Subgroups — C₇₉×#13013 #34124702

Order 20224.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SD₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#358×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#357×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#1970	C₂	1	1	yes	maximal, characteristic
6	C₇₉×#1380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
11	C₂×SD₃₂×C₇₉	—	2	2	no	—
12	C₂×SD₃₂×C₇₉	—	2	2	no	—
13	C₂×SD₃₂×C₇₉	C₄	1	4	yes	complemented
14	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₇₉	—	2	2	no	—
17	C₄×Q₁₆×C₇₉	—	2	2	no	—
18	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#103×C₇₉	—	2	1	no	—
21	C₂×#102×C₇₉	—	2	1	no	—
22	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	#390×C₇₉	—	2	1	no	—
24	#358×C₇₉	—	2	2	no	—
25	#357×C₇₉	—	2	2	no	—
26	C₂²×Q₈×C₇₉	—	2	1	no	—
27	C₂²×D₄×C₇₉	—	2	1	no	—
28	C₂×Q₁₆×C₇₉	—	2	1	no	—
29	C₂×Q₁₆×C₇₉	—	2	1	no	—
30	C₂×Q₁₆×C₇₉	—	2	1	no	—
31	C₂×Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
32	C₂×Q₁₆×C₇₉	D₄	1	2	yes	—
33	C₂×Q₁₆×C₇₉	D₄	1	2	yes	—
34	C₂×D₈×C₇₉	—	2	1	no	—
35	C₂×D₈×C₇₉	—	2	1	no	—
36	C₂×D₈×C₇₉	—	2	1	no	—
37	C₂×D₈×C₇₉	—	2	1	no	—
38	C₂×D₈×C₇₉	—	2	1	no	—
39	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₇₉	—	2	4	no	—
43	C₄×Q₈×C₇₉	—	4	2	no	—
44	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
47	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
48	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
49	C₂×C₄²×C₇₉	—	4	1	no	—
50	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
51	SD₃₂×C₇₉	—	2	8	no	—
52	C₂×C₁₆×C₇₉	—	2	1	no	—
53	C₂×C₁₆×C₇₉	—	2	1	no	—
54	C₂×C₁₆×C₇₉	—	2	1	no	—
55	C₂×C₁₆×C₇₉	—	2	1	no	—
56	C₂×C₁₆×C₇₉	—	2	1	no	—
57	C₂×C₁₆×C₇₉	C₂×C₄	1	2	yes	—
58	#107×C₇₉	—	2	1	no	—
59	#107×C₇₉	—	2	1	no	—
60	#107×C₇₉	—	2	1	no	—
61	#107×C₇₉	D₄	1	2	yes	—
62	#103×C₇₉	—	2	4	no	—
63	#102×C₇₉	—	4	2	no	—
64	C₄×C₈×C₇₉	—	2	1	no	—
65	C₄×C₈×C₇₉	—	2	1	no	—
66	C₂⁴×C₇₉	—	4	1	no	—
67	C₂×Q₈×C₇₉	—	2	2	no	—
68	C₂×Q₈×C₇₉	—	2	2	no	—
69	C₂×Q₈×C₇₉	—	2	2	no	—
70	C₂×Q₈×C₇₉	—	4	1	no	—
71	C₂×Q₈×C₇₉	—	4	1	no	—
72	C₂×Q₈×C₇₉	—	4	1	no	—
73	C₂×D₄×C₇₉	—	2	2	no	—
74	C₂×D₄×C₇₉	—	4	1	no	—
75	C₂×D₄×C₇₉	—	4	1	no	—
76	C₂×D₄×C₇₉	—	4	1	no	—
77	C₂×D₄×C₇₉	—	4	1	no	—
78	C₂×D₄×C₇₉	—	4	1	no	—
79	C₂²×C₄×C₇₉	—	4	1	no	—
80	C₂²×C₄×C₇₉	—	4	1	no	—
81	C₂²×C₄×C₇₉	—	4	1	no	—
82	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
85	Q₁₆×C₇₉	—	2	2	no	—
86	Q₁₆×C₇₉	—	2	2	no	—
87	Q₁₆×C₇₉	—	2	2	no	—
88	Q₁₆×C₇₉	C₂²⋊C₄	1	4	yes	complemented
89	D₈×C₇₉	—	2	2	no	—
90	D₈×C₇₉	—	2	2	no	—
91	D₈×C₇₉	—	4	1	no	—
92	D₈×C₇₉	—	4	1	no	—
93	C₂×C₈×C₇₉	—	2	1	no	—
94	C₂×C₈×C₇₉	—	2	1	no	—
95	C₂×C₈×C₇₉	—	2	1	no	—
96	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
101	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
