Group #14568097 — subgroups

Subgroups — #14568097

Order 2432.

568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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	C₂×#10597376	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597372	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926460	C₂	1	4	yes	maximal, complemented
4	#11926446	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926446	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926436	C₂	1	4	yes	maximal, complemented
7	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
12	C₂²×D₇₆	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
17	#10597376	—	2	4	no	—
18	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
19	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
20	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
21	#10597372	—	2	4	no	—
22	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
26	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
27	C₁₉×#95	C₂²	1	2	yes	—
28	C₁₉⋊#95	C₂²	1	4	yes	—
29	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
30	C₂³×D₁₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	D₄	1	4	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊D₁₉	—	2	4	no	—
39	C₂×C₂²⋊D₁₉	—	4	4	no	—
40	C₂²×Dic₁₉	C₂³	1	2	yes	—
41	C₂²×Dic₁₉	C₂³	1	2	yes	—
42	C₂²×Dic₁₉	C₂³	1	2	yes	—
43	C₂×D₇₆	—	2	2	no	—
44	C₂×D₇₆	—	2	2	no	—
45	C₂×D₇₆	—	2	2	no	—
46	C₂²⋊C₄×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₂²⋊Dic₁₉	—	2	4	no	—
50	(C₂×D₁₉)⋊C₄	—	2	4	no	—
51	(C₂×D₁₉)⋊C₄	—	2	8	no	—
52	(C₂×D₁₉)⋊C₄	—	4	4	no	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	C₄⋊Dic₁₉	—	2	2	no	—
55	C₄⋊Dic₁₉	—	2	2	no	—
56	C₄⋊Dic₁₉	—	4	4	no	—
57	C₄×Dic₁₉	—	2	4	no	—
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	2	1	no	—
60	C₂³×C₁₉	—	2	1	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	C₂×D₄	1	2	yes	—
63	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
64	C₂²×D₁₉	—	2	2	no	—
65	C₂²×D₁₉	—	2	4	no	—
66	C₂²×D₁₉	—	2	2	no	—
67	C₂²×D₁₉	—	2	2	no	—
68	C₂²×D₁₉	—	2	4	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	8	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₉	#41	1	4	yes	—
80	C₂×C₄×C₁₉	#41	1	2	yes	—
81	C₂×C₄×C₁₉	#41	1	2	yes	—
82	C₂²⋊D₁₉	—	4	8	no	—
83	C₂×Dic₁₉	—	2	2	no	—
84	C₂×Dic₁₉	—	2	2	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	4	no	—
87	C₂×Dic₁₉	—	2	4	no	—
88	C₂×Dic₁₉	—	2	4	no	—
89	D₇₆	—	4	4	no	—
90	#2500	—	19	1	no	maximal, Sylow
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	—	4	2	no	—
96	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
97	C₂²×C₁₉	C₂×#41	1	2	yes	—
98	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
99	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
100	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
101	C₂×D₁₉	—	4	2	no	—
102	C₂×D₁₉	—	4	2	no	—
103	C₂×D₁₉	—	4	2	no	—
104	C₂×D₁₉	—	4	4	no	—
105	C₂×D₁₉	—	4	4	no	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	2	4	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	#123	1	4	yes	—
110	Dic₁₉	—	4	2	no	—
111	Dic₁₉	—	4	2	no	—
112	Dic₁₉	—	4	2	no	—
113	C₂×#121	—	19	1	no	—
114	C₂×#117	—	19	1	no	—
115	#394	—	19	4	no	—
