Group #34205153 — subgroups

Subgroups — #34205153

Order 20224.

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

normal subgroups only

This group has 488 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	#23772092	C₂	1	1	yes	maximal, characteristic
2	#23765021	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765010	C₂	1	2	yes	maximal, complemented
4	#23761485	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
7	#19099070	C₄	1	1	yes	characteristic
8	C₂×#14579101	C₂²	1	2	yes	—
9	#19098632	—	2	2	no	—
10	C₈×C₂²⋊D₇₉	—	2	2	no	—
11	#19098591	C₄	1	1	yes	characteristic
12	#19098530	C₄	1	1	yes	characteristic
13	#19098526	C₄	1	1	yes	characteristic
14	#19098518	C₂²	1	1	yes	characteristic
15	#19098345	—	2	2	no	—
16	(C₂×D₇₉)⋊C₁₆	—	2	4	no	—
17	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
18	#504×C₇₉	—	2	4	no	—
19	C₂×M₃₂×C₇₉	—	2	2	no	—
20	C₂×M₃₂×C₇₉	C₂²	1	2	yes	—
21	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#11929608	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₇₉	—	2	1	no	—
25	C₂×C₈×D₇₉	—	2	1	no	—
26	C₂×C₈×D₇₉	—	2	2	no	—
27	C₂×C₈×D₇₉	—	2	2	no	—
28	#14579142	C₈	1	2	yes	—
29	#14579137	—	2	1	no	—
30	#14579132	—	2	1	no	—
31	#14579129	C₈	1	2	yes	—
32	C₄×C₂²⋊D₇₉	—	2	2	no	—
33	#14579120	C₂×C₄	1	1	yes	characteristic
34	#14579101	—	2	2	no	—
35	#14579101	—	2	2	no	—
36	C₂×C₇₉⋊C₁₆	—	2	2	no	—
37	Dic₇₉⋊C₈	—	2	2	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
39	(C₂×D₇₉)⋊C₈	—	2	2	no	—
40	#14579071	—	2	1	no	—
41	C₈×Dic₇₉	—	2	1	no	—
42	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
43	#131×C₇₉	—	2	2	no	—
44	#131×C₇₉	—	2	2	no	—
45	C₂×M₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₇₉	D₄	1	2	yes	—
47	C₂²×C₈×C₇₉	D₄	1	2	yes	—
48	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
49	M₃₂×C₇₉	—	2	4	no	—
50	M₃₂×C₇₉	—	2	2	no	—
51	M₃₂×C₇₉	—	2	2	no	—
52	C₂×C₁₆×C₇₉	—	2	4	no	—
53	C₂×C₁₆×C₇₉	D₄	1	4	yes	complemented
54	C₂³×D₇₉	C₂×C₈	1	1	yes	characteristic
55	C₂×C₂²⋊D₇₉	—	2	2	no	—
56	C₂²×Dic₇₉	C₂×C₈	1	1	yes	characteristic
57	C₂×C₄×D₇₉	—	2	1	no	—
58	C₂×C₄×D₇₉	—	2	2	no	—
59	C₂×C₄×D₇₉	—	2	1	no	—
60	C₂×C₄×D₇₉	—	2	2	no	—
61	#11929608	—	2	2	no	—
62	C₂×C₇₉⋊C₈	—	2	1	no	—
63	C₂×C₇₉⋊C₈	—	2	1	no	—
64	C₂×C₇₉⋊C₈	—	2	2	no	—
65	C₈×D₇₉	—	4	1	no	—
66	C₈×D₇₉	—	4	2	no	—
67	C₈×D₇₉	—	4	1	no	—
68	C₄⋊Dic₇₉	—	2	1	no	—
69	Dic₇₉⋊C₄	—	2	2	no	—
70	C₂²⋊Dic₇₉	—	2	2	no	—
71	C₂²⋊Dic₇₉	C₂×C₈	1	2	yes	—
72	(C₂×D₇₉)⋊C₄	—	2	2	no	—
73	C₄×Dic₇₉	—	2	1	no	—
74	C₇₉⋊C₁₆	—	4	2	no	—
75	#41×C₇₉	—	2	2	no	—
76	#41×C₇₉	—	2	2	no	—
77	C₂×Q₈×C₇₉	M₁₆	1	1	yes	characteristic
78	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
79	C₂×D₄×C₇₉	M₁₆	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
82	M₁₆×C₇₉	—	2	4	no	—
83	M₁₆×C₇₉	—	2	2	no	—
84	C₂×C₈×C₇₉	—	2	2	no	—
