Subgroups — C₇₉×#61803 #34173492

Order 20224.

1732 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3506	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#3353	C₂	1	2	yes	maximal, complemented
4	C₇₉×#3350	C₂	1	4	yes	maximal, complemented
5	C₇₉×#3340	C₂	1	2	yes	maximal, complemented
6	C₇₉×#3329	C₂	1	2	yes	maximal, complemented
7	C₇₉×#3320	C₂	1	4	yes	maximal, complemented
8	C₇₉×#3298	C₂	1	2	yes	maximal, complemented
9	C₇₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3200	C₂	1	4	yes	maximal, complemented
12	C₇₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#3097	C₂	1	4	yes	maximal, complemented
15	C₇₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	#563×C₇₉	—	2	2	no	—
17	#559×C₇₉	—	2	1	no	—
18	#559×C₇₉	—	2	2	no	—
19	Q₈²×C₇₉	—	2	1	no	—
20	#556×C₇₉	—	2	1	no	—
21	#556×C₇₉	C₂²	1	2	yes	complemented
22	#556×C₇₉	C₂²	1	2	yes	complemented
23	#555×C₇₉	C₂²	1	2	yes	—
24	#553×C₇₉	C₂²	1	4	yes	—
25	#550×C₇₉	—	2	1	no	—
26	D₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
28	#547×C₇₉	C₂²	1	2	yes	—
29	#542×C₇₉	—	2	2	no	—
30	#542×C₇₉	—	2	2	no	—
31	#538×C₇₉	—	2	2	no	—
32	#536×C₇₉	C₂²	1	4	yes	—
33	#535×C₇₉	C₂²	1	2	yes	—
34	#533×C₇₉	C₂²	1	1	yes	characteristic
35	#533×C₇₉	C₂²	1	1	yes	characteristic
36	#533×C₇₉	C₂²	1	1	yes	characteristic
37	#532×C₇₉	C₂²	1	1	yes	characteristic
38	#525×C₇₉	—	2	2	no	—
39	#520×C₇₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
41	#501×C₇₉	C₂²	1	2	yes	complemented
42	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#498×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#491×C₇₉	C₂²	1	2	yes	complemented
45	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	#485×C₇₉	C₂²	1	4	yes	—
48	#485×C₇₉	C₂²	1	4	yes	—
49	#485×C₇₉	C₂²	1	4	yes	complemented
50	#485×C₇₉	C₂²	1	4	yes	complemented
51	#484×C₇₉	C₂²	1	2	yes	—
52	#484×C₇₉	C₂²	1	4	yes	complemented
53	#483×C₇₉	C₂²	1	2	yes	—
54	#483×C₇₉	C₂²	1	4	yes	complemented
55	#482×C₇₉	C₂²	1	4	yes	—
56	#482×C₇₉	C₂²	1	4	yes	—
57	#479×C₇₉	C₂²	1	4	yes	complemented
58	#477×C₇₉	C₂²	1	2	yes	complemented
59	#476×C₇₉	C₂²	1	2	yes	—
60	#475×C₇₉	C₂²	1	2	yes	complemented
61	#474×C₇₉	C₂²	1	2	yes	—
62	#468×C₇₉	C₂²	1	4	yes	—
63	#468×C₇₉	C₂²	1	4	yes	—
64	#465×C₇₉	C₂²	1	4	yes	—
65	#465×C₇₉	C₂²	1	4	yes	—
66	#461×C₇₉	C₂²	1	2	yes	—
67	#461×C₇₉	C₂²	1	2	yes	—
68	#450×C₇₉	C₂²	1	2	yes	—
69	#450×C₇₉	C₂²	1	2	yes	—
70	#448×C₇₉	C₂²	1	4	yes	—
71	#448×C₇₉	C₂²	1	4	yes	—
72	#440×C₇₉	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
75	#436×C₇₉	C₂²	1	2	yes	complemented
