Group #18081705 — subgroups

Subgroups — #18081705

Order 4864.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14574221	C₂	1	1	yes	maximal, characteristic
2	#14564579	C₂	1	2	yes	maximal
3	C₄×#10597274	C₂	1	1	yes	maximal, characteristic
4	#14562135	C₂	1	2	yes	maximal
5	C₁₉×#1451	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926924	C₄	1	1	yes	characteristic, complemented
9	#11926895	C₄	1	2	yes	complemented
10	#11926785	—	2	1	no	—
11	#11926785	—	2	1	no	—
12	C₄×Dic₇₆	—	2	1	no	—
13	C₄×Dic₇₆	—	2	1	no	—
14	C₂×#10597274	—	2	1	no	—
15	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	#11926307	—	2	1	no	—
17	#11926305	—	2	4	no	—
18	#11926282	—	2	4	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#322	—	2	1	no	—
23	C₁₉×#322	—	2	1	no	—
24	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597372	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	#10597370	—	2	2	no	—
31	#10597370	—	2	2	no	—
32	C₂×C₄×Dic₁₉	—	2	2	no	—
33	C₂×Dic₇₆	—	2	1	no	—
34	C₂×Dic₇₆	—	2	1	no	—
35	#10597316	—	2	2	no	—
36	#10597315	C₂×C₄	1	2	yes	—
37	#10597315	C₂×C₄	1	2	yes	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₄×Dic₃₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
42	C₁₉×#97	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	—	2	1	no	—
45	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₁₉⋊#95	—	2	2	no	—
50	#10597275	—	2	1	no	—
51	#10597275	—	2	1	no	—
52	#10597274	—	2	4	no	—
53	#10597273	—	2	2	no	—
54	#10597273	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₉	—	4	2	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	C₂×Dic₃₈	—	2	2	no	—
61	M₁₆×C₁₉	—	2	4	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₂²⋊Dic₁₉	—	4	2	no	—
75	C₄⋊Dic₁₉	—	2	4	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₄⋊Dic₁₉	—	4	2	no	—
81	Dic₁₉⋊C₄	—	4	2	no	—
82	Dic₁₉⋊C₄	—	4	2	no	—
83	C₄×Dic₁₉	—	4	2	no	—
84	C₄×Dic₁₉	—	4	4	no	—
85	Dic₇₆	—	4	2	no	—
86	Dic₇₆	—	4	2	no	—
87	#9720	—	19	1	no	maximal, Sylow
88	C₂³×C₁₉	#127	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#137	1	4	yes	—
99	C₂×Dic₁₉	—	4	4	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	8	2	no	—
103	C₂×Dic₁₉	—	8	2	no	—
104	Dic₃₈	—	4	2	no	—
105	Dic₃₈	—	4	2	no	—
106	Dic₃₈	—	8	2	no	—
107	C₈×C₁₉	—	2	1	no	—
108	C₈×C₁₉	—	2	1	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	4	2	no	—
111	C₈×C₁₉	—	4	2	no	—
112	C₈×C₁₉	#104	1	2	yes	—
113	#3170	—	19	1	no	—
114	#1986	—	19	2	no	—
115	C₄×#106	—	19	1	no	—
116	#1503	—	19	2	no	—
117	#1451	D₁₉	1	1	yes	characteristic
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	#390	1	1	yes	characteristic
121	C₂²×C₁₉	#497	1	2	yes	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
126	C₄×C₁₉	#421	1	1	yes	characteristic
127	C₄×C₁₉	#441	1	2	yes	—
128	C₄×C₁₉	#470	1	2	yes	—
129	Dic₁₉	—	8	4	no	—
130	Dic₁₉	—	8	2	no	—
131	Dic₁₉	—	8	2	no	—
132	#533	—	19	2	no	—
133	#500	—	19	1	no	—
134	#494	—	19	1	no	—
135	#487	—	19	2	no	—
136	#467	—	38	1	no	—
137	#467	—	38	1	no	—
138	C₄×Q₁₆	—	38	1	no	—
139	C₄×Q₁₆	—	38	1	no	—
140	#431	C₂×D₁₉	1	1	yes	characteristic
141	C₂×#106	—	38	1	no	—
142	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