85	C₂×C₈×C₇₉	—	2	2	no	—
86	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
87	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₇₉	#41	1	2	yes	—
91	C₁₆×C₇₉	—	2	4	no	—
92	C₂³×C₇₉	C₂²⋊C₈	1	2	yes	—
93	C₂³×C₇₉	C₂²×C₈	1	1	yes	characteristic
94	C₂²×D₇₉	—	2	1	no	—
95	C₂²×D₇₉	—	2	2	no	—
96	C₂²×D₇₉	—	4	2	no	—
97	Q₈×C₇₉	—	2	2	no	—
98	D₄×C₇₉	—	2	4	no	—
99	D₄×C₇₉	—	2	2	no	—
100	C₂×C₄×C₇₉	—	2	2	no	—
101	C₂×C₄×C₇₉	—	2	2	no	—
102	C₂×C₄×C₇₉	C₂²⋊C₈	1	2	yes	—
103	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₇₉	#131	1	2	yes	—
107	C₂²⋊D₇₉	—	4	4	no	—
108	C₂×Dic₇₉	—	2	2	no	—
109	C₂×Dic₇₉	—	2	1	no	—
110	C₂×Dic₇₉	—	2	2	no	—
111	C₄×D₇₉	—	4	1	no	—
112	C₄×D₇₉	—	4	1	no	—
113	C₄×D₇₉	—	4	2	no	—
114	C₈×C₇₉	—	2	2	no	—
115	C₈×C₇₉	#120	1	1	yes	characteristic
116	C₈×C₇₉	#121	1	2	yes	—
117	C₈×C₇₉	#123	1	1	yes	characteristic
118	C₇₉⋊C₈	—	4	1	no	—
119	C₇₉⋊C₈	—	4	1	no	—
120	C₂²×C₇₉	—	2	2	no	—
121	C₂²×C₇₉	—	4	1	no	—
122	C₂²×C₇₉	—	4	2	no	—
123	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
124	C₂²×C₇₉	C₈×D₄	1	2	yes	—
125	C₂×D₇₉	—	2	2	no	—
126	C₂×D₇₉	—	2	4	no	—
127	C₂×D₇₉	—	4	1	no	—
128	C₂×D₇₉	—	4	2	no	—
129	C₂×D₇₉	—	4	1	no	—
130	C₄×C₇₉	—	2	2	no	—
131	C₄×C₇₉	#386	1	1	yes	characteristic
132	C₄×C₇₉	#408	1	1	yes	characteristic
133	C₄×C₇₉	#435	1	2	yes	—
134	Dic₇₉	—	4	2	no	—
135	Dic₇₉	—	4	1	no	—
136	#12981	—	79	1	no	maximal, Sylow
137	C₂×C₇₉	—	2	1	no	—
138	C₂×C₇₉	—	2	2	no	—
139	C₂×C₇₉	—	4	2	no	—
140	C₂×C₇₉	#1869	1	1	yes	characteristic
141	D₇₉	—	4	2	no	—
142	#3407	D₇₉	1	1	yes	characteristic, complemented
143	#2929	—	79	1	no	—
144	#2115	—	79	1	no	—
145	#2112	—	79	2	no	—
146	#1378	—	79	2	no	—
147	C₇₉	#12981	1	1	yes	characteristic, complemented, Sylow
148	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
149	C₂³×C₈	—	79	1	no	—
150	#525	—	79	1	no	—
151	#504	—	2	4	no	—
152	C₂×M₃₂	—	2	2	no	—
153	C₂×M₃₂	—	79	2	no	—
154	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
155	#435	—	158	2	no	—
156	C₈×D₄	—	158	2	no	—
157	#424	—	79	1	no	—
158	#408	—	79	1	no	—
159	#407	—	79	1	no	—
160	#405	—	79	1	no	—
161	#349	—	158	2	no	—
162	C₂²⋊C₁₆	—	158	4	no	—
163	C₂×#41	C₄×D₇₉	1	1	yes	characteristic
164	C₂³×C₄	—	79	1	no	—
165	#131	—	2	2	no	—
166	#131	—	2	2	no	—
167	C₂×M₁₆	—	79	1	no	—
168	C₂×M₁₆	C₄×D₇₉	1	1	yes	characteristic
169	C₂×M₁₆	D₃₁₆	1	2	yes	—
170	C₂²×C₈	—	79	1	no	—
171	C₂²×C₈	—	158	2	no	—
172	C₂²×C₈	—	158	1	no	—
173	C₂²×C₈	—	158	1	no	—
174	C₂²×C₈	—	158	2	no	—
175	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
176	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
177	#123	—	79	2	no	—
178	C₂²⋊Q₈	—	158	1	no	—
179	#121	—	158	1	no	—
180	#120	—	79	2	no	—
181	C₄×D₄	—	158	2	no	—
182	#117	—	79	1	no	—
183	M₃₂	—	2	4	no	—
184	M₃₂	—	2	2	no	—
185	M₃₂	—	2	2	no	—
