Subgroups — #1706×D₇₉ #34275908

Order 20224.

1046 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#493×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#492×D₇₉	C₂	1	2	yes	maximal, complemented
4	#486×D₇₉	C₂	1	2	yes	maximal, complemented
5	#23762993	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762992	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762991	C₂	1	2	yes	maximal, complemented
8	#23762990	C₂	1	2	yes	maximal, complemented
9	#23762989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈²×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₇₉	—	2	4	no	—
13	C₂×D₈×D₇₉	—	2	2	no	—
14	C₄⋊Q₈×D₇₉	C₂²	1	2	yes	—
15	#127×D₇₉	C₂²	1	2	yes	—
16	#19098968	C₂²	1	1	yes	characteristic, complemented
17	#19098967	—	2	2	no	—
18	#19098966	C₂²	1	2	yes	complemented
19	#19098940	C₂²	1	1	yes	characteristic
20	#19098939	C₂²	1	2	yes	—
21	#19098938	—	2	2	no	—
22	#19098937	C₂²	1	2	yes	complemented
23	#19098936	C₂²	1	2	yes	complemented
24	#19098935	C₂²	1	2	yes	complemented
25	#19098934	—	2	4	no	—
26	#19098911	C₂²	1	2	yes	complemented
27	#19098910	C₂²	1	2	yes	complemented
28	#19098909	C₂²	1	2	yes	complemented
29	#19098908	—	2	4	no	—
30	#107×D₇₉	—	2	2	no	—
31	#102×D₇₉	—	2	4	no	—
32	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
35	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#493×C₇₉	C₂²	1	1	yes	characteristic
40	#492×C₇₉	C₂²	1	2	yes	complemented
41	#486×C₇₉	C₂²	1	2	yes	complemented
42	C₈²×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×Q₈×D₇₉	—	2	2	no	—
44	C₂×D₄×D₇₉	—	2	2	no	—
45	C₂×D₄×D₇₉	—	2	2	no	—
46	C₂×D₄×D₇₉	—	2	2	no	—
47	C₂×#11929613	—	2	4	no	—
48	C₂×#11929612	—	2	4	no	—
49	C₂×#11929611	—	2	4	no	—
50	SD₁₆×D₇₉	—	4	16	no	—
51	C₂×D₆₃₂	—	2	2	no	—
52	C₂×#11929609	—	2	4	no	—
53	D₈×D₇₉	—	4	8	no	—
54	C₂×C₈×D₇₉	D₄	1	2	yes	—
55	C₂×C₈×D₇₉	D₄	1	2	yes	—
56	C₂×C₈×D₇₉	D₄	1	2	yes	—
57	#14579161	C₂³	1	2	yes	—
58	#14579160	—	2	2	no	—
59	#14579160	—	2	2	no	—
60	#14579159	—	2	2	no	—
61	#14579158	C₂³	1	2	yes	—
62	#14579157	—	2	2	no	—
63	#14579157	—	2	2	no	—
64	#14579157	—	2	2	no	—
65	C₄⋊C₄×D₇₉	—	2	2	no	—
66	C₄⋊C₄×D₇₉	—	2	2	no	—
67	C₄²×D₇₉	C₂³	1	1	yes	characteristic
68	#14579095	—	2	2	no	—
69	#14579094	—	2	4	no	—
70	#14579083	—	2	4	no	—
71	#14579082	—	2	4	no	—
72	#14579081	—	2	4	no	—
73	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₈×Dic₇₉	D₄	1	2	yes	—
77	C₈×Dic₇₉	D₄	1	2	yes	—
