Group #18069158 — subgroups

Subgroups — #18069158

Order 4864.

476 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 59 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	#14561559	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂⁴×C₄×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
6	C₂×C₁₉×C₂²⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
8	C₂⁵×C₁₉	C₈	1	1	yes	characteristic
9	C₂³×C₄×C₁₉	—	2	1	no	—
10	C₂³×C₄×C₁₉	—	2	1	no	—
11	C₂³×C₄×C₁₉	—	4	4	no	—
12	C₂³×C₄×C₁₉	—	4	1	no	—
13	C₂³×C₄×C₁₉	—	4	1	no	—
14	C₂³×C₄×C₁₉	C₈	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	2	1	no	—
17	C₂²×C₈×C₁₉	D₄	1	2	yes	—
18	C₁₉×C₂²⋊C₈	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	4	no	—
20	C₁₉×C₂²⋊C₈	—	4	1	no	—
21	C₂×C₁₉⋊C₁₆	—	4	2	no	—
22	C₂⁴×C₁₉	—	2	1	no	—
23	C₂⁴×C₁₉	—	2	1	no	—
24	C₂⁴×C₁₉	—	4	2	no	—
25	C₂⁴×C₁₉	—	4	1	no	—
26	C₂⁴×C₁₉	—	4	2	no	—
27	C₂⁴×C₁₉	—	4	1	no	—
28	C₂⁴×C₁₉	C₁₆	1	2	yes	complemented
29	C₂⁴×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	—	2	4	no	—
31	C₂²×C₄×C₁₉	—	2	1	no	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄×C₁₉	—	4	2	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	—	4	2	no	—
39	C₂²×C₄×C₁₉	—	4	2	no	—
40	C₂²×C₄×C₁₉	—	4	4	no	—
41	C₂²×C₄×C₁₉	—	4	4	no	—
42	C₂²×C₄×C₁₉	—	4	4	no	—
43	C₂²×C₄×C₁₉	—	4	1	no	—
44	C₂²×C₄×C₁₉	—	4	1	no	—
45	C₂²×C₄×C₁₉	—	4	1	no	—
46	C₂²×C₄×C₁₉	—	4	4	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₉	—	2	2	no	—
50	C₂×C₈×C₁₉	—	4	2	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	C₁₉⋊C₁₆	—	8	2	no	—
54	#7054	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	—	2	2	no	—
56	C₂³×C₁₉	—	2	2	no	—
57	C₂³×C₁₉	—	2	1	no	—
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	2	1	no	—
60	C₂³×C₁₉	—	4	1	no	—
61	C₂³×C₁₉	—	4	4	no	—
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	—	4	1	no	—
64	C₂³×C₁₉	—	4	1	no	—
65	C₂³×C₁₉	—	4	1	no	—
66	C₂³×C₁₉	—	4	4	no	—
67	C₂³×C₁₉	—	4	2	no	—
68	C₂³×C₁₉	—	4	2	no	—
69	C₂³×C₁₉	—	4	2	no	—
70	C₂³×C₁₉	—	4	2	no	—
71	C₂³×C₁₉	—	4	8	no	—
72	C₂³×C₁₉	—	4	2	no	—
73	C₂³×C₁₉	—	4	1	no	—
74	C₂³×C₁₉	—	4	1	no	—
75	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
76	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
77	C₂³×C₁₉	M₃₂	1	1	yes	characteristic
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	4	4	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	4	8	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	—	4	4	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
93	C₈×C₁₉	—	4	2	no	—
94	C₈×C₁₉	—	8	1	no	—
95	#1779	D₁₉	1	1	yes	characteristic
96	#1314	—	19	2	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	2	4	no	—
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	4	1	no	—
103	C₂²×C₁₉	—	4	1	no	—
104	C₂²×C₁₉	—	4	2	no	—
105	C₂²×C₁₉	—	4	2	no	—
106	C₂²×C₁₉	—	4	2	no	—
107	C₂²×C₁₉	—	4	2	no	—
108	C₂²×C₁₉	—	4	4	no	—
109	C₂²×C₁₉	—	4	4	no	—
110	C₂²×C₁₉	—	4	4	no	—
111	C₂²×C₁₉	—	4	4	no	—
112	C₂²×C₁₉	—	4	2	no	—
113	C₂²×C₁₉	—	4	2	no	—
114	C₂²×C₁₉	—	4	1	no	—
115	C₂²×C₁₉	—	4	2	no	—
116	C₂²×C₁₉	—	4	1	no	—
117	C₂²×C₁₉	#323	1	1	yes	characteristic
118	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
119	C₂²×C₁₉	#349	1	1	yes	characteristic
120	C₄×C₁₉	—	2	1	no	—
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	—	4	1	no	—