186	M₃₂	—	158	2	no	—
187	M₃₂	—	158	2	no	—
188	C₂×C₁₆	—	2	4	no	—
189	C₂×C₁₆	—	158	2	no	—
190	C₂×C₁₆	C₂²⋊D₇₉	1	4	yes	complemented
191	C₄⋊C₈	—	158	2	no	—
192	C₂²⋊C₈	—	158	2	no	—
193	C₂²⋊C₈	—	158	2	no	—
194	#97	—	158	1	no	—
195	C₄×C₈	—	158	1	no	—
196	C₂⁴	—	79	1	no	—
197	#41	—	2	2	no	—
198	#41	—	2	2	no	—
199	C₂×Q₈	#11929607	1	1	yes	characteristic
200	C₂×D₄	—	158	2	no	—
201	C₂×D₄	C₈×D₇₉	1	2	yes	—
202	C₂×D₄	#11929607	1	1	yes	characteristic
203	C₂²×C₄	—	79	1	no	—
204	C₂²×C₄	—	158	1	no	—
205	C₂²×C₄	—	158	2	no	—
206	C₂²×C₄	—	158	1	no	—
207	C₂²×C₄	—	158	2	no	—
208	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
209	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
210	M₁₆	—	2	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	158	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	316	1	no	—
216	C₂×C₈	—	316	2	no	—
217	C₂×C₈	—	316	1	no	—
218	C₂×C₈	—	158	1	no	—
219	C₂×C₈	—	158	1	no	—
220	C₂×C₈	—	158	2	no	—
221	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
222	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
223	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
224	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
225	C₂×C₈	#11929624	1	2	yes	—
226	C₄⋊C₄	—	158	2	no	—
227	C₄⋊C₄	—	158	1	no	—
228	C₂²⋊C₄	—	79	2	no	—
229	C₂²⋊C₄	—	158	2	no	—
230	C₂²⋊C₄	—	158	2	no	—
231	C₄²	—	158	1	no	—
232	C₁₆	—	2	4	no	—
233	C₁₆	—	316	2	no	—
234	C₂³	—	316	2	no	—
235	C₂³	—	158	2	no	—
236	C₂³	—	158	1	no	—
237	C₂³	(C₂×D₇₉)⋊C₈	1	2	yes	—
238	C₂³	C₂×C₈×D₇₉	1	1	yes	characteristic
239	Q₈	—	2	2	no	—
240	D₄	—	2	4	no	—
241	D₄	—	2	2	no	—
242	D₄	—	316	4	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	316	2	no	—
246	C₂×C₄	—	316	1	no	—
247	C₂×C₄	—	316	1	no	—
248	C₂×C₄	—	158	2	no	—
249	C₂×C₄	—	158	2	no	—
250	C₂×C₄	—	158	1	no	—
251	C₂×C₄	(C₂×D₇₉)⋊C₈	1	2	yes	—
252	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
253	C₂×C₄	C₄×C₂²⋊D₇₉	1	2	yes	—
254	C₂×C₄	C₂×#11929607	1	1	yes	characteristic
255	C₂×C₄	#14579167	1	2	yes	—
256	C₈	—	2	2	no	—
257	C₈	—	316	1	no	—
258	C₈	—	316	1	no	—
259	C₈	#14579130	1	1	yes	characteristic
260	C₈	#14579135	1	2	yes	—
261	C₈	#14579144	1	1	yes	characteristic
262	C₂²	—	2	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	316	1	no	—
266	C₂²	—	316	2	no	—
267	C₂²	—	316	1	no	—
268	C₂²	—	158	2	no	—
269	C₂²	—	158	4	no	—
270	C₂²	C₂×(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
271	C₂²	C₈×C₂²⋊D₇₉	1	2	yes	—
272	C₄	—	2	2	no	—
273	C₄	—	316	2	no	—
274	C₄	—	316	1	no	—
275	C₄	#19098442	1	1	yes	characteristic
276	C₄	#19098529	1	1	yes	characteristic
277	C₄	#19098634	1	2	yes	—
278	C₂	—	2	1	no	—
279	C₂	—	2	2	no	—
280	C₂	—	4	2	no	—
281	C₂	—	316	2	no	—
282	C₂	#23763692	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772092

