Group #14570594 — subgroups

Subgroups — #14570594

Order 2432.

476 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597325	C₂	1	2	yes	maximal, complemented
2	#11926480	C₂	1	2	yes	maximal, complemented
3	#11926467	C₂	1	2	yes	maximal, complemented
4	#11926458	C₂	1	2	yes	maximal
5	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926439	C₂	1	2	yes	maximal, complemented
8	#11926437	C₂	1	2	yes	maximal, complemented
9	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
24	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
26	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
27	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
28	#10597325	—	2	8	no	—
29	C₁₉⋊#95	C₂²	1	2	yes	—
30	C₁₉⋊#95	C₂²	1	2	yes	—
31	C₁₉⋊#95	C₂²	1	2	yes	—
32	C₂⁴×C₁₉	C₂³	1	2	yes	—
33	C₂×D₄×C₁₉	—	2	2	no	—
34	C₂×D₄×C₁₉	—	4	1	no	—
35	C₂×D₄×C₁₉	—	4	1	no	—
36	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×Dic₁₉	C₂³	1	2	yes	—
41	C₂²×Dic₁₉	C₂³	1	2	yes	—
42	C₂²×Dic₁₉	C₂³	1	2	yes	—
43	C₂²×Dic₁₉	C₂³	1	2	yes	—
44	C₄⋊C₄×C₁₉	—	4	1	no	—
45	C₂²⋊C₄×C₁₉	—	2	4	no	—
46	C₂²⋊C₄×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	4	1	no	—
48	C₂²⋊Dic₁₉	—	2	4	no	—
49	C₂²⋊Dic₁₉	—	2	4	no	—
50	C₂²⋊Dic₁₉	—	4	2	no	—
51	C₂²⋊Dic₁₉	—	4	2	no	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	—	4	1	no	—
54	C₄⋊Dic₁₉	—	4	1	no	—
55	C₄⋊Dic₁₉	D₄	1	4	yes	complemented
56	Dic₁₉⋊C₄	—	2	4	no	—
57	Dic₁₉⋊C₄	—	2	4	no	—
58	Dic₁₉⋊C₄	—	2	4	no	—
59	Dic₁₉⋊C₄	—	4	2	no	—
60	C₄×Dic₁₉	—	2	4	no	—
61	C₂³×C₁₉	—	2	2	no	—
62	C₂³×C₁₉	—	2	2	no	—
63	C₂³×C₁₉	—	2	2	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	—	2	2	no	—
66	C₂³×C₁₉	—	2	2	no	—
67	C₂³×C₁₉	—	2	2	no	—
68	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
69	D₄×C₁₉	—	4	4	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₁₉	#41	1	2	yes	—
81	C₂×C₄×C₁₉	#41	1	2	yes	—
82	C₂×Dic₁₉	—	2	2	no	—
83	C₂×Dic₁₉	—	2	2	no	—
84	C₂×Dic₁₉	—	2	2	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	2	no	—
87	C₂×Dic₁₉	—	2	2	no	—
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	—	2	2	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
94	#2727	—	19	1	no	maximal, Sylow
95	C₂²×C₁₉	—	4	2	no	—
96	C₂²×C₁₉	—	4	2	no	—
97	C₂²×C₁₉	—	4	2	no	—
98	C₂²×C₁₉	—	4	2	no	—
99	C₂²×C₁₉	—	4	2	no	—
100	C₂²×C₁₉	—	4	2	no	—
101	C₂²×C₁₉	—	4	2	no	—
102	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
103	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
104	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
105	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
106	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
107	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
108	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	4	2	no	—
113	Dic₁₉	—	2	4	no	—
114	Dic₁₉	—	4	2	no	—
115	Dic₁₉	—	4	2	no	—
116	Dic₁₉	—	4	2	no	—
117	C₂×#126	—	19	2	no	—
118	#399	—	19	2	no	—
119	#396	—	19	2	no	—
120	#394	—	19	2	no	—
121	#390	D₁₉	1	1	yes	characteristic
122	#389	—	19	2	no	—
123	#389	—	19	1	no	—
124	#389	—	19	1	no	—
125	#388	—	19	2	no	—
126	C₂×C₁₉	—	8	2	no	—
127	C₂×C₁₉	#537	1	1	yes	characteristic
128	C₂×C₁₉	#538	1	1	yes	characteristic