78	C₈×Dic₇₉	D₄	1	2	yes	—
79	C₂×SD₁₆×C₇₉	—	2	4	no	—
80	C₂×D₈×C₇₉	—	2	2	no	—
81	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
82	#127×C₇₉	C₂³	1	2	yes	—
83	#107×C₇₉	—	2	2	no	—
84	#102×C₇₉	—	2	4	no	—
85	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂³×D₇₉	—	4	2	no	—
89	C₂×Dic₁₅₈	—	2	2	no	—
90	C₂×Dic₁₅₈	—	4	2	no	—
91	Q₈×D₇₉	—	4	8	no	—
92	C₂×D₃₁₆	—	2	2	no	—
93	C₂×D₃₁₆	—	2	2	no	—
94	C₂×D₃₁₆	—	2	2	no	—
95	C₂×C₂²⋊D₇₉	—	4	2	no	—
96	C₂×C₂²⋊D₇₉	—	4	2	no	—
97	C₂×C₂²⋊D₇₉	—	4	2	no	—
98	D₄×D₇₉	—	4	8	no	—
99	D₄×D₇₉	—	4	8	no	—
100	D₄×D₇₉	—	4	8	no	—
101	C₂×C₄×D₇₉	—	4	2	no	—
102	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
105	#11929613	—	4	8	no	—
106	#11929612	—	4	8	no	—
107	#11929611	—	4	8	no	—
108	D₆₃₂	—	4	4	no	—
109	#11929609	—	4	8	no	—
110	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
111	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
112	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
113	C₈×D₇₉	—	2	4	no	—
114	C₈×D₇₉	D₈	1	8	yes	complemented
115	C₈×D₇₉	SD₁₆	1	8	yes	complemented
116	C₄⋊Dic₇₉	—	2	2	no	—
117	C₄⋊Dic₇₉	—	2	2	no	—
118	Dic₇₉⋊C₄	—	4	2	no	—
119	Dic₇₉⋊C₄	—	4	2	no	—
120	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	SD₁₆×C₇₉	—	4	8	no	—
128	D₈×C₇₉	—	4	4	no	—
129	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₇₉	—	2	2	no	—
133	C₄⋊C₄×C₇₉	—	2	2	no	—
134	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
135	C₂³×C₇₉	—	4	2	no	—
136	C₂²×D₇₉	—	4	2	no	—
137	C₂²×D₇₉	—	8	4	no	—
138	C₂²×D₇₉	—	8	4	no	—
139	C₂²×D₇₉	—	8	4	no	—
140	C₂²×D₇₉	#127	1	1	yes	characteristic
141	Q₈×C₇₉	—	4	4	no	—
142	D₄×C₇₉	—	4	4	no	—
143	D₄×C₇₉	—	4	4	no	—
144	D₄×C₇₉	—	4	4	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₇₉	—	8	4	no	—
150	C₂²⋊D₇₉	—	8	4	no	—
151	C₂²⋊D₇₉	—	8	4	no	—
152	C₂×Dic₇₉	—	4	2	no	—
153	C₂×Dic₇₉	#127	1	1	yes	characteristic
154	C₂×Dic₇₉	#127	1	1	yes	characteristic
155	C₂×Dic₇₉	#127	1	1	yes	characteristic
156	D₃₁₆	—	4	4	no	—
157	D₃₁₆	—	4	4	no	—
158	D₃₁₆	—	4	4	no	—
159	C₄×D₇₉	—	8	4	no	—
160	C₄×D₇₉	C₂×D₈	1	4	yes	—
161	C₄×D₇₉	C₂×SD₁₆	1	4	yes	—
162	C₄×D₇₉	#135	1	4	yes	—
163	Dic₁₅₈	—	4	4	no	—
164	Dic₁₅₈	—	8	4	no	—
165	C₈×C₇₉	—	2	2	no	—
166	C₈×C₇₉	C₂×D₈	1	4	yes	complemented
167	C₈×C₇₉	C₂×SD₁₆	1	4	yes	complemented
168	C₇₉⋊C₈	—	2	2	no	—
169	C₇₉⋊C₈	C₂×D₈	1	4	yes	complemented
170	C₇₉⋊C₈	C₂×SD₁₆	1	4	yes	complemented
171	C₂²×C₇₉	—	8	2	no	—
172	C₂²×C₇₉	—	8	2	no	—
173	C₂²×C₇₉	—	8	2	no	—
