Group #34204210 — subgroups

Subgroups — #34204210

Order 20224.

538 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 139 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×C₄×C₈×D₇₉	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×C₈×D₇₉	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₇₉	C₄	1	1	yes	characteristic
9	C₂×#14579101	C₂²	1	2	yes	—
10	C₂×C₄×C₇₉⋊C₈	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₇₉	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×D₇₉	—	2	4	no	—
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	—	2	1	no	—
19	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₇₉	—	2	2	no	—
23	C₂×C₈×D₇₉	—	2	2	no	—
24	C₂×C₈×D₇₉	—	2	2	no	—
25	C₂×C₈×D₇₉	—	2	2	no	—
26	C₂×C₈×D₇₉	C₈	1	4	yes	—
27	C₂×C₈×D₇₉	D₄	1	2	yes	—
28	C₂×C₈×D₇₉	Q₈	1	2	yes	—
29	C₂×C₄×Dic₇₉	—	2	1	no	—
30	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×D₇₉	—	2	2	no	—
32	C₄²×D₇₉	—	2	2	no	—
33	#14579101	—	2	2	no	—
34	#14579101	—	2	2	no	—
35	C₂×C₇₉⋊C₁₆	—	2	2	no	—
36	C₄×C₇₉⋊C₈	—	2	2	no	—
37	C₈×Dic₇₉	—	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	4	no	—
50	C₂×C₄×D₇₉	—	2	8	no	—
51	C₂×C₄×D₇₉	—	2	1	no	—
52	C₂×C₄×D₇₉	—	2	1	no	—
53	C₂×C₄×D₇₉	—	2	1	no	—
54	C₂×C₄×D₇₉	—	2	1	no	—
55	C₂×C₄×D₇₉	C₄⋊C₄	1	2	yes	—
56	C₂×C₄×D₇₉	C₂×C₈	1	2	yes	—
57	C₂×C₇₉⋊C₈	—	2	1	no	—
58	C₂×C₇₉⋊C₈	—	2	1	no	—
59	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
60	C₂×C₇₉⋊C₈	C₄⋊C₄	1	2	yes	—
61	C₂×C₇₉⋊C₈	C₂×C₈	1	2	yes	—
62	C₂×C₇₉⋊C₈	M₁₆	1	2	yes	—
63	C₈×D₇₉	—	2	4	no	—
64	C₈×D₇₉	—	2	4	no	—
65	C₈×D₇₉	—	2	8	no	—
66	C₄×Dic₇₉	—	2	4	no	—
67	C₄×Dic₇₉	—	2	1	no	—
68	C₄×Dic₇₉	C₂²⋊C₄	1	2	yes	—
69	C₇₉⋊C₁₆	—	4	2	no	—
70	C₂²×C₄×C₇₉	—	2	1	no	—
71	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₇₉	—	2	1	no	—
73	C₂×C₈×C₇₉	—	2	1	no	—
74	C₂×C₈×C₇₉	C₂×C₈	1	2	yes	—
75	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₈×C₇₉	#41	1	2	yes	—
79	C₄²×C₇₉	—	2	1	no	—
80	C₄²×C₇₉	M₁₆	1	2	yes	—
81	C₁₆×C₇₉	—	4	2	no	—
82	C₂³×C₇₉	C₂×M₁₆	1	1	yes	characteristic
83	C₂²×D₇₉	—	2	1	no	—
84	C₂²×D₇₉	—	2	1	no	—
85	C₂²×D₇₉	—	2	4	no	—
86	C₂²×D₇₉	C₄⋊C₈	1	2	yes	—
87	C₂×C₄×C₇₉	—	2	4	no	—
88	C₂×C₄×C₇₉	—	2	2	no	—
89	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
93	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
94	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
95	C₂×Dic₇₉	—	2	4	no	—
96	C₂×Dic₇₉	—	2	1	no	—
97	C₂×Dic₇₉	—	2	2	no	—
98	C₂×Dic₇₉	—	2	1	no	—
99	C₂×Dic₇₉	C₄⋊C₈	1	2	yes	—
100	C₄×D₇₉	—	2	16	no	—
101	C₄×D₇₉	—	2	2	no	—
102	C₄×D₇₉	—	2	2	no	—
103	C₄×D₇₉	—	2	2	no	—
104	C₄×D₇₉	—	2	2	no	—
105	C₈×C₇₉	—	2	2	no	—
106	C₈×C₇₉	#121	1	2	yes	—
107	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
108	C₇₉⋊C₈	—	2	2	no	—
109	C₇₉⋊C₈	C₂²⋊C₈	1	4	yes	—
110	C₂²×C₇₉	—	2	2	no	—
111	C₂²×C₇₉	#407	1	1	yes	characteristic
112	C₂²×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
113	C₂²×C₇₉	#432	1	1	yes	characteristic
114	C₂×D₇₉	—	2	4	no	—
115	C₂×D₇₉	—	2	4	no	—
116	C₂×D₇₉	—	2	2	no	—
117	C₂×D₇₉	—	2	2	no	—
118	C₂×D₇₉	#364	1	4	yes	complemented
119	C₄×C₇₉	—	2	4	no	—
120	C₄×C₇₉	#380	1	1	yes	characteristic
121	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
122	C₄×C₇₉	#423	1	1	yes	characteristic
123	C₄×C₇₉	#431	1	1	yes	characteristic
124	Dic₇₉	—	2	4	no	—
125	Dic₇₉	—	2	2	no	—
126	#12788	—	79	1	no	maximal, Sylow
127	C₂×C₇₉	—	2	1	no	—
128	C₂×C₇₉	—	2	1	no	—
129	C₂×C₇₉	#1797	1	1	yes	characteristic
130	C₂×C₇₉	C₂×#364	1	2	yes	—
131	D₇₉	—	2	4	no	—
132	C₂²×C₄×C₈	—	79	1	no	—
133	C₂×#364	—	79	2	no	—
134	#2112	—	79	2	no	—
135	#1376	—	79	1	no	—
