Group #14567943 — subgroups

Subgroups — #14567943

Order 2432.

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

normal subgroups only

This group has 624 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	C₂×#10597381	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926474	C₂	1	2	yes	maximal, complemented
4	#11926469	C₂	1	2	yes	maximal, complemented
5	#11926442	C₂	1	2	yes	maximal, complemented
6	#11926405	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	#10597381	—	2	8	no	—
22	C₂×C₄⋊Dic₁₉	—	2	4	no	—
23	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
26	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
27	C₁₉⋊#95	C₂²	1	4	yes	—
28	C₁₉⋊#95	C₂²	1	2	yes	—
29	C₁₉⋊#95	C₂²	1	4	yes	—
30	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
31	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×D₄×C₁₉	—	2	2	no	—
33	C₂×D₄×C₁₉	—	2	2	no	—
34	C₂×D₄×C₁₉	D₄	1	4	yes	—
35	C₂²×C₄×C₁₉	—	2	4	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	4	no	—
38	C₂²×C₄×C₁₉	D₄	1	4	yes	—
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×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×Dic₁₉	—	2	4	no	—
45	C₂²×Dic₁₉	—	2	4	no	—
46	C₂²×Dic₁₉	—	2	4	no	—
47	C₂²×Dic₁₉	C₂³	1	4	yes	—
48	C₂²×Dic₁₉	C₂³	1	4	yes	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂²⋊C₄×C₁₉	—	2	2	no	—
51	C₂²⋊C₄×C₁₉	—	2	2	no	—
52	C₄²×C₁₉	—	2	2	no	—
53	C₂²⋊Dic₁₉	—	2	4	no	—
54	C₂²⋊Dic₁₉	—	2	8	no	—
55	C₄⋊Dic₁₉	—	2	4	no	—
56	C₄⋊Dic₁₉	—	2	4	no	—
57	C₄⋊Dic₁₉	—	2	4	no	—
58	Dic₁₉⋊C₄	—	2	8	no	—
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	—	2	1	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	2	1	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	C₂×D₄	1	2	yes	—
66	C₂³×C₁₉	C₂×D₄	1	2	yes	—
67	C₂³×C₁₉	C₂×D₄	1	2	yes	—
68	C₂³×C₁₉	#41	1	2	yes	—
69	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
70	D₄×C₁₉	—	2	8	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	8	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₁₉	#41	1	4	yes	—
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	—	2	4	no	—
89	C₂×Dic₁₉	—	2	4	no	—
90	C₂×Dic₁₉	—	4	8	no	—
91	#2486	—	19	1	no	maximal, Sylow
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	4	no	—
95	C₂²×C₁₉	—	2	4	no	—
96	C₂²×C₁₉	—	2	2	no	—
97	C₂²×C₁₉	—	2	4	no	—
98	C₂²×C₁₉	—	4	1	no	—
99	C₂²×C₁₉	—	4	1	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	#121	1	4	yes	—
102	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
103	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
104	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×#41	1	2	yes	—
106	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	2	2	no	—
109	C₄×C₁₉	—	4	1	no	—
110	C₄×C₁₉	—	4	1	no	—
111	C₄×C₁₉	#123	1	4	yes	complemented
112	Dic₁₉	—	4	4	no	—
113	Dic₁₉	—	4	4	no	—
114	C₂×#123	—	19	2	no	—
115	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic
116	C₂²×C₄⋊C₄	—	19	1	no	—
117	#398	—	19	2	no	—
118	#397	—	19	2	no	—
119	#389	—	19	2	no	—
120	#381	—	19	2	no	—
121	#380	—	19	2	no	—
122	#380	—	19	1	no	—
123	C₂×C₁₉	—	2	4	no	—
124	C₂×C₁₉	—	4	2	no	—
125	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