76	#435×C₇₉	C₂²	1	4	yes	complemented
77	C₈×D₄×C₇₉	C₂²	1	2	yes	complemented
78	#432×C₇₉	C₂²	1	1	yes	characteristic
79	#431×C₇₉	C₂²	1	1	yes	characteristic
80	#428×C₇₉	C₂²	1	4	yes	complemented
81	#427×C₇₉	C₂²	1	4	yes	complemented
82	#419×C₇₉	C₂²	1	4	yes	complemented
83	C₂×#103×C₇₉	C₂²	1	4	yes	complemented
84	#408×C₇₉	C₂²	1	4	yes	—
85	C₂×#41×C₇₉	—	2	2	no	—
86	C₂×#41×C₇₉	C₂³	1	2	yes	—
87	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
88	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇₉	—	2	1	no	—
90	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
91	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₇₉	C₂³	1	4	yes	—
93	C₂×M₁₆×C₇₉	C₂³	1	4	yes	—
94	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₇₉	—	2	4	no	—
96	C₄⋊Q₈×C₇₉	—	2	2	no	—
97	C₄⋊Q₈×C₇₉	—	2	2	no	—
98	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
105	#127×C₇₉	—	2	2	no	—
106	#127×C₇₉	D₄	1	1	yes	characteristic
107	#126×C₇₉	—	2	4	no	—
108	#126×C₇₉	—	2	4	no	—
109	#126×C₇₉	—	2	4	no	—
110	#125×C₇₉	—	2	1	no	—
111	#125×C₇₉	—	2	1	no	—
112	#125×C₇₉	C₂³	1	2	yes	—
113	#124×C₇₉	—	2	2	no	—
114	#124×C₇₉	—	2	4	no	—
115	#124×C₇₉	—	2	2	no	—
116	#124×C₇₉	—	2	2	no	—
117	#124×C₇₉	—	2	4	no	—
118	#124×C₇₉	D₄	1	2	yes	—
119	#123×C₇₉	—	2	4	no	—
120	#123×C₇₉	—	2	4	no	—
121	#123×C₇₉	—	2	4	no	—
122	#123×C₇₉	—	2	4	no	—
123	C₂²⋊Q₈×C₇₉	—	2	1	no	—
124	C₂²⋊Q₈×C₇₉	—	2	1	no	—
125	C₂²⋊Q₈×C₇₉	—	2	1	no	—
126	C₂²⋊Q₈×C₇₉	—	2	1	no	—
127	C₂²⋊Q₈×C₇₉	—	2	2	no	—
128	C₂²⋊Q₈×C₇₉	—	2	4	no	—
129	C₂²⋊Q₈×C₇₉	—	2	4	no	—
130	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
131	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
132	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
133	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
134	#121×C₇₉	—	2	2	no	—
135	#121×C₇₉	—	2	4	no	—
136	#121×C₇₉	D₄	1	2	yes	—
137	#121×C₇₉	D₄	1	2	yes	—
138	#121×C₇₉	C₂³	1	4	yes	—
139	#121×C₇₉	C₂³	1	4	yes	—
140	#120×C₇₉	—	2	4	no	—
141	C₄×Q₈×C₇₉	—	2	2	no	—
142	C₄×Q₈×C₇₉	—	2	2	no	—
143	C₄×Q₈×C₇₉	—	2	2	no	—
144	C₄×Q₈×C₇₉	—	2	1	no	—
145	C₄×Q₈×C₇₉	—	2	1	no	—
146	C₄×Q₈×C₇₉	—	2	1	no	—
147	C₄×Q₈×C₇₉	—	2	1	no	—
148	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
149	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
150	C₄×D₄×C₇₉	—	2	4	no	—
151	C₄×D₄×C₇₉	—	2	2	no	—
152	C₄×D₄×C₇₉	—	2	2	no	—
153	C₄×D₄×C₇₉	—	2	2	no	—
154	C₄×D₄×C₇₉	—	2	4	no	—
155	C₄×D₄×C₇₉	—	2	1	no	—
156	C₄×D₄×C₇₉	—	2	1	no	—
157	C₄×D₄×C₇₉	C₂³	1	2	yes	—
158	C₄×D₄×C₇₉	C₂³	1	2	yes	—
159	C₄×D₄×C₇₉	C₂³	1	2	yes	—
160	C₄×D₄×C₇₉	C₂³	1	2	yes	—