136	#1376	D₇₉	1	1	yes	characteristic, complemented
137	C₇₉	#12788	1	1	yes	characteristic, complemented, Sylow
138	C₂³×C₈	—	79	1	no	—
139	C₂³×C₈	—	79	1	no	—
140	C₂²×C₄²	—	79	1	no	—
141	C₂×M₃₂	—	79	2	no	—
142	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
143	C₂×C₄×C₈	—	79	1	no	—
144	C₂×C₄×C₈	—	79	1	no	—
145	C₂×C₄×C₈	—	79	1	no	—
146	C₂×C₄×C₈	—	158	4	no	—
147	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
148	#364	—	158	4	no	—
149	C₂²⋊C₁₆	—	158	4	no	—
150	C₂³×C₄	—	79	1	no	—
151	C₂³×C₄	—	158	1	no	—
152	C₂²×C₈	—	79	1	no	—
153	C₂²×C₈	—	79	1	no	—
154	C₂²×C₈	—	79	4	no	—
155	C₂²×C₈	—	79	2	no	—
156	C₂²×C₈	—	79	2	no	—
157	C₂²×C₈	—	158	2	no	—
158	C₂²×C₈	—	158	2	no	—
159	C₂²×C₈	—	158	2	no	—
160	C₂²×C₈	—	158	2	no	—
161	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
163	C₂×C₄²	—	79	1	no	—
164	C₂×C₄²	—	158	2	no	—
165	C₂×C₄²	—	158	1	no	—
166	C₂×C₄²	—	158	2	no	—
167	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
168	M₃₂	—	2	2	no	—
169	M₃₂	—	2	2	no	—
170	M₃₂	—	158	2	no	—
171	M₃₂	—	158	2	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	158	2	no	—
174	C₄×C₈	—	2	2	no	—
175	C₄×C₈	—	79	4	no	—
176	C₄×C₈	—	158	2	no	—
177	C₄×C₈	—	158	2	no	—
178	C₂⁴	—	79	1	no	—
179	C₂²×C₄	—	2	1	no	—
180	C₂²×C₄	—	79	1	no	—
181	C₂²×C₄	—	79	2	no	—
182	C₂²×C₄	—	79	2	no	—
183	C₂²×C₄	—	158	4	no	—
184	C₂²×C₄	—	158	8	no	—
185	C₂²×C₄	—	158	1	no	—
186	C₂²×C₄	—	158	1	no	—
187	C₂²×C₄	—	158	1	no	—
188	C₂²×C₄	—	158	1	no	—
189	C₂²×C₄	—	158	1	no	—
190	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	79	2	no	—
194	C₂×C₈	—	79	2	no	—
195	C₂×C₈	—	79	2	no	—
196	C₂×C₈	—	79	2	no	—
197	C₂×C₈	—	158	8	no	—
198	C₂×C₈	—	158	1	no	—
199	C₂×C₈	—	158	1	no	—
200	C₂×C₈	—	158	4	no	—
201	C₂×C₈	—	158	4	no	—
202	C₂×C₈	C₈×D₇₉	1	2	yes	—
203	C₂×C₈	D₄×D₇₉	1	2	yes	—
204	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
205	C₂×C₈	Q₈×D₇₉	1	1	yes	characteristic
206	C₂×C₈	#11929624	1	2	yes	—
207	C₄²	—	2	1	no	—
208	C₄²	—	79	2	no	—
209	C₄²	—	158	4	no	—
210	C₄²	—	158	1	no	—
211	C₄²	#11929607	1	2	yes	—
212	C₁₆	—	4	2	no	—
213	C₁₆	—	316	2	no	—
214	C₂³	—	79	2	no	—
215	C₂³	—	158	4	no	—
216	C₂³	—	158	1	no	—
217	C₂³	—	158	1	no	—
218	C₂³	M₁₆×D₇₉	1	1	yes	characteristic
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	79	2	no	—
222	C₂×C₄	—	158	16	no	—
223	C₂×C₄	—	158	4	no	—
224	C₂×C₄	—	158	2	no	—
225	C₂×C₄	—	158	1	no	—
226	C₂×C₄	—	158	1	no	—
227	C₂×C₄	—	158	2	no	—
228	C₂×C₄	—	158	2	no	—
229	C₂×C₄	—	158	2	no	—
230	C₂×C₄	—	158	2	no	—
231	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
232	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
233	C₂×C₄	#14579118	1	1	yes	characteristic
234	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
235	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
236	C₂×C₄	C₂×#11929607	1	1	yes	characteristic
237	C₈	—	2	2	no	—
238	C₈	—	79	4	no	—
239	C₈	—	158	2	no	—
240	C₈	#14579134	1	2	yes	—
241	C₈	#14579139	1	2	yes	—
242	C₂²	—	2	2	no	—
243	C₂²	—	79	4	no	—
244	C₂²	—	158	4	no	—
245	C₂²	—	158	4	no	—
246	C₂²	—	158	2	no	—
247	C₂²	—	158	2	no	—
248	C₂²	#19098525	1	1	yes	characteristic
249	C₂²	C₄⋊C₈×D₇₉	1	1	yes	characteristic
250	C₂²	#19098618	1	1	yes	characteristic
251	C₄	—	2	4	no	—
252	C₄	—	158	4	no	—
253	C₄	—	158	2	no	—
254	C₄	#19098422	1	1	yes	characteristic
255	C₄	C₂²⋊C₈×D₇₉	1	1	yes	characteristic
256	C₄	#19098585	1	1	yes	characteristic
257	C₄	#19098614	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	158	4	no	—
261	C₂	#23763379	1	1	yes	characteristic
262	C₂	#364×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈×D₇₉

