Group #14574242 — subgroups

Subgroups — #14574242

Order 2432.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926954	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926939	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926914	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926903	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926800	C₂	1	2	yes	maximal, complemented
7	#11926788	C₂	1	2	yes	maximal
8	C₄×#64528	C₂	1	2	yes	maximal, complemented
9	C₄×#64526	C₂	1	2	yes	maximal, complemented
10	C₄×#64520	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#529	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#126	—	2	1	no	—
13	C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₁₉×#124	C₂²	1	1	yes	characteristic
15	C₁₉×#123	—	2	1	no	—
16	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×D₄×C₁₉	—	2	1	no	—
20	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#117	—	2	1	no	—
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×#64528	C₂²	1	2	yes	—
24	C₂×#64526	C₂²	1	2	yes	—
25	#10597372	—	2	1	no	—
26	#10597370	—	2	1	no	—
27	#10597370	C₂²	1	2	yes	—
28	C₂×#64520	C₂²	1	2	yes	—
29	#10597316	—	2	1	no	—
30	#10597315	C₂²	1	1	yes	characteristic
31	#10597315	C₂²	1	1	yes	characteristic
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	C₂²	1	2	yes	—
34	#10597292	C₂²	1	2	yes	—
35	#10597289	C₂²	1	2	yes	—
36	#10597267	C₂²	1	2	yes	—
37	#10597267	C₂²	1	2	yes	—
38	#10597265	C₂²	1	2	yes	—
39	#10597264	C₂²	1	2	yes	—
40	#10597260	C₂²	1	1	yes	characteristic
41	#10597260	C₂²	1	1	yes	characteristic
42	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
43	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₁₉	—	2	1	no	—
45	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×Dic₃₈	—	2	1	no	—
51	C₂×Dic₃₈	C₂³	1	2	yes	—
52	C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	D₄	1	1	yes	characteristic
65	C₄²×C₁₉	D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²⋊Dic₁₉	—	2	2	no	—
69	#64528	—	2	4	no	—
70	#64526	—	2	4	no	—
71	C₄⋊Dic₁₉	—	2	1	no	—
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	—	2	1	no	—
74	C₄⋊Dic₁₉	C₂³	1	2	yes	—
75	Dic₁₉⋊C₄	—	2	2	no	—
76	Dic₁₉⋊C₄	—	2	2	no	—
77	C₄×Dic₁₉	—	2	2	no	—
78	#64520	—	2	4	no	—
79	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
80	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
81	C₂³×C₁₉	—	2	1	no	—
82	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₁₉	—	2	2	no	—
84	D₄×C₁₉	—	2	2	no	—
85	D₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	4	1	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	Dic₃₈	—	2	2	no	—
102	Dic₃₈	—	2	2	no	—
103	Dic₃₈	—	4	2	no	—
104	C₁₉⋊C₈	—	2	2	no	—
105	C₁₉⋊C₈	#41	1	4	yes	—
106	#3172	—	19	1	no	maximal, Sylow
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	—	2	1	no	—
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	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	4	1	no	—
119	C₄×C₁₉	—	4	1	no	—
120	C₄×C₁₉	—	4	1	no	—
121	C₄×C₁₉	#137	1	2	yes	—
122	C₄×C₁₉	C₂×#41	1	2	yes	—
123	Dic₁₉	—	4	2	no	—
124	Dic₁₉	—	4	2	no	—
125	#533	—	19	1	no	—
126	#529	D₁₉	1	1	yes	characteristic
127	#501	—	19	1	no	—