C₂

yes

maximal, characteristic

#23765021

C₂

yes

maximal, characteristic, complemented

#23765010

C₂

yes

maximal, complemented

#23761485

C₂

yes

maximal, complemented

C₇₉×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₇₉

C₂²

yes

characteristic

#19099070

C₄

yes

characteristic

C₂×#14579101

C₂²

yes

—

#19098632

—

C₈×C₂²⋊D₇₉

—

#19098591

C₄

yes

characteristic

#19098530

C₄

yes

characteristic

#19098526

C₄

yes

characteristic

#19098518

C₂²

yes

characteristic

#19098345

—

(C₂×D₇₉)⋊C₁₆

—

C₂×#131×C₇₉

C₂²

yes

characteristic

#504×C₇₉

—

C₂×M₃₂×C₇₉

—

C₂×M₃₂×C₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂×C₄

yes

characteristic

C₂×#11929608

C₂×C₄

yes

characteristic

C₂²×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

C₂×C₈×D₇₉

—

#14579142

C₈

yes

—

#14579137

—

#14579132

—

#14579129

C₈

yes

—

C₄×C₂²⋊D₇₉

—

#14579120

C₂×C₄

yes

characteristic

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

—

Dic₇₉⋊C₈

—

C₂²⋊(C₇₉⋊C₈)