116	#390	—	19	1	no	—
117	#390	—	19	1	no	—
118	#388	—	19	4	no	—
119	#384	—	19	1	no	—
120	#382	—	19	1	no	—
121	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic, complemented
122	C₂×C₁₉	—	4	2	no	—
123	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
124	C₂×C₁₉	#532	1	1	yes	characteristic
125	C₂×C₁₉	#535	1	1	yes	characteristic
126	C₂×C₁₉	#553	1	2	yes	—
127	C₂×C₁₉	#555	1	2	yes	—
128	D₁₉	—	8	2	no	—
129	C₂²×D₄	—	19	2	no	—
130	C₂²×D₄	—	19	1	no	—
131	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
132	#121	—	38	4	no	—
133	#117	—	38	4	no	—
134	C₂×C₄⋊C₄	—	19	1	no	—
135	C₂×C₄⋊C₄	—	19	1	no	—
136	C₂×C₄⋊C₄	—	19	1	no	—
137	C₂×C₄⋊C₄	—	19	4	no	—
138	C₂×C₂²⋊C₄	—	19	2	no	—
139	C₂×C₂²⋊C₄	—	19	2	no	—
140	C₂×C₂²⋊C₄	—	19	4	no	—
141	C₂×C₂²⋊C₄	—	19	4	no	—
142	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
143	C₂×C₄²	—	19	2	no	—
144	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
146	#95	—	19	4	no	—
147	#95	C₂×D₁₉	1	2	yes	—
148	C₁₉	#2500	1	1	yes	characteristic, complemented, Sylow
149	C₂⁴	—	19	2	no	—
150	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
151	C₂×D₄	—	38	4	no	—
152	C₂×D₄	—	38	2	no	—
153	C₂×D₄	—	38	2	no	—
154	C₂×D₄	—	38	2	no	—
155	C₂×D₄	—	76	4	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	19	2	no	—
159	C₂²×C₄	—	19	2	no	—
160	C₂²×C₄	—	19	2	no	—
161	C₂²×C₄	D₇₆	1	4	yes	—
162	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
163	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
165	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₄	—	38	2	no	—
167	C₄⋊C₄	—	38	2	no	—
168	C₄⋊C₄	—	38	2	no	—
169	C₄⋊C₄	—	76	4	no	—
170	C₂²⋊C₄	—	2	4	no	—
171	C₂²⋊C₄	—	38	4	no	—
172	C₂²⋊C₄	—	38	4	no	—
173	C₂²⋊C₄	—	38	8	no	—
174	C₂²⋊C₄	—	76	4	no	—
175	C₄²	—	2	2	no	—
176	C₄²	—	2	2	no	—
177	C₄²	—	38	4	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	2	1	no	—
180	C₂³	—	2	1	no	—
181	C₂³	—	2	2	no	—
182	C₂³	—	38	2	no	—
183	C₂³	—	38	4	no	—
184	C₂³	—	38	2	no	—
185	C₂³	—	38	2	no	—
186	C₂³	—	38	4	no	—
187	C₂³	C₂×D₇₆	1	2	yes	—
188	C₂³	C₂³×D₁₉	1	1	yes	characteristic
189	D₄	—	76	8	no	—
190	D₄	—	76	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	38	2	no	—
200	C₂×C₄	—	38	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	38	4	no	—
203	C₂×C₄	—	38	4	no	—
204	C₂×C₄	—	38	4	no	—
205	C₂×C₄	C₂×D₇₆	1	2	yes	—
206	C₂×C₄	C₂×D₇₆	1	2	yes	—
207	C₂×C₄	#64541	1	4	yes	—
208	C₂×C₄	#64543	1	2	yes	—
209	C₂×C₄	#64543	1	2	yes	—
210	C₂²	—	2	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	76	2	no	—
216	C₂²	—	76	2	no	—
217	C₂²	—	76	2	no	—
218	C₂²	—	76	4	no	—
219	C₂²	—	76	4	no	—
220	C₂²	C₂²×D₇₆	1	1	yes	characteristic
221	C₂²	C₂×#64541	1	2	yes	—
222	C₂²	C₂×#64543	1	1	yes	characteristic
223	C₂²	C₂×#64543	1	1	yes	characteristic
224	C₂²	#10597435	1	2	yes	—
225	C₄	—	2	2	no	—
226	C₄	—	2	4	no	—
227	C₄	—	4	2	no	—
228	C₄	—	76	2	no	—
229	C₄	—	76	2	no	—
230	C₄	—	76	2	no	—
231	C₄	#10597332	1	4	yes	—
232	C₂	—	4	2	no	—
233	C₂	—	152	2	no	—
234	C₂	C₂×#10597332	1	1	yes	characteristic
235	C₂	#11927094	1	1	yes	characteristic
236	C₂	#11927113	1	1	yes	characteristic
237	C₂	#11927240	1	2	yes	—
238	C₂	#11927259	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597376