128	#497	—	19	1	no	—
129	#491	—	19	1	no	—
130	#489	—	19	1	no	—
131	#470	—	19	2	no	—
132	#468	—	19	2	no	—
133	C₄×Q₁₆	—	19	2	no	—
134	C₄×SD₁₆	—	19	2	no	—
135	C₄×M₁₆	—	19	1	no	—
136	C₂×C₁₉	—	4	1	no	—
137	C₂×C₁₉	—	8	1	no	—
138	C₂×C₁₉	#532	1	1	yes	characteristic
139	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
140	C₂×C₁₉	#575	1	1	yes	characteristic
141	C₂×Q₁₆	—	19	2	no	—
142	C₂×SD₁₆	—	19	2	no	—
143	C₂×M₁₆	—	19	2	no	—
144	C₄⋊Q₈	—	19	1	no	—
145	C₄⋊Q₈	—	19	1	no	—
146	#126	—	2	1	no	—
147	#125	—	38	1	no	—
148	#125	C₂×D₁₉	1	1	yes	characteristic
149	#124	C₂×D₁₉	1	1	yes	characteristic
150	#123	—	2	1	no	—
151	C₂²⋊Q₈	—	19	2	no	—
152	C₂²⋊Q₈	—	38	1	no	—
153	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
154	#121	C₂×D₁₉	1	1	yes	characteristic
155	C₄×Q₈	—	19	2	no	—
156	C₄×Q₈	—	38	1	no	—
157	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
158	C₄×D₄	—	2	1	no	—
159	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
160	#117	—	2	1	no	—
161	#117	—	38	1	no	—
162	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
163	#107	—	19	2	no	—
164	#106	—	19	2	no	—
165	#103	—	19	2	no	—
166	#103	—	19	2	no	—
167	#103	—	19	2	no	—
168	#102	—	19	2	no	—
169	#97	—	19	1	no	—
170	#97	—	19	1	no	—
171	C₄×C₈	—	19	2	no	—
172	C₁₉	#3172	1	1	yes	characteristic, complemented, Sylow
173	C₂×Q₈	—	19	2	no	—
174	C₂×Q₈	—	38	1	no	—
175	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
178	C₂²×C₄	—	2	1	no	—
179	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
182	Q₁₆	—	38	4	no	—
183	SD₁₆	—	38	4	no	—
184	M₁₆	—	38	4	no	—
185	C₂×C₈	—	19	2	no	—
186	C₂×C₈	—	19	2	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	—	19	2	no	—
192	C₄⋊C₄	—	38	2	no	—
193	C₄⋊C₄	—	38	2	no	—
194	C₄⋊C₄	—	38	1	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄⋊C₄	—	38	1	no	—
197	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
198	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	2	1	no	—
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	38	2	no	—
205	C₄²	—	2	1	no	—
206	C₄²	—	38	2	no	—
207	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
208	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
209	C₄²	C₂²×D₁₉	1	1	yes	characteristic
210	C₄²	C₂²×D₁₉	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
213	Q₈	—	2	2	no	—
214	Q₈	—	38	2	no	—
215	Q₈	—	38	2	no	—
216	Q₈	—	76	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	38	2	no	—
227	C₂×C₄	—	38	2	no	—
228	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
231	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
232	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
234	C₈	—	19	4	no	—
235	C₈	—	38	2	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	1	no	—
241	C₂²	—	4	1	no	—
242	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	2	1	no	—
247	C₄	—	4	1	no	—
248	C₄	—	4	1	no	—
249	C₄	—	4	1	no	—
250	C₄	—	76	2	no	—
251	C₄	—	76	2	no	—
252	C₄	#10597397	1	2	yes	—
253	C₄	#41×D₁₉	1	2	yes	—
254	C₂	—	4	1	no	—
255	C₂	—	8	1	no	—
256	C₂	#11927090	1	1	yes	characteristic
257	C₂	C₂×#10597397	1	1	yes	characteristic
258	C₂	#11927342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic, complemented