—

(C₂×D₇₉)⋊C₈

—

#14579071

—

C₈×Dic₇₉

—

C₂×#41×C₇₉

C₂×C₄

yes

characteristic

#131×C₇₉

—

#131×C₇₉

—

C₂×M₁₆×C₇₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

C₂³

yes

characteristic

M₃₂×C₇₉

—

M₃₂×C₇₉

—

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

complemented

C₂³×D₇₉

C₂×C₈

yes

characteristic

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

C₂×C₈

yes

characteristic

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₈×D₇₉

—

C₈×D₇₉

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

C₂×C₈

yes

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

M₁₆

yes

characteristic

C₂×D₄×C₇₉

C₂×C₈

yes

—

C₂×D₄×C₇₉

M₁₆

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

#41

yes

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂²⋊C₈

yes

—

C₂³×C₇₉

C₂²×C₈

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

C₂²⋊C₈

yes

—

103

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₇₉

C₄×D₄

yes

—

105

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₇₉

#131

yes

—

107

C₂²⋊D₇₉

—

108

C₂×Dic₇₉

—

109

C₂×Dic₇₉

—

110

C₂×Dic₇₉

—

111

C₄×D₇₉

—

112

C₄×D₇₉

—

113

C₄×D₇₉

—

114

C₈×C₇₉

—

115

C₈×C₇₉

#120

yes

characteristic

116

C₈×C₇₉

#121

yes

—

117

C₈×C₇₉

#123

yes

characteristic

118

C₇₉⋊C₈

—

119

C₇₉⋊C₈

—

120

C₂²×C₇₉

—

121

C₂²×C₇₉

—

122

C₂²×C₇₉

—

123

C₂²×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

124

C₂²×C₇₉

C₈×D₄

yes

—

125

C₂×D₇₉

—

126

C₂×D₇₉

—

127

C₂×D₇₉

—

128

C₂×D₇₉

—

129

C₂×D₇₉

—

130

C₄×C₇₉

—

131

C₄×C₇₉

#386

yes

characteristic

132

C₄×C₇₉

#408

yes

characteristic

133

C₄×C₇₉

#435

yes

—

134

Dic₇₉

—

135

Dic₇₉

—

136

#12981

—

maximal, Sylow

137

C₂×C₇₉

—

138

C₂×C₇₉

—

139

C₂×C₇₉

—

140

C₂×C₇₉

#1869

yes

characteristic

141

D₇₉

—

142

#3407

D₇₉

yes

characteristic, complemented

143

#2929

—

144

#2115

—

145

#2112

—

146

#1378

—

147

C₇₉

#12981

yes

characteristic, complemented, Sylow

148

C₂×#131

C₂×D₇₉

yes

characteristic

149

C₂³×C₈

—

150

#525

—

151

#504

—

152

C₂×M₃₂

—

153

C₂×M₃₂

—

154

C₂×M₃₂

C₂×D₇₉

yes

—

155

#435

—

158

—

156

C₈×D₄

—

158

—

157

#424

—

158

#408

—

159

#407

—

160

#405

—

161

#349

—

158

—

162

C₂²⋊C₁₆

—

158

—

163

C₂×#41

C₄×D₇₉

yes

characteristic

164

C₂³×C₄

—

165

#131

—

166

#131

—

167

C₂×M₁₆

—

168

C₂×M₁₆

C₄×D₇₉

yes

characteristic

169

C₂×M₁₆

D₃₁₆

yes

—

170

C₂²×C₈

—

171

C₂²×C₈

—

158

—

172

C₂²×C₈

—

158

—

173

C₂²×C₈

—

158

—

174

C₂²×C₈

—

158

—

175

C₂²×C₈

C₂²⋊D₇₉

yes

—

176

C₂²×C₈

C₂²×D₇₉

yes

characteristic

177

#123

—

178

C₂²⋊Q₈

—

158

—

179

#121

—

158

—

180

#120

—

181

C₄×D₄

—

158

—

182

#117

—

183

M₃₂

—

184

M₃₂

—

185

M₃₂

—

186

M₃₂

—

158

—

187

M₃₂

—

158

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

158

—

190

C₂×C₁₆

C₂²⋊D₇₉

yes

complemented

191

C₄⋊C₈

—

158

—

192

C₂²⋊C₈

—

158

—

193

C₂²⋊C₈

—

158

—

194

#97

—

158

—

195

C₄×C₈

—

158

—

196

C₂⁴

—

197

#41

—

198

#41

—

199

C₂×Q₈

#11929607

yes

characteristic

200

C₂×D₄

—

158

—

201

C₂×D₄

C₈×D₇₉

yes

—

202

C₂×D₄

#11929607

yes

characteristic

203

C₂²×C₄

—

204

C₂²×C₄

—

158

—

