Group #18084895 — subgroups

Subgroups — #18084895

Order 4864.

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

normal subgroups only

This group has 560 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×#11926840	C₂	1	2	yes	maximal
2	#14569008	C₂	1	1	yes	maximal, characteristic
3	#14564436	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926274	C₂	1	2	yes	maximal
5	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
8	#11926840	—	2	4	no	—
9	#11926840	—	2	4	no	—
10	C₂×#10597275	—	2	2	no	—
11	C₂×#10597273	—	2	2	no	—
12	C₂×#10597267	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926474	—	2	2	no	—
15	#11926449	—	2	2	no	—
16	#11926443	—	2	2	no	—
17	#11926274	—	2	4	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	D₄	1	2	yes	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	—	2	2	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	#10597315	—	2	2	no	—
33	#10597315	—	2	1	no	—
34	#10597315	D₄	1	2	yes	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	2	no	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	#10597275	—	2	8	no	—
44	#10597273	—	2	8	no	—
45	#10597267	—	4	4	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂²×Dic₁₉	—	4	1	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	—	2	2	no	—
55	C₂×Dic₃₈	—	2	2	no	—
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	C₂×Dic₃₈	—	2	2	no	—
59	C₂×Dic₃₈	—	4	2	no	—
60	C₂×Dic₃₈	—	4	2	no	—
61	C₂×Dic₃₈	—	4	1	no	—
62	C₂×Dic₃₈	Q₁₆	1	4	yes	—
63	C₂×C₈×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	2	no	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄⋊Dic₁₉	—	2	4	no	—
73	C₄⋊Dic₁₉	—	2	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	8	2	no	—
77	Dic₁₉⋊C₄	—	4	2	no	—
78	Dic₁₉⋊C₄	—	4	2	no	—
79	C₄×Dic₁₉	—	4	2	no	—
80	C₄×Dic₁₉	—	4	2	no	—
81	C₂×C₁₉⋊C₈	—	2	2	no	—
82	C₂×C₁₉⋊C₈	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	#10237	—	19	1	no	maximal, Sylow
85	C₂³×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	4	4	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	#120	1	2	yes	—
91	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	2	yes	—
93	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₁₉	#135	1	2	yes	—
96	C₂×C₄×C₁₉	#137	1	2	yes	—
97	C₂×C₄×C₁₉	#137	1	2	yes	—
98	C₂×Dic₁₉	—	2	4	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	C₂×Dic₁₉	—	4	2	no	—
101	C₂×Dic₁₉	—	4	2	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	8	1	no	—
106	C₂×Dic₁₉	—	8	1	no	—
107	Dic₃₈	—	2	4	no	—
108	Dic₃₈	—	2	4	no	—
109	Dic₃₈	—	4	2	no	—
110	Dic₃₈	—	4	2	no	—
111	Dic₃₈	—	4	4	no	—
112	Dic₃₈	—	8	2	no	—
113	C₈×C₁₉	—	4	4	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	C₂×#477	—	19	2	no	—
116	#2582	—	19	1	no	—
117	#1956	—	19	1	no	—
118	C₂×Q₈⋊C₈	—	19	2	no	—
119	#1296	D₁₉	1	1	yes	characteristic
120	C₂²×C₁₉	#392	1	1	yes	characteristic
121	C₂²×C₁₉	#451	1	2	yes	—
122	C₂²×C₁₉	#452	1	2	yes	—
123	C₂²×C₁₉	#453	1	1	yes	characteristic
124	C₂²×C₁₉	#454	1	1	yes	characteristic
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	8	2	no	—
128	C₄×C₁₉	#451	1	2	yes	—
129	C₄×C₁₉	#452	1	2	yes	—
130	C₄×C₁₉	#467	1	2	yes	—
131	C₄×C₁₉	#470	1	2	yes	—
132	Dic₁₉	—	4	4	no	—
133	Dic₁₉	—	8	2	no	—
134	Dic₁₉	—	8	2	no	—
135	C₂×C₄⋊Q₈	—	19	1	no	—
136	C₂×C₄×Q₈	—	19	2	no	—
137	#477	—	38	4	no	—
138	#477	—	38	4	no	—
139	C₂×#107	—	38	2	no	—
140	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
141	C₂×#103	—	38	2	no	—
142	C₂×#103	—	38	2	no	—
