Group #34204214 — subgroups

Subgroups — #34204214

Order 20224.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19098517	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098383	C₂	1	2	yes	maximal, complemented
3	#23765010	C₂	1	2	yes	maximal
4	#23761482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11929607	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
8	C₂×#14579118	C₄	1	1	yes	characteristic
9	C₂×#14579101	C₂²	1	2	yes	—
10	#19098517	—	2	4	no	—
11	C₂×#14579072	C₄	1	1	yes	characteristic
12	C₂×#14579071	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
14	#19098383	—	2	4	no	—
15	(C₂×D₇₉)⋊C₁₆	—	2	4	no	—
16	C₂×M₃₂×C₇₉	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
19	C₂×#11929607	—	2	2	no	—
20	C₂×#11929607	—	2	2	no	—
21	C₂×#11929607	C₈	1	4	yes	—
22	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₇₉	—	2	2	no	—
25	C₂×C₈×D₇₉	—	2	2	no	—
26	C₂×C₈×D₇₉	D₄	1	2	yes	—
27	C₂×C₈×D₇₉	Q₈	1	2	yes	—
28	#14579118	—	2	2	no	—
29	#14579118	—	2	2	no	—
30	C₂×Dic₇₉⋊C₄	—	2	1	no	—
31	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
32	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
33	#14579101	—	2	2	no	—
34	#14579101	—	2	2	no	—
35	C₂×C₇₉⋊C₁₆	—	2	2	no	—
36	#14579072	—	2	2	no	—
37	#14579071	—	2	2	no	—
38	C₈×Dic₇₉	D₄	1	4	yes	—
39	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
42	M₃₂×C₇₉	—	2	2	no	—
43	M₃₂×C₇₉	—	2	2	no	—
44	C₂×C₁₆×C₇₉	—	2	2	no	—
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₂³×D₇₉	M₁₆	1	1	yes	characteristic
47	C₂²×Dic₇₉	—	2	1	no	—
48	C₂²×Dic₇₉	M₁₆	1	1	yes	characteristic
49	C₂×C₄×D₇₉	—	2	1	no	—
50	C₂×C₄×D₇₉	—	2	1	no	—
51	C₂×C₄×D₇₉	—	2	1	no	—
52	C₂×C₄×D₇₉	—	2	1	no	—
53	C₂×C₄×D₇₉	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×D₇₉	C₂×C₈	1	2	yes	—
55	#11929607	—	2	8	no	—
56	C₂×C₇₉⋊C₈	—	2	1	no	—
57	C₂×C₇₉⋊C₈	—	2	1	no	—
58	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
59	C₂×C₇₉⋊C₈	C₄⋊C₄	1	2	yes	—
60	C₂×C₇₉⋊C₈	C₂×C₈	1	2	yes	—
61	C₂×C₇₉⋊C₈	M₁₆	1	2	yes	—
62	C₈×D₇₉	—	2	4	no	—
63	C₈×D₇₉	—	2	4	no	—
64	Dic₇₉⋊C₄	—	2	4	no	—
65	(C₂×D₇₉)⋊C₄	—	2	4	no	—
66	C₄×Dic₇₉	—	2	1	no	—
67	C₄×Dic₇₉	C₂²⋊C₄	1	2	yes	—
68	C₇₉⋊C₁₆	—	4	2	no	—
69	C₂²×C₄×C₇₉	—	2	1	no	—
70	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₉	—	2	1	no	—
72	C₂×C₈×C₇₉	—	2	1	no	—
73	C₂×C₈×C₇₉	C₂×C₈	1	2	yes	—
74	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
77	C₂×C₈×C₇₉	#41	1	2	yes	—
78	C₄²×C₇₉	—	2	1	no	—
79	C₄²×C₇₉	M₁₆	1	2	yes	—