126	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
127	C₂×C₁₉	#536	1	1	yes	characteristic
128	C₂×C₁₉	#547	1	2	yes	—
129	C₂×C₁₉	#552	1	2	yes	—
130	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
131	C₂³×C₄	—	19	2	no	—
132	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
133	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
134	#123	—	38	8	no	—
135	C₄×D₄	—	2	4	no	—
136	C₂×C₄⋊C₄	—	19	2	no	—
137	C₂×C₄⋊C₄	—	19	2	no	—
138	C₂×C₄⋊C₄	—	19	4	no	—
139	C₂×C₄⋊C₄	—	19	2	no	—
140	C₂×C₄⋊C₄	—	38	4	no	—
141	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₂²⋊C₄	—	19	2	no	—
143	C₂×C₂²⋊C₄	—	19	4	no	—
144	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
146	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
147	#95	—	19	4	no	—
148	#95	—	19	2	no	—
149	#95	—	19	4	no	—
150	C₁₉	#2486	1	1	yes	characteristic, complemented, Sylow
151	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
152	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	D₇₆	1	4	yes	—
156	C₂²×C₄	—	2	4	no	—
157	C₂²×C₄	—	2	4	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	19	4	no	—
160	C₂²×C₄	—	19	4	no	—
161	C₂²×C₄	—	38	4	no	—
162	C₂²×C₄	—	38	4	no	—
163	C₂²×C₄	—	38	4	no	—
164	C₂²×C₄	C₂²⋊D₁₉	1	4	yes	—
165	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
166	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
167	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
168	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
169	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	38	8	no	—
172	C₄⋊C₄	—	38	4	no	—
173	C₄⋊C₄	—	38	4	no	—
174	C₄⋊C₄	—	38	4	no	—
175	C₂²⋊C₄	—	2	2	no	—
176	C₂²⋊C₄	—	2	2	no	—
177	C₂²⋊C₄	—	38	4	no	—
178	C₂²⋊C₄	—	38	8	no	—
179	C₄²	—	2	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	1	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	2	1	no	—
186	C₂³	C₂×D₇₆	1	2	yes	—
187	C₂³	C₂×D₇₆	1	2	yes	—
188	C₂³	#64541	1	2	yes	—
189	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
190	C₂³	C₂³×D₁₉	1	1	yes	characteristic
191	D₄	—	2	8	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	38	4	no	—
202	C₂×C₄	—	38	4	no	—
203	C₂×C₄	—	38	4	no	—
204	C₂×C₄	—	38	4	no	—
205	C₂×C₄	—	38	4	no	—
206	C₂×C₄	—	38	4	no	—
207	C₂×C₄	—	76	8	no	—
208	C₂×C₄	C₂×D₇₆	1	2	yes	—
209	C₂×C₄	#64543	1	4	yes	—
210	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
211	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	2	4	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	4	1	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	2	no	—
221	C₂²	#10597376	1	4	yes	—
222	C₂²	C₂²×D₇₆	1	1	yes	characteristic
223	C₂²	C₂×#64541	1	1	yes	characteristic
224	C₂²	C₂×#64543	1	2	yes	—
225	C₂²	#10597436	1	2	yes	—
226	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	76	4	no	—
232	C₄	—	76	4	no	—
233	C₄	#10597381	1	4	yes	complemented
234	C₂	—	2	4	no	—
235	C₂	—	4	2	no	—
236	C₂	C₂×#10597376	1	1	yes	characteristic
237	C₂	C₂×#10597381	1	1	yes	characteristic
238	C₂	#11927115	1	1	yes	characteristic
239	C₂	#11927198	1	2	yes	—
240	C₂	#11927234	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597381