143	C₂×C₄×C₈	—	19	1	no	—
144	#398	—	38	2	no	—
145	#391	—	38	2	no	—
146	#389	—	38	2	no	—
147	#384	C₂×D₁₉	1	1	yes	characteristic
148	Q₈⋊C₈	—	38	4	no	—
149	C₂×C₁₉	#1630	1	1	yes	characteristic
150	C₂×C₁₉	#1633	1	1	yes	characteristic
151	C₂×C₁₉	#1636	1	2	yes	—
152	C₂×C₁₉	#2001	1	2	yes	—
153	C₂×C₁₉	#2006	1	1	yes	characteristic
154	C₂²×Q₈	—	19	2	no	—
155	C₂²×Q₈	—	38	1	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	38	1	no	—
158	C₄⋊Q₈	—	19	2	no	—
159	C₄⋊Q₈	—	38	2	no	—
160	C₄⋊Q₈	—	38	1	no	—
161	C₄×Q₈	—	38	2	no	—
162	C₄×Q₈	—	38	2	no	—
163	C₄×Q₈	—	38	2	no	—
164	C₄×Q₈	—	38	2	no	—
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	19	2	no	—
167	C₂×C₄⋊C₄	—	38	2	no	—
168	C₂×C₄⋊C₄	—	38	2	no	—
169	C₂×C₄⋊C₄	—	38	2	no	—
170	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
171	C₂×C₄²	—	38	2	no	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	#107	—	38	8	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	D₇₆	1	4	yes	—
176	#103	—	38	8	no	—
177	#103	—	76	4	no	—
178	C₄×C₈	—	38	2	no	—
179	#95	—	38	4	no	—
180	#95	—	38	2	no	—
181	C₁₉	#10237	1	1	yes	characteristic, complemented, Sylow
182	C₂×Q₈	—	19	4	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂×Q₈	—	38	2	no	—
185	C₂×Q₈	—	38	2	no	—
186	C₂×Q₈	—	38	2	no	—
187	C₂×Q₈	—	38	2	no	—
188	C₂×Q₈	—	38	2	no	—
189	C₂×Q₈	—	76	2	no	—
190	C₂×Q₈	—	76	2	no	—
191	C₂×Q₈	—	76	1	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	38	2	no	—
194	C₂²×C₄	—	38	2	no	—
195	C₂²×C₄	—	76	1	no	—
196	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
197	C₂²×C₄	D₄×D₁₉	1	2	yes	—
198	C₂×C₈	—	2	4	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	38	2	no	—
202	C₂×C₈	—	76	1	no	—
203	C₂×C₈	—	76	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	38	4	no	—
208	C₄⋊C₄	—	38	2	no	—
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	76	2	no	—
211	C₄⋊C₄	—	76	2	no	—
212	C₄⋊C₄	—	76	2	no	—
213	C₄⋊C₄	—	152	2	no	—
214	C₄²	—	76	2	no	—
215	C₄²	—	76	2	no	—
216	C₄²	C₂×D₇₆	1	2	yes	—
217	C₄²	D₄×D₁₉	1	1	yes	characteristic
218	C₄²	#64545	1	1	yes	characteristic
219	C₂³	#10597328	1	1	yes	characteristic
220	Q₈	—	38	4	no	—
221	Q₈	—	38	4	no	—
222	Q₈	—	76	4	no	—
223	Q₈	—	76	2	no	—
224	Q₈	—	76	2	no	—
225	Q₈	—	152	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	4	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	38	4	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	76	2	no	—
234	C₂×C₄	—	76	2	no	—
235	C₂×C₄	—	76	2	no	—
236	C₂×C₄	—	76	2	no	—
237	C₂×C₄	—	152	1	no	—
238	C₂×C₄	—	152	1	no	—
239	C₂×C₄	#10597320	1	1	yes	characteristic
240	C₂×C₄	#10597328	1	2	yes	—
241	C₂×C₄	#10597341	1	1	yes	characteristic
242	C₂×C₄	#10597341	1	2	yes	—
243	C₂×C₄	#10597358	1	2	yes	—
244	C₂×C₄	#10597361	1	2	yes	—
245	C₂×C₄	#10597361	1	2	yes	—
246	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
247	C₈	—	4	4	no	—
248	C₈	—	76	2	no	—
249	C₂²	#11926454	1	1	yes	characteristic
250	C₂²	#11926701	1	2	yes	—
251	C₂²	#11926707	1	2	yes	—
252	C₂²	#11926714	1	1	yes	characteristic
253	C₂²	#11926719	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	8	2	no	—
257	C₄	—	76	4	no	—
258	C₄	—	152	2	no	—
259	C₄	—	152	2	no	—
260	C₄	#11926701	1	2	yes	—
261	C₄	#11926707	1	2	yes	—
262	C₄	#11926786	1	2	yes	—
263	C₄	#11926803	1	2	yes	—
264	C₂	#14562757	1	1	yes	characteristic
265	C₂	#14562776	1	1	yes	characteristic
266	C₂	#14562794	1	2	yes	—
267	C₂	#14564646	1	2	yes	—
268	C₂	#14564679	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926840