123	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	2	yes	—
124	C₂⁴×C₄	Dic₁₉	1	1	yes	characteristic
125	C₂×C₂²⋊C₈	—	2	2	no	—
126	C₂×C₂²⋊C₈	Dic₁₉	1	1	yes	characteristic
127	C₂×C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₂²⋊C₁₆	—	38	2	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	—	4	4	no	—
132	C₂×C₁₉	—	4	1	no	—
133	C₂×C₁₉	—	4	1	no	—
134	C₂×C₁₉	#1314	1	1	yes	characteristic
135	C₂×C₁₉	#1316	1	1	yes	characteristic
136	C₂×C₁₉	#1320	1	1	yes	characteristic
137	C₂⁵	C₁₉⋊C₈	1	1	yes	characteristic
138	C₂³×C₄	—	2	1	no	—
139	C₂³×C₄	—	2	1	no	—
140	C₂³×C₄	—	4	4	no	—
141	C₂³×C₄	—	4	1	no	—
142	C₂³×C₄	—	4	1	no	—
143	C₂³×C₄	C₁₉⋊C₈	1	1	yes	characteristic
144	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
147	C₂×C₁₆	—	76	2	no	—
148	C₂²⋊C₈	—	4	1	no	—
149	C₂²⋊C₈	—	4	4	no	—
150	C₂²⋊C₈	—	4	1	no	—
151	C₁₉	#7054	1	1	yes	characteristic, complemented, Sylow
152	C₂⁴	—	2	1	no	—
153	C₂⁴	—	2	1	no	—
154	C₂⁴	—	4	2	no	—
155	C₂⁴	—	4	1	no	—
156	C₂⁴	—	4	2	no	—
157	C₂⁴	—	4	1	no	—
158	C₂⁴	C₁₉⋊C₁₆	1	2	yes	complemented
159	C₂⁴	C₂×C₁₉⋊C₈	1	1	yes	characteristic
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	4	2	no	—
165	C₂²×C₄	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	4	2	no	—
168	C₂²×C₄	—	4	2	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	—	4	4	no	—
171	C₂²×C₄	—	4	4	no	—
172	C₂²×C₄	—	4	4	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	—	4	1	no	—
175	C₂²×C₄	—	4	1	no	—
176	C₂²×C₄	—	4	4	no	—
177	C₂²×C₄	#64520	1	1	yes	characteristic
178	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₁₆	—	152	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	2	2	no	—
186	C₂³	—	2	2	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	1	no	—
190	C₂³	—	4	4	no	—
191	C₂³	—	4	2	no	—
192	C₂³	—	4	1	no	—
193	C₂³	—	4	1	no	—
194	C₂³	—	4	1	no	—
195	C₂³	—	4	4	no	—
196	C₂³	—	4	2	no	—
197	C₂³	—	4	2	no	—
198	C₂³	—	4	2	no	—
199	C₂³	—	4	2	no	—
200	C₂³	—	4	8	no	—
201	C₂³	—	4	2	no	—
202	C₂³	—	4	1	no	—
203	C₂³	—	4	1	no	—
204	C₂³	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
205	C₂³	#10597269	1	1	yes	characteristic
206	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	8	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	#10597290	1	1	yes	characteristic
221	C₂×C₄	#10597291	1	1	yes	characteristic
222	C₈	—	4	2	no	—
223	C₈	—	8	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	4	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	4	2	no	—
232	C₂²	—	4	2	no	—
233	C₂²	—	4	2	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	4	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	4	no	—
238	C₂²	—	4	4	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	1	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	1	no	—
244	C₂²	#11926268	1	1	yes	characteristic
245	C₂²	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
246	C₂²	#11926326	1	1	yes	characteristic
247	C₄	—	2	1	no	—
248	C₄	—	4	2	no	—
249	C₄	—	4	1	no	—
250	C₄	#11926331	1	2	yes	—
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	4	4	no	—
254	C₂	—	4	1	no	—
255	C₂	—	4	1	no	—
256	C₂	#14561559	1	1	yes	characteristic
257	C₂	#14561563	1	1	yes	characteristic
258	C₂	#14561571	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561559