205

C₂²×C₄

—

158

—

206

C₂²×C₄

—

158

—

207

C₂²×C₄

—

158

—

208

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

—

209

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

210

M₁₆

—

211

M₁₆

—

212

M₁₆

—

158

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

316

—

216

C₂×C₈

—

316

—

217

C₂×C₈

—

316

—

218

C₂×C₈

—

158

—

219

C₂×C₈

—

158

—

220

C₂×C₈

—

158

—

221

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

222

C₂×C₈

C₂×C₂²⋊D₇₉

yes

—

223

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

224

C₂×C₈

C₂×D₃₁₆

yes

characteristic

225

C₂×C₈

#11929624

yes

—

226

C₄⋊C₄

—

158

—

227

C₄⋊C₄

—

158

—

228

C₂²⋊C₄

—

229

C₂²⋊C₄

—

158

—

230

C₂²⋊C₄

—

158

—

231

C₄²

—

158

—

232

C₁₆

—

233

C₁₆

—

316

—

234

C₂³

—

316

—

235

C₂³

—

158

—

236

C₂³

—

158

—

237

C₂³

(C₂×D₇₉)⋊C₈

yes

—

238

C₂³

C₂×C₈×D₇₉

yes

characteristic

239

Q₈

—

240

D₄

—

241

D₄

—

242

D₄

—

316

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

316

—

246

C₂×C₄

—

316

—

247

C₂×C₄

—

316

—

248

C₂×C₄

—

158

—

249

C₂×C₄

—

158

—

250

C₂×C₄

—

158

—

251

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

—

252

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

253

C₂×C₄

C₄×C₂²⋊D₇₉

yes

—

254

C₂×C₄

C₂×#11929607

yes

characteristic

255

C₂×C₄

#14579167

yes

—

256

C₈

—

257

C₈

—

316

—

258

C₈

—

316

—

259

C₈

#14579130

yes

characteristic

260

C₈

#14579135

yes

—

261

C₈

#14579144

yes

characteristic

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

316

—

266

C₂²

—

316

—

267

C₂²

—

316

—

268

C₂²

—

158

—

269

C₂²

—

158

—

270

C₂²

C₂×(C₂×D₇₉)⋊C₈

yes

characteristic

271

C₂²

C₈×C₂²⋊D₇₉

yes

—

272

C₄

—

273

C₄

—

316

—

274

C₄

—

316

—

275

C₄

#19098442

yes

characteristic

276

C₄

#19098529

yes

characteristic

277

C₄

#19098634

yes

—

278

C₂

—

279

C₂

—

280

C₂

—

281

C₂

—

316

—

282

C₂

#23763692

yes

characteristic

	subgroup	G/H
center	C₈	#14579130
commutator	C₂³×C₇₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#3407	C₂
socle	C₂×C₇₉	#1869
prime radical	#19099070	C₄
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#3407	D₇₉
hypocenter	C₇₉	#12981
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

subgroup

G/H

center

C₈

#14579130

commutator

C₂³×C₇₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#3407

C₂

C₂×C₇₉

C₄

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

N	H ≅ G/N	type
2. #23765021	C₂	semidirect
3. #23765010	C₂	semidirect
4. #23761485	C₂	semidirect
5. C₇₉×#3407	C₂	semidirect
53. C₂×C₁₆×C₇₉	D₄	semidirect
142. #3407	D₇₉	semidirect
147. C₇₉	#12981	semidirect
190. C₂×C₁₆	C₂²⋊D₇₉	semidirect

H ≅ G/N

type

2. #23765021

C₂

semidirect

3. #23765010

C₂

semidirect

4. #23761485

C₂

semidirect

5. C₇₉×#3407

C₂

semidirect

53. C₂×C₁₆×C₇₉

D₄

semidirect

142. #3407

D₇₉

semidirect

147. C₇₉

#12981

semidirect

190. C₂×C₁₆

C₂²⋊D₇₉

semidirect

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

subgroup	index
#23772092	2
#23765021	2
#23765010	2
#23761485	2
C₇₉×#3407	2
#12981	79

subgroup

index

C₇₉×#3407

Subgroups — #34205153

Conjugacy classes of subgroups

Complements

Maximal subgroups