Group #34119321 — subgroups

Subgroups — C₇₉×#7632 #34119321

Order 20224.

590 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 142 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	C₇₉×#2296	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#1728	C₂	1	2	yes	maximal
3	C₇₉×#1271	C₂	1	4	yes	maximal, complemented
4	C₂²×M₁₆×C₇₉	—	2	2	no	—
5	C₂×#117×C₇₉	C₄	1	1	yes	characteristic
6	C₂×#117×C₇₉	C₄	1	1	yes	characteristic
7	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
8	#389×C₇₉	C₄	1	2	yes	—
9	#389×C₇₉	C₂²	1	2	yes	—
10	#385×C₇₉	—	2	2	no	—
11	C₄×C₄⋊C₄×C₇₉	—	2	2	no	—
12	#336×C₇₉	—	2	2	no	—
13	#336×C₇₉	C₂²	1	4	yes	—
14	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₇₉	D₄	1	2	yes	—
16	C₂×M₁₆×C₇₉	—	2	8	no	—
17	C₂×M₁₆×C₇₉	—	4	4	no	—
18	C₂×M₁₆×C₇₉	—	4	4	no	—
19	C₂²×C₈×C₇₉	—	2	4	no	—
20	#117×C₇₉	—	2	4	no	—
21	#117×C₇₉	—	4	2	no	—
22	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
24	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
25	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
26	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
27	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
28	C₂×C₄²×C₇₉	—	2	1	no	—
29	C₂×C₄²×C₇₉	—	2	1	no	—
30	C₂×C₄²×C₇₉	—	4	2	no	—
31	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₇₉	D₄	1	2	yes	—
33	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
34	#95×C₇₉	—	2	2	no	—
35	#95×C₇₉	—	2	2	no	—
36	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₇₉	—	2	2	no	—
38	C₂²×C₄×C₇₉	—	2	4	no	—
39	C₂²×C₄×C₇₉	—	2	2	no	—
40	C₂²×C₄×C₇₉	—	2	4	no	—
41	C₂²×C₄×C₇₉	—	2	2	no	—
42	C₂²×C₄×C₇₉	—	2	2	no	—
43	C₂²×C₄×C₇₉	—	2	2	no	—
44	C₂²×C₄×C₇₉	—	2	2	no	—
45	C₂²×C₄×C₇₉	—	2	2	no	—
46	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
50	M₁₆×C₇₉	—	4	16	no	—
51	C₂×C₈×C₇₉	—	2	8	no	—
52	C₂×C₈×C₇₉	—	4	4	no	—
53	C₂×C₈×C₇₉	—	4	4	no	—
54	C₄⋊C₄×C₇₉	—	2	2	no	—
55	C₄⋊C₄×C₇₉	—	4	2	no	—
56	C₄⋊C₄×C₇₉	—	4	4	no	—
57	C₄⋊C₄×C₇₉	—	4	2	no	—
58	C₄⋊C₄×C₇₉	—	4	2	no	—
59	C₄⋊C₄×C₇₉	M₁₆	1	4	yes	complemented
60	C₂²⋊C₄×C₇₉	—	2	4	no	—
61	C₂²⋊C₄×C₇₉	—	4	2	no	—
62	C₄²×C₇₉	—	2	4	no	—
63	C₄²×C₇₉	—	4	1	no	—
64	C₄²×C₇₉	—	4	2	no	—
65	C₄²×C₇₉	—	4	1	no	—
66	C₄²×C₇₉	—	4	2	no	—
67	C₂³×C₇₉	—	2	1	no	—
68	C₂³×C₇₉	—	2	1	no	—
69	C₂³×C₇₉	—	2	2	no	—
70	C₂³×C₇₉	—	2	2	no	—
71	C₂³×C₇₉	#99	1	2	yes	—
72	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₇₉	—	2	8	no	—
74	C₂×C₄×C₇₉	—	2	8	no	—
75	C₂×C₄×C₇₉	—	2	8	no	—
76	C₂×C₄×C₇₉	—	2	1	no	—
77	C₂×C₄×C₇₉	—	2	1	no	—
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	2	2	no	—
80	C₂×C₄×C₇₉	—	2	2	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	2	no	—
83	C₂×C₄×C₇₉	—	2	2	no	—
84	C₂×C₄×C₇₉	—	2	4	no	—
85	C₂×C₄×C₇₉	—	4	2	no	—
86	C₂×C₄×C₇₉	—	4	2	no	—
87	C₂×C₄×C₇₉	—	4	2	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	—	4	2	no	—
90	C₂×C₄×C₇₉	#101	1	2	yes	—
91	C₂×C₄×C₇₉	#104	1	4	yes	—
92	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
93	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×C₄×C₇₉	#137	1	2	yes	—
95	C₈×C₇₉	—	4	8	no	—
96	C₂²×C₇₉	—	2	2	no	—
97	C₂²×C₇₉	—	2	4	no	—
98	C₂²×C₇₉	—	4	1	no	—
99	C₂²×C₇₉	—	4	2	no	—
100	C₂²×C₇₉	—	4	1	no	—
101	C₂²×C₇₉	#407	1	1	yes	characteristic
102	C₂²×C₇₉	C₂×#99	1	1	yes	characteristic
103	C₂²×C₇₉	C₂×#101	1	1	yes	characteristic