C₂

yes

maximal, characteristic

C₂×#10597372

C₂

yes

maximal, characteristic, complemented

#11926460

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, characteristic, complemented

#11926446

C₂

yes

maximal, characteristic, complemented

#11926436

C₂

yes

maximal, complemented

#11926414

C₂

yes

maximal, characteristic, complemented

#11926410

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×C₂²⋊D₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597376

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

#2500

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

100

C₂²×C₁₉

H(5,𝔽₂)

yes

—

101

C₂×D₁₉

—

102

C₂×D₁₉

—

103

C₂×D₁₉

—

104

C₂×D₁₉

—

105

C₂×D₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#123

yes

—

110

Dic₁₉

—

111

Dic₁₉

—

112

Dic₁₉

—

113

C₂×#121

—

114

C₂×#117

—

115

#394

—

116

#390

—

117

#390

—

118

#388

—

119

#384

—

120

#382

—

121

C₄×C₂²⋊C₄

D₁₉

yes

characteristic, complemented

122

C₂×C₁₉

—

123

C₂×C₁₉

C₂×#123

yes

characteristic

124

C₂×C₁₉

#532

yes

characteristic

125

C₂×C₁₉

#535

yes

characteristic

126

C₂×C₁₉

#553

yes

—

127

C₂×C₁₉

#555

yes

—

128

D₁₉

—

129

C₂²×D₄

—

130

C₂²×D₄

—

131

C₂³×C₄

C₂×D₁₉

yes

characteristic

132

#121

—

133

#117

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

143

C₂×C₄²

—

144

C₂×C₄²

C₂×D₁₉

yes

characteristic

145

C₂×C₄²

C₂×D₁₉

yes

characteristic

146

#95

—

147

#95

C₂×D₁₉

yes

—

148

C₁₉

#2500

yes

characteristic, complemented, Sylow

149

C₂⁴

—

150

C₂⁴

C₂²×D₁₉

yes

characteristic

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

D₇₆

yes

—

162

C₂²×C₄

C₂²×D₁₉

yes

—

163

C₂²×C₄

C₂²×D₁₉

yes

characteristic

164

C₂²×C₄

C₂²×D₁₉

yes

—

165

C₂²×C₄

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₂²⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

C₂×D₇₆

yes

—

188

C₂³

C₂³×D₁₉

yes

characteristic

189

D₄

—

190

D₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

C₂×D₇₆

yes

—

206

C₂×C₄

C₂×D₇₆

yes

—

207

C₂×C₄

#64541

yes

—

208

C₂×C₄

#64543

yes

—

209

C₂×C₄

#64543

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₂²×D₇₆

yes

characteristic

221

C₂²

C₂×#64541

yes

—

222

C₂²

C₂×#64543

yes

characteristic

223

C₂²

C₂×#64543

yes

characteristic

224

C₂²

#10597435

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

#10597332

yes

—

232

C₂

—

233

C₂

—

152

—

234

C₂

C₂×#10597332

yes

characteristic

235

C₂

#11927094

yes

characteristic

236

C₂

#11927113

yes

characteristic

237

C₂

#11927240

yes

—

238

C₂

#11927259

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
prime radical	C₂×#10597376	C₂
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#2500
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄×C₂²⋊C₄×C₁₉

C₂

prime radical

C₂×#10597376

C₂

hypercenter

C₄×C₂²⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
2. C₂×#10597372	C₂	semidirect
3. #11926460	C₂	semidirect
4. #11926446	C₂	semidirect
5. #11926446	C₂	semidirect
6. #11926436	C₂	semidirect
7. #11926414	C₂	semidirect
8. #11926410	C₂	semidirect
9. C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
121. C₄×C₂²⋊C₄	D₁₉	semidirect
148. C₁₉	#2500	semidirect

H ≅ G/N

type

2. C₂×#10597372

C₂

semidirect

3. #11926460

C₂

semidirect

4. #11926446

C₂

semidirect

5. #11926446

C₂

semidirect

6. #11926436

C₂

semidirect

7. #11926414

C₂

semidirect

8. #11926410

C₂

semidirect

9. C₄×C₂²⋊C₄×C₁₉

C₂

semidirect

121. C₄×C₂²⋊C₄

D₁₉

semidirect

148. C₁₉

#2500

semidirect

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

subgroup	index
C₂×#10597376	2
C₂×#10597372	2
#11926460	2
#11926446	2
#11926436	2
#11926414	2
#11926410	2
C₄×C₂²⋊C₄×C₁₉	2
#2500	19

subgroup

index

C₄×C₂²⋊C₄×C₁₉

Subgroups — #14568097

Conjugacy classes of subgroups

Complements

Maximal subgroups