Group #18085324 — subgroups

Subgroups — #18085324

Order 4864.

754 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 151 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×#11926921	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926892	C₂	1	2	yes	maximal, complemented
3	#14564440	C₂	1	2	yes	maximal, complemented
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₅₂	—	2	2	no	—
7	C₂×#10597320	C₂²	1	2	yes	—
8	#11926921	—	2	4	no	—
9	#11926892	—	2	4	no	—
10	#11926892	—	2	4	no	—
11	C₂×#10597266	—	2	4	no	—
12	C₂×#10597266	—	2	4	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#103	—	2	2	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#384	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	2	1	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₂²×D₇₆	—	2	2	no	—
21	C₂²×D₇₆	—	2	2	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
31	C₂×D₁₅₂	—	2	8	no	—
32	C₂×D₁₅₂	—	4	4	no	—
33	C₂×D₁₅₂	—	4	4	no	—
34	#10597320	—	2	2	no	—
35	#10597320	—	2	2	no	—
36	#10597320	—	2	2	no	—
37	#10597320	D₄	1	4	yes	—
38	C₁₉×#103	—	4	4	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	#10597266	—	2	16	no	—
41	#10597266	—	4	8	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂³×D₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	4	1	no	—
47	C₂×Q₈×C₁₉	—	4	2	no	—
48	C₂×Q₈×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×D₇₆	—	2	4	no	—
54	C₂×D₇₆	—	2	4	no	—
55	C₂×D₇₆	—	2	4	no	—
56	C₂×D₇₆	—	4	4	no	—
57	C₂×D₇₆	—	4	4	no	—
58	C₂×D₇₆	—	4	4	no	—
59	C₂×D₇₆	—	4	4	no	—
60	C₂×D₇₆	—	4	4	no	—
61	C₂×D₇₆	—	4	4	no	—
62	C₂×D₇₆	—	4	2	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	2	no	—
67	C₂×C₈×C₁₉	D₈	1	4	yes	—
68	C₄⋊C₄×C₁₉	—	2	4	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	4	no	—
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	2	yes	—
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₂×C₁₉⋊C₈	—	2	4	no	—
76	C₂×C₁₉⋊C₈	—	2	4	no	—
77	C₂×C₁₉⋊C₈	—	2	4	no	—
78	D₁₅₂	—	4	16	no	—
79	#10307	—	19	1	no	maximal, Sylow
80	C₂³×C₁₉	#127	1	1	yes	characteristic
81	C₂²×D₁₉	—	4	4	no	—
82	C₂²×D₁₉	—	8	2	no	—
83	C₂²×D₁₉	—	8	2	no	—
84	C₂²×D₁₉	—	8	2	no	—
85	C₂²×D₁₉	—	8	2	no	—
86	C₂²×D₁₉	—	8	2	no	—
87	C₂²×D₁₉	—	8	2	no	—
88	Q₈×C₁₉	—	4	4	no	—
89	Q₈×C₁₉	—	8	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	—	8	1	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	8	2	no	—
