Group #23774739 — subgroups

Subgroups — #23774739

Order 10112.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19099118	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099095	C₂	1	1	yes	maximal, characteristic
3	#19098869	C₂	1	2	yes	maximal, complemented
4	#19098845	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098805	C₂	1	2	yes	maximal, complemented
6	#19098791	C₂	1	2	yes	maximal
7	#19098784	C₂	1	2	yes	maximal, complemented
8	#19098774	C₂	1	1	yes	maximal, characteristic, complemented
9	#19098768	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#474×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₃₁₆	C₂²	1	2	yes	—
13	C₂×#11929612	C₂²	1	2	yes	—
14	C₂×C₈×D₇₉	C₂²	1	2	yes	—
15	#14579161	C₂²	1	1	yes	characteristic
16	#14579154	—	2	1	no	—
17	#14579152	—	2	1	no	—
18	#14579152	C₂²	1	1	yes	characteristic
19	#14579148	C₂²	1	1	yes	characteristic
20	#14579143	—	2	1	no	—
21	#14579141	C₂²	1	2	yes	—
22	#14579141	C₂²	1	1	yes	characteristic
23	#14579137	—	2	1	no	—
24	#14579132	C₂²	1	1	yes	characteristic
25	Q₈×Dic₇₉	—	2	1	no	—
26	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
27	#14579126	C₂²	1	2	yes	—
28	C₄×C₂²⋊D₇₉	—	2	1	no	—
29	#14579120	—	2	1	no	—
30	#14579119	—	2	1	no	—
31	C₄²×D₇₉	C₂²	1	1	yes	characteristic
32	#14579092	C₂²	1	2	yes	—
33	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	Dic₇₉⋊C₈	C₂²	1	2	yes	—
35	#14579086	C₂²	1	2	yes	—
36	#14579084	C₂²	1	2	yes	—
37	#14579084	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#107×C₇₉	C₂²	1	2	yes	—
41	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
42	#102×C₇₉	C₂²	1	2	yes	—
43	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₅₈	C₂³	1	2	yes	—
45	C₂×C₂²⋊D₇₉	—	2	1	no	—
46	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
47	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
48	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
49	Dic₃₁₆	—	4	2	no	—
50	#11929612	—	4	2	no	—
51	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
52	C₈×D₇₉	—	4	2	no	—
53	C₄⋊Dic₇₉	—	2	1	no	—
54	C₄⋊Dic₇₉	—	2	1	no	—
55	C₄⋊Dic₇₉	—	2	2	no	—
56	C₄⋊Dic₇₉	—	2	1	no	—
57	C₄⋊Dic₇₉	—	2	1	no	—
58	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
59	Dic₇₉⋊C₄	—	2	1	no	—
60	Dic₇₉⋊C₄	—	2	2	no	—
61	Dic₇₉⋊C₄	—	2	1	no	—
62	C₂²⋊Dic₇₉	—	2	1	no	—
63	C₂²⋊Dic₇₉	—	2	1	no	—
64	C₂²⋊Dic₇₉	—	2	1	no	—
65	(C₂×D₇₉)⋊C₄	—	2	2	no	—
66	(C₂×D₇₉)⋊C₄	—	2	1	no	—
67	C₄×Dic₇₉	—	2	2	no	—
68	C₄×Dic₇₉	—	2	1	no	—
69	C₄×Dic₇₉	D₄	1	1	yes	characteristic
70	C₄×Dic₇₉	D₄	1	1	yes	characteristic
71	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₇₉	—	2	1	no	—
73	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₇₉	—	2	1	no	—
75	C₂×C₈×C₇₉	C₂³	1	2	yes	—
76	C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²⋊C₄×C₇₉	—	2	1	no	—
80	C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₂³×C₇₉	—	2	1	no	—
82	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₇₉	—	4	2	no	—
84	D₄×C₇₉	—	2	1	no	—
85	D₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	2	no	—
87	C₂×C₄×C₇₉	—	2	1	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
92	C₂²⋊D₇₉	—	4	2	no	—
93	C₂×Dic₇₉	—	2	1	no	—
94	C₂×Dic₇₉	—	2	2	no	—
95	C₂×Dic₇₉	—	2	1	no	—
96	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
99	C₄×D₇₉	—	2	2	no	—
100	C₄×D₇₉	—	2	2	no	—
101	C₄×D₇₉	—	2	1	no	—
102	C₄×D₇₉	—	2	1	no	—
103	Dic₁₅₈	—	2	2	no	—
104	Dic₁₅₈	—	2	1	no	—
105	Dic₁₅₈	—	2	1	no	—
106	Dic₁₅₈	—	2	2	no	—
107	C₈×C₇₉	—	2	2	no	—
108	C₇₉⋊C₈	—	2	2	no	—
109	C₂²×C₇₉	—	4	1	no	—
110	C₂²×C₇₉	—	4	1	no	—
111	C₂²×C₇₉	—	4	1	no	—
112	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
113	C₂×D₇₉	—	2	1	no	—
114	C₂×D₇₉	—	2	1	no	—
115	C₂×D₇₉	#137	1	2	yes	—
116	C₄×C₇₉	—	2	1	no	—
117	C₄×C₇₉	—	4	1	no	—
118	C₄×C₇₉	—	4	2	no	—
119	C₄×C₇₉	#135	1	2	yes	—
120	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
121	C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