80	C₁₆×C₇₉	—	4	2	no	—
81	C₂³×C₇₉	C₂×M₁₆	1	1	yes	characteristic
82	C₂²×D₇₉	—	2	1	no	—
83	C₂²×D₇₉	—	2	1	no	—
84	C₂²×D₇₉	—	4	2	no	—
85	C₂²×D₇₉	C₄⋊C₈	1	2	yes	—
86	C₂×C₄×C₇₉	—	2	2	no	—
87	C₂×C₄×C₇₉	—	4	2	no	—
88	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₇₉	—	2	1	no	—
95	C₂×Dic₇₉	—	2	1	no	—
96	C₂×Dic₇₉	—	2	2	no	—
97	C₂×Dic₇₉	—	4	2	no	—
98	C₂×Dic₇₉	C₄⋊C₈	1	2	yes	—
99	C₄×D₇₉	—	2	2	no	—
100	C₄×D₇₉	—	2	2	no	—
101	C₄×D₇₉	—	2	2	no	—
102	C₄×D₇₉	—	2	2	no	—
103	C₈×C₇₉	—	2	2	no	—
104	C₈×C₇₉	#121	1	2	yes	—
105	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
106	C₇₉⋊C₈	—	2	2	no	—
107	C₇₉⋊C₈	C₂²⋊C₈	1	4	yes	—
108	C₂²×C₇₉	—	2	2	no	—
109	C₂²×C₇₉	#407	1	1	yes	characteristic
110	C₂²×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
111	C₂²×C₇₉	#432	1	1	yes	characteristic
112	C₂×D₇₉	—	2	2	no	—
113	C₂×D₇₉	—	2	4	no	—
114	C₂×D₇₉	—	4	2	no	—
115	C₂×D₇₉	—	4	2	no	—
116	C₄×C₇₉	—	4	2	no	—
117	C₄×C₇₉	#380	1	1	yes	characteristic
118	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₄×C₇₉	#423	1	1	yes	characteristic
120	C₄×C₇₉	#431	1	1	yes	characteristic
121	Dic₇₉	—	2	2	no	—
122	Dic₇₉	—	4	2	no	—
123	#12789	—	79	1	no	maximal, Sylow
124	C₂×C₇₉	—	2	1	no	—
125	C₂×C₇₉	—	2	1	no	—
126	C₂×C₇₉	#1797	1	1	yes	characteristic
127	C₂×C₇₉	#2153	1	2	yes	—
128	D₇₉	—	4	2	no	—
129	C₂×#405	—	79	1	no	—
130	C₂×#364	—	79	2	no	—
131	#2112	—	79	2	no	—
132	#1376	—	79	1	no	—
133	#1376	D₇₉	1	1	yes	characteristic, complemented
134	C₇₉	#12789	1	1	yes	characteristic, complemented, Sylow
135	C₂²×M₁₆	—	79	1	no	—
136	C₂³×C₈	—	79	1	no	—
137	C₂×#117	—	79	1	no	—
138	C₂×M₃₂	—	79	2	no	—
139	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
140	#405	—	158	4	no	—
141	C₂×#97	—	79	1	no	—
142	C₂×#97	—	79	1	no	—
143	C₂×C₄×C₈	—	79	1	no	—
144	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
145	#364	—	158	4	no	—
146	C₂²⋊C₁₆	—	158	4	no	—
147	C₂³×C₄	—	79	1	no	—
148	C₂×M₁₆	—	79	4	no	—
149	C₂×M₁₆	—	158	2	no	—
150	C₂×M₁₆	—	158	2	no	—
151	C₂²×C₈	—	79	1	no	—
152	C₂²×C₈	—	79	1	no	—
153	C₂²×C₈	—	79	2	no	—
154	C₂²×C₈	—	79	2	no	—
155	C₂²×C₈	—	158	2	no	—
156	C₂²×C₈	—	158	2	no	—
157	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
159	#117	—	158	2	no	—
160	#117	—	158	2	no	—
161	C₂×C₄⋊C₄	—	158	1	no	—
162	C₂×C₂²⋊C₄	—	158	1	no	—
163	C₂×C₄²	—	79	1	no	—
164	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	158	2	no	—
168	M₃₂	—	158	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	158	2	no	—