161	#117×C₇₉	—	2	1	no	—
162	#117×C₇₉	—	2	1	no	—
163	#117×C₇₉	—	2	2	no	—
164	#117×C₇₉	C₂³	1	4	yes	—
165	#117×C₇₉	C₂³	1	4	yes	—
166	#117×C₇₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
170	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
171	#107×C₇₉	C₂³	1	4	yes	—
172	#107×C₇₉	C₂³	1	4	yes	—
173	#107×C₇₉	C₂³	1	4	yes	—
174	#106×C₇₉	C₂³	1	2	yes	—
175	#106×C₇₉	C₂³	1	4	yes	—
176	#106×C₇₉	C₂³	1	2	yes	—
177	#106×C₇₉	C₂³	1	4	yes	—
178	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
179	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
180	#103×C₇₉	C₂³	1	2	yes	—
181	#103×C₇₉	C₂³	1	4	yes	—
182	#103×C₇₉	C₂³	1	4	yes	—
183	#103×C₇₉	C₂³	1	4	yes	—
184	#103×C₇₉	C₂³	1	2	yes	—
185	#103×C₇₉	C₂³	1	4	yes	—
186	#103×C₇₉	C₂³	1	4	yes	—
187	#102×C₇₉	C₂³	1	2	yes	—
188	#102×C₇₉	C₂³	1	2	yes	—
189	#102×C₇₉	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
194	#97×C₇₉	C₂³	1	2	yes	—
195	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
197	C₂⁴×C₇₉	—	2	1	no	—
198	#41×C₇₉	—	4	4	no	—
199	#41×C₇₉	—	8	4	no	—
200	C₂×Q₈×C₇₉	—	2	1	no	—
201	C₂×Q₈×C₇₉	—	2	1	no	—
202	C₂×Q₈×C₇₉	—	2	1	no	—
203	C₂×Q₈×C₇₉	—	2	1	no	—
204	C₂×Q₈×C₇₉	—	2	4	no	—
205	C₂×Q₈×C₇₉	—	4	4	no	—
206	C₂×Q₈×C₇₉	—	4	4	no	—
207	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
210	C₂×D₄×C₇₉	—	2	4	no	—
211	C₂×D₄×C₇₉	—	2	4	no	—
212	C₂×D₄×C₇₉	—	2	1	no	—
213	C₂×D₄×C₇₉	—	4	2	no	—
214	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₇₉	C₂×D₄	1	4	yes	—
217	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₇₉	—	2	1	no	—
220	C₂²×C₄×C₇₉	—	2	4	no	—
221	C₂²×C₄×C₇₉	—	2	4	no	—
222	C₂²×C₄×C₇₉	—	2	2	no	—
223	C₂²×C₄×C₇₉	—	2	2	no	—
224	C₂²×C₄×C₇₉	—	8	2	no	—
225	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
229	SD₁₆×C₇₉	—	4	2	no	—
230	SD₁₆×C₇₉	—	4	4	no	—
231	SD₁₆×C₇₉	—	4	2	no	—
232	M₁₆×C₇₉	—	4	4	no	—
233	C₂×C₈×C₇₉	—	4	4	no	—
234	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
235	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
236	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₇₉	—	2	1	no	—
238	C₄⋊C₄×C₇₉	—	2	4	no	—
239	C₄⋊C₄×C₇₉	—	2	1	no	—
240	C₄⋊C₄×C₇₉	—	2	1	no	—
241	C₄⋊C₄×C₇₉	—	2	1	no	—
242	C₄⋊C₄×C₇₉	—	2	1	no	—
243	C₄⋊C₄×C₇₉	—	2	1	no	—
244	C₄⋊C₄×C₇₉	—	2	2	no	—
245	C₄⋊C₄×C₇₉	—	2	1	no	—
246	C₄⋊C₄×C₇₉	—	2	1	no	—
247	C₄⋊C₄×C₇₉	—	2	2	no	—
248	C₄⋊C₄×C₇₉	—	2	4	no	—
249	C₄⋊C₄×C₇₉	—	2	4	no	—
250	C₄⋊C₄×C₇₉	—	2	1	no	—
251	C₄⋊C₄×C₇₉	—	2	2	no	—
252	C₄⋊C₄×C₇₉	—	2	2	no	—
253	C₄⋊C₄×C₇₉	—	2	2	no	—
254	C₄⋊C₄×C₇₉	—	2	2	no	—
255	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₇₉	—	2	2	no	—