122	Dic₇₉	—	2	1	no	—
123	Dic₇₉	—	2	1	no	—
124	Dic₇₉	—	2	1	no	—
125	Dic₇₉	—	4	2	no	—
126	Dic₇₉	—	4	1	no	—
127	Dic₇₉	—	4	1	no	—
128	C₂×C₇₉	—	8	1	no	—
129	C₂×C₇₉	#537	1	1	yes	characteristic
130	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
131	C₂×C₇₉	C₂×#137	1	1	yes	characteristic
132	D₇₉	—	2	2	no	—
133	#3248	—	79	1	no	maximal, Sylow
134	C₇₉	#3248	1	1	yes	characteristic, complemented, Sylow
135	#533	—	79	1	no	—
136	#529	—	79	1	no	—
137	#479	—	79	2	no	—
138	#475	—	79	1	no	—
139	#474	D₇₉	1	1	yes	characteristic, complemented
140	#467	—	79	2	no	—
141	#465	—	79	2	no	—
142	#464	—	79	2	no	—
143	#462	—	79	1	no	—
144	#461	—	79	1	no	—
145	C₂×C₄⋊C₈	—	79	1	no	—
146	C₂×Q₁₆	—	79	2	no	—
147	C₂×SD₁₆	—	79	2	no	—
148	C₂²×C₈	—	79	2	no	—
149	C₄⋊Q₈	—	79	1	no	—
150	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
151	#126	—	158	1	no	—
152	#125	—	79	1	no	—
153	#125	—	158	1	no	—
154	#124	—	79	1	no	—
155	#123	—	158	1	no	—
156	C₂²⋊Q₈	—	79	1	no	—
157	C₂²⋊Q₈	—	79	2	no	—
158	C₂²⋊Q₈	—	158	1	no	—
159	#121	—	79	1	no	—
160	C₄×Q₈	—	79	2	no	—
161	C₄×Q₈	—	79	1	no	—
162	C₄×Q₈	—	158	1	no	—
163	C₄×D₄	—	158	1	no	—
164	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
165	#117	—	158	1	no	—
166	#117	—	158	1	no	—
167	C₂×C₄²	—	79	1	no	—
168	#107	C₂×D₇₉	1	2	yes	—
169	#106	—	79	2	no	—
170	C₄⋊C₈	—	79	2	no	—
171	C₄⋊C₈	—	79	1	no	—
172	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
173	#103	—	79	2	no	—
174	#103	—	79	2	no	—
175	#103	—	79	2	no	—
176	#102	C₂×D₇₉	1	2	yes	—
177	C₂×Q₈	—	2	1	no	—
178	C₂×Q₈	—	79	1	no	—
179	C₂×Q₈	—	79	2	no	—
180	C₂×D₄	—	158	1	no	—
181	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	79	1	no	—
184	C₂²×C₄	—	79	1	no	—
185	C₂²×C₄	—	79	1	no	—
186	Q₁₆	—	316	2	no	—
187	SD₁₆	—	316	2	no	—
188	C₂×C₈	—	316	2	no	—
189	C₂×C₈	—	79	2	no	—
190	C₂×C₈	C₂²×D₇₉	1	2	yes	—
191	C₄⋊C₄	—	2	1	no	—
192	C₄⋊C₄	—	79	1	no	—
193	C₄⋊C₄	—	158	1	no	—
194	C₄⋊C₄	—	158	2	no	—
195	C₄⋊C₄	—	158	1	no	—
196	C₄⋊C₄	—	158	1	no	—
197	C₄⋊C₄	—	158	2	no	—
198	C₄⋊C₄	—	158	1	no	—
199	C₄⋊C₄	—	158	1	no	—
200	C₄⋊C₄	—	158	1	no	—
201	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
202	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
203	C₂²⋊C₄	—	2	1	no	—
204	C₂²⋊C₄	—	158	2	no	—
205	C₂²⋊C₄	—	158	1	no	—
206	C₂²⋊C₄	—	158	1	no	—
207	C₂²⋊C₄	—	158	1	no	—
208	C₂²⋊C₄	—	158	1	no	—
209	C₄²	—	79	1	no	—
210	C₄²	—	79	1	no	—
211	C₄²	—	79	1	no	—
212	C₄²	—	158	2	no	—
213	C₄²	—	158	1	no	—
214	C₄²	C₂²×D₇₉	1	1	yes	characteristic
215	C₂³	—	2	1	no	—
216	C₂³	—	79	1	no	—
217	Q₈	—	4	2	no	—
218	Q₈	—	158	2	no	—
219	Q₈	—	158	1	no	—
220	Q₈	—	158	1	no	—
221	Q₈	—	158	2	no	—
222	D₄	—	2	1	no	—
223	D₄	—	2	1	no	—
224	D₄	—	316	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	79	1	no	—
229	C₂×C₄	—	79	1	no	—
230	C₂×C₄	—	79	1	no	—
231	C₂×C₄	—	158	2	no	—
232	C₂×C₄	—	158	1	no	—
233	C₂×C₄	—	158	1	no	—
234	C₂×C₄	—	158	2	no	—
235	C₂×C₄	—	158	1	no	—
236	C₂×C₄	—	158	1	no	—
237	C₂×C₄	—	158	2	no	—
238	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
239	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
240	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
241	C₈	—	2	2	no	—
242	C₈	—	158	2	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	1	no	—
246	C₂²	—	79	2	no	—
247	C₂²	—	158	1	no	—
248	C₂²	—	158	1	no	—
249	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	4	1	no	—
252	C₄	—	4	2	no	—
253	C₄	—	316	1	no	—
254	C₄	—	316	2	no	—
255	C₄	—	316	1	no	—
256	C₄	—	158	1	no	—
257	C₄	—	158	1	no	—
258	C₄	—	158	1	no	—
259	C₄	#14579180	1	2	yes	—
260	C₄	#14579207	1	1	yes	characteristic
261	C₄	#14579209	1	1	yes	characteristic
262	C₂	—	8	1	no	—
263	C₂	—	158	2	no	—
264	C₂	#19099143	1	1	yes	characteristic
265	C₂	C₂×#14579180	1	1	yes	characteristic
266	C₂	#137×D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal, characteristic, complemented