143	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
144	C₄×C₄⋊C₄	—	19	2	no	—
145	#340	—	38	1	no	—
146	#339	—	38	4	no	—
147	#328	—	38	4	no	—
148	#322	—	2	1	no	—
149	#322	—	2	1	no	—
150	C₂×C₁₉	—	2	2	no	—
151	C₂×C₁₉	#1971	1	1	yes	characteristic
152	C₂×C₁₉	#1976	1	1	yes	characteristic
153	C₂×C₁₉	#1980	1	1	yes	characteristic
154	C₂×Q₁₆	—	38	1	no	—
155	C₂×Q₁₆	—	38	1	no	—
156	C₂×M₁₆	D₇₆	1	2	yes	—
157	C₂²×C₈	D₇₆	1	1	yes	characteristic
158	C₂²×C₈	D₇₆	1	1	yes	characteristic
159	C₄⋊Q₈	—	19	2	no	—
160	C₄⋊Q₈	—	19	2	no	—
161	#125	—	38	2	no	—
162	C₂²⋊Q₈	—	38	2	no	—
163	C₂²⋊Q₈	—	38	2	no	—
164	C₄×Q₈	—	38	2	no	—
165	C₄×Q₈	—	38	2	no	—
166	#117	—	38	2	no	—
167	C₂×C₄⋊C₄	—	38	2	no	—
168	C₂×C₄²	—	38	2	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	#107	—	38	1	no	—
171	#107	—	38	1	no	—
172	#106	—	38	4	no	—
173	C₄⋊C₈	—	2	1	no	—
174	#103	—	38	2	no	—
175	#103	—	38	2	no	—
176	C₂²⋊C₈	D₇₆	1	2	yes	—
177	#97	—	2	1	no	—
178	C₄×C₈	—	2	1	no	—
179	C₄×C₈	—	2	1	no	—
180	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
181	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
182	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	#95	—	38	2	no	—
185	C₁₉	#9720	1	1	yes	characteristic, complemented, Sylow
186	C₂×Q₈	—	38	2	no	—
187	C₂×Q₈	—	38	2	no	—
188	C₂²×C₄	—	76	2	no	—
189	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
192	Q₁₆	—	76	2	no	—
193	Q₁₆	—	76	2	no	—
194	M₁₆	—	2	4	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₄⋊C₄	—	38	4	no	—
204	C₄⋊C₄	—	38	2	no	—
205	C₄⋊C₄	—	38	2	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	76	2	no	—
209	C₄⋊C₄	—	76	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₂²⋊C₄	—	76	2	no	—
212	C₄²	—	76	2	no	—
213	C₄²	—	76	4	no	—
214	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
215	C₄²	#64541	1	1	yes	characteristic
216	C₄²	#64541	1	1	yes	characteristic
217	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	C₂³	#10597320	1	1	yes	characteristic
219	Q₈	—	76	2	no	—
220	Q₈	—	76	2	no	—
221	Q₈	—	152	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	76	4	no	—
226	C₂×C₄	—	76	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	—	152	2	no	—
229	C₂×C₄	—	152	2	no	—
230	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
231	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
232	C₂×C₄	#10597321	1	1	yes	characteristic
233	C₂×C₄	#10597355	1	4	yes	—
234	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
235	C₂×C₄	#10597376	1	1	yes	characteristic
236	C₂×C₄	#10597376	1	1	yes	characteristic
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	4	2	no	—
241	C₈	—	4	2	no	—
242	C₈	#10597282	1	2	yes	—
243	C₂²	—	2	1	no	—
244	C₂²	—	2	1	no	—
245	C₂²	#11926446	1	1	yes	characteristic
246	C₂²	#11926938	1	2	yes	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	152	4	no	—
251	C₄	—	152	2	no	—
252	C₄	—	152	2	no	—
253	C₄	C₂×#10597282	1	1	yes	characteristic
254	C₄	#11926560	1	1	yes	characteristic
255	C₄	#11926652	1	2	yes	—
256	C₄	#11926802	1	2	yes	—
257	C₂	—	2	2	no	—
258	C₂	#14564506	1	1	yes	characteristic
259	C₂	#14564533	1	1	yes	characteristic
260	C₂	#14564554	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574221

