Group #18087416 — subgroups

Subgroups — #18087416

Order 4864.

298 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14563651	C₂	1	1	yes	maximal, characteristic
2	#14563628	C₂	1	1	yes	maximal, characteristic
3	#14562405	C₂	1	1	yes	maximal, characteristic
4	#14562029	C₂	1	1	yes	maximal, characteristic
5	#14561495	C₂	1	1	yes	maximal, characteristic
6	#14561494	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926568	C₂²	1	1	yes	characteristic
11	C₂×#10597273	—	2	1	no	—
12	C₂×#10597281	—	2	1	no	—
13	#11926410	C₂²	1	1	yes	characteristic
14	#11926312	—	2	1	no	—
15	#11926307	—	2	1	no	—
16	#11926294	—	2	2	no	—
17	#11926274	—	2	2	no	—
18	C₁₉×#431	C₂²	1	1	yes	characteristic
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	—	2	1	no	—
26	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
27	C₂×Dic₁₉⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₁₉	—	2	1	no	—
29	C₂×#64520	—	2	1	no	—
30	C₄×Dic₃₈	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₄×Dic₃₈	—	2	1	no	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	—	2	1	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₂²⋊C₈	—	2	1	no	—
40	C₄×C₈×C₁₉	—	2	1	no	—
41	C₁₉⋊#95	—	2	1	no	—
42	C₁₉⋊#95	—	2	1	no	—
43	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
44	#10597281	—	4	2	no	—
45	#10597273	—	4	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	—	2	1	no	—
55	C₂²×Dic₁₉	—	4	1	no	—
56	C₂×Dic₃₈	—	2	1	no	—
57	C₂×Dic₃₈	—	2	1	no	—
58	C₂×Dic₃₈	—	2	1	no	—
59	C₂×Dic₃₈	—	2	1	no	—
60	C₂×Dic₃₈	—	2	1	no	—
61	C₂×Dic₃₈	SD₁₆	1	2	yes	—
62	M₁₆×C₁₉	—	4	1	no	—
63	M₁₆×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₂×C₈×C₁₉	—	4	1	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	—	4	1	no	—
68	C₂×C₈×C₁₉	—	4	1	no	—
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	1	yes	characteristic
72	C₄²×C₁₉	#41	1	1	yes	characteristic
73	C₄⋊Dic₁₉	—	2	1	no	—
74	C₄⋊Dic₁₉	—	2	1	no	—
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	Dic₁₉⋊C₄	—	4	1	no	—
78	Dic₁₉⋊C₄	—	4	1	no	—
79	C₄×Dic₁₉	—	4	1	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	#64520	—	4	1	no	—
82	#64520	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	#10644	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	#123	1	1	yes	characteristic
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
97	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	4	1	no	—
101	C₂×Dic₁₉	—	4	1	no	—
102	C₂×Dic₁₉	—	4	1	no	—
103	C₂×Dic₁₉	—	8	1	no	—
104	C₂×Dic₁₉	—	8	1	no	—
105	C₂×Dic₁₉	—	8	1	no	—
106	C₂×Dic₁₉	—	8	1	no	—
107	Dic₃₈	—	2	2	no	—
108	Dic₃₈	—	2	2	no	—
109	Dic₃₈	—	4	1	no	—
110	Dic₃₈	—	4	1	no	—
111	C₈×C₁₉	—	8	1	no	—
112	C₈×C₁₉	—	8	1	no	—
113	C₈×C₁₉	—	8	1	no	—
114	C₁₉⋊C₈	—	4	2	no	—
115	C₁₉⋊C₈	—	8	1	no	—
116	#1805	—	19	1	no	—
117	#1801	—	19	1	no	—
118	#1570	—	19	1	no	—
119	#1479	—	19	1	no	—
120	#1301	D₁₉	1	1	yes	characteristic
121	#1286	—	19	1	no	—
122	#1286	—	19	1	no	—
123	C₂²×C₁₉	—	2	1	no	—
124	C₂²×C₁₉	—	2	1	no	—
125	C₂²×C₁₉	#397	1	1	yes	characteristic
126	C₂²×C₁₉	#481	1	1	yes	characteristic
127	C₂²×C₁₉	#485	1	1	yes	characteristic
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	#465	1	1	yes	characteristic
133	C₄×C₁₉	#468	1	1	yes	characteristic
134	C₄×C₁₉	#482	1	1	yes	characteristic
135	C₄×C₁₉	#483	1	1	yes	characteristic
136	Dic₁₉	—	4	2	no	—
137	Dic₁₉	—	8	1	no	—
138	Dic₁₉	—	16	1	no	—
139	C₂×C₄×Q₈	—	19	1	no	—
140	#431	—	19	1	no	—
141	#431	C₂×D₁₉	1	1	yes	characteristic
142	#423	—	19	1	no	—
143	#423	C₂×D₁₉	1	1	yes	characteristic