263	C₂²⋊C₄×C₇₉	—	2	2	no	—
264	C₂²⋊C₄×C₇₉	—	2	2	no	—
265	C₂²⋊C₄×C₇₉	—	2	4	no	—
266	C₂²⋊C₄×C₇₉	—	2	4	no	—
267	C₂²⋊C₄×C₇₉	—	2	4	no	—
268	C₂²⋊C₄×C₇₉	—	2	4	no	—
269	C₂²⋊C₄×C₇₉	—	2	2	no	—
270	C₂²⋊C₄×C₇₉	—	2	2	no	—
271	C₂²⋊C₄×C₇₉	—	2	4	no	—
272	C₂²⋊C₄×C₇₉	—	2	4	no	—
273	C₂²⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
275	C₄²×C₇₉	—	2	4	no	—
276	C₄²×C₇₉	—	2	2	no	—
277	C₄²×C₇₉	—	2	2	no	—
278	C₄²×C₇₉	—	2	2	no	—
279	C₄²×C₇₉	—	2	4	no	—
280	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
283	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
284	C₂³×C₇₉	—	2	2	no	—
285	C₂³×C₇₉	—	4	2	no	—
286	C₂³×C₇₉	—	8	1	no	—
287	C₂³×C₇₉	—	8	1	no	—
288	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
290	Q₈×C₇₉	—	2	2	no	—
291	Q₈×C₇₉	—	2	4	no	—
292	Q₈×C₇₉	—	2	2	no	—
293	Q₈×C₇₉	—	4	2	no	—
294	Q₈×C₇₉	—	4	2	no	—
295	Q₈×C₇₉	—	4	2	no	—
296	Q₈×C₇₉	—	4	2	no	—
297	Q₈×C₇₉	—	8	1	no	—
298	Q₈×C₇₉	—	8	4	no	—
299	D₄×C₇₉	—	2	4	no	—
300	D₄×C₇₉	—	2	2	no	—
301	D₄×C₇₉	—	2	2	no	—
302	D₄×C₇₉	—	4	2	no	—
303	D₄×C₇₉	—	4	2	no	—
304	D₄×C₇₉	—	4	4	no	—
305	D₄×C₇₉	—	4	2	no	—
306	D₄×C₇₉	—	8	4	no	—
307	D₄×C₇₉	—	8	4	no	—
308	C₂×C₄×C₇₉	—	2	2	no	—
309	C₂×C₄×C₇₉	—	2	4	no	—
310	C₂×C₄×C₇₉	—	2	4	no	—
311	C₂×C₄×C₇₉	—	2	2	no	—
312	C₂×C₄×C₇₉	—	2	2	no	—
313	C₂×C₄×C₇₉	—	2	2	no	—
314	C₂×C₄×C₇₉	—	2	2	no	—
315	C₂×C₄×C₇₉	—	2	2	no	—
316	C₂×C₄×C₇₉	—	2	2	no	—
317	C₂×C₄×C₇₉	—	2	2	no	—
318	C₂×C₄×C₇₉	—	2	2	no	—
319	C₂×C₄×C₇₉	—	4	1	no	—
320	C₂×C₄×C₇₉	—	4	4	no	—
321	C₂×C₄×C₇₉	—	8	2	no	—
322	C₂×C₄×C₇₉	—	8	1	no	—
323	C₂×C₄×C₇₉	—	8	4	no	—
324	C₂×C₄×C₇₉	—	8	4	no	—
325	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
332	C₈×C₇₉	—	2	2	no	—
333	C₈×C₇₉	—	2	4	no	—
334	C₈×C₇₉	—	2	2	no	—
335	C₂²×C₇₉	—	2	1	no	—
336	C₂²×C₇₉	—	2	4	no	—
337	C₂²×C₇₉	—	2	4	no	—
338	C₂²×C₇₉	—	2	1	no	—
339	C₂²×C₇₉	—	2	1	no	—
340	C₂²×C₇₉	—	2	4	no	—
341	C₂²×C₇₉	—	4	2	no	—
342	C₂²×C₇₉	—	4	2	no	—
343	C₂²×C₇₉	—	4	2	no	—
344	C₂²×C₇₉	—	8	4	no	—
345	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₇₉	—	2	1	no	—
347	C₄×C₇₉	—	2	1	no	—
348	C₄×C₇₉	—	2	1	no	—
349	C₄×C₇₉	—	2	4	no	—
350	C₄×C₇₉	—	2	1	no	—
351	C₄×C₇₉	—	4	2	no	—
352	C₄×C₇₉	—	4	2	no	—
353	C₄×C₇₉	—	4	2	no	—
354	C₄×C₇₉	—	4	2	no	—
355	C₄×C₇₉	—	4	2	no	—
356	C₄×C₇₉	—	4	2	no	—
357	C₄×C₇₉	—	4	2	no	—
358	C₄×C₇₉	#577	1	2	yes	—
359	C₄×C₇₉	#585	1	2	yes	—
360	#61803	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₇₉	—	4	4	no	—
362	C₂×C₇₉	—	4	1	no	—
363	C₂×C₇₉	—	8	2	no	—
364	C₂×C₇₉	#3485	1	1	yes	characteristic
365	C₂×C₇₉	C₂×#577	1	1	yes	characteristic