129	C₂×C₁₉	#539	1	1	yes	characteristic
130	C₂×C₁₉	#547	1	1	yes	characteristic
131	C₂×C₁₉	#550	1	1	yes	characteristic
132	C₂×C₁₉	#556	1	1	yes	characteristic
133	C₂×C₁₉	#563	1	1	yes	characteristic
134	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
135	#126	—	38	8	no	—
136	C₂×C₄⋊C₄	—	19	1	no	—
137	C₂×C₄⋊C₄	—	19	2	no	—
138	C₂×C₄⋊C₄	—	19	2	no	—
139	C₂×C₄⋊C₄	—	19	2	no	—
140	C₂×C₄⋊C₄	—	19	1	no	—
141	C₂×C₄⋊C₄	—	19	1	no	—
142	C₂×C₄⋊C₄	—	19	1	no	—
143	C₂×C₄⋊C₄	—	19	2	no	—
144	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	19	2	no	—
146	C₂×C₂²⋊C₄	—	19	2	no	—
147	C₂×C₂²⋊C₄	—	19	2	no	—
148	C₂×C₂²⋊C₄	—	19	2	no	—
149	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
150	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
151	C₂×C₄²	—	19	2	no	—
152	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
153	#95	—	19	2	no	—
154	#95	—	19	2	no	—
155	#95	—	19	2	no	—
156	C₁₉	#2727	1	1	yes	characteristic, complemented, Sylow
157	C₂⁴	C₂²×D₁₉	1	2	yes	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	4	1	no	—
160	C₂×D₄	—	4	1	no	—
161	C₂²×C₄	—	19	2	no	—
162	C₂²×C₄	—	19	2	no	—
163	C₂²×C₄	—	19	2	no	—
164	C₂²×C₄	—	19	2	no	—
165	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
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	C₄⋊C₄	—	4	1	no	—
170	C₄⋊C₄	—	19	4	no	—
171	C₄⋊C₄	—	38	4	no	—
172	C₄⋊C₄	—	38	4	no	—
173	C₄⋊C₄	—	38	4	no	—
174	C₄⋊C₄	—	38	2	no	—
175	C₄⋊C₄	—	76	2	no	—
176	C₄⋊C₄	—	76	1	no	—
177	C₄⋊C₄	—	76	1	no	—
178	C₂²⋊C₄	—	2	4	no	—
179	C₂²⋊C₄	—	2	4	no	—
180	C₂²⋊C₄	—	38	4	no	—
181	C₂²⋊C₄	—	38	4	no	—
182	C₂²⋊C₄	—	76	2	no	—
183	C₂²⋊C₄	—	76	2	no	—
184	C₄²	—	4	1	no	—
185	C₄²	—	38	4	no	—
186	C₂³	—	2	2	no	—
187	C₂³	—	2	2	no	—
188	C₂³	—	2	2	no	—
189	C₂³	—	2	2	no	—
190	C₂³	—	2	2	no	—
191	C₂³	—	2	2	no	—
192	C₂³	—	2	2	no	—
193	C₂³	C₂³×D₁₉	1	1	yes	characteristic
194	D₄	—	4	4	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	19	4	no	—
205	C₂×C₄	—	38	2	no	—
206	C₂×C₄	—	38	2	no	—
207	C₂×C₄	—	38	2	no	—
208	C₂×C₄	—	38	2	no	—
209	C₂×C₄	—	38	2	no	—
210	C₂×C₄	—	38	2	no	—
211	C₂×C₄	—	38	2	no	—
212	C₂×C₄	—	38	2	no	—
213	C₂×C₄	—	38	2	no	—
214	C₂×C₄	—	38	2	no	—
215	C₂×C₄	—	38	2	no	—
216	C₂×C₄	#64541	1	2	yes	—
217	C₂×C₄	D₄×D₁₉	1	2	yes	—
218	C₂×C₄	#64543	1	2	yes	—
219	C₂²	—	4	2	no	—
220	C₂²	—	4	2	no	—
221	C₂²	—	4	2	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	2	no	—
226	C₂²	C₂×#64541	1	1	yes	characteristic
227	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
228	C₂²	C₂×#64543	1	1	yes	characteristic
229	C₂²	#10597430	1	1	yes	characteristic
230	C₂²	#10597430	1	1	yes	characteristic
231	C₂²	#10597436	1	1	yes	characteristic
232	C₂²	#10597436	1	1	yes	characteristic
233	C₄	—	2	2	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	4	2	no	—
237	C₄	—	38	4	no	—
238	C₄	—	76	2	no	—
239	C₄	—	76	2	no	—
240	C₄	—	76	2	no	—
241	C₂	—	8	2	no	—
242	C₂	#11927121	1	1	yes	characteristic
243	C₂	#11927132	1	1	yes	characteristic
244	C₂	#11927139	1	1	yes	characteristic
245	C₂	#11927199	1	1	yes	characteristic
246	C₂	#11927214	1	1	yes	characteristic
247	C₂	#11927264	1	1	yes	characteristic
248	C₂	#11927294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597325