102	C₄⋊C₄×C₇₉	—	2	2	no	—
103	C₄⋊C₄×C₇₉	—	4	4	no	—
104	C₄⋊C₄×C₇₉	—	4	1	no	—
105	C₄⋊C₄×C₇₉	—	4	1	no	—
106	C₄⋊C₄×C₇₉	—	4	1	no	—
107	C₂²⋊C₄×C₇₉	—	8	2	no	—
108	C₂²⋊C₄×C₇₉	—	8	2	no	—
109	C₄²×C₇₉	—	2	1	no	—
110	C₄²×C₇₉	—	2	1	no	—
111	C₄²×C₇₉	—	4	4	no	—
112	C₁₆×C₇₉	—	2	2	no	—
113	C₁₆×C₇₉	—	4	1	no	—
114	C₂³×C₇₉	—	4	2	no	—
115	C₂³×C₇₉	—	8	1	no	—
116	C₂³×C₇₉	—	8	1	no	—
117	C₂³×C₇₉	—	8	1	no	—
118	C₂³×C₇₉	—	8	1	no	—
119	C₂³×C₇₉	—	8	1	no	—
120	C₂³×C₇₉	—	8	1	no	—
121	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
122	Q₈×C₇₉	—	2	4	no	—
123	Q₈×C₇₉	—	4	2	no	—
124	Q₈×C₇₉	—	4	2	no	—
125	Q₈×C₇₉	—	4	2	no	—
126	D₄×C₇₉	—	4	2	no	—
127	D₄×C₇₉	—	4	2	no	—
128	D₄×C₇₉	—	8	1	no	—
129	D₄×C₇₉	—	8	1	no	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	—	2	1	no	—
132	C₂×C₄×C₇₉	—	2	1	no	—
133	C₂×C₄×C₇₉	—	2	1	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	4	2	no	—
136	C₂×C₄×C₇₉	—	4	2	no	—
137	C₂×C₄×C₇₉	—	4	2	no	—
138	C₂×C₄×C₇₉	—	4	2	no	—
139	C₂×C₄×C₇₉	—	8	1	no	—
140	C₂×C₄×C₇₉	—	8	1	no	—
141	C₂×C₄×C₇₉	—	8	1	no	—
142	C₂×C₄×C₇₉	—	8	1	no	—
143	C₂×C₄×C₇₉	—	8	1	no	—
144	C₂×C₄×C₇₉	SD₃₂	1	2	yes	complemented
145	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
147	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
149	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₈×C₇₉	—	4	1	no	—
152	C₈×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
154	C₈×C₇₉	#121	1	1	yes	characteristic
155	C₈×C₇₉	#123	1	1	yes	characteristic
156	C₂²×C₇₉	—	8	2	no	—
157	C₂²×C₇₉	—	8	2	no	—
158	C₂²×C₇₉	—	8	2	no	—
159	C₂²×C₇₉	—	16	1	no	—
160	C₂²×C₇₉	—	16	1	no	—
161	C₂²×C₇₉	—	16	1	no	—
162	C₂²×C₇₉	—	16	1	no	—
163	C₂²×C₇₉	C₄×D₈	1	1	yes	characteristic
164	C₂²×C₇₉	#447	1	1	yes	characteristic
165	C₂²×C₇₉	#459	1	1	yes	characteristic
166	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
167	C₂²×C₇₉	#508	1	1	yes	characteristic
168	C₂²×C₇₉	#509	1	1	yes	characteristic
169	C₂²×C₇₉	#510	1	1	yes	characteristic
170	C₄×C₇₉	—	2	2	no	—
171	C₄×C₇₉	—	4	4	no	—
172	C₄×C₇₉	—	4	1	no	—
173	C₄×C₇₉	—	8	2	no	—
174	C₄×C₇₉	—	16	1	no	—
175	C₄×C₇₉	#386	1	1	yes	characteristic
176	C₄×C₇₉	#442	1	1	yes	characteristic
177	C₄×C₇₉	#449	1	1	yes	characteristic
178	C₄×C₇₉	#463	1	1	yes	characteristic
179	#13013	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₇₉	—	16	2	no	—
181	C₂×C₇₉	#1879	1	1	yes	characteristic
182	C₂×C₇₉	C₄×SD₃₂	1	1	yes	characteristic
183	C₂×C₇₉	#2175	1	1	yes	characteristic
184	C₂×C₇₉	#2185	1	1	yes	characteristic
185	C₂×C₇₉	#2186	1	1	yes	characteristic
186	C₂×C₇₉	#2207	1	1	yes	characteristic
187	C₂×C₇₉	#2211	1	1	yes	characteristic
188	C₂²×SD₃₂	C₂×C₇₉	1	1	yes	characteristic
189	C₂×C₄×Q₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
190	C₂×#358	C₂×C₇₉	1	1	yes	characteristic, complemented