171	#97	—	158	2	no	—
172	#97	—	158	2	no	—
173	C₄×C₈	—	2	2	no	—
174	C₄×C₈	—	79	4	no	—
175	C₂⁴	—	79	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	79	1	no	—
178	C₂²×C₄	—	79	2	no	—
179	C₂²×C₄	—	79	2	no	—
180	C₂²×C₄	—	158	1	no	—
181	C₂²×C₄	—	158	1	no	—
182	C₂²×C₄	—	158	1	no	—
183	C₂²×C₄	—	158	1	no	—
184	C₂²×C₄	—	158	1	no	—
185	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
186	M₁₆	—	158	8	no	—
187	C₂×C₈	—	2	1	no	—
188	C₂×C₈	—	2	1	no	—
189	C₂×C₈	—	79	2	no	—
190	C₂×C₈	—	79	2	no	—
191	C₂×C₈	—	79	2	no	—
192	C₂×C₈	—	79	2	no	—
193	C₂×C₈	—	158	1	no	—
194	C₂×C₈	—	158	1	no	—
195	C₂×C₈	—	158	4	no	—
196	C₂×C₈	—	158	4	no	—
197	C₂×C₈	C₈×D₇₉	1	2	yes	—
198	C₂×C₈	D₄×D₇₉	1	2	yes	—
199	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
200	C₂×C₈	Q₈×D₇₉	1	1	yes	characteristic
201	C₂×C₈	#11929624	1	2	yes	—
202	C₄⋊C₄	—	158	4	no	—
203	C₂²⋊C₄	—	158	4	no	—
204	C₄²	—	2	1	no	—
205	C₄²	—	79	2	no	—
206	C₄²	—	158	1	no	—
207	C₄²	#11929607	1	2	yes	—
208	C₁₆	—	4	2	no	—
209	C₁₆	—	316	2	no	—
210	C₂³	—	316	2	no	—
211	C₂³	—	79	2	no	—
212	C₂³	—	158	1	no	—
213	C₂³	—	158	1	no	—
214	C₂³	M₁₆×D₇₉	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	316	2	no	—
218	C₂×C₄	—	79	2	no	—
219	C₂×C₄	—	158	2	no	—
220	C₂×C₄	—	158	1	no	—
221	C₂×C₄	—	158	1	no	—
222	C₂×C₄	—	158	2	no	—
223	C₂×C₄	—	158	2	no	—
224	C₂×C₄	—	158	2	no	—
225	C₂×C₄	—	158	2	no	—
226	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
227	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
228	C₂×C₄	#14579118	1	1	yes	characteristic
229	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
230	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
231	C₂×C₄	C₂×#11929607	1	1	yes	characteristic
232	C₈	—	2	2	no	—
233	C₈	—	79	4	no	—
234	C₈	—	158	2	no	—
235	C₈	#14579134	1	2	yes	—
236	C₈	#14579139	1	2	yes	—
237	C₂²	—	2	2	no	—
238	C₂²	—	316	2	no	—
239	C₂²	—	316	2	no	—
240	C₂²	—	158	4	no	—
241	C₂²	—	158	2	no	—
242	C₂²	#19098525	1	1	yes	characteristic
243	C₂²	C₄⋊C₈×D₇₉	1	1	yes	characteristic
244	C₂²	#19098618	1	1	yes	characteristic
245	C₄	—	4	2	no	—
246	C₄	—	316	2	no	—
247	C₄	—	158	2	no	—
248	C₄	#19098422	1	1	yes	characteristic
249	C₄	C₂²⋊C₈×D₇₉	1	1	yes	characteristic
250	C₄	#19098585	1	1	yes	characteristic
251	C₄	#19098614	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	—	316	2	no	—
255	C₂	#23763379	1	1	yes	characteristic
256	C₂	#23765164	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098517