C₂

yes

maximal, complemented

C₁₉×#1779

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂⁴×C₄×C₁₉

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×C₂²⋊C₈

C₄

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

C₂²

yes

characteristic

C₂⁵×C₁₉

C₈

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₁₆

yes

complemented

C₂⁴×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₁₉⋊C₁₆

—

#7054

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂³×C₁₉

C₂×C₁₆

yes

characteristic

C₂³×C₁₉

M₃₂

yes

characteristic

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1779

D₁₉

yes

characteristic

#1314

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

#323

yes

characteristic

118

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

119

C₂²×C₁₉

#349

yes

characteristic

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

—

124

C₂⁴×C₄

Dic₁₉

yes

characteristic

125

C₂×C₂²⋊C₈

—

126

C₂×C₂²⋊C₈

Dic₁₉

yes

characteristic

127

C₂×C₂²⋊C₈

C₂×D₁₉

yes

characteristic

128

C₂²⋊C₁₆

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

—

132

C₂×C₁₉

—

133

C₂×C₁₉

—

134

C₂×C₁₉

#1314

yes

characteristic

135

C₂×C₁₉

#1316

yes

characteristic

136

C₂×C₁₉

#1320

yes

characteristic

137

C₂⁵

C₁₉⋊C₈

yes

characteristic

138

C₂³×C₄

—

139

C₂³×C₄

—

140

C₂³×C₄

—

141

C₂³×C₄

—

142

C₂³×C₄

—

143

C₂³×C₄

C₁₉⋊C₈

yes

characteristic

144

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

145

C₂²×C₈

—

146

C₂²×C₈

C₂²⋊D₁₉

yes

—

147

C₂×C₁₆

—

148

C₂²⋊C₈

—

149

C₂²⋊C₈

—

150

C₂²⋊C₈

—

151

C₁₉

#7054

yes

characteristic, complemented, Sylow

152

C₂⁴

—

153

C₂⁴

—

154

C₂⁴

—

155

C₂⁴

—

156

C₂⁴

—

157

C₂⁴

—

158

C₂⁴

C₁₉⋊C₁₆

yes

complemented

159

C₂⁴

C₂×C₁₉⋊C₈

yes

characteristic

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

#64520

yes

characteristic

178

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₁₆

—

152

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

C₂×C₁₉⋊C₁₆

yes

characteristic

205

C₂³

#10597269

yes

characteristic

206

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

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

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#10597290

yes

characteristic

221

C₂×C₄

#10597291

yes

characteristic

222

C₈

—

223

C₈

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#11926268

yes

characteristic

245

C₂²

C₂²⋊(C₁₉⋊C₁₆)

yes

characteristic

246

C₂²

#11926326

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

#11926331

yes

—

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

—

255

C₂

—

256

C₂

#14561559

yes

characteristic

257

C₂

#14561563

yes

characteristic

258

C₂

#14561571

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂³×C₁₉	C₂×C₁₆
Frattini	C₂×C₂²⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1779	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂⁵×C₁₉	C₈
cosocle	C₂×C₁₉×C₂²⋊C₈	C₂²
hypercenter	#1779	D₁₉
hypocenter	C₁₉	#7054
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1779

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂³×C₁₉

C₂×C₁₆

Frattini

C₂×C₂²⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1779

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂⁵×C₁₉

C₈

cosocle

C₂×C₁₉×C₂²⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1779

N	H ≅ G/N	type
1. #14561559	C₂	semidirect
28. C₂⁴×C₁₉	C₁₆	semidirect
151. C₁₉	#7054	semidirect
158. C₂⁴	C₁₉⋊C₁₆	semidirect

H ≅ G/N

type

1. #14561559

C₂

semidirect

28. C₂⁴×C₁₉

C₁₆

semidirect

151. C₁₉

#7054

semidirect

158. C₂⁴

C₁₉⋊C₁₆

semidirect

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

subgroup	index
#14561559	2
C₁₉×#1779	2
#7054	19

subgroup

index

#14561559

C₁₉×#1779

#7054

Subgroups — #18069158

Conjugacy classes of subgroups

Complements

Maximal subgroups