366	C₂×C₇₉	#3586	1	1	yes	characteristic
367	#3550	C₂×C₇₉	1	1	yes	characteristic, complemented
368	#3506	C₂×C₇₉	1	1	yes	characteristic
369	#3353	C₂×C₇₉	1	2	yes	complemented
370	#3350	C₂×C₇₉	1	4	yes	complemented
371	#3340	C₂×C₇₉	1	2	yes	complemented
372	#3329	C₂×C₇₉	1	2	yes	complemented
373	#3320	C₂×C₇₉	1	4	yes	complemented
374	#3298	C₂×C₇₉	1	2	yes	complemented
375	#3237	C₂×C₇₉	1	1	yes	characteristic, complemented
376	#3231	C₂×C₇₉	1	1	yes	characteristic, complemented
377	#3200	C₂×C₇₉	1	4	yes	complemented
378	#3110	C₂×C₇₉	1	1	yes	characteristic, complemented
379	#3101	C₂×C₇₉	1	1	yes	characteristic, complemented
380	#3097	C₂×C₇₉	1	4	yes	complemented
381	#2981	C₂×C₇₉	1	1	yes	characteristic, complemented
382	C₇₉	#61803	1	1	yes	characteristic, direct product factor, Sylow
383	#563	—	2	2	no	—
384	#559	—	2	1	no	—
385	#559	—	2	2	no	—
386	Q₈²	—	2	1	no	—
387	#556	—	2	1	no	—
388	#556	C₂²×C₇₉	1	2	yes	complemented
389	#556	C₂²×C₇₉	1	2	yes	complemented
390	#555	C₂²×C₇₉	1	2	yes	—
391	#553	C₂²×C₇₉	1	4	yes	—
392	#550	—	2	1	no	—
393	D₄×Q₈	C₂²×C₇₉	1	2	yes	complemented
394	D₄×Q₈	C₂²×C₇₉	1	2	yes	complemented
395	#547	C₂²×C₇₉	1	2	yes	—
396	#542	—	2	2	no	—
397	#542	—	2	2	no	—
398	#538	—	2	2	no	—
399	#536	C₂²×C₇₉	1	4	yes	—
400	#535	C₂²×C₇₉	1	2	yes	—
401	#533	C₂²×C₇₉	1	1	yes	characteristic
402	#533	C₂²×C₇₉	1	1	yes	characteristic
403	#533	C₂²×C₇₉	1	1	yes	characteristic
404	#532	C₂²×C₇₉	1	1	yes	characteristic
405	#525	—	2	2	no	—
406	#520	C₂²×C₇₉	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
408	#501	C₂²×C₇₉	1	2	yes	complemented
409	#500	C₂²×C₇₉	1	1	yes	characteristic, complemented
410	#498	C₂²×C₇₉	1	1	yes	characteristic, complemented
411	#491	C₂²×C₇₉	1	2	yes	complemented
412	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
413	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
414	#485	C₂²×C₇₉	1	4	yes	—
415	#485	C₂²×C₇₉	1	4	yes	—
416	#485	C₂²×C₇₉	1	4	yes	complemented
417	#485	C₂²×C₇₉	1	4	yes	complemented
418	#484	C₂²×C₇₉	1	2	yes	—
419	#484	C₂²×C₇₉	1	4	yes	complemented
420	#483	C₂²×C₇₉	1	2	yes	—
421	#483	C₂²×C₇₉	1	4	yes	complemented
422	#482	C₂²×C₇₉	1	4	yes	—
423	#482	C₂²×C₇₉	1	4	yes	—
424	#479	C₂²×C₇₉	1	4	yes	complemented
425	#477	C₂²×C₇₉	1	2	yes	complemented
426	#476	C₂²×C₇₉	1	2	yes	—
427	#475	C₂²×C₇₉	1	2	yes	complemented
428	#474	C₂²×C₇₉	1	2	yes	—
429	#468	C₂²×C₇₉	1	4	yes	—
430	#468	C₂²×C₇₉	1	4	yes	—
431	#465	C₂²×C₇₉	1	4	yes	—
432	#465	C₂²×C₇₉	1	4	yes	—
433	#461	C₂²×C₇₉	1	2	yes	—
434	#461	C₂²×C₇₉	1	2	yes	—
435	#450	C₂²×C₇₉	1	2	yes	—
436	#450	C₂²×C₇₉	1	2	yes	—