104	C₂²×C₇₉	#417	1	2	yes	—
105	C₂²×C₇₉	C₂×#104	1	2	yes	—
106	C₄×C₇₉	—	2	2	no	—
107	C₄×C₇₉	—	2	2	no	—
108	C₄×C₇₉	—	2	4	no	—
109	C₄×C₇₉	—	2	2	no	—
110	C₄×C₇₉	—	2	2	no	—
111	C₄×C₇₉	—	4	4	no	—
112	C₄×C₇₉	—	8	2	no	—
113	#7632	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂×C₇₉	—	4	2	no	—
115	C₂×C₇₉	#1463	1	1	yes	characteristic
116	C₂×C₇₉	#1489	1	2	yes	—
117	C₂×C₇₉	#1504	1	2	yes	—
118	C₂×C₇₉	#1526	1	1	yes	characteristic
119	C₂×C₇₉	#1561	1	1	yes	characteristic
120	#2296	C₂×C₇₉	1	1	yes	characteristic
121	#1728	C₂×C₇₉	1	2	yes	—
122	#1271	C₂×C₇₉	1	4	yes	complemented
123	C₇₉	#7632	1	1	yes	characteristic, direct product factor, Sylow
124	C₂²×M₁₆	—	2	2	no	—
125	C₂×#117	C₄×C₇₉	1	1	yes	characteristic
126	C₂×#117	C₄×C₇₉	1	1	yes	characteristic
127	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
128	#389	C₄×C₇₉	1	2	yes	—
129	#389	C₂²×C₇₉	1	2	yes	—
130	#385	—	2	2	no	—
131	C₄×C₄⋊C₄	—	2	2	no	—
132	#336	—	2	2	no	—
133	#336	C₂²×C₇₉	1	4	yes	—
134	C₂³×C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
135	C₂³×C₄	D₄×C₇₉	1	2	yes	—
136	C₂×M₁₆	—	2	8	no	—
137	C₂×M₁₆	—	4	4	no	—
138	C₂×M₁₆	—	4	4	no	—
139	C₂²×C₈	—	2	4	no	—
140	#117	—	2	4	no	—
141	#117	—	4	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	—
145	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	—
146	C₂×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	—	4	2	no	—
151	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
152	C₂×C₄²	D₄×C₇₉	1	2	yes	—
153	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
154	#95	—	2	2	no	—
155	#95	—	2	2	no	—
156	C₂⁴	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
167	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
168	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
169	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
170	M₁₆	—	4	16	no	—
171	C₂×C₈	—	2	8	no	—
172	C₂×C₈	—	4	4	no	—
173	C₂×C₈	—	4	4	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	4	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	M₁₆×C₇₉	1	4	yes	complemented
180	C₂²⋊C₄	—	2	4	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	2	4	no	—
183	C₄²	—	4	1	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	4	1	no	—
186	C₄²	—	4	2	no	—
187	C₂³	—	2	2	no	—
188	C₂³	—	2	2	no	—
189	C₂³	—	2	1	no	—
190	C₂³	—	2	1	no	—
191	C₂³	#99×C₇₉	1	2	yes	—
192	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
193	C₂×C₄	—	2	8	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	#101×C₇₉	1	2	yes	—
211	C₂×C₄	#104×C₇₉	1	4	yes	—
212	C₂×C₄	C₂×M₁₆×C₇₉	1	2	yes	—
213	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
214	C₂×C₄	#137×C₇₉	1	2	yes	—
215	C₈	—	4	8	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	#407×C₇₉	1	1	yes	characteristic
222	C₂²	C₂×#99×C₇₉	1	1	yes	characteristic
223	C₂²	C₂×#101×C₇₉	1	1	yes	characteristic
224	C₂²	#417×C₇₉	1	2	yes	—
225	C₂²	C₂×#104×C₇₉	1	2	yes	—
226	C₄	—	2	2	no	—
227	C₄	—	2	4	no	—
228	C₄	—	2	2	no	—
229	C₄	—	2	2	no	—
230	C₄	—	2	2	no	—
231	C₄	—	4	4	no	—
232	C₄	—	8	2	no	—
233	C₂	—	4	2	no	—
234	C₂	C₇₉×#1463	1	1	yes	characteristic
235	C₂	C₇₉×#1489	1	2	yes	—
236	C₂	C₇₉×#1504	1	2	yes	—
237	C₂	C₇₉×#1526	1	1	yes	characteristic
238	C₂	C₇₉×#1561	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₉×#2296

