Group #14567952 — subgroups

Subgroups — #14567952

Order 2432.

584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂²×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926483	C₂	1	2	yes	maximal, complemented
3	#11926480	C₂	1	2	yes	maximal, complemented
4	#11926442	C₂	1	2	yes	maximal, complemented
5	#11926424	C₂	1	2	yes	maximal
6	#11926416	C₂	1	2	yes	maximal, complemented
7	#11926404	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926404	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×Dic₁₉	C₂²	1	2	yes	—
14	C₄×D₄×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
21	C₂×C₄⋊Dic₁₉	—	2	4	no	—
22	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
23	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
26	C₁₉⋊#95	C₂²	1	4	yes	—
27	C₁₉⋊#95	C₂²	1	2	yes	—
28	C₁₉⋊#95	C₂²	1	4	yes	—
29	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
30	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×D₄×C₁₉	—	2	2	no	—
32	C₂×D₄×C₁₉	—	2	2	no	—
33	C₂×D₄×C₁₉	Q₈	1	4	yes	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	D₄	1	4	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	4	no	—
44	C₂²×Dic₁₉	—	4	4	no	—
45	C₂²×Dic₁₉	C₂³	1	4	yes	—
46	C₂²×Dic₁₉	C₂³	1	4	yes	—
47	C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂²⋊C₄×C₁₉	—	2	2	no	—
49	C₂²⋊C₄×C₁₉	—	2	2	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₂²⋊Dic₁₉	—	2	4	no	—
52	C₂²⋊Dic₁₉	—	4	4	no	—
53	C₄⋊Dic₁₉	—	2	4	no	—
54	C₄⋊Dic₁₉	—	2	4	no	—
55	C₄⋊Dic₁₉	—	2	4	no	—
56	Dic₁₉⋊C₄	—	4	4	no	—
57	C₂³×C₁₉	—	2	2	no	—
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	2	1	no	—
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	C₂×D₄	1	2	yes	—
64	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
65	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
66	C₂³×C₁₉	#41	1	2	yes	—
67	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
68	D₄×C₁₉	—	2	8	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	8	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	4	4	no	—
78	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
81	C₂×C₄×C₁₉	#41	1	4	yes	—
82	C₂×Dic₁₉	—	2	4	no	—
83	C₂×Dic₁₉	—	2	4	no	—
84	C₂×Dic₁₉	—	2	4	no	—
85	C₂×Dic₁₉	—	2	4	no	—
86	C₂×Dic₁₉	—	2	4	no	—
87	C₂×Dic₁₉	—	2	4	no	—
88	C₂×Dic₁₉	—	4	8	no	—
89	#2487	—	19	1	no	maximal, Sylow
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	2	4	no	—
93	C₂²×C₁₉	—	2	4	no	—
94	C₂²×C₁₉	—	2	2	no	—
95	C₂²×C₁₉	—	2	4	no	—
96	C₂²×C₁₉	—	4	1	no	—
97	C₂²×C₁₉	—	4	1	no	—
98	C₂²×C₁₉	—	4	2	no	—
99	C₂²×C₁₉	C₂²⋊Q₈	1	4	yes	—
100	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
101	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
102	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
103	C₂²×C₁₉	C₂×#41	1	2	yes	—
104	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	4	1	no	—
108	C₄×C₁₉	—	4	1	no	—
109	C₄×C₁₉	#123	1	4	yes	—
110	Dic₁₉	—	4	4	no	—
111	Dic₁₉	—	4	4	no	—
112	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic
113	C₂²×C₄⋊C₄	—	19	1	no	—
114	#400	—	19	2	no	—
115	#399	—	19	2	no	—
116	#389	—	19	2	no	—
117	#386	—	19	2	no	—
118	#385	—	19	2	no	—
119	#380	—	19	2	no	—
120	#380	—	19	1	no	—
121	C₂×C₁₉	—	2	4	no	—