437	#448	C₂²×C₇₉	1	4	yes	—
438	#448	C₂²×C₇₉	1	4	yes	—
439	#440	C₂²×C₇₉	1	4	yes	—
440	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
441	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
442	#436	C₂²×C₇₉	1	2	yes	complemented
443	#435	C₂²×C₇₉	1	4	yes	complemented
444	C₈×D₄	C₂²×C₇₉	1	2	yes	complemented
445	#432	C₂²×C₇₉	1	1	yes	characteristic
446	#431	C₂²×C₇₉	1	1	yes	characteristic
447	#428	C₂²×C₇₉	1	4	yes	complemented
448	#427	C₂²×C₇₉	1	4	yes	complemented
449	#419	C₂²×C₇₉	1	4	yes	complemented
450	C₂×#103	C₂²×C₇₉	1	4	yes	complemented
451	#408	C₂²×C₇₉	1	4	yes	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	C₂³×C₇₉	1	2	yes	—
454	C₂²×Q₈	C₂³×C₇₉	1	4	yes	—
455	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
459	C₂×SD₁₆	C₂³×C₇₉	1	4	yes	—
460	C₂×M₁₆	C₂³×C₇₉	1	4	yes	—
461	C₂²×C₈	C₂³×C₇₉	1	4	yes	—
462	C₄⋊Q₈	—	2	4	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
471	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
472	#127	—	2	2	no	—
473	#127	D₄×C₇₉	1	1	yes	characteristic
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#126	—	2	4	no	—
477	#125	—	2	1	no	—
478	#125	—	2	1	no	—
479	#125	C₂³×C₇₉	1	2	yes	—
480	#124	—	2	2	no	—
481	#124	—	2	4	no	—
482	#124	—	2	2	no	—
483	#124	—	2	2	no	—
484	#124	—	2	4	no	—
485	#124	D₄×C₇₉	1	2	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
499	C₂²⋊Q₈	C₂³×C₇₉	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₇₉	1	4	yes	—
501	#121	—	2	2	no	—
502	#121	—	2	4	no	—
503	#121	D₄×C₇₉	1	2	yes	—
504	#121	D₄×C₇₉	1	2	yes	—
505	#121	C₂³×C₇₉	1	4	yes	—
506	#121	C₂³×C₇₉	1	4	yes	—
507	#120	—	2	4	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
516	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	C₂³×C₇₉	1	2	yes	—
525	C₄×D₄	C₂³×C₇₉	1	2	yes	—
526	C₄×D₄	C₂³×C₇₉	1	2	yes	—
527	C₄×D₄	C₂³×C₇₉	1	2	yes	—
528	#117	—	2	1	no	—
529	#117	—	2	1	no	—
530	#117	—	2	2	no	—
531	#117	C₂³×C₇₉	1	2	yes	—
532	#117	C₂³×C₇₉	1	4	yes	—
533	#117	C₂³×C₇₉	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
538	#107	C₂³×C₇₉	1	4	yes	—
539	#107	C₂³×C₇₉	1	4	yes	—
540	#107	C₂³×C₇₉	1	4	yes	—
541	#106	C₂³×C₇₉	1	2	yes	—
542	#106	C₂³×C₇₉	1	4	yes	—
543	#106	C₂³×C₇₉	1	2	yes	—
544	#106	C₂³×C₇₉	1	4	yes	—
545	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
546	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
547	#103	C₂³×C₇₉	1	2	yes	—
548	#103	C₂³×C₇₉	1	4	yes	—
549	#103	C₂³×C₇₉	1	4	yes	—
550	#103	C₂³×C₇₉	1	4	yes	—
551	#103	C₂³×C₇₉	1	2	yes	—
552	#103	C₂³×C₇₉	1	4	yes	—
553	#103	C₂³×C₇₉	1	4	yes	—
