgroup	index
#11927099	2
#11927076	2
#11926853	2
#11926840	2
#11926834	2
#11926801	2
#11926787	2
#11926764	2
#11926751	2
#11926566	2
C₁₉×#461	2
#3252	19

subgroup

index

C₁₉×#461

Subgroups — #14575004

Conjugacy classes of subgroups

Complements

Maximal subgroups