95	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#120	1	2	yes	—
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#121	1	2	yes	—
99	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
100	C₂×C₄×C₁₉	#135	1	4	yes	—
101	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
103	D₇₆	—	4	8	no	—
104	D₇₆	—	4	8	no	—
105	D₇₆	—	4	8	no	—
106	D₇₆	—	8	4	no	—
107	D₇₆	—	8	4	no	—
108	D₇₆	—	8	4	no	—
109	C₈×C₁₉	—	2	4	no	—
110	C₁₉⋊C₈	—	4	4	no	—
111	C₂×#493	—	19	1	no	—
112	C₂×#486	—	19	2	no	—
113	#1957	—	19	2	no	—
114	#1956	D₁₉	1	1	yes	characteristic, complemented
115	#1273	—	19	1	no	—
116	C₂²×C₁₉	#392	1	1	yes	characteristic
117	C₂²×C₁₉	#493	1	1	yes	characteristic
118	C₂²×C₁₉	#495	1	2	yes	—
119	C₂²×C₁₉	#496	1	2	yes	—
120	C₂²×C₁₉	#496	1	1	yes	characteristic
121	C₂×D₁₉	—	8	4	no	—
122	C₂×D₁₉	—	8	4	no	—
123	C₂×D₁₉	—	8	4	no	—
124	C₂×D₁₉	—	16	2	no	—
125	C₂×D₁₉	—	16	2	no	—
126	C₂×D₁₉	—	16	2	no	—
127	C₂×D₁₉	—	16	2	no	—
128	C₄×C₁₉	—	8	2	no	—
129	C₄×C₁₉	—	16	1	no	—
130	C₄×C₁₉	#447	1	2	yes	—
131	C₄×C₁₉	#449	1	4	yes	—
132	C₄×C₁₉	#459	1	2	yes	—
133	C₄×C₁₉	#463	1	4	yes	—
134	C₂²×D₈	—	38	2	no	—
135	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
136	C₂×#127	—	19	2	no	—
137	#493	—	38	4	no	—
138	#486	—	38	4	no	—
139	#486	—	38	4	no	—
140	C₂×#103	—	2	2	no	—
141	C₂×#102	—	38	4	no	—
142	C₂×#102	—	38	4	no	—
143	C₂×C₄×C₈	—	19	2	no	—
144	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
145	#384	C₂×D₁₉	1	1	yes	characteristic
146	C₂×C₁₉	#1709	1	1	yes	characteristic
147	C₂×C₁₉	#1717	1	2	yes	—
148	C₂×C₁₉	#1721	1	1	yes	characteristic
149	C₂×C₁₉	#2011	1	1	yes	characteristic
150	C₂×C₁₉	#2012	1	2	yes	—
151	D₁₉	—	16	4	no	—
152	C₂²×Q₈	—	2	1	no	—
153	C₂²×D₄	—	38	2	no	—
154	C₂²×D₄	—	38	2	no	—
155	C₂²×D₄	—	38	2	no	—
156	C₂×D₈	—	38	8	no	—
157	C₂×D₈	—	76	4	no	—
158	C₂×D₈	—	76	4	no	—
159	C₂²×C₈	—	19	4	no	—
160	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	D₇₆	1	2	yes	—
164	#127	—	19	4	no	—
165	#127	—	38	2	no	—
166	#127	—	38	2	no	—
167	#127	—	38	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄⋊C₄	—	2	2	no	—
170	C₂×C₄⋊C₄	—	2	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	#103	—	4	4	no	—
173	#102	—	38	16	no	—
174	#102	—	76	8	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	—	38	2	no	—
177	C₄×C₈	—	38	2	no	—
178	C₁₉	#10307	1	1	yes	characteristic, complemented, Sylow