174	C₂²×C₇₉	C₂×#127	1	1	yes	characteristic
175	C₂×D₇₉	—	8	2	no	—
176	C₂×D₇₉	—	8	2	no	—
177	C₂×D₇₉	—	8	2	no	—
178	C₂×D₇₉	—	16	8	no	—
179	C₂×D₇₉	#492	1	2	yes	—
180	C₂×D₇₉	#493	1	2	yes	—
181	C₂×D₇₉	#495	1	2	yes	—
182	C₄×C₇₉	—	8	2	no	—
183	C₄×C₇₉	C₂²×D₈	1	2	yes	—
184	C₄×C₇₉	C₂²×SD₁₆	1	2	yes	—
185	C₄×C₇₉	C₂×#135	1	2	yes	—
186	Dic₇₉	—	8	2	no	—
187	Dic₇₉	#492	1	2	yes	—
188	Dic₇₉	#493	1	2	yes	—
189	Dic₇₉	#495	1	2	yes	—
190	C₂×#1706	—	79	1	no	maximal, Sylow
191	C₂×C₇₉	—	16	2	no	—
192	C₂×C₇₉	C₂×#492	1	1	yes	characteristic
193	C₂×C₇₉	C₂×#493	1	1	yes	characteristic
194	C₂×C₇₉	C₂×#495	1	1	yes	characteristic
195	D₇₉	—	16	2	no	—
196	D₇₉	#1706	1	4	yes	direct product factor
197	C₂×#500	—	79	1	no	—
198	C₂×#493	—	79	1	no	—
199	C₂×#492	—	79	2	no	—
200	C₂×#486	—	79	2	no	—
201	#1706	—	79	1	no	—
202	#1706	—	79	1	no	—
203	#1706	—	79	2	no	—
204	#1706	—	79	2	no	—
205	#1706	—	79	1	no	—
206	#1706	D₇₉	1	1	yes	characteristic, direct product factor
207	C₂×C₈²	—	79	1	no	—
208	C₇₉	C₂×#1706	1	1	yes	characteristic, complemented, Sylow
209	C₂²×SD₁₆	—	158	4	no	—
210	C₂²×D₈	—	158	2	no	—
211	C₂×C₄⋊Q₈	—	79	2	no	—
212	C₂×#127	—	79	2	no	—
213	#500	—	79	2	no	—
214	#500	—	79	1	no	—
215	#500	—	158	2	no	—
216	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
217	#493	—	79	2	no	—
218	#493	—	79	1	no	—
219	#493	—	158	2	no	—
220	#493	C₂×D₇₉	1	1	yes	characteristic
221	#492	—	79	2	no	—
222	#492	—	79	2	no	—
223	#492	—	79	2	no	—
224	#492	—	158	4	no	—
225	#492	C₂×D₇₉	1	2	yes	complemented
226	#486	—	79	2	no	—
227	#486	—	79	2	no	—
228	#486	—	79	2	no	—
229	#486	—	158	4	no	—
230	#486	C₂×D₇₉	1	2	yes	complemented
231	C₂×#107	—	158	2	no	—
232	C₂×#102	—	158	4	no	—
233	C₂×C₄×C₈	—	79	1	no	—
234	C₂×C₄×C₈	—	79	1	no	—
235	C₂×C₄×C₈	—	79	1	no	—
236	C₈²	—	79	1	no	—
237	C₈²	—	79	1	no	—
238	C₈²	—	79	1	no	—
239	C₈²	C₂×D₇₉	1	1	yes	characteristic, complemented
240	C₂²×Q₈	—	158	2	no	—
241	C₂²×D₄	—	158	2	no	—
242	C₂²×D₄	—	158	2	no	—
243	C₂²×D₄	—	158	2	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	316	16	no	—
246	C₂×SD₁₆	—	158	4	no	—
247	C₂×SD₁₆	—	158	4	no	—
248	C₂×SD₁₆	—	158	4	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	316	8	no	—
251	C₂×D₈	—	158	4	no	—
252	C₂×D₈	—	158	2	no	—
253	C₂²×C₈	—	79	2	no	—
254	C₂²×C₈	—	79	2	no	—
255	C₂²×C₈	—	79	2	no	—
256	C₄⋊Q₈	—	79	2	no	—
257	C₄⋊Q₈	—	158	2	no	—
258	C₄⋊Q₈	—	158	2	no	—
259	C₄⋊Q₈	—	158	2	no	—