C₂

yes

maximal, characteristic

C₇₉×#1728

C₂

yes

maximal

C₇₉×#1271

C₂

yes

maximal, complemented

C₂²×M₁₆×C₇₉

—

C₂×#117×C₇₉

C₄

yes

characteristic

C₂×#117×C₇₉

C₄

yes

characteristic

C₂²×C₄²×C₇₉

C₂²

yes

characteristic

#389×C₇₉

C₄

yes

—

#389×C₇₉

C₂²

yes

—

#385×C₇₉

—

C₄×C₄⋊C₄×C₇₉

—

#336×C₇₉

—

#336×C₇₉

C₂²

yes

—

C₂³×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₉

D₄

yes

—

C₂×M₁₆×C₇₉

—

C₂×M₁₆×C₇₉

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

—

#117×C₇₉

—

#117×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

C₂⁴×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

M₁₆

yes

complemented

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

#99

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#101

yes

—

C₂×C₄×C₇₉

#104

yes

—

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₈×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#407

yes

characteristic

102

C₂²×C₇₉

C₂×#99

yes

characteristic

103

C₂²×C₇₉

C₂×#101

yes

characteristic

104

C₂²×C₇₉

#417

yes

—

105

C₂²×C₇₉

C₂×#104

yes

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

—

113

#7632

C₇₉

yes

maximal, characteristic, direct product factor, Sylow

114

C₂×C₇₉

—

115

C₂×C₇₉

#1463

yes

characteristic

116

C₂×C₇₉

#1489

yes

—

117

C₂×C₇₉

#1504

yes

—

118

C₂×C₇₉

#1526

yes

characteristic

119

C₂×C₇₉

#1561

yes

characteristic

120

#2296

C₂×C₇₉

yes

characteristic

121

#1728

C₂×C₇₉

yes

—

122

#1271

C₂×C₇₉

yes

complemented

123

C₇₉

#7632

yes

characteristic, direct product factor, Sylow

124

C₂²×M₁₆

—

125

C₂×#117

C₄×C₇₉

yes

characteristic

126

C₂×#117

C₄×C₇₉

yes

characteristic

127

C₂²×C₄²

C₂²×C₇₉

yes

characteristic

128

#389

C₄×C₇₉

yes

—

129

#389

C₂²×C₇₉

yes

—

130

#385

—

131

C₄×C₄⋊C₄

—

132

#336

—

133

#336

C₂²×C₇₉

yes

—

134

C₂³×C₄

C₂×C₄×C₇₉

yes

characteristic

135

C₂³×C₄

D₄×C₇₉

yes

—

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

C₂×M₁₆

—

139

C₂²×C₈

—

140

#117

—

141

#117

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

C₂×C₄×C₇₉

yes

—

145

C₂×C₄⋊C₄

C₂×C₄×C₇₉

yes

—

146

C₂×C₂²⋊C₄

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

C₂×C₄×C₇₉

yes