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×C₈×D₇₉

C₄

yes

characteristic

C₂²×C₈×D₇₉

C₂²

yes

characteristic

C₂×C₄²×D₇₉

C₄

yes

characteristic

C₂×#14579101

C₂²

yes

—

C₂×C₄×C₇₉⋊C₈

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₂²

yes

characteristic

C₄×C₈×D₇₉

—

#19098383

—

(C₂×D₇₉)⋊C₁₆

—

C₂×M₃₂×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×C₄×D₇₉

—

C₂²×C₄×D₇₉

C₂×C₄

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

C₈

yes

—

C₂×C₈×D₇₉

D₄

yes

—

C₂×C₈×D₇₉

Q₈

yes

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₄²×D₇₉

—

C₄²×D₇₉

—

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

—

C₄×C₇₉⋊C₈

—

C₈×Dic₇₉

—

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

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₄⋊C₄

yes

—

C₂×C₄×D₇₉

C₂×C₈

yes

—

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

—

C₈×D₇₉

—

C₄×Dic₇₉

—

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

—

100

C₄×D₇₉

—

101

C₄×D₇₉

—

102

C₄×D₇₉

—

103

C₄×D₇₉

—

104

C₄×D₇₉

—

105

C₈×C₇₉

—

106

C₈×C₇₉

#121

yes

—

107

C₈×C₇₉

C₂²⋊Q₈

yes

—

108

C₇₉⋊C₈

—

109

C₇₉⋊C₈

C₂²⋊C₈

yes

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

#407

yes

characteristic

112

C₂²×C₇₉

C₂×C₄⋊C₈

yes

characteristic

113

C₂²×C₇₉

#432

yes

characteristic

114

C₂×D₇₉

—

115

C₂×D₇₉

—

116

C₂×D₇₉

—

117

C₂×D₇₉

—

118

C₂×D₇₉

#364

yes

complemented

119

C₄×C₇₉

—

120

C₄×C₇₉

#380

yes

characteristic

121

C₄×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

122

C₄×C₇₉

#423

yes

characteristic

123

C₄×C₇₉

#431

yes

characteristic

124

Dic₇₉

—

125

Dic₇₉

—

126

#12788

—

maximal, Sylow

127

C₂×C₇₉

—

128

C₂×C₇₉

—

129

C₂×C₇₉

#1797

yes

characteristic

130

C₂×C₇₉

C₂×#364

yes

—

131

D₇₉

—

132

C₂²×C₄×C₈

—

133

C₂×#364

—

134

#2112

—

135

#1376

—

136

#1376

D₇₉

yes

characteristic, complemented

137

C₇₉

#12788

yes

characteristic, complemented, Sylow

138

C₂³×C₈

—

139

C₂³×C₈

—

140

C₂²×C₄²

—

141

C₂×M₃₂

—

142

C₂×M₃₂

C₂×D₇₉

yes

—

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

—

145

C₂×C₄×C₈

—

146

C₂×C₄×C₈

—

158

—

147

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

148

#364

—

158

—

149

C₂²⋊C₁₆

—

158

—

150

C₂³×C₄

—

151

C₂³×C₄

—

158

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

—

158

C₂²×C₈

—

158

—

159

C₂²×C₈

—

158

—

160

C₂²×C₈

—

158

—

161

C₂²×C₈

C₄×D₇₉

yes

characteristic

162

C₂²×C₈

C₂²×D₇₉

yes

characteristic

163

C₂×C₄²

—

164

C₂×C₄²

—

158

—

165

C₂×C₄²

—

158

—

166

C₂×C₄²

—

158

—

167

C₂×C₄²

C₄×D₇₉

yes

characteristic

168

M₃₂

—

169

M₃₂

—

170

M₃₂

—

158

—

171

M₃₂

—

158

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

