Subgroups — C₇₉×#12990 #34124679

Order 20224.

518 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	C₇₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#359×C₇₉	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1382	C₂	1	2	yes	maximal, complemented
6	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₇₉	—	2	1	no	—
8	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	#525×C₇₉	—	2	1	no	—
10	C₂²×C₁₆×C₇₉	C₂²	1	2	yes	—
11	#467×C₇₉	C₄	1	1	yes	characteristic
12	#467×C₇₉	C₄	1	1	yes	characteristic
13	#466×C₇₉	C₄	1	1	yes	characteristic
14	#466×C₇₉	C₄	1	1	yes	characteristic
15	#465×C₇₉	—	2	1	no	—
16	#465×C₇₉	—	2	1	no	—
17	C₂×#108×C₇₉	—	2	1	no	—
18	C₂×#108×C₇₉	—	2	4	no	—
19	C₂×#108×C₇₉	C₂²	1	2	yes	—
20	#427×C₇₉	C₂²	1	1	yes	characteristic
21	#416×C₇₉	—	2	1	no	—
22	#359×C₇₉	—	2	4	no	—
23	C₂²⋊C₁₆×C₇₉	—	2	1	no	—
24	C₂²⋊C₁₆×C₇₉	—	2	1	no	—
25	C₂×#41×C₇₉	—	2	1	no	—
26	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
27	#135×C₇₉	—	2	2	no	—
28	#135×C₇₉	—	2	2	no	—
29	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂×SD₁₆×C₇₉	—	2	1	no	—
31	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₇₉	—	2	4	no	—
33	C₂×M₁₆×C₇₉	—	2	2	no	—
34	C₂×M₁₆×C₇₉	—	4	2	no	—
35	C₂×M₁₆×C₇₉	—	4	1	no	—
36	C₂²×C₈×C₇₉	—	2	2	no	—
37	C₂²×C₈×C₇₉	—	2	2	no	—
38	C₂²×C₈×C₇₉	—	4	1	no	—
39	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
45	#123×C₇₉	—	4	1	no	—
46	C₂²⋊Q₈×C₇₉	—	2	1	no	—
47	C₂²⋊Q₈×C₇₉	—	2	1	no	—
48	#121×C₇₉	—	2	1	no	—
49	#121×C₇₉	—	2	1	no	—
50	#120×C₇₉	—	4	1	no	—
51	C₄×D₄×C₇₉	—	4	1	no	—
52	C₄×D₄×C₇₉	—	4	1	no	—
53	#117×C₇₉	—	2	1	no	—
54	C₂×C₁₆×C₇₉	—	2	2	no	—
55	C₂×C₁₆×C₇₉	—	2	2	no	—
56	C₂×C₁₆×C₇₉	—	2	2	no	—
57	#108×C₇₉	—	2	4	no	—
58	#108×C₇₉	—	2	2	no	—
59	#108×C₇₉	D₄	1	4	yes	complemented
60	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
61	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
62	#106×C₇₉	—	2	1	no	—
63	#103×C₇₉	—	2	1	no	—
64	#103×C₇₉	—	2	1	no	—
65	#102×C₇₉	—	2	1	no	—
66	#102×C₇₉	—	2	1	no	—
67	C₂⁴×C₇₉	SD₁₆	1	1	yes	characteristic
68	#41×C₇₉	—	4	1	no	—
69	#41×C₇₉	—	4	1	no	—
70	#41×C₇₉	—	4	1	no	—
71	#41×C₇₉	—	4	1	no	—
72	C₂×Q₈×C₇₉	—	2	1	no	—
73	C₂×D₄×C₇₉	—	2	1	no	—
74	C₂×D₄×C₇₉	—	4	1	no	—
75	C₂×D₄×C₇₉	—	4	1	no	—
76	C₂×D₄×C₇₉	—	4	1	no	—
77	C₂²×C₄×C₇₉	—	2	1	no	—
78	C₂²×C₄×C₇₉	—	2	1	no	—
79	C₂²×C₄×C₇₉	—	2	1	no	—
80	C₂²×C₄×C₇₉	—	2	1	no	—
81	C₂²×C₄×C₇₉	—	4	1	no	—
82	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
85	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
88	Q₁₆×C₇₉	—	2	2	no	—
89	SD₁₆×C₇₉	—	4	2	no	—
90	D₈×C₇₉	—	2	2	no	—
91	M₁₆×C₇₉	—	2	4	no	—
92	M₁₆×C₇₉	—	4	4	no	—
93	M₁₆×C₇₉	—	4	2	no	—
94	C₂×C₈×C₇₉	—	2	2	no	—
95	C₂×C₈×C₇₉	—	2	2	no	—
96	C₂×C₈×C₇₉	—	2	2	no	—
97	C₂×C₈×C₇₉	—	2	2	no	—
98	C₂×C₈×C₇₉	—	2	1	no	—
99	C₂×C₈×C₇₉	—	2	1	no	—
100	C₂×C₈×C₇₉	—	4	4	no	—
101	C₂×C₈×C₇₉	—	4	2	no	—
102	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₇₉	#41	1	2	yes	—
108	C₄⋊C₄×C₇₉	—	2	1	no	—
109	C₄⋊C₄×C₇₉	—	2	1	no	—
110	C₄⋊C₄×C₇₉	—	4	1	no	—
111	C₄⋊C₄×C₇₉	—	4	1	no	—
112	C₂²⋊C₄×C₇₉	—	4	1	no	—
113	C₂²⋊C₄×C₇₉	—	4	1	no	—
114	C₂²⋊C₄×C₇₉	—	4	1	no	—
115	C₂²⋊C₄×C₇₉	—	4	1	no	—
116	C₂²⋊C₄×C₇₉	—	4	1	no	—
117	C₄²×C₇₉	—	4	1	no	—
118	C₁₆×C₇₉	—	4	2	no	—
119	C₂³×C₇₉	—	2	2	no	—
120	C₂³×C₇₉	—	2	1	no	—
121	C₂³×C₇₉	—	2	1	no	—
122	C₂³×C₇₉	—	4	1	no	—
123	C₂³×C₇₉	—	4	1	no	—
124	C₂³×C₇₉	#102	1	1	yes	characteristic
125	C₂³×C₇₉	#102	1	1	yes	characteristic