179	C₂⁴	—	76	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	4	1	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×D₄	—	38	4	no	—
185	C₂×D₄	—	38	4	no	—
186	C₂×D₄	—	38	4	no	—
187	C₂×D₄	—	76	2	no	—
188	C₂×D₄	—	76	4	no	—
189	C₂×D₄	—	76	4	no	—
190	C₂×D₄	—	76	2	no	—
191	C₂×D₄	—	76	2	no	—
192	C₂×D₄	—	76	4	no	—
193	C₂×D₄	—	76	4	no	—
194	C₂×D₄	—	76	4	no	—
195	C₂×D₄	—	76	4	no	—
196	C₂²×C₄	—	4	1	no	—
197	C₂²×C₄	—	4	1	no	—
198	C₂²×C₄	D₄×D₁₉	1	2	yes	—
199	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
200	D₈	—	76	16	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	38	4	no	—
204	C₂×C₈	—	38	4	no	—
205	C₂×C₈	—	38	4	no	—
206	C₂×C₈	#64525	1	4	yes	—
207	C₄⋊C₄	—	2	4	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₄⋊C₄	—	4	2	no	—
210	C₄⋊C₄	—	4	4	no	—
211	C₄²	C₂×D₇₆	1	1	yes	characteristic
212	C₄²	#64541	1	1	yes	characteristic
213	C₄²	D₄×D₁₉	1	2	yes	—
214	C₂³	—	76	4	no	—
215	C₂³	—	152	2	no	—
216	C₂³	—	152	2	no	—
217	C₂³	—	152	2	no	—
218	C₂³	—	152	2	no	—
219	C₂³	—	152	2	no	—
220	C₂³	—	152	2	no	—
221	C₂³	#10597386	1	1	yes	characteristic
222	Q₈	—	4	4	no	—
223	Q₈	—	8	2	no	—
224	D₄	—	76	8	no	—
225	D₄	—	76	8	no	—
226	D₄	—	76	8	no	—
227	D₄	—	152	4	no	—
228	D₄	—	152	4	no	—
229	D₄	—	152	4	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	8	2	no	—
235	C₂×C₄	#10597328	1	2	yes	—
236	C₂×C₄	#10597330	1	2	yes	—
237	C₂×C₄	#10597360	1	4	yes	—
238	C₂×C₄	#10597365	1	4	yes	—
239	C₂×C₄	#10597376	1	1	yes	characteristic
240	C₂×C₄	C₂×#64525	1	2	yes	—
241	C₂×C₄	#10597383	1	1	yes	characteristic
242	C₂×C₄	#10597395	1	2	yes	—
243	C₈	—	2	4	no	—
244	C₈	—	76	4	no	—
245	C₂²	—	304	2	no	—
246	C₂²	—	304	2	no	—
247	C₂²	—	304	2	no	—
248	C₂²	—	304	2	no	—
249	C₂²	—	152	4	no	—
250	C₂²	—	152	4	no	—
251	C₂²	—	152	4	no	—
252	C₂²	#11926453	1	1	yes	characteristic
253	C₂²	#11926920	1	1	yes	characteristic
254	C₂²	#11926929	1	2	yes	—
255	C₂²	#11926930	1	2	yes	—
256	C₂²	#11926934	1	1	yes	characteristic
257	C₄	—	8	2	no	—
258	C₄	—	16	1	no	—
259	C₄	#11926677	1	2	yes	—
260	C₄	#11926692	1	4	yes	—
261	C₄	#11926739	1	2	yes	—
262	C₄	#11926762	1	4	yes	—
263	C₂	—	304	4	no	—
264	C₂	#14563242	1	1	yes	characteristic
265	C₂	#14563277	1	2	yes	—
266	C₂	#14563299	1	1	yes	characteristic
267	C₂	#14564705	1	1	yes	characteristic
268	C₂	#14564713	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926921