144	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
145	C₂×#103	—	38	1	no	—
146	C₂×#101	—	38	1	no	—
147	#382	—	19	1	no	—
148	#343	—	38	1	no	—
149	#340	—	38	1	no	—
150	#334	—	38	2	no	—
151	Q₈⋊C₈	—	38	2	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	#2077	1	1	yes	characteristic
155	C₂×C₁₉	#2080	1	1	yes	characteristic
156	C₂×C₁₉	#2082	1	1	yes	characteristic
157	C₂²×Q₈	—	19	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂×M₁₆	—	38	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₄×Q₈	—	38	1	no	—
162	C₄×Q₈	—	38	1	no	—
163	C₄×Q₈	—	38	1	no	—
164	C₄×Q₈	—	38	1	no	—
165	C₂×C₄⋊C₄	—	19	1	no	—
166	C₂×C₄⋊C₄	—	38	1	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄²	—	38	1	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	38	1	no	—
176	C₄⋊C₈	—	38	1	no	—
177	C₄⋊C₈	—	38	1	no	—
178	#103	—	76	2	no	—
179	#101	—	76	2	no	—
180	C₂²⋊C₈	—	2	1	no	—
181	C₂²⋊C₈	—	38	1	no	—
182	C₄×C₈	—	2	1	no	—
183	C₄×C₈	—	19	2	no	—
184	#95	—	38	1	no	—
185	#95	—	38	1	no	—
186	C₁₉	#10644	1	1	yes	characteristic, complemented, Sylow
187	C₂×Q₈	—	19	2	no	—
188	C₂×Q₈	—	38	1	no	—
189	C₂×Q₈	—	38	1	no	—
190	C₂×Q₈	—	38	1	no	—
191	C₂×Q₈	—	38	1	no	—
192	C₂×Q₈	—	38	1	no	—
193	C₂²×C₄	—	38	1	no	—
194	C₂²×C₄	—	38	1	no	—
195	C₂²×C₄	—	76	1	no	—
196	C₂²×C₄	#64541	1	1	yes	characteristic
197	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
198	C₂²×C₄	#64545	1	1	yes	characteristic
199	M₁₆	—	4	1	no	—
200	M₁₆	—	4	1	no	—
201	M₁₆	—	76	1	no	—
202	M₁₆	—	76	1	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	1	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	4	1	no	—
208	C₂×C₈	—	38	2	no	—
209	C₂×C₈	—	76	1	no	—
210	C₄⋊C₄	—	38	1	no	—
211	C₄⋊C₄	—	38	1	no	—
212	C₄⋊C₄	—	76	1	no	—
213	C₄⋊C₄	—	76	1	no	—
214	C₄⋊C₄	—	76	1	no	—
215	C₄⋊C₄	—	76	1	no	—
216	C₄²	—	76	1	no	—
217	C₄²	—	76	1	no	—
218	C₄²	#64541	1	1	yes	characteristic
219	C₄²	#64541	1	1	yes	characteristic
220	C₄²	D₄×D₁₉	1	1	yes	characteristic
221	C₄²	#64543	1	1	yes	characteristic
222	C₂³	#10597340	1	1	yes	characteristic
223	Q₈	—	38	2	no	—
224	Q₈	—	38	2	no	—
225	Q₈	—	76	1	no	—
226	Q₈	—	76	1	no	—
227	C₂×C₄	—	4	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	76	1	no	—
231	C₂×C₄	—	76	1	no	—
232	C₂×C₄	—	76	1	no	—
233	C₂×C₄	—	152	1	no	—
234	C₂×C₄	—	152	1	no	—
235	C₂×C₄	—	152	1	no	—
236	C₂×C₄	—	152	1	no	—
237	C₂×C₄	#10597322	1	1	yes	characteristic
238	C₂×C₄	#10597329	1	1	yes	characteristic
239	C₂×C₄	#10597330	1	1	yes	characteristic
240	C₂×C₄	#10597331	1	1	yes	characteristic
241	C₂×C₄	#10597340	1	1	yes	characteristic
242	C₂×C₄	#10597344	1	1	yes	characteristic
243	C₂×C₄	#10597358	1	1	yes	characteristic
244	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
245	C₂×C₄	#10597360	1	1	yes	characteristic
246	C₂×C₄	#10597364	1	1	yes	characteristic
247	C₈	—	8	1	no	—
248	C₈	—	8	1	no	—
249	C₈	—	8	1	no	—
250	C₈	—	76	2	no	—
251	C₈	—	152	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	#11926473	1	1	yes	characteristic
255	C₂²	#11926864	1	1	yes	characteristic
256	C₂²	#11926887	1	1	yes	characteristic
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	304	1	no	—
262	C₄	—	76	2	no	—
263	C₄	—	152	1	no	—
264	C₄	#11926772	1	1	yes	characteristic
265	C₄	#11926793	1	1	yes	characteristic
266	C₄	#11926866	1	1	yes	characteristic
267	C₄	#11926873	1	1	yes	characteristic
268	C₂	—	2	1	no	—
269	C₂	—	2	1	no	—
270	C₂	#14565073	1	1	yes	characteristic
271	C₂	#14565091	1	1	yes	characteristic
272	C₂	#14565105	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563651

