Subgroups — C₇₉×#61927 #34173616

Order 20224.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3401	C₂	1	2	yes	maximal, complemented
4	C₇₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#3394	C₂	1	2	yes	maximal, complemented
7	C₇₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#3371	C₂	1	2	yes	maximal, complemented
10	C₇₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#3365	C₂	1	2	yes	maximal, complemented
13	C₇₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3224	C₂	1	2	yes	maximal, complemented
16	C₇₉×#3222	C₂	1	2	yes	maximal, complemented
17	C₇₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₉×#3125	C₂	1	2	yes	maximal, complemented
20	C₇₉×#3120	C₂	1	2	yes	maximal, complemented
21	C₇₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#563×C₇₉	—	2	2	no	—
25	#559×C₇₉	C₂²	1	2	yes	—
26	#559×C₇₉	C₂²	1	2	yes	—
27	Q₈²×C₇₉	C₂²	1	1	yes	characteristic, complemented
28	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#557×C₇₉	C₂²	1	2	yes	complemented
30	#556×C₇₉	—	2	1	no	—
31	#556×C₇₉	C₂²	1	1	yes	characteristic
32	#556×C₇₉	C₂²	1	1	yes	characteristic
33	#556×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	#556×C₇₉	C₂²	1	2	yes	complemented
35	#555×C₇₉	—	2	1	no	—
36	#554×C₇₉	C₂²	1	1	yes	characteristic, complemented
37	#553×C₇₉	—	2	2	no	—
38	#552×C₇₉	—	2	1	no	—
39	#550×C₇₉	C₂²	1	1	yes	characteristic
40	#550×C₇₉	C₂²	1	1	yes	characteristic
41	#547×C₇₉	—	2	1	no	—
42	#544×C₇₉	—	2	1	no	—
43	#542×C₇₉	C₂²	1	2	yes	—
44	#541×C₇₉	—	2	1	no	—
45	#541×C₇₉	—	2	2	no	—
46	#541×C₇₉	C₂²	1	2	yes	—
47	#538×C₇₉	—	2	2	no	—
48	#535×C₇₉	C₂²	1	2	yes	—
49	#533×C₇₉	C₂²	1	1	yes	characteristic
50	#533×C₇₉	C₂²	1	1	yes	characteristic
51	#532×C₇₉	C₂²	1	1	yes	characteristic
52	#529×C₇₉	C₂²	1	1	yes	characteristic
53	#525×C₇₉	—	2	1	no	—
54	#525×C₇₉	—	2	1	no	—
55	#520×C₇₉	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
57	#497×C₇₉	C₂²	1	2	yes	—
58	#496×C₇₉	C₂²	1	2	yes	—
59	#495×C₇₉	C₂²	1	2	yes	—
60	#495×C₇₉	C₂²	1	2	yes	complemented
61	#494×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	#492×C₇₉	C₂²	1	2	yes	—
63	#492×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	#490×C₇₉	C₂²	1	2	yes	—
65	#489×C₇₉	C₂²	1	2	yes	—
66	#488×C₇₉	C₂²	1	2	yes	—
67	#488×C₇₉	C₂²	1	2	yes	complemented
68	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
69	#486×C₇₉	C₂²	1	2	yes	—
70	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
71	#484×C₇₉	C₂²	1	1	yes	characteristic
72	#483×C₇₉	C₂²	1	2	yes	—
73	#481×C₇₉	C₂²	1	1	yes	characteristic
74	#479×C₇₉	C₂²	1	2	yes	complemented
75	#478×C₇₉	C₂²	1	1	yes	characteristic
76	#478×C₇₉	C₂²	1	1	yes	characteristic
77	#478×C₇₉	C₂²	1	2	yes	complemented
78	#476×C₇₉	C₂²	1	1	yes	characteristic
79	#476×C₇₉	C₂²	1	1	yes	characteristic
80	#476×C₇₉	C₂²	1	2	yes	complemented
81	#475×C₇₉	C₂²	1	2	yes	complemented
82	#464×C₇₉	C₂²	1	2	yes	—
83	#464×C₇₉	C₂²	1	2	yes	—
84	#464×C₇₉	C₂²	1	2	yes	—
85	#464×C₇₉	C₂²	1	2	yes	complemented
86	#464×C₇₉	C₂²	1	2	yes	complemented
87	#464×C₇₉	C₂²	1	2	yes	complemented
88	#463×C₇₉	C₂²	1	2	yes	—
89	#463×C₇₉	C₂²	1	1	yes	characteristic
90	#463×C₇₉	C₂²	1	1	yes	characteristic
91	#463×C₇₉	C₂²	1	2	yes	complemented
92	#462×C₇₉	C₂²	1	1	yes	characteristic, complemented
93	#462×C₇₉	C₂²	1	2	yes	complemented
94	#461×C₇₉	C₂²	1	1	yes	characteristic
95	#461×C₇₉	C₂²	1	1	yes	characteristic
96	#461×C₇₉	C₂²	1	1	yes	characteristic, complemented
97	#461×C₇₉	C₂²	1	2	yes	complemented
98	#460×C₇₉	C₂²	1	2	yes	—
99	#460×C₇₉	C₂²	1	2	yes	—
100	#460×C₇₉	C₂²	1	2	yes	—