122	C₂×C₁₉	—	4	2	no	—
123	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
124	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
125	C₂×C₁₉	#535	1	1	yes	characteristic
126	C₂×C₁₉	#553	1	2	yes	—
127	C₂×C₁₉	#554	1	2	yes	—
128	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
129	C₂³×C₄	—	19	2	no	—
130	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
131	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
132	C₄×D₄	—	2	4	no	—
133	C₂×C₄⋊C₄	—	19	2	no	—
134	C₂×C₄⋊C₄	—	19	2	no	—
135	C₂×C₄⋊C₄	—	19	2	no	—
136	C₂×C₄⋊C₄	—	19	4	no	—
137	C₂×C₄⋊C₄	—	38	4	no	—
138	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
139	C₂×C₂²⋊C₄	—	19	2	no	—
140	C₂×C₂²⋊C₄	—	19	4	no	—
141	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
143	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
144	#95	—	19	4	no	—
145	#95	—	19	2	no	—
146	#95	—	19	4	no	—
147	C₁₉	#2487	1	1	yes	characteristic, complemented, Sylow
148	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
149	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
150	C₂×D₄	—	2	2	no	—
151	C₂×D₄	—	2	2	no	—
152	C₂×D₄	Dic₃₈	1	4	yes	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	19	4	no	—
157	C₂²×C₄	—	19	4	no	—
158	C₂²×C₄	—	38	4	no	—
159	C₂²×C₄	—	76	4	no	—
160	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
161	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
162	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
163	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	38	4	no	—
168	C₄⋊C₄	—	38	4	no	—
169	C₄⋊C₄	—	38	4	no	—
170	C₄⋊C₄	—	76	4	no	—
171	C₂²⋊C₄	—	2	2	no	—
172	C₂²⋊C₄	—	2	2	no	—
173	C₂²⋊C₄	—	38	4	no	—
174	C₂²⋊C₄	—	76	4	no	—
175	C₄²	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	—	2	2	no	—
178	C₂³	—	2	1	no	—
179	C₂³	—	2	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	1	no	—
182	C₂³	C₂×Dic₃₈	1	2	yes	—
183	C₂³	C₂×Dic₃₈	1	2	yes	—
184	C₂³	#64541	1	2	yes	—
185	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
186	C₂³	C₂³×D₁₉	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	8	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	38	4	no	—
198	C₂×C₄	—	38	4	no	—
199	C₂×C₄	—	38	4	no	—
200	C₂×C₄	—	38	4	no	—
201	C₂×C₄	—	38	4	no	—
202	C₂×C₄	—	38	4	no	—
203	C₂×C₄	—	76	8	no	—
204	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
205	C₂×C₄	#64543	1	4	yes	—
206	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	4	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	4	1	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	2	no	—
217	C₂²	#10597370	1	4	yes	—
218	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
219	C₂²	C₂×#64541	1	1	yes	characteristic
220	C₂²	C₂×#64543	1	2	yes	—
221	C₂²	#10597435	1	2	yes	—
222	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	1	no	—
226	C₄	—	4	1	no	—
227	C₄	—	76	4	no	—
228	C₄	—	76	4	no	—
229	C₄	#10597381	1	4	yes	—
230	C₂	—	2	4	no	—
231	C₂	—	4	2	no	—
232	C₂	C₂×#10597370	1	1	yes	characteristic
233	C₂	C₂×#10597381	1	1	yes	characteristic
234	C₂	#11927108	1	1	yes	characteristic
235	C₂	#11927240	1	2	yes	—
236	C₂	#11927251	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic, complemented