C₂

yes

maximal

#14569008

C₂

yes

maximal, characteristic

#14564436

C₂

yes

maximal, characteristic

C₂×#11926274

C₂

yes

maximal

C₁₉×#1296

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂²×Dic₃₈

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

#10597315

—

#10597315

—

#10597315

D₄

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

#10597275

—

#10597273

—

#10597267

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

Dic₃₈

—

110

Dic₃₈

—

111

Dic₃₈

—

112

Dic₃₈

—

113

C₈×C₁₉

—

114

C₁₉⋊C₈

—

115

C₂×#477

—

116

#2582

—

117

#1956

—

118

C₂×Q₈⋊C₈

—

119

#1296

D₁₉

yes

characteristic

120

C₂²×C₁₉

#392

yes

characteristic

121

C₂²×C₁₉

#451

yes

—

122

C₂²×C₁₉

#452

yes

—

123

C₂²×C₁₉

#453

yes

characteristic

124

C₂²×C₁₉

#454

yes

characteristic

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

#451

yes

—

129

C₄×C₁₉

#452

yes

—

130

C₄×C₁₉

#467

yes

—

131

C₄×C₁₉

#470

yes

—

132

Dic₁₉

—

133

Dic₁₉

—

134

Dic₁₉

—

135

C₂×C₄⋊Q₈

—

136

C₂×C₄×Q₈

—

137

#477

—

138

#477

—

139

C₂×#107

—

140

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

141

C₂×#103

—

142

C₂×#103

—

143

C₂×C₄×C₈

—

144

#398

—

145

#391

—

146

#389

—

147

#384

C₂×D₁₉

yes

characteristic

148

Q₈⋊C₈

—

149

C₂×C₁₉

#1630

yes

characteristic

150

C₂×C₁₉

#1633

yes

characteristic

151

C₂×C₁₉

#1636

yes

—

152

C₂×C₁₉

#2001

yes

—

153

C₂×C₁₉

#2006

yes

characteristic

154

C₂²×Q₈

—

155

C₂²×Q₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

D₇₆

yes

—

171

C₂×C₄²

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

#107

—

174

C₄⋊C₈

—

175

C₄⋊C₈

D₇₆

yes

—

176

#103

—

177

#103

—

178

C₄×C₈

—

179

#95

—

180

#95

—

181

C₁₉

#10237

yes

characteristic, complemented, Sylow

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

C₂×D₇₆

yes

characteristic

197

C₂²×C₄

D₄×D₁₉

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

152

—

214

C₄²

—

215

C₄²

—

216

C₄²

C₂×D₇₆

yes

—

217

C₄²

D₄×D₁₉

yes

characteristic

218

C₄²

#64545

yes

characteristic

219

C₂³

#10597328

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

223

Q₈

—

224

Q₈

—

225

Q₈

—

152

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

152

—

238

C₂×C₄

—

152

—

239

C₂×C₄

#10597320

yes

characteristic

240

C₂×C₄

#10597328

yes

—

241

C₂×C₄

#10597341

yes

characteristic

242

C₂×C₄

#10597341

yes

—

243

C₂×C₄

#10597358

yes

—

244

C₂×C₄

#10597361

yes

—

245

C₂×C₄

#10597361

yes

—

246

C₂×C₄

Q₁₆×D₁₉

yes

—

247

C₈

—

248

C₈

—

249

C₂²

#11926454

yes

characteristic

250

C₂²

#11926701

yes

—

251

C₂²

#11926707

yes

—

252

C₂²

#11926714

yes

characteristic

253

C₂²

#11926719

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

152

—

259

C₄

—

152

—

260

C₄

#11926701

yes

—

261

C₄

#11926707

yes

—

262

C₄

#11926786

yes

—

263

C₄

#11926803

yes

—

264

C₂

#14562757

yes

characteristic

265

C₂

#14562776

yes

characteristic

266

C₂

#14562794

yes

—

267

C₂

#14564646

yes

—

268

C₂

#14564679

yes

characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle, prime radical	C₂³×C₁₉	#120
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#10237
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#10597328

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1296

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
181. C₁₉	#10237	semidirect

H ≅ G/N

type

181. C₁₉

#10237

semidirect

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

subgroup	index
C₂×#11926840	2
#14569008	2
#14564436	2
C₂×#11926274	2
C₁₉×#1296	2
#10237	19

subgroup

index

C₁₉×#1296

Subgroups — #18084895

Conjugacy classes of subgroups

Complements

Maximal subgroups