C₂

yes

maximal, characteristic

C₂×#19098383

C₂

yes

maximal, complemented

#23765010

C₂

yes

maximal

#23761482

C₂

yes

maximal, characteristic, complemented

C₇₉×#1376

C₂

yes

maximal, characteristic, complemented

C₂²×#11929607

C₄

yes

characteristic

C₂²×C₈×D₇₉

C₂²

yes

characteristic

C₂×#14579118

C₄

yes

characteristic

C₂×#14579101

C₂²

yes

—

#19098517

—

C₂×#14579072

C₄

yes

characteristic

C₂×#14579071

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₂²

yes

characteristic

#19098383

—

(C₂×D₇₉)⋊C₁₆

—

C₂×M₃₂×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×C₄×D₇₉

C₂×C₄

yes

—

—

C₈

yes

—

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

D₄

yes

—

C₂×C₈×D₇₉

Q₈

yes

—

#14579118

—

#14579118

—

C₂×Dic₇₉⋊C₄

—

C₂×(C₂×D₇₉)⋊C₄

—

C₂×C₄×Dic₇₉

C₂×C₄

yes

characteristic

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

—

#14579072

—

#14579071

—

C₈×Dic₇₉

D₄

yes

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

M₃₂×C₇₉

—

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₄×C₈×C₇₉

—

C₂³×D₇₉

M₁₆

yes

characteristic

C₂²×Dic₇₉

—

C₂²×Dic₇₉

M₁₆

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₄⋊C₄

yes

—

C₂×C₄×D₇₉

C₂×C₈

yes

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₇₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₇₉⋊C₈