#19099095

C₂

yes

maximal, characteristic

#19098869

C₂

yes

maximal, complemented

#19098845

C₂

yes

maximal, characteristic, complemented

#19098805

C₂

yes

maximal, complemented

#19098791

C₂

yes

maximal

#19098784

C₂

yes

maximal, complemented

#19098774

C₂

yes

maximal, characteristic, complemented

#19098768

C₂

yes

maximal, characteristic, complemented

C₄⋊C₈×D₇₉

C₂

yes

maximal, characteristic, complemented

#474×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₃₁₆

C₂²

yes

—

C₂×#11929612

C₂²

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

—

—

C₂²

yes

characteristic

#14579148

C₂²

yes

characteristic

#14579143

—

#14579141

C₂²

yes

—

#14579141

C₂²

yes

characteristic

#14579137

—

#14579132

C₂²

yes

characteristic

Q₈×Dic₇₉

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579126

C₂²

yes

—

C₄×C₂²⋊D₇₉

—

#14579120

—

#14579119

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579092

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

C₂²

yes

—

#14579086

C₂²

yes

—

#14579084

C₂²

yes

—

#14579084

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#102×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

C₂³

yes

characteristic

C₂×Dic₁₅₈

C₂³

yes

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

C₂³

yes

characteristic

Dic₃₁₆

—

#11929612

—

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

100

C₄×D₇₉

—

101

C₄×D₇₉

—

102

C₄×D₇₉

—

103

Dic₁₅₈

—

104

Dic₁₅₈

—

105

Dic₁₅₈

—

106

Dic₁₅₈

—

107

C₈×C₇₉

—

108

C₇₉⋊C₈

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

C₂²×D₄

yes

characteristic

113

C₂×D₇₉

—

114

C₂×D₇₉

—

115

C₂×D₇₉

#137

yes

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

#135

yes

—

120

C₄×C₇₉

H(5,𝔽₂)