#11926954

C₂

yes

maximal, characteristic, complemented

#11926939

C₂

yes

maximal, characteristic, complemented

#11926914

C₂

yes

maximal, characteristic, complemented

#11926903

C₂

yes

maximal, characteristic, complemented

#11926800

C₂

yes

maximal, complemented

#11926788

C₂

yes

maximal

C₄×#64528

C₂

yes

maximal, complemented

C₄×#64526

C₂

yes

maximal, complemented

C₄×#64520

C₂

yes

maximal, characteristic, complemented

C₁₉×#529

C₂

yes

maximal, characteristic

C₁₉×#126

—

C₁₉×#125

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

C₂²

yes

characteristic

C₁₉×#121

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64528

C₂²

yes

—

C₂×#64526

C₂²

yes

—

#10597372

—

#10597370

—

#10597370

C₂²

yes

—

C₂×#64520

C₂²

yes

—

#10597316

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

#10597267

C₂²

yes

—

#10597267

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

#10597260

C₂²

yes

characteristic

#10597260

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

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×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

Dic₃₈

—

102

Dic₃₈

—

103

Dic₃₈

—

104

C₁₉⋊C₈

—

105

C₁₉⋊C₈

#41

yes

—

106

#3172

—

maximal, Sylow

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

C₂²×D₄

yes

characteristic

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

#137

yes

—

122

C₄×C₁₉

C₂×#41

yes

—

123

Dic₁₉

—

124

Dic₁₉

—

125

#533

—

126

#529

D₁₉

yes

characteristic

127

#501

—

128

#497

—

129

#491

—

130

#489

—

131

#470

—

132

#468

—

133

C₄×Q₁₆

—

134

C₄×SD₁₆

—

135

C₄×M₁₆

—

136

C₂×C₁₉

—

137

C₂×C₁₉

—

138

C₂×C₁₉

#532

yes

characteristic

139

C₂×C₁₉

C₂×#137

yes

characteristic

140

C₂×C₁₉

#575

yes

characteristic

141

C₂×Q₁₆

—

142

C₂×SD₁₆

—

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

#126

—

147

#125

—

148

#125

C₂×D₁₉

yes

characteristic

149

#124

C₂×D₁₉

yes

characteristic

150

#123

—

151

C₂²⋊Q₈

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

C₂×D₁₉

yes

characteristic

154

#121

C₂×D₁₉

yes

characteristic

155

C₄×Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

C₂×D₁₉

yes

characteristic

158

C₄×D₄

—

159

C₄×D₄

C₂×D₁₉

yes

characteristic

160

#117

—

161

#117

—

162

C₂×C₄²

C₂×D₁₉

yes

characteristic

163

#107

—

164

#106

—

165

#103

—

166

#103

—

167

#103

—

168

#102

—

169

#97

—

170

#97

—

171

C₄×C₈

—

172

C₁₉

#3172

yes

characteristic, complemented, Sylow

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

C₂²×D₁₉

yes

characteristic

176

C₂×D₄

—

177

C₂×D₄

C₂²×D₁₉

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

180

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

181

C₂²×C₄

C₂²×D₁₉

yes

characteristic

182

Q₁₆

—

183

SD₁₆

—

184

M₁₆

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

198

C₄⋊C₄

C₂²×D₁₉

yes

characteristic

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂²⋊D₁₉

yes

characteristic

208

C₄²

C₂²⋊D₁₉

yes

characteristic

209

C₄²

C₂²×D₁₉

yes

characteristic

210

C₄²

C₂²×D₁₉

yes

characteristic

211

C₂³

—

212

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

230

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

231

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

232

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

233

C₂×C₄

C₂³×D₁₉

yes

characteristic

234

C₈

—

235

C₈

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#10597397

yes

—

253

C₄

#41×D₁₉

yes

—

254

C₂

—

255

C₂

—

256

C₂

#11927090

yes

characteristic

257

C₂

C₂×#10597397

yes

characteristic

258

C₂

#11927342

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#529	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₁₉×#121	C₂²
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3172
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#529

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₁₉×#121

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

N	H ≅ G/N	type
1. #11927101	C₂	semidirect
2. #11926954	C₂	semidirect
3. #11926939	C₂	semidirect
4. #11926914	C₂	semidirect
5. #11926903	C₂	semidirect
6. #11926800	C₂	semidirect
8. C₄×#64528	C₂	semidirect
9. C₄×#64526	C₂	semidirect
10. C₄×#64520	C₂	semidirect
172. C₁₉	#3172	semidirect

H ≅ G/N

type

1. #11927101

C₂

semidirect

2. #11926954

C₂

semidirect

3. #11926939

C₂

semidirect

4. #11926914

C₂

semidirect

5. #11926903

C₂

semidirect

6. #11926800

C₂

semidirect

8. C₄×#64528

C₂

semidirect

9. C₄×#64526

C₂

semidirect

10. C₄×#64520

C₂

semidirect

172. C₁₉

#3172

semidirect

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

subgroup	index
#11927101	2
#11926954	2
#11926939	2
#11926914	2
#11926903	2
#11926800	2
#11926788	2
C₄×#64528	2
C₄×#64526	2
C₄×#64520	2
C₁₉×#529	2
#3172	19

subgroup

index

C₁₉×#529

Subgroups — #14574242

Conjugacy classes of subgroups

Complements

Maximal subgroups