126	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
127	Q₈×C₇₉	—	4	1	no	—
128	Q₈×C₇₉	—	4	1	no	—
129	D₄×C₇₉	—	4	1	no	—
130	D₄×C₇₉	—	4	1	no	—
131	D₄×C₇₉	—	8	2	no	—
132	D₄×C₇₉	—	8	2	no	—
133	D₄×C₇₉	—	8	1	no	—
134	D₄×C₇₉	—	8	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	1	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	4	1	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	—	4	1	no	—
148	C₂×C₄×C₇₉	—	8	1	no	—
149	C₂×C₄×C₇₉	—	8	1	no	—
150	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
151	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
158	C₈×C₇₉	—	2	1	no	—
159	C₈×C₇₉	—	2	1	no	—
160	C₈×C₇₉	—	4	4	no	—
161	C₈×C₇₉	C₄×D₄	1	2	yes	—
162	C₈×C₇₉	#121	1	2	yes	—
163	C₂²×C₇₉	—	2	1	no	—
164	C₂²×C₇₉	—	2	1	no	—
165	C₂²×C₇₉	—	2	1	no	—
166	C₂²×C₇₉	—	2	1	no	—
167	C₂²×C₇₉	—	2	1	no	—
168	C₂²×C₇₉	—	2	1	no	—
169	C₂²×C₇₉	—	2	1	no	—
170	C₂²×C₇₉	—	4	2	no	—
171	C₂²×C₇₉	—	4	2	no	—
172	C₂²×C₇₉	—	8	1	no	—
173	C₂²×C₇₉	—	8	1	no	—
174	C₂²×C₇₉	—	8	1	no	—
175	C₂²×C₇₉	#359	1	2	yes	complemented
176	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
177	C₂²×C₇₉	#448	1	1	yes	characteristic
178	C₂²×C₇₉	#481	1	1	yes	characteristic
179	C₄×C₇₉	—	2	1	no	—
180	C₄×C₇₉	—	2	1	no	—
181	C₄×C₇₉	—	8	1	no	—
182	C₄×C₇₉	—	8	1	no	—
183	C₄×C₇₉	—	8	1	no	—
184	C₄×C₇₉	#386	1	1	yes	characteristic
185	C₄×C₇₉	#417	1	1	yes	characteristic
186	C₄×C₇₉	#447	1	1	yes	characteristic
187	C₄×C₇₉	#480	1	1	yes	characteristic
188	#12990	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₇₉	—	2	2	no	—
190	C₂×C₇₉	—	2	1	no	—
191	C₂×C₇₉	—	2	1	no	—
192	C₂×C₇₉	—	4	1	no	—
193	C₂×C₇₉	—	16	1	no	—
194	C₂×C₇₉	#1874	1	1	yes	characteristic
195	C₂×C₇₉	C₂×#359	1	1	yes	characteristic
196	C₂×C₇₉	#2143	1	1	yes	characteristic
197	#3050	C₂×C₇₉	1	1	yes	characteristic
198	C₂²×#108	C₂×C₇₉	1	1	yes	characteristic, complemented
199	C₂×#359	C₂×C₇₉	1	2	yes	complemented
200	C₂×C₂²⋊C₁₆	C₂×C₇₉	1	1	yes	characteristic, complemented
201	#1382	C₂×C₇₉	1	2	yes	complemented
202	C₇₉	#12990	1	1	yes	characteristic, direct product factor, Sylow
203	C₂×#135	C₂²×C₇₉	1	1	yes	characteristic
204	C₂²×M₁₆	—	2	1	no	—
205	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
206	#525	—	2	1	no	—
207	C₂²×C₁₆	C₂²×C₇₉	1	2	yes	—
208	#467	C₄×C₇₉	1	1	yes	characteristic
209	#467	C₄×C₇₉	1	1	yes	characteristic
210	#466	C₄×C₇₉	1	1	yes	characteristic
211	#466	C₄×C₇₉	1	1	yes	characteristic
212	#465	—	2	1	no	—
213	#465	—	2	1	no	—
214	C₂×#108	—	2	1	no	—
215	C₂×#108	—	2	4	no	—
216	C₂×#108	C₂²×C₇₉	1	2	yes	—
217	#427	C₂²×C₇₉	1	1	yes	characteristic
218	#416	—	2	1	no	—
219	#359	—	2	4	no	—
220	C₂²⋊C₁₆	—	2	1	no	—
221	C₂²⋊C₁₆	—	2	1	no	—
222	C₂×#41	—	2	1	no	—
223	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
224	#135	—	2	2	no	—
225	#135	—	2	2	no	—
226	C₂×Q₁₆	C₂×C₄×C₇₉	1	1	yes	characteristic
227	C₂×SD₁₆	—	2	1	no	—
228	C₂×D₈	C₂×C₄×C₇₉	1	1	yes	characteristic
229	C₂×M₁₆	—	2	4	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	4	2	no	—
232	C₂×M₁₆	—	4	1	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	4	1	no	—
236	C₂²×C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
237	C₂²×C₈	C₂×C₄×C₇₉	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
242	#123	—	4	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	—	2	1	no	—
245	#121	—	2	1	no	—
246	#121	—	2	1	no	—
247	#120	—	4	1	no	—
248	C₄×D₄	—	4	1	no	—