158

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

158

—

177

C₄×C₈

—

158

—

178

C₂⁴

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

158

—

184

C₂²×C₄

—

158

—

185

C₂²×C₄

—

158

—

186

C₂²×C₄

—

158

—

187

C₂²×C₄

—

158

—

188

C₂²×C₄

—

158

—

189

C₂²×C₄

—

158

—

190

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

158

—

198

C₂×C₈

—

158

—

199

C₂×C₈

—

158

—

200

C₂×C₈

—

158

—

201

C₂×C₈

—

158

—

202

C₂×C₈

C₈×D₇₉

yes

—

203

C₂×C₈

D₄×D₇₉

yes

—

204

C₂×C₈

D₄×D₇₉

yes

characteristic

205

C₂×C₈

Q₈×D₇₉

yes

characteristic

206

C₂×C₈

#11929624

yes

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

158

—

210

C₄²

—

158

—

211

C₄²

#11929607

yes

—

212

C₁₆

—

213

C₁₆

—

316

—

214

C₂³

—

215

C₂³

—

158

—

216

C₂³

—

158

—

217

C₂³

—

158

—

218

C₂³

M₁₆×D₇₉

yes

characteristic

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

158

—

223

C₂×C₄

—

158

—

224

C₂×C₄

—

158

—

225

C₂×C₄

—

158

—

226

C₂×C₄

—

158

—

227

C₂×C₄

—

158

—

228

C₂×C₄

—

158

—

229

C₂×C₄

—

158

—

230

C₂×C₄

—

158

—

231

C₂×C₄

C₂²⋊C₄×D₇₉

yes

characteristic

232

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

233

C₂×C₄

#14579118

yes

characteristic

234

C₂×C₄

C₂×C₈×D₇₉

yes

characteristic

235

C₂×C₄

M₁₆×D₇₉

yes

characteristic

236

C₂×C₄

C₂×#11929607

yes

characteristic

237

C₈

—

238

C₈

—

239

C₈

—

158

—

240

C₈

#14579134

yes

—

241

C₈

#14579139

yes

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

158

—

245

C₂²

—

158

—

246

C₂²

—

158

—

247

C₂²

—

158

—

248

C₂²

#19098525

yes

characteristic

249

C₂²

C₄⋊C₈×D₇₉

yes

characteristic

250

C₂²

#19098618

yes

characteristic

251

C₄

—

252

C₄

—

158

—

253

C₄

—

158

—

254

C₄

#19098422

yes

characteristic

255

C₄

C₂²⋊C₈×D₇₉

yes

characteristic

256

C₄

#19098585

yes

characteristic

257

C₄

#19098614

yes

characteristic

258

C₂

—

259

C₂

—

260

C₂

—

158

—

261

C₂

#23763379

yes

characteristic

262

C₂

#364×D₇₉

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	#12788
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
118. C₂×D₇₉	#364	semidirect
136. #1376	D₇₉	semidirect
137. C₇₉	#12788	semidirect

H ≅ G/N

type

2. C₂×#19098383

C₂

semidirect

4. #23761482

C₂

semidirect

5. C₇₉×#1376

C₂

semidirect

118. C₂×D₇₉

#364

semidirect

136. #1376

D₇₉

semidirect

137. C₇₉

#12788

semidirect

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

subgroup	index
C₂×C₄×C₈×D₇₉	2
C₂×#19098383	2
#23765010	2
#23761482	2
C₇₉×#1376	2
#12788	79

subgroup

index

C₂×C₄×C₈×D₇₉

C₇₉×#1376

Subgroups — #34204210

Conjugacy classes of subgroups

Complements

Maximal subgroups