C₂

yes

maximal, complemented

#11926480

C₂

yes

maximal, complemented

#11926467

C₂

yes

maximal, complemented

#11926458

C₂

yes

maximal

#11926442

C₂

yes

maximal, characteristic, complemented

#11926442

C₂

yes

maximal, characteristic, complemented

#11926439

C₂

yes

maximal, complemented

#11926437

C₂

yes

maximal, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597325

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

complemented

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

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

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

#2727

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

C₂²×D₄

yes

characteristic

103

C₂²×C₁₉

C₂×#41

yes

characteristic

104

C₂²×C₁₉

C₂×#41

yes

characteristic

105

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

106

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

107

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

108

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

Dic₁₉

—

114

Dic₁₉

—

115

Dic₁₉

—

116

Dic₁₉

—

117

C₂×#126

—

118

#399

—

119

#396

—

120

#394

—

121

#390

D₁₉

yes

characteristic

122

#389

—

123

#389

—

124

#389

—

125

#388

—

126

C₂×C₁₉

—

127

C₂×C₁₉

#537

yes

characteristic

128

C₂×C₁₉

#538

yes

characteristic

129

C₂×C₁₉

#539

yes

characteristic

130

C₂×C₁₉

#547

yes

characteristic

131

C₂×C₁₉

#550

yes

characteristic

132

C₂×C₁₉

#556

yes

characteristic

133

C₂×C₁₉

#563

yes

characteristic

134

C₂²×D₄

C₂×D₁₉

yes

characteristic

135

#126

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₂²⋊C₄

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

150

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂×D₁₉

yes

characteristic

153

#95

—

154

#95

—

155

#95

—

156

C₁₉

#2727

yes

characteristic, complemented, Sylow

157

C₂⁴

C₂²×D₁₉

yes

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

C₂²×D₁₉

yes

—

166

C₂²×C₄

C₂²×D₁₉

yes

characteristic

167

C₂²×C₄

C₂²×D₁₉

yes

characteristic

168

C₂²×C₄

C₂²×D₁₉

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₂²⋊C₄

—

180

C₂²⋊C₄

—

181

C₂²⋊C₄

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

C₂³×D₁₉

yes

characteristic

194

D₄

—

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

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

#64541

yes

—

217

C₂×C₄

D₄×D₁₉

yes

—

218

C₂×C₄

#64543

yes

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

C₂×#64541

yes

characteristic

227

C₂²

C₂×D₄×D₁₉

yes

characteristic

228

C₂²

C₂×#64543

yes

characteristic

229

C₂²

#10597430

yes

characteristic

230

C₂²

#10597430

yes

characteristic

231

C₂²

#10597436

yes

characteristic

232

C₂²

#10597436

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₂

—

242

C₂

#11927121

yes

characteristic

243

C₂

#11927132

yes

characteristic

244

C₂

#11927139

yes

characteristic

245

C₂

#11927199

yes

characteristic

246

C₂

#11927214

yes

characteristic

247

C₂

#11927264

yes

characteristic

248

C₂

#11927294

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#390	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2727
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #390

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#390

C₂

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #390

N	H ≅ G/N	type
1. C₂×#10597325	C₂	semidirect
2. #11926480	C₂	semidirect
3. #11926467	C₂	semidirect
5. #11926442	C₂	semidirect
6. #11926442	C₂	semidirect
7. #11926439	C₂	semidirect
8. #11926437	C₂	semidirect
55. C₄⋊Dic₁₉	D₄	semidirect
156. C₁₉	#2727	semidirect

H ≅ G/N

type

1. C₂×#10597325

C₂

semidirect

2. #11926480

C₂

semidirect

3. #11926467

C₂

semidirect

5. #11926442

C₂

semidirect

6. #11926442

C₂

semidirect

7. #11926439

C₂

semidirect

8. #11926437

C₂

semidirect

55. C₄⋊Dic₁₉

D₄

semidirect

156. C₁₉

#2727

semidirect

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

subgroup	index
C₂×#10597325	2
#11926480	2
#11926467	2
#11926458	2
#11926442	2
#11926439	2
#11926437	2
C₁₉×#390	2
#2727	19

subgroup

index

C₁₉×#390

Subgroups — #14570594

Conjugacy classes of subgroups

Complements

Maximal subgroups