C₂

yes

maximal, characteristic

#14563628

C₂

yes

maximal, characteristic

#14562405

C₂

yes

maximal, characteristic

#14562029

C₂

yes

maximal, characteristic

#14561495

C₂

yes

maximal, characteristic

#14561494

C₂

yes

maximal, characteristic

C₁₉×#1301

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

—

—

C₂²

yes

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂²×Dic₃₈

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597281

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

SD₁₆

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×SD₁₆

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

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

Dic₃₈

—

110

Dic₃₈

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

C₁₉⋊C₈

—

115

C₁₉⋊C₈

—

116

#1805

—

117

#1801

—

118

#1570

—

119

#1479

—

120

#1301

D₁₉

yes

characteristic

121

#1286

—

122

#1286

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#397

yes

characteristic

126

C₂²×C₁₉

#481

yes

characteristic

127

C₂²×C₁₉

#485

yes

characteristic

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#465

yes

characteristic

133

C₄×C₁₉

#468

yes

characteristic

134

C₄×C₁₉

#482

yes

characteristic

135

C₄×C₁₉

#483

yes

characteristic

136

Dic₁₉

—

137

Dic₁₉

—

138

Dic₁₉

—

139

C₂×C₄×Q₈

—

140

#431

—

141

#431

C₂×D₁₉

yes

characteristic

142

#423

—

143

#423

C₂×D₁₉

yes

characteristic

144

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

145

C₂×#103

—

146

C₂×#101

—

147

#382

—

148

#343

—

149

#340

—

150

#334

—

151

Q₈⋊C₈

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

#2077

yes

characteristic

155

C₂×C₁₉

#2080

yes

characteristic

156

C₂×C₁₉

#2082

yes

characteristic

157

C₂²×Q₈

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

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×C₄²

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

#103

—

179

#101

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

C₄×C₈

—

183

C₄×C₈

—

184

#95

—

185

#95

—

186

C₁₉

#10644

yes

characteristic, complemented, Sylow

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂×Q₈

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

#64541

yes

characteristic

197

C₂²×C₄

D₄×D₁₉

yes

characteristic

198

C₂²×C₄

#64545

yes

characteristic

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄²

—

217

C₄²

—

218

C₄²

#64541

yes

characteristic

219

C₄²

#64541

yes

characteristic

220

C₄²

D₄×D₁₉

yes

characteristic

221

C₄²

#64543

yes

characteristic

222

C₂³

#10597340

yes

characteristic

223

Q₈

—

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

152

—

234

C₂×C₄

—

152

—

235

C₂×C₄

—

152

—

236

C₂×C₄

—

152

—

237

C₂×C₄

#10597322

yes

characteristic

238

C₂×C₄

#10597329

yes

characteristic

239

C₂×C₄

#10597330

yes

characteristic

240

C₂×C₄

#10597331

yes

characteristic

241

C₂×C₄

#10597340

yes

characteristic

242

C₂×C₄

#10597344

yes

characteristic

243

C₂×C₄

#10597358

yes

characteristic

244

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

245

C₂×C₄

#10597360

yes

characteristic

246

C₂×C₄

#10597364

yes

characteristic

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

152

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11926473

yes

characteristic

255

C₂²

#11926864

yes

characteristic

256

C₂²

#11926887

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

304

—

262

C₄

—

263

C₄

—

152

—

264

C₄

#11926772

yes

characteristic

265

C₄

#11926793

yes

characteristic

266

C₄

#11926866

yes

characteristic

267

C₄

#11926873

yes

characteristic

268

C₂

—

269

C₂

—

270

C₂

#14565073

yes

characteristic

271

C₂

#14565091

yes

characteristic

272

C₂

#14565105

yes

characteristic

	subgroup	G/H
center	C₂²	#11926473
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1301	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#123
hypercenter	#1301	D₁₉
hypocenter	C₁₉	#10644
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂²

#11926473

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1301

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
186. C₁₉	#10644	semidirect

H ≅ G/N

type

186. C₁₉

#10644

semidirect

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

subgroup	index
#14563651	2
#14563628	2
#14562405	2
#14562029	2
#14561495	2
#14561494	2
C₁₉×#1301	2
#10644	19

subgroup

index

C₁₉×#1301

Subgroups — #18087416

Conjugacy classes of subgroups

Complements

Maximal subgroups