C₂

yes

maximal, characteristic

#14564579

C₂

yes

maximal

C₄×#10597274

C₂

yes

maximal, characteristic

#14562135

C₂

yes

maximal

C₁₉×#1451

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926924

C₄

yes

characteristic, complemented

#11926895

C₄

yes

complemented

#11926785

—

#11926785

—

C₄×Dic₇₆

—

C₄×Dic₇₆

—

C₂×#10597274

—

C₄×C₄⋊Dic₁₉

C₂²

yes

—

#11926307

—

#11926305

—

#11926282

—

C₁₉×#431

C₂²

yes

characteristic

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₁₉×#322

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

—

C₂×C₄×Dic₁₉

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

—

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉⋊#95

—

—

—

—

—

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

Dic₃₈

—

105

Dic₃₈

—

106

Dic₃₈

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

#104

yes

—

113

#3170

—

114

#1986

—

115

C₄×#106

—

116

#1503

—

117

#1451

D₁₉

yes

characteristic

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

#390

yes

characteristic

121

C₂²×C₁₉

#497

yes

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

C₂×#104

yes

characteristic

126

C₄×C₁₉

#421

yes

characteristic

127

C₄×C₁₉

#441

yes

—

128

C₄×C₁₉

#470

yes

—

129

Dic₁₉

—

130

Dic₁₉

—

131

Dic₁₉

—

132

#533

—

133

#500

—

134

#494

—

135

#487

—

136

#467

—

137

#467

—

138

C₄×Q₁₆

—

139

C₄×Q₁₆

—

140

#431

C₂×D₁₉

yes

characteristic

141

C₂×#106

—

142

C₄×M₁₆

C₂×D₁₉

yes

characteristic

143

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

144

C₄×C₄⋊C₄

—

145

#340

—

146

#339

—

147

#328

—

148

#322

—

149

#322

—

150

C₂×C₁₉

—

151

C₂×C₁₉

#1971

yes

characteristic

152

C₂×C₁₉

#1976

yes

characteristic

153

C₂×C₁₉

#1980

yes

characteristic

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×M₁₆

D₇₆

yes

—

157

C₂²×C₈

D₇₆

yes

characteristic

158

C₂²×C₈

D₇₆

yes

characteristic

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

#125

—

162

C₂²⋊Q₈

—

163

C₂²⋊Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

#117

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄²

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

#107

—

171

#107

—

172

#106

—

173

C₄⋊C₈

—

174

#103

—

175

#103

—

176

C₂²⋊C₈

D₇₆

yes

—

177

#97

—

178

C₄×C₈

—

179

C₄×C₈

—

180

C₄×C₈

C₄×D₁₉

yes

characteristic

181

C₄×C₈

C₄×D₁₉

yes

characteristic

182

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

183

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

184

#95

—

185

C₁₉

#9720

yes

characteristic, complemented, Sylow

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×D₇₆

yes

characteristic

190

C₂²×C₄

C₂×D₇₆

yes

characteristic

191

C₂²×C₄

C₂×D₇₆

yes

characteristic

192

Q₁₆

—

193

Q₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

201

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

202

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

C₂×C₄×D₁₉

yes

characteristic

215

C₄²

#64541

yes

characteristic

216

C₄²

#64541

yes

characteristic

217

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

218

C₂³

#10597320

yes

characteristic

219

Q₈

—

220

Q₈

—

221

Q₈

—

152

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

152

—

229

C₂×C₄

—

152

—

230

C₂×C₄

C₄×D₇₆

yes

characteristic

231

C₂×C₄

C₄×D₇₆

yes

characteristic

232

C₂×C₄

#10597321

yes

characteristic

233

C₂×C₄

#10597355

yes

—

234

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

235

C₂×C₄

#10597376

yes

characteristic

236

C₂×C₄

#10597376

yes

characteristic

237

C₈

—

238

C₈

—

239

C₈

—

240

C₈

—

241

C₈

—

242

C₈

#10597282

yes

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926446

yes

characteristic

246

C₂²

#11926938

yes

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

152

—

251

C₄

—

152

—

252

C₄

—

152

—

253

C₄

C₂×#10597282

yes

characteristic

254

C₄

#11926560

yes

characteristic

255

C₄

#11926652

yes

—

256

C₄

#11926802

yes

—

257

C₂

—

258

C₂

#14564506

yes

characteristic

259

C₂

#14564533

yes

characteristic

260

C₂

#14564554

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1451	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1451	D₁₉
hypocenter	C₁₉	#9720
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1451

subgroup

G/H

center

C₂×C₄

#10597376

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1451

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1451

N	H ≅ G/N	type
7. #11926949	C₄	semidirect
8. #11926924	C₄	semidirect
9. #11926895	C₄	semidirect
185. C₁₉	#9720	semidirect

H ≅ G/N

type

7. #11926949

C₄

semidirect

8. #11926924

C₄

semidirect

9. #11926895

C₄

semidirect

185. C₁₉

#9720

semidirect

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

subgroup	index
#14574221	2
#14564579	2
C₄×#10597274	2
#14562135	2
C₁₉×#1451	2
#9720	19

subgroup

index

C₁₉×#1451

Subgroups — #18081705

Conjugacy classes of subgroups

Complements

Maximal subgroups