C₂

yes

maximal, characteristic

C₂×#11926892

C₂

yes

maximal, complemented

#14564440

C₂

yes

maximal, complemented

C₁₉⋊#1273

C₂

yes

maximal, characteristic, complemented

C₁₉×#1956

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₅₂

—

C₂×#10597320

C₂²

yes

—

—

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

—

—

—

D₄

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597266

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

100

C₂×C₄×C₁₉

#135

yes

—

101

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

102

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

103

D₇₆

—

104

D₇₆

—

105

D₇₆

—

106

D₇₆

—

107

D₇₆

—

108

D₇₆

—

109

C₈×C₁₉

—

110

C₁₉⋊C₈

—

111

C₂×#493

—

112

C₂×#486

—

113

#1957

—

114

#1956

D₁₉

yes

characteristic, complemented

115

#1273

—

116

C₂²×C₁₉

#392

yes

characteristic

117

C₂²×C₁₉

#493

yes

characteristic

118

C₂²×C₁₉

#495

yes

—

119

C₂²×C₁₉

#496

yes

—

120

C₂²×C₁₉

#496

yes

characteristic

121

C₂×D₁₉

—

122

C₂×D₁₉

—

123

C₂×D₁₉

—

124

C₂×D₁₉

—

125

C₂×D₁₉

—

126

C₂×D₁₉

—

127

C₂×D₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#447

yes

—

131

C₄×C₁₉

#449

yes

—

132

C₄×C₁₉

#459

yes

—

133

C₄×C₁₉

#463

yes

—

134

C₂²×D₈

—

135

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

136

C₂×#127

—

137

#493

—

138

#486

—

139

#486

—

140

C₂×#103

—

141

C₂×#102

—

142

C₂×#102

—

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

145

#384

C₂×D₁₉

yes

characteristic

146

C₂×C₁₉

#1709

yes

characteristic

147

C₂×C₁₉

#1717

yes

—

148

C₂×C₁₉

#1721

yes

characteristic

149

C₂×C₁₉

#2011

yes

characteristic

150

C₂×C₁₉

#2012

yes

—

151

D₁₉

—

152

C₂²×Q₈

—

153

C₂²×D₄

—

154

C₂²×D₄

—

155

C₂²×D₄

—

156

C₂×D₈

—

157

C₂×D₈

—

158

C₂×D₈

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²⋊D₁₉

yes

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

D₇₆

yes

—

164

#127

—

165

#127

—

166

#127

—

167

#127

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

#103

—

173

#102

—

174

#102

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₁₉

#10307

yes

characteristic, complemented, Sylow

179

C₂⁴

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

D₄×D₁₉

yes

—

199

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

200

D₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

#64525

yes

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄²

C₂×D₇₆

yes

characteristic

212

C₄²

#64541

yes

characteristic

213

C₄²

D₄×D₁₉

yes

—

214

C₂³

—

215

C₂³

—

152

—

216

C₂³

—

152

—

217

C₂³

—

152

—

218

C₂³

—

152

—

219

C₂³

—

152

—

220

C₂³

—

152

—

221

C₂³

#10597386

yes

characteristic

222

Q₈

—

223

Q₈

—

224

D₄

—

225

D₄

—

226

D₄

—

227

D₄

—

152

—

228

D₄

—

152

—

229

D₄

—

152

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

#10597328

yes

—

236

C₂×C₄

#10597330

yes

—

237

C₂×C₄

#10597360

yes

—

238

C₂×C₄

#10597365

yes

—

239

C₂×C₄

#10597376

yes

characteristic

240

C₂×C₄

C₂×#64525

yes

—

241

C₂×C₄

#10597383

yes

characteristic

242

C₂×C₄

#10597395

yes

—

243

C₈

—

244

C₈

—

245

C₂²

—

304

—

246

C₂²

—

304

—

247

C₂²

—

304

—

248

C₂²

—

304

—

249

C₂²

—

152

—

250

C₂²

—

152

—

251

C₂²

—

152

—

252

C₂²

#11926453

yes

characteristic

253

C₂²

#11926920

yes

characteristic

254

C₂²

#11926929

yes

—

255

C₂²

#11926930

yes

—

256

C₂²

#11926934

yes

characteristic

257

C₄

—

258

C₄

—

259

C₄

#11926677

yes

—

260

C₄

#11926692

yes

—

261

C₄

#11926739

yes

—

262

C₄

#11926762

yes

—

263

C₂

—

304

—

264

C₂

#14563242

yes

characteristic

265

C₂

#14563277

yes

—

266

C₂

#14563299

yes

characteristic

267

C₂

#14564705

yes

characteristic

268

C₂

#14564713

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#11926921	C₂
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#10307
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1956

C₂

C₂³×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
2. C₂×#11926892	C₂	semidirect
3. #14564440	C₂	semidirect
4. C₁₉⋊#1273	C₂	semidirect
5. C₁₉×#1956	C₂	semidirect
114. #1956	D₁₉	semidirect
178. C₁₉	#10307	semidirect

H ≅ G/N

type

2. C₂×#11926892

C₂

semidirect

3. #14564440

C₂

semidirect

4. C₁₉⋊#1273

C₂

semidirect

5. C₁₉×#1956

C₂

semidirect

114. #1956

D₁₉

semidirect

178. C₁₉

#10307

semidirect

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

subgroup	index
C₂×#11926921	2
C₂×#11926892	2
#14564440	2
C₁₉⋊#1273	2
C₁₉×#1956	2
#10307	19

subgroup

index

C₂×#11926921

C₂×#11926892

#14564440

C₁₉⋊#1273

C₁₉×#1956

#10307

Subgroups — #18085324

Conjugacy classes of subgroups

Complements

Maximal subgroups