191	C₂×#357	C₂×C₇₉	1	1	yes	characteristic
192	#1970	C₂×C₇₉	1	1	yes	characteristic
193	#1380	C₂×C₇₉	1	1	yes	characteristic, complemented
194	#1374	C₂×C₇₉	1	1	yes	characteristic, complemented
195	C₇₉	#13013	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
197	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
198	C₂×C₄×Q₈	—	2	1	no	—
199	C₂×SD₃₂	—	2	2	no	—
200	C₂×SD₃₂	—	2	2	no	—
201	C₂×SD₃₂	C₄×C₇₉	1	4	yes	complemented
202	C₂²×C₁₆	C₂²×C₇₉	1	1	yes	characteristic
203	C₂²×C₁₆	C₂²×C₇₉	1	1	yes	characteristic
204	C₄×Q₁₆	—	2	2	no	—
205	C₄×Q₁₆	—	2	2	no	—
206	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
207	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
208	C₂×#103	—	2	1	no	—
209	C₂×#102	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
211	#390	—	2	1	no	—
212	#358	—	2	2	no	—
213	#357	—	2	2	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂×Q₁₆	—	2	1	no	—
217	C₂×Q₁₆	—	2	1	no	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	C₂×C₄×C₇₉	1	2	yes	—
220	C₂×Q₁₆	D₄×C₇₉	1	2	yes	—
221	C₂×Q₁₆	D₄×C₇₉	1	2	yes	—
222	C₂×D₈	—	2	1	no	—
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	—	2	1	no	—
225	C₂×D₈	—	2	1	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	C₂×C₄×C₇₉	1	2	yes	—
228	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
230	C₄×Q₈	—	2	4	no	—
231	C₄×Q₈	—	4	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	4	1	no	—
235	C₂×C₂²⋊C₄	—	4	1	no	—
236	C₂×C₂²⋊C₄	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
239	SD₃₂	—	2	8	no	—
240	C₂×C₁₆	—	2	1	no	—
241	C₂×C₁₆	—	2	1	no	—
242	C₂×C₁₆	—	2	1	no	—
243	C₂×C₁₆	—	2	1	no	—
244	C₂×C₁₆	—	2	1	no	—
245	C₂×C₁₆	C₂×C₄×C₇₉	1	2	yes	—
246	#107	—	2	1	no	—
247	#107	—	2	1	no	—
248	#107	—	2	1	no	—
249	#107	D₄×C₇₉	1	2	yes	—
250	#103	—	2	4	no	—
251	#102	—	4	2	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₂⁴	—	4	1	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	1	no	—
266	C₂×D₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
271	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
273	Q₁₆	—	2	2	no	—
274	Q₁₆	—	2	2	no	—
275	Q₁₆	—	2	2	no	—
276	Q₁₆	C₂²⋊C₄×C₇₉	1	4	yes	complemented
277	D₈	—	2	2	no	—
278	D₈	—	2	2	no	—
279	D₈	—	4	1	no	—
280	D₈	—	4	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
285	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
288	C₂×C₈	#41×C₇₉	1	1	yes	characteristic
289	C₂×C₈	#41×C₇₉	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₂²⋊C₄	—	8	2	no	—
296	C₂²⋊C₄	—	8	2	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	4	4	no	—
300	C₁₆	—	2	2	no	—
301	C₁₆	—	4	1	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	8	1	no	—
304	C₂³	—	8	1	no	—
305	C₂³	—	8	1	no	—
306	C₂³	—	8	1	no	—
307	C₂³	—	8	1	no	—
308	C₂³	—	8	1	no	—