characteristic

152

C₂×C₄²

D₄×C₇₉

yes

—

153

C₂×C₄²

C₂³×C₇₉

yes

characteristic

154

#95

—

155

#95

—

156

C₂⁴

C₂²⋊C₄×C₇₉

yes

characteristic

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂²⋊C₄×C₇₉

yes

characteristic

167

C₂²×C₄

C₂²⋊C₄×C₇₉

yes

—

168

C₂²×C₄

C₂²×C₄×C₇₉

yes

characteristic

169

C₂²×C₄

C₂×D₄×C₇₉

yes

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

M₁₆×C₇₉

yes

complemented

180

C₂²⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

#99×C₇₉

yes

—

192

C₂³

C₂×C₂²⋊C₄×C₇₉

yes

characteristic

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#101×C₇₉

yes

—

211

C₂×C₄

#104×C₇₉

yes

—

212

C₂×C₄

C₂×M₁₆×C₇₉

yes

—

213

C₂×C₄

AGL(1,ℤ/8)×C₇₉

yes

—

214

C₂×C₄

#137×C₇₉

yes

—

215

C₈

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#407×C₇₉

yes

characteristic

222

C₂²

C₂×#99×C₇₉

yes

characteristic

223

C₂²

C₂×#101×C₇₉

yes

characteristic

224

C₂²

#417×C₇₉

yes

—

225

C₂²

C₂×#104×C₇₉

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₂

—

234

C₂

C₇₉×#1463

yes

characteristic

235

C₂

C₇₉×#1489

yes

—

236

C₂

C₇₉×#1504

yes

—

237

C₂

C₇₉×#1526

yes

characteristic

238

C₂

C₇₉×#1561

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
prime radical	C₂⁴×C₇₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₉

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₇₉

Frattini, cosocle

C₂×C₄²

C₂³×C₇₉

prime radical

C₂⁴×C₇₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

N	H ≅ G/N	type
3. C₇₉×#1271	C₂	semidirect
59. C₄⋊C₄×C₇₉	M₁₆	semidirect
113. #7632	C₇₉	direct (N × H)
122. #1271	C₂×C₇₉	semidirect
123. C₇₉	#7632	direct (N × H)
179. C₄⋊C₄	M₁₆×C₇₉	semidirect

H ≅ G/N

type

3. C₇₉×#1271

C₂

semidirect

59. C₄⋊C₄×C₇₉

M₁₆

semidirect

113. #7632

C₇₉

direct (N × H)

122. #1271

C₂×C₇₉

semidirect

123. C₇₉

#7632

direct (N × H)

179. C₄⋊C₄

M₁₆×C₇₉

semidirect

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

subgroup	index
C₇₉×#2296	2
C₇₉×#1728	2
C₇₉×#1271	2
#7632	79

subgroup

index

C₇₉×#2296

C₇₉×#1728

C₇₉×#1271

#7632

Subgroups — C₇₉×#7632 #34119321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C79×#7632 #34119321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#7632 #34119321