554	#102	C₂³×C₇₉	1	2	yes	—
555	#102	C₂³×C₇₉	1	2	yes	—
556	#102	C₂³×C₇₉	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
560	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
561	#97	C₂³×C₇₉	1	2	yes	—
562	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
564	C₂⁴	—	2	1	no	—
565	#41	—	4	4	no	—
566	#41	—	8	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
575	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
582	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₇₉	1	4	yes	—
584	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
585	C₂×D₄	C₂⁴×C₇₉	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
596	SD₁₆	—	4	2	no	—
597	SD₁₆	—	4	4	no	—
598	SD₁₆	—	4	2	no	—
599	M₁₆	—	4	4	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
602	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
603	C₂×C₈	C₂⁴×C₇₉	1	4	yes	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
623	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
625	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
641	C₂²⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	4	no	—
647	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
649	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
650	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
651	C₂³	—	2	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	8	1	no	—
654	C₂³	—	8	1	no	—
655	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
656	C₂³	C₂²×D₄×C₇₉	1	4	yes	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	—	8	1	no	—
665	Q₈	—	8	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	2	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	2	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	1	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
695	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
698	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
699	C₈	—	2	2	no	—
700	C₈	—	2	4	no	—
701	C₈	—	2	2	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	8	4	no	—
712	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	#577×C₇₉	1	2	yes	—
726	C₄	#585×C₇₉	1	2	yes	—
727	C₂	—	4	1	no	—
728	C₂	—	4	4	no	—
729	C₂	—	8	2	no	—
730	C₂	C₇₉×#3485	1	1	yes	characteristic
731	C₂	C₂×#577×C₇₉	1	1	yes	characteristic
732	C₂	C₇₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
prime radical	C₇₉×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ #532×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3550	C₂	semidirect
3. C₇₉×#3353	C₂	semidirect
4. C₇₉×#3350	C₂	semidirect