260	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
261	#127	—	79	2	no	—
262	#127	—	158	2	no	—
263	#127	—	158	2	no	—
264	#127	—	158	2	no	—
265	#127	C₂²×D₇₉	1	2	yes	—
266	C₂×C₄⋊C₄	—	158	2	no	—
267	C₂×C₄⋊C₄	—	158	2	no	—
268	C₂×C₄²	—	79	1	no	—
269	#107	—	2	2	no	—
270	#107	—	158	4	no	—
271	#107	—	158	2	no	—
272	#102	—	2	4	no	—
273	#102	—	158	4	no	—
274	#102	—	158	4	no	—
275	#102	—	158	4	no	—
276	C₄×C₈	—	79	2	no	—
277	C₄×C₈	—	79	2	no	—
278	C₄×C₈	—	79	2	no	—
279	C₄×C₈	—	79	1	no	—
280	C₄×C₈	—	79	1	no	—
281	C₄×C₈	—	79	1	no	—
282	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
285	C₂⁴	—	316	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	316	2	no	—
288	C₂×Q₈	—	316	8	no	—
289	C₂×Q₈	—	158	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	316	8	no	—
294	C₂×D₄	—	316	8	no	—
295	C₂×D₄	—	316	8	no	—
296	C₂×D₄	—	316	2	no	—
297	C₂×D₄	—	316	2	no	—
298	C₂×D₄	—	316	2	no	—
299	C₂×D₄	—	158	2	no	—
300	C₂×D₄	—	158	2	no	—
301	C₂×D₄	—	158	2	no	—
302	C₂²×C₄	—	316	2	no	—
303	C₂²×C₄	—	79	1	no	—
304	C₂²×C₄	—	79	1	no	—
305	C₂²×C₄	—	79	1	no	—
306	SD₁₆	—	4	8	no	—
307	SD₁₆	—	316	8	no	—
308	SD₁₆	—	316	8	no	—
309	SD₁₆	—	316	8	no	—
310	D₈	—	4	4	no	—
311	D₈	—	316	8	no	—
312	D₈	—	316	4	no	—
313	C₂×C₈	—	79	2	no	—
314	C₂×C₈	—	79	2	no	—
315	C₂×C₈	—	79	8	no	—
316	C₂×C₈	—	79	8	no	—
317	C₂×C₈	—	79	2	no	—
318	C₂×C₈	—	158	4	no	—
319	C₂×C₈	D₄×D₇₉	1	2	yes	—
320	C₂×C₈	D₄×D₇₉	1	2	yes	—
321	C₂×C₈	D₄×D₇₉	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	316	2	no	—
325	C₄⋊C₄	—	316	2	no	—
326	C₄⋊C₄	—	158	2	no	—
327	C₄⋊C₄	—	158	2	no	—
328	C₄²	—	79	1	no	—
329	C₄²	—	79	1	no	—
330	C₄²	—	79	1	no	—
331	C₄²	C₂³×D₇₉	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	316	2	no	—
334	C₂³	—	79	1	no	—
335	C₂³	—	632	4	no	—
336	C₂³	—	632	4	no	—
337	C₂³	—	632	4	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	316	4	no	—
340	Q₈	—	632	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	316	4	no	—
345	D₄	—	316	4	no	—
346	D₄	—	316	4	no	—
347	D₄	—	632	4	no	—
348	D₄	—	632	4	no	—
349	D₄	—	632	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	316	2	no	—
352	C₂×C₄	—	79	1	no	—
353	C₂×C₄	—	79	1	no	—
354	C₂×C₄	—	79	1	no	—
355	C₂×C₄	—	79	4	no	—
356	C₂×C₄	—	79	4	no	—
357	C₂×C₄	—	79	4	no	—
358	C₂×C₄	—	632	4	no	—
359	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
361	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	79	4	no	—
364	C₈	—	79	4	no	—
365	C₈	—	158	2	no	—