249	C₄×D₄	—	4	1	no	—
250	#117	—	2	1	no	—
251	C₂×C₁₆	—	2	2	no	—
252	C₂×C₁₆	—	2	2	no	—
253	C₂×C₁₆	—	2	2	no	—
254	#108	—	2	4	no	—
255	#108	—	2	2	no	—
256	#108	D₄×C₇₉	1	4	yes	complemented
257	#107	C₂×C₄×C₇₉	1	1	yes	characteristic
258	#107	C₂×C₄×C₇₉	1	1	yes	characteristic
259	#106	—	2	1	no	—
260	#103	—	2	1	no	—
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	1	no	—
264	C₂⁴	SD₁₆×C₇₉	1	1	yes	characteristic
265	#41	—	4	1	no	—
266	#41	—	4	1	no	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
281	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
282	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
283	C₂²×C₄	SD₁₆×C₇₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	4	2	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	4	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
300	C₂×C₈	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₇₉	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
304	C₂×C₈	#41×C₇₉	1	2	yes	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₁₆	—	4	2	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	#102×C₇₉	1	1	yes	characteristic
322	C₂³	#102×C₇₉	1	1	yes	characteristic
323	C₂³	C₂×SD₁₆×C₇₉	1	1	yes	characteristic
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	4	1	no	—
327	D₄	—	4	1	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	1	no	—
330	D₄	—	8	1	no	—
331	D₄	—	8	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	#102×C₇₉	1	1	yes	characteristic
348	C₂×C₄	#102×C₇₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
350	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
351	C₂×C₄	#123×C₇₉	1	1	yes	characteristic
352	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
353	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
354	C₂×C₄	#137×C₇₉	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	4	4	no	—
358	C₈	C₄×D₄×C₇₉	1	2	yes	—
359	C₈	#121×C₇₉	1	2	yes	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	#359×C₇₉	1	2	yes	complemented
373	C₂²	C₂×#102×C₇₉	1	1	yes	characteristic
374	C₂²	#448×C₇₉	1	1	yes	characteristic
375	C₂²	#481×C₇₉	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	#386×C₇₉	1	1	yes	characteristic
382	C₄	#417×C₇₉	1	1	yes	characteristic
383	C₄	#447×C₇₉	1	1	yes	characteristic
384	C₄	#480×C₇₉	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	4	1	no	—
389	C₂	—	16	1	no	—
390	C₂	C₇₉×#1874	1	1	yes	characteristic
391	C₂	C₂×#359×C₇₉	1	1	yes	characteristic
392	C₂	C₇₉×#2143	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₇₉
Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
socle	C₂²×C₇₉	C₂×#102
prime radical	C₇₉×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ C₂³×C₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₇₉	C₂	semidirect
3. C₂×#359×C₇₉	C₂	semidirect
4. C₂×C₂²⋊C₁₆×C₇₉	C₂	semidirect
5. C₇₉×#1382	C₂	semidirect
59. #108×C₇₉	D₄	semidirect
175. C₂²×C₇₉	#359	semidirect
188. #12990	C₇₉	direct (N × H)
198. C₂²×#108	C₂×C₇₉	semidirect
199. C₂×#359	C₂×C₇₉	semidirect
200. C₂×C₂²⋊C₁₆	C₂×C₇₉	semidirect
201. #1382	C₂×C₇₉	semidirect
202. C₇₉	#12990	direct (N × H)
256. #108	D₄×C₇₉	semidirect
372. C₂²	#359×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3050	2
C₂²×#108×C₇₉	2
C₂×#359×C₇₉	2
C₂×C₂²⋊C₁₆×C₇₉	2
C₇₉×#1382	2
#12990	79

Subgroups — C79×#12990 #34124679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#12990 #34124679