C₂×C₈

yes

—

C₂×C₇₉⋊C₈

M₁₆

yes

—

C₈×D₇₉

—

C₈×D₇₉

—

Dic₇₉⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂²⋊C₄

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₈

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₇₉

#41

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

M₁₆

yes

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×M₁₆

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₄⋊C₈

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

#117

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄⋊C₈

yes

—

C₄×D₇₉

—

100

C₄×D₇₉

—

101

C₄×D₇₉

—

102

C₄×D₇₉

—

103

C₈×C₇₉

—

104

C₈×C₇₉

#121

yes

—

105

C₈×C₇₉

C₂²⋊Q₈

yes

—

106

C₇₉⋊C₈

—

107

C₇₉⋊C₈

C₂²⋊C₈

yes

—

108

C₂²×C₇₉

—

109

C₂²×C₇₉

#407

yes

characteristic

110

C₂²×C₇₉

C₂×C₄⋊C₈

yes

characteristic

111

C₂²×C₇₉

#432

yes

characteristic

112

C₂×D₇₉

—

113

C₂×D₇₉

—

114

C₂×D₇₉

—

115

C₂×D₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

#380

yes

characteristic

118

C₄×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

119

C₄×C₇₉

#423

yes

characteristic

120

C₄×C₇₉

#431

yes

characteristic

121

Dic₇₉

—

122

Dic₇₉

—

123

#12789

—

maximal, Sylow

124

C₂×C₇₉

—

125

C₂×C₇₉

—

126

C₂×C₇₉

#1797

yes

characteristic

127

C₂×C₇₉

#2153

yes

—

128

D₇₉

—

129

C₂×#405

—

130

C₂×#364

—

131

#2112

—

132

#1376

—

133

#1376

D₇₉

yes

characteristic, complemented

134

C₇₉

#12789

yes

characteristic, complemented, Sylow

135

C₂²×M₁₆

—

136

C₂³×C₈

—

137

C₂×#117

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₇₉

yes

—

140

#405

—

158

—

141

C₂×#97

—

142

C₂×#97

—

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

145

#364

—

158

—

146

C₂²⋊C₁₆

—

158

—

147

C₂³×C₄

—

148

C₂×M₁₆

—

149

C₂×M₁₆

—

158

—

150

C₂×M₁₆

—

158

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

158

—

156

C₂²×C₈

—

158

—

157

C₂²×C₈

C₄×D₇₉

yes

characteristic

158

C₂²×C₈

C₂²×D₇₉

yes

characteristic

159

#117

—

158

—

160

#117

—

158

—

161

C₂×C₄⋊C₄

—

158

—

162

C₂×C₂²⋊C₄

—

158

—

163

C₂×C₄²

—

164

C₂×C₄²

C₄×D₇₉

yes

characteristic

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

158

—

168

M₃₂

—

158

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

158

—

171

#97

—

158

—

172

#97

—

158

—

173

C₄×C₈

—

174

C₄×C₈

—

175

C₂⁴

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

158

—

181

C₂²×C₄

—

158

—

182

C₂²×C₄

—

158

—

183

C₂²×C₄

—

158

—

184

C₂²×C₄

—

158

—

185

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

186

M₁₆

—

158

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

158

—

194

C₂×C₈

—

158

—

195

C₂×C₈

—

158

—

196

C₂×C₈

—

158

—

197

C₂×C₈

C₈×D₇₉

yes

—

198

C₂×C₈

D₄×D₇₉

yes

—

199

C₂×C₈

D₄×D₇₉

yes

characteristic

200

C₂×C₈

Q₈×D₇₉

yes

characteristic

201

C₂×C₈

#11929624

yes

—

202

C₄⋊C₄

—

158

—

203

C₂²⋊C₄

—

158

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

158

—

207

C₄²

#11929607

yes

—

208

C₁₆

—

209

C₁₆

—

316

—

210

C₂³

—

316

—

211

C₂³

—

212

C₂³

—

158

—

213

C₂³

—

158

—

214

C₂³

M₁₆×D₇₉

yes

characteristic

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

316

—

218

C₂×C₄

—

219

C₂×C₄

—

158

—

220

C₂×C₄

—

158

—

221

C₂×C₄

—

158

—

222

C₂×C₄

—

158

—

223

C₂×C₄

—

158

—

224

C₂×C₄

—

158

—

225

C₂×C₄

—

158

—

226

C₂×C₄

C₂²⋊C₄×D₇₉

yes

characteristic

227

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

228

C₂×C₄

#14579118

yes

characteristic

229

C₂×C₄

C₂×C₈×D₇₉

yes

characteristic

230

C₂×C₄

M₁₆×D₇₉

yes

characteristic

231

C₂×C₄

C₂×#11929607

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

158

—

235

C₈

#14579134

yes

—

236

C₈

#14579139

yes

—

237

C₂²

—

238

C₂²

—

316

—

239

C₂²

—

316

—

240

C₂²

—

158

—

241

C₂²

—

158

—

242

C₂²

#19098525

yes

characteristic

243

C₂²

C₄⋊C₈×D₇₉

yes

characteristic

244

C₂²

#19098618

yes

characteristic

245

C₄

—

246

C₄

—

316

—

247

C₄

—

158

—

248

C₄

#19098422

yes

characteristic

249

C₄

C₂²⋊C₈×D₇₉

yes

characteristic

250

C₄

#19098585

yes

characteristic

251

C₄

#19098614

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

—

316

—

255

C₂

#23763379

yes

characteristic

256

C₂

#23765164

yes

—

	subgroup	G/H
center	C₂×C₈	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1376	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₈
prime radical	C₂³×D₇₉	M₁₆
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#1376	D₇₉
hypocenter	C₇₉	#12789
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1376

subgroup

G/H

center

C₂×C₈

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1376

C₂

socle

C₂²×C₇₉

C₂×C₄⋊C₈

prime radical

C₂³×D₇₉

M₁₆

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1376

N	H ≅ G/N	type
2. C₂×#19098383	C₂	semidirect
4. #23761482	C₂	semidirect
5. C₇₉×#1376	C₂	semidirect
133. #1376	D₇₉	semidirect
134. C₇₉	#12789	semidirect

H ≅ G/N

type

2. C₂×#19098383

C₂

semidirect

4. #23761482

C₂

semidirect

5. C₇₉×#1376

C₂

semidirect

133. #1376

D₇₉

semidirect

134. C₇₉

#12789

semidirect

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

subgroup	index
C₂×#19098517	2
C₂×#19098383	2
#23765010	2
#23761482	2
C₇₉×#1376	2
#12789	79

subgroup

index

C₇₉×#1376

Subgroups — #34204214

Conjugacy classes of subgroups

Complements

Maximal subgroups