yes

characteristic

121

C₄×C₇₉

2₋¹⁺⁴

yes

characteristic

122

Dic₇₉

—

123

Dic₇₉

—

124

Dic₇₉

—

125

Dic₇₉

—

126

Dic₇₉

—

127

Dic₇₉

—

128

C₂×C₇₉

—

129

C₂×C₇₉

#537

yes

characteristic

130

C₂×C₇₉

C₂×#135

yes

characteristic

131

C₂×C₇₉

C₂×#137

yes

characteristic

132

D₇₉

—

133

#3248

—

maximal, Sylow

134

C₇₉

#3248

yes

characteristic, complemented, Sylow

135

#533

—

136

#529

—

137

#479

—

138

#475

—

139

#474

D₇₉

yes

characteristic, complemented

140

#467

—

141

#465

—

142

#464

—

143

#462

—

144

#461

—

145

C₂×C₄⋊C₈

—

146

C₂×Q₁₆

—

147

C₂×SD₁₆

—

148

C₂²×C₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

151

#126

—

158

—

152

#125

—

153

#125

—

158

—

154

#124

—

155

#123

—

158

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₂²⋊Q₈

—

158

—

159

#121

—

160

C₄×Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

158

—

163

C₄×D₄

—

158

—

164

C₄×D₄

C₂×D₇₉

yes

characteristic

165

#117

—

158

—

166

#117

—

158

—

167

C₂×C₄²

—

168

#107

C₂×D₇₉

yes

—

169

#106

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

C₂×D₇₉

yes

characteristic

173

#103

—

174

#103

—

175

#103

—

176

#102

C₂×D₇₉

yes

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

158

—

181

C₂×D₄

C₂²×D₇₉

yes

characteristic

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

Q₁₆

—

316

—

187

SD₁₆

—

316

—

188

C₂×C₈

—

316

—

189

C₂×C₈

—

190

C₂×C₈

C₂²×D₇₉

yes

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

158

—

194

C₄⋊C₄

—

158

—

195

C₄⋊C₄

—

158

—

196

C₄⋊C₄

—

158

—

197

C₄⋊C₄

—

158

—

198

C₄⋊C₄

—

158

—

199

C₄⋊C₄

—

158

—

200

C₄⋊C₄

—

158

—

201

C₄⋊C₄

C₂²×D₇₉

yes

—

202

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

158

—

205

C₂²⋊C₄

—

158

—

206

C₂²⋊C₄

—

158

—

207

C₂²⋊C₄

—

158

—

208

C₂²⋊C₄

—

158

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

158

—

213

C₄²

—

158

—

214

C₄²

C₂²×D₇₉

yes

characteristic

215

C₂³

—

216

C₂³

—

217

Q₈

—

218

Q₈

—

158

—

219

Q₈

—

158

—

220

Q₈

—

158

—

221

Q₈

—

158

—

222

D₄

—

223

D₄

—

224

D₄

—

316

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

158

—

232

C₂×C₄

—

158

—

233

C₂×C₄

—

158

—

234

C₂×C₄

—

158

—

235

C₂×C₄

—

158

—

236

C₂×C₄

—

158

—

237

C₂×C₄

—

158

—

238

C₂×C₄

D₄×D₇₉

yes

characteristic

239

C₂×C₄

D₄×D₇₉

yes

characteristic

240

C₂×C₄

C₂³×D₇₉

yes

characteristic

241

C₈

—

242

C₈

—

158

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

158

—

248

C₂²

—

158

—

249

C₂²

C₂×D₄×D₇₉

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

316

—

254

C₄

—

316

—

255

C₄

—

316

—

256

C₄

—

158

—

257

C₄

—

158

—

258

C₄

—

158

—

259

C₄

#14579180

yes

—

260

C₄

#14579207

yes

characteristic

261

C₄

#14579209

yes

characteristic

262

C₂

—

263

C₂

—

158

—

264

C₂

#19099143

yes

characteristic

265

C₂

C₂×#14579180

yes

characteristic

266

C₂

#137×D₇₉

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#474×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	#14579132	C₂²
hypercenter	#474	D₇₉
hypocenter	C₇₉	#3248
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#474×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #474

N	H ≅ G/N	type
1. #19099118	C₂	semidirect
3. #19098869	C₂	semidirect
4. #19098845	C₂	semidirect
5. #19098805	C₂	semidirect
7. #19098784	C₂	semidirect
8. #19098774	C₂	semidirect
9. #19098768	C₂	semidirect
10. C₄⋊C₈×D₇₉	C₂	semidirect
11. #474×C₇₉	C₂	semidirect
134. C₇₉	#3248	semidirect
139. #474	D₇₉	semidirect

H ≅ G/N

type

1. #19099118

C₂

semidirect

3. #19098869

C₂

semidirect

4. #19098845

C₂

semidirect

5. #19098805

C₂

semidirect

7. #19098784

C₂

semidirect

8. #19098774

C₂

semidirect

9. #19098768

C₂

semidirect

10. C₄⋊C₈×D₇₉

C₂

semidirect

11. #474×C₇₉

C₂

semidirect

134. C₇₉

#3248

semidirect

139. #474

D₇₉

semidirect

Subgroups — #23774739

Conjugacy classes of subgroups

Complements