366	C₈	D₈×D₇₉	1	4	yes	complemented
367	C₈	SD₁₆×D₇₉	1	4	yes	complemented
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	79	2	no	—
372	C₂²	—	79	2	no	—
373	C₂²	—	79	2	no	—
374	C₂²	—	632	2	no	—
375	C₂²	—	632	2	no	—
376	C₂²	—	632	2	no	—
377	C₂²	—	1264	8	no	—
378	C₂²	#127×D₇₉	1	1	yes	characteristic
379	C₄	—	8	2	no	—
380	C₄	—	79	2	no	—
381	C₄	—	79	2	no	—
382	C₄	—	79	2	no	—
383	C₄	—	632	2	no	—
384	C₄	C₂×D₈×D₇₉	1	2	yes	—
385	C₄	C₂×SD₁₆×D₇₉	1	2	yes	—
386	C₄	#135×D₇₉	1	2	yes	—
387	C₂	—	16	2	no	—
388	C₂	—	79	4	no	—
389	C₂	—	1264	2	no	—
390	C₂	#492×D₇₉	1	1	yes	characteristic
391	C₂	#493×D₇₉	1	1	yes	characteristic
392	C₂	#495×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₇₉
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1706	C₂
socle	C₂²×C₇₉	C₂×#127
prime radical	#493×D₇₉	C₂
hypercenter	#1706	D₇₉
hypocenter	C₇₉	C₂×#1706
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1706

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #500×D₇₉	C₂	semidirect
3. #492×D₇₉	C₂	semidirect
4. #486×D₇₉	C₂	semidirect
5. #23762993	C₂	semidirect
6. #23762992	C₂	semidirect
7. #23762991	C₂	semidirect
8. #23762990	C₂	semidirect
9. #23762989	C₂	semidirect
10. C₈²×D₇₉	C₂	semidirect
11. C₇₉×#1706	C₂	semidirect
16. #19098968	C₂²	semidirect
18. #19098966	C₂²	semidirect
22. #19098937	C₂²	semidirect
23. #19098936	C₂²	semidirect
24. #19098935	C₂²	semidirect
26. #19098911	C₂²	semidirect
27. #19098910	C₂²	semidirect
28. #19098909	C₂²	semidirect
35. C₈×C₇₉⋊C₈	C₂²	semidirect
36. C₈×C₇₉⋊C₈	C₂²	semidirect
37. C₈×C₇₉⋊C₈	C₂²	semidirect
38. #500×C₇₉	C₂²	semidirect
40. #492×C₇₉	C₂²	semidirect
41. #486×C₇₉	C₂²	semidirect
42. C₈²×C₇₉	C₂²	semidirect
114. C₈×D₇₉	D₈	semidirect
115. C₈×D₇₉	SD₁₆	semidirect
166. C₈×C₇₉	C₂×D₈	semidirect
167. C₈×C₇₉	C₂×SD₁₆	semidirect
169. C₇₉⋊C₈	C₂×D₈	semidirect
170. C₇₉⋊C₈	C₂×SD₁₆	semidirect
196. D₇₉	#1706	direct (N × H)
206. #1706	D₇₉	direct (N × H)
208. C₇₉	C₂×#1706	semidirect
216. #500	C₂×D₇₉	semidirect
225. #492	C₂×D₇₉	semidirect
230. #486	C₂×D₇₉	semidirect
239. C₈²	C₂×D₇₉	semidirect
366. C₈	D₈×D₇₉	semidirect
367. C₈	SD₁₆×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₇₉	2
#493×D₇₉	2
#492×D₇₉	2
#486×D₇₉	2
#23762993	2
#23762992	2
#23762991	2
#23762990	2
#23762989	2
C₈²×D₇₉	2
C₇₉×#1706	2
C₂×#1706	79

Subgroups — #1706×D79 #34275908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1706×D₇₉ #34275908