309	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
310	Q₈	—	2	4	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	8	1	no	—
317	D₄	—	8	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	8	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	—	8	1	no	—
332	C₂×C₄	SD₃₂×C₇₉	1	2	yes	complemented
333	C₂×C₄	C₄×D₄×C₇₉	1	1	yes	characteristic
334	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
335	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
336	C₂×C₄	#135×C₇₉	1	1	yes	characteristic
337	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
338	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
339	C₈	—	4	1	no	—
340	C₈	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
341	C₈	C₄×D₄×C₇₉	1	1	yes	characteristic
342	C₈	#121×C₇₉	1	1	yes	characteristic
343	C₈	#123×C₇₉	1	1	yes	characteristic
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	—	16	1	no	—
348	C₂²	—	16	1	no	—
349	C₂²	—	16	1	no	—
350	C₂²	—	16	1	no	—
351	C₂²	C₄×D₈×C₇₉	1	1	yes	characteristic
352	C₂²	#447×C₇₉	1	1	yes	characteristic
353	C₂²	#459×C₇₉	1	1	yes	characteristic
354	C₂²	C₂×SD₃₂×C₇₉	1	1	yes	characteristic
355	C₂²	#508×C₇₉	1	1	yes	characteristic
356	C₂²	#509×C₇₉	1	1	yes	characteristic
357	C₂²	#510×C₇₉	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	1	no	—
361	C₄	—	8	2	no	—
362	C₄	—	16	1	no	—
363	C₄	#386×C₇₉	1	1	yes	characteristic
364	C₄	#442×C₇₉	1	1	yes	characteristic
365	C₄	#449×C₇₉	1	1	yes	characteristic
366	C₄	#463×C₇₉	1	1	yes	characteristic
367	C₂	—	16	2	no	—
368	C₂	C₇₉×#1879	1	1	yes	characteristic
369	C₂	C₄×SD₃₂×C₇₉	1	1	yes	characteristic
370	C₂	C₇₉×#2175	1	1	yes	characteristic
371	C₂	C₇₉×#2185	1	1	yes	characteristic
372	C₂	C₇₉×#2186	1	1	yes	characteristic
373	C₂	C₇₉×#2207	1	1	yes	characteristic
374	C₂	C₇₉×#2211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₇₉
Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
prime radical	C₂²×D₈×C₇₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ C₂×C₄×C₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₇₉	C₂	semidirect
3. C₂×#358×C₇₉	C₂	semidirect
6. C₇₉×#1380	C₂	semidirect
7. C₇₉×#1374	C₂	semidirect
13. C₂×SD₃₂×C₇₉	C₄	semidirect
88. Q₁₆×C₇₉	C₂²⋊C₄	semidirect
144. C₂×C₄×C₇₉	SD₃₂	semidirect
179. #13013	C₇₉	direct (N × H)
189. C₂×C₄×Q₁₆	C₂×C₇₉	semidirect
190. C₂×#358	C₂×C₇₉	semidirect
193. #1380	C₂×C₇₉	semidirect
194. #1374	C₂×C₇₉	semidirect
195. C₇₉	#13013	direct (N × H)
201. C₂×SD₃₂	C₄×C₇₉	semidirect
276. Q₁₆	C₂²⋊C₄×C₇₉	semidirect
332. C₂×C₄	SD₃₂×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×SD₃₂×C₇₉	2
C₂×C₄×Q₁₆×C₇₉	2
C₂×#358×C₇₉	2
C₂×#357×C₇₉	2
C₇₉×#1970	2
C₇₉×#1380	2
C₇₉×#1374	2
#13013	79

Subgroups — C79×#13013 #34124702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#13013 #34124702