#11926483

C₂

yes

maximal, complemented

#11926480

C₂

yes

maximal, complemented

#11926442

C₂

yes

maximal, complemented

#11926424

C₂

yes

maximal

#11926416

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, characteristic, complemented

#11926404

C₂

yes

maximal, complemented

C₂×C₄×D₄×C₁₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

D₄×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×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2487

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

—

100

C₂²×C₁₉

C₂²×D₄

yes

characteristic

101

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

102

C₂²×C₁₉

C₂×#41

yes

characteristic

103

C₂²×C₁₉

C₂×#41

yes

—

104

C₂²×C₁₉

H(5,𝔽₂)

yes

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#123

yes

—

110

Dic₁₉

—

111

Dic₁₉

—

112

C₂×C₄×D₄

D₁₉

yes

characteristic

113

C₂²×C₄⋊C₄

—

114

#400

—

115

#399

—

116

#389

—

117

#386

—

118

#385

—

119

#380

—

120

#380

—

121

C₂×C₁₉

—

122

C₂×C₁₉

—

123

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

124

C₂×C₁₉

C₂×#123

yes

characteristic

125

C₂×C₁₉

#535

yes

characteristic

126

C₂×C₁₉

#553

yes

—

127

C₂×C₁₉

#554

yes

—

128

C₂²×D₄

C₂×D₁₉

yes

characteristic

129

C₂³×C₄

—

130

C₂³×C₄

C₂×D₁₉

yes

characteristic

131

C₂³×C₄

C₂×D₁₉

yes

characteristic

132

C₄×D₄

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

139

C₂×C₂²⋊C₄

—

140

C₂×C₂²⋊C₄

—

141

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

142

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

143

C₂×C₄²

C₂×D₁₉

yes

characteristic

144

#95

—

145

#95

—

146

#95

—

147

C₁₉

#2487

yes

characteristic, complemented, Sylow

148

C₂⁴

C₂²×D₁₉

yes

characteristic

149

C₂⁴

C₂²×D₁₉

yes

characteristic

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

Dic₃₈

yes

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

C₂²⋊D₁₉

yes

—

161

C₂²×C₄

C₂²×D₁₉

yes

characteristic

162

C₂²×C₄

C₂²×D₁₉

yes

characteristic

163

C₂²×C₄

C₂²×D₁₉

yes

characteristic

164

C₂²×C₄

C₂²×D₁₉

yes

characteristic

165

C₂²×C₄

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₂²⋊C₄

—

172

C₂²⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

C₂×Dic₃₈

yes

—

183

C₂³

C₂×Dic₃₈

yes

—

184

C₂³

#64541

yes

—

185

C₂³

C₂×C₂²⋊D₁₉

yes

—

186

C₂³

C₂³×D₁₉

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

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

C₂×Dic₃₈

yes

—

205

C₂×C₄

#64543

yes

—

206

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

207

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

#10597370

yes

—

218

C₂²

C₂²×Dic₃₈

yes

characteristic

219

C₂²

C₂×#64541

yes

characteristic

220

C₂²

C₂×#64543

yes

—

221

C₂²

#10597435

yes

—

222

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

#10597381

yes

—

230

C₂

—

231

C₂

—

232

C₂

C₂×#10597370

yes

characteristic

233

C₂

C₂×#10597381

yes

characteristic

234

C₂

#11927108

yes

characteristic

235

C₂

#11927240

yes

—

236

C₂

#11927251

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₄×D₄×C₁₉	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#2487
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₄×D₄×C₁₉

C₂

prime radical

C₂²×D₄×C₁₉

C₂²

hypercenter

C₂×C₄×D₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄×D₄

N	H ≅ G/N	type
1. C₂²×C₄⋊Dic₁₉	C₂	semidirect
2. #11926483	C₂	semidirect
3. #11926480	C₂	semidirect
4. #11926442	C₂	semidirect
6. #11926416	C₂	semidirect
7. #11926404	C₂	semidirect
8. #11926404	C₂	semidirect
147. C₁₉	#2487	semidirect

H ≅ G/N

type

1. C₂²×C₄⋊Dic₁₉

C₂

semidirect

2. #11926483

C₂

semidirect

3. #11926480

C₂

semidirect

4. #11926442

C₂

semidirect

6. #11926416

C₂

semidirect

7. #11926404

C₂

semidirect

8. #11926404

C₂

semidirect

147. C₁₉

#2487

semidirect

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

subgroup	index
C₂²×C₄⋊Dic₁₉	2
#11926483	2
#11926480	2
#11926442	2
#11926424	2
#11926416	2
#11926404	2
C₂×C₄×D₄×C₁₉	2
#2487	19

subgroup

index

C₂²×C₄⋊Dic₁₉

C₂×C₄×D₄×C₁₉

Subgroups — #14567952

Conjugacy classes of subgroups

Complements

Maximal subgroups