C₂

yes

maximal

C₂²×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic, complemented

#11926474

C₂

yes

maximal, complemented

#11926469

C₂

yes

maximal, complemented

#11926442

C₂

yes

maximal, complemented

#11926405

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

—

#10597381

—

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

D₄

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

—

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×D₄

yes

—

C₂³×C₁₉

C₂×D₄

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×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2486

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

#121

yes

—

102

C₂²×C₁₉

C₂²×D₄

yes

characteristic

103

C₂²×C₁₉

C₂²×D₄

yes

characteristic

104

C₂²×C₁₉

C₂×#41

yes

characteristic

105

C₂²×C₁₉

C₂×#41

yes

—

106

C₂²×C₁₉

2₋¹⁺⁴

yes

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

#123

yes

complemented

112

Dic₁₉

—

113

Dic₁₉

—

114

C₂×#123

—

115

C₂×C₄×D₄

D₁₉

yes

characteristic

116

C₂²×C₄⋊C₄

—

117

#398

—

118

#397

—

119

#389

—

120

#381

—

121

#380

—

122

#380

—

123

C₂×C₁₉

—

124

C₂×C₁₉

—

125

C₂×C₁₉

C₂×#121

yes

characteristic

126

C₂×C₁₉

C₂×#123

yes

characteristic

127

C₂×C₁₉

#536

yes

characteristic

128

C₂×C₁₉

#547

yes

—

129

C₂×C₁₉

#552

yes

—

130

C₂²×D₄

C₂×D₁₉

yes

characteristic

131

C₂³×C₄

—

132

C₂³×C₄

C₂×D₁₉

yes

characteristic

133

C₂³×C₄

C₂×D₁₉

yes

characteristic

134

#123

—

135

C₄×D₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

142

C₂×C₂²⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

145

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

146

C₂×C₄²

C₂×D₁₉

yes

characteristic

147

#95

—

148

#95

—

149

#95

—

150

C₁₉

#2486

yes

characteristic, complemented, Sylow

151

C₂⁴

C₂²×D₁₉

yes

characteristic

152

C₂⁴

C₂²×D₁₉

yes

characteristic

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

D₇₆

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂²⋊D₁₉

yes

—

165

C₂²×C₄

C₂²×D₁₉

yes

characteristic

166

C₂²×C₄

C₂²×D₁₉

yes

characteristic

167

C₂²×C₄

C₂²×D₁₉

yes

characteristic

168

C₂²×C₄

C₂²×D₁₉

yes

characteristic

169

C₂²×C₄

C₂²×D₁₉

yes

characteristic

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

C₂×D₇₆

yes

—

187

C₂³

C₂×D₇₆

yes

—

188

C₂³

#64541

yes

—

189

C₂³

C₂×C₂²⋊D₁₉

yes

—

190

C₂³

C₂³×D₁₉

yes

characteristic

191

D₄

—

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

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

C₂×D₇₆

yes

—

209

C₂×C₄

#64543

yes

—

210

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

211

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#10597376

yes

—

222

C₂²

C₂²×D₇₆

yes

characteristic

223

C₂²

C₂×#64541

yes

characteristic

224

C₂²

C₂×#64543

yes

—

225

C₂²

#10597436

yes

—

226

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

#10597381

yes

complemented

234

C₂

—

235

C₂

—

236

C₂

C₂×#10597376

yes

characteristic

237

C₂

C₂×#10597381

yes

characteristic

238

C₂

#11927115

yes

characteristic

239

C₂

#11927198

yes

—

240

C₂

#11927234

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	#2486
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
2. C₂²×C₄⋊Dic₁₉	C₂	semidirect
3. #11926474	C₂	semidirect
4. #11926469	C₂	semidirect
5. #11926442	C₂	semidirect
6. #11926405	C₂	semidirect
7. #11926404	C₂	semidirect
8. #11926404	C₂	semidirect
111. C₄×C₁₉	#123	semidirect
150. C₁₉	#2486	semidirect
233. C₄	#10597381	semidirect

H ≅ G/N

type

2. C₂²×C₄⋊Dic₁₉

C₂

semidirect

3. #11926474

C₂

semidirect

4. #11926469

C₂

semidirect

5. #11926442

C₂

semidirect

6. #11926405

C₂

semidirect

7. #11926404

C₂

semidirect

8. #11926404

C₂

semidirect

111. C₄×C₁₉

#123

semidirect

150. C₁₉

#2486

semidirect

233. C₄

#10597381

semidirect

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

subgroup	index
C₂×#10597381	2
C₂²×C₄⋊Dic₁₉	2
#11926474	2
#11926469	2
#11926442	2
#11926405	2
#11926404	2
C₂×C₄×D₄×C₁₉	2
#2486	19

subgroup

index

C₂²×C₄⋊Dic₁₉

C₂×C₄×D₄×C₁₉

Subgroups — #14567943

Conjugacy classes of subgroups

Complements

Maximal subgroups