5. C₇₉×#3340	C₂	semidirect
6. C₇₉×#3329	C₂	semidirect
7. C₇₉×#3320	C₂	semidirect
8. C₇₉×#3298	C₂	semidirect
9. C₇₉×#3237	C₂	semidirect
10. C₇₉×#3231	C₂	semidirect
11. C₇₉×#3200	C₂	semidirect
12. C₇₉×#3110	C₂	semidirect
13. C₇₉×#3101	C₂	semidirect
14. C₇₉×#3097	C₂	semidirect
15. C₇₉×#2981	C₂	semidirect
21. #556×C₇₉	C₂²	semidirect
22. #556×C₇₉	C₂²	semidirect
26. D₄×Q₈×C₇₉	C₂²	semidirect
27. D₄×Q₈×C₇₉	C₂²	semidirect
41. #501×C₇₉	C₂²	semidirect
42. #500×C₇₉	C₂²	semidirect
43. #498×C₇₉	C₂²	semidirect
44. #491×C₇₉	C₂²	semidirect
45. #487×C₇₉	C₂²	semidirect
46. #487×C₇₉	C₂²	semidirect
49. #485×C₇₉	C₂²	semidirect
50. #485×C₇₉	C₂²	semidirect
52. #484×C₇₉	C₂²	semidirect
54. #483×C₇₉	C₂²	semidirect
57. #479×C₇₉	C₂²	semidirect
58. #477×C₇₉	C₂²	semidirect
60. #475×C₇₉	C₂²	semidirect
75. #436×C₇₉	C₂²	semidirect
76. #435×C₇₉	C₂²	semidirect
77. C₈×D₄×C₇₉	C₂²	semidirect
80. #428×C₇₉	C₂²	semidirect
81. #427×C₇₉	C₂²	semidirect
82. #419×C₇₉	C₂²	semidirect
83. C₂×#103×C₇₉	C₂²	semidirect
360. #61803	C₇₉	direct (N × H)
367. #3550	C₂×C₇₉	semidirect
369. #3353	C₂×C₇₉	semidirect
370. #3350	C₂×C₇₉	semidirect
371. #3340	C₂×C₇₉	semidirect
372. #3329	C₂×C₇₉	semidirect
373. #3320	C₂×C₇₉	semidirect
374. #3298	C₂×C₇₉	semidirect
375. #3237	C₂×C₇₉	semidirect
376. #3231	C₂×C₇₉	semidirect
377. #3200	C₂×C₇₉	semidirect
378. #3110	C₂×C₇₉	semidirect
379. #3101	C₂×C₇₉	semidirect
380. #3097	C₂×C₇₉	semidirect
381. #2981	C₂×C₇₉	semidirect
382. C₇₉	#61803	direct (N × H)
388. #556	C₂²×C₇₉	semidirect
389. #556	C₂²×C₇₉	semidirect
393. D₄×Q₈	C₂²×C₇₉	semidirect
394. D₄×Q₈	C₂²×C₇₉	semidirect
408. #501	C₂²×C₇₉	semidirect
409. #500	C₂²×C₇₉	semidirect
410. #498	C₂²×C₇₉	semidirect
411. #491	C₂²×C₇₉	semidirect
412. #487	C₂²×C₇₉	semidirect
413. #487	C₂²×C₇₉	semidirect
416. #485	C₂²×C₇₉	semidirect
417. #485	C₂²×C₇₉	semidirect
419. #484	C₂²×C₇₉	semidirect
421. #483	C₂²×C₇₉	semidirect
424. #479	C₂²×C₇₉	semidirect
425. #477	C₂²×C₇₉	semidirect
427. #475	C₂²×C₇₉	semidirect
442. #436	C₂²×C₇₉	semidirect
443. #435	C₂²×C₇₉	semidirect
444. C₈×D₄	C₂²×C₇₉	semidirect
447. #428	C₂²×C₇₉	semidirect
448. #427	C₂²×C₇₉	semidirect
449. #419	C₂²×C₇₉	semidirect
450. C₂×#103	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3550	2
C₇₉×#3506	2
C₇₉×#3353	2
C₇₉×#3350	2
C₇₉×#3340	2
C₇₉×#3329	2
C₇₉×#3320	2
C₇₉×#3298	2
C₇₉×#3237	2
C₇₉×#3231	2
C₇₉×#3200	2
C₇₉×#3110	2
C₇₉×#3101	2
C₇₉×#3097	2
C₇₉×#2981	2
#61803	79

Subgroups — C79×#61803 #34173492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#61803 #34173492