101	#460×C₇₉	C₂²	1	1	yes	characteristic, complemented
102	#459×C₇₉	C₂²	1	2	yes	—
103	#459×C₇₉	C₂²	1	1	yes	characteristic, complemented
104	#452×C₇₉	C₂²	1	2	yes	—
105	#452×C₇₉	C₂²	1	2	yes	—
106	#452×C₇₉	C₂²	1	2	yes	—
107	#450×C₇₉	C₂²	1	2	yes	—
108	#450×C₇₉	C₂²	1	1	yes	characteristic
109	#449×C₇₉	C₂²	1	2	yes	—
110	#447×C₇₉	C₂²	1	1	yes	characteristic
111	#446×C₇₉	C₂²	1	1	yes	characteristic, complemented
112	#446×C₇₉	C₂²	1	1	yes	characteristic, complemented
113	#446×C₇₉	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
117	#442×C₇₉	C₂²	1	2	yes	complemented
118	#441×C₇₉	C₂²	1	2	yes	complemented
119	#441×C₇₉	C₂²	1	2	yes	complemented
120	#440×C₇₉	C₂²	1	2	yes	complemented
121	C₄×Q₁₆×C₇₉	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	complemented
129	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
131	#433×C₇₉	C₂²	1	2	yes	—
132	#433×C₇₉	C₂²	1	2	yes	—
133	#431×C₇₉	C₂²	1	1	yes	characteristic
134	#431×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₇₉	—	2	1	no	—
136	C₂×#41×C₇₉	—	2	1	no	—
137	C₂×#41×C₇₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇₉	—	2	1	no	—
140	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
151	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₇₉	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₇₉	—	2	2	no	—
155	C₄⋊Q₈×C₇₉	—	2	2	no	—
156	C₄⋊Q₈×C₇₉	—	2	1	no	—
157	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
159	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
164	#127×C₇₉	C₂³	1	2	yes	—
165	#127×C₇₉	C₂³	1	1	yes	characteristic
166	#127×C₇₉	C₂³	1	2	yes	—
167	#126×C₇₉	—	2	2	no	—
168	#126×C₇₉	—	2	2	no	—
169	#126×C₇₉	—	2	2	no	—
170	#126×C₇₉	—	2	2	no	—
171	#126×C₇₉	—	2	2	no	—
172	#126×C₇₉	—	2	2	no	—
173	#126×C₇₉	—	2	2	no	—
174	#126×C₇₉	—	2	2	no	—
175	#126×C₇₉	—	2	1	no	—
176	#125×C₇₉	—	2	2	no	—
177	#125×C₇₉	—	2	2	no	—
178	#125×C₇₉	—	2	2	no	—
179	#125×C₇₉	—	2	2	no	—
180	#125×C₇₉	—	2	2	no	—
181	#125×C₇₉	—	2	1	no	—
182	#125×C₇₉	—	2	1	no	—
183	#125×C₇₉	D₄	1	2	yes	—
184	#125×C₇₉	C₂³	1	1	yes	characteristic
185	#125×C₇₉	C₂³	1	2	yes	—
186	#124×C₇₉	—	2	2	no	—
187	#124×C₇₉	—	2	2	no	—
188	#124×C₇₉	—	2	2	no	—
189	#124×C₇₉	C₂³	1	1	yes	characteristic
190	#124×C₇₉	C₂³	1	2	yes	—
191	#124×C₇₉	C₂³	1	2	yes	—
192	#124×C₇₉	C₂³	1	2	yes	—
193	#124×C₇₉	C₂³	1	2	yes	—
194	#123×C₇₉	—	2	1	no	—
195	#123×C₇₉	—	2	2	no	—
196	#123×C₇₉	—	2	2	no	—
197	#123×C₇₉	—	2	2	no	—
198	#123×C₇₉	—	2	2	no	—
199	#123×C₇₉	—	2	2	no	—
200	C₂²⋊Q₈×C₇₉	—	2	1	no	—
201	C₂²⋊Q₈×C₇₉	—	2	1	no	—
202	C₂²⋊Q₈×C₇₉	—	2	1	no	—
203	C₂²⋊Q₈×C₇₉	—	2	1	no	—
204	C₂²⋊Q₈×C₇₉	—	2	2	no	—
205	C₂²⋊Q₈×C₇₉	—	2	1	no	—
206	C₂²⋊Q₈×C₇₉	—	2	2	no	—
207	C₂²⋊Q₈×C₇₉	—	2	2	no	—
208	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
211	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
213	#121×C₇₉	—	2	1	no	—
214	#121×C₇₉	—	2	1	no	—
215	#121×C₇₉	—	2	1	no	—
216	#121×C₇₉	—	2	1	no	—
217	#121×C₇₉	—	2	2	no	—
218	#121×C₇₉	—	2	2	no	—
219	#121×C₇₉	—	2	2	no	—
220	#121×C₇₉	—	2	2	no	—
221	#121×C₇₉	C₂³	1	1	yes	characteristic
222	#120×C₇₉	—	2	2	no	—
223	#120×C₇₉	—	2	2	no	—
224	C₄×Q₈×C₇₉	—	2	1	no	—
225	C₄×Q₈×C₇₉	—	2	1	no	—
226	C₄×Q₈×C₇₉	—	2	2	no	—
227	C₄×Q₈×C₇₉	—	2	1	no	—
228	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
233	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
234	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
235	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
238	C₄×D₄×C₇₉	—	2	1	no	—
239	C₄×D₄×C₇₉	—	2	2	no	—
240	C₄×D₄×C₇₉	—	2	2	no	—
241	C₄×D₄×C₇₉	—	2	2	no	—
242	C₄×D₄×C₇₉	—	2	2	no	—
243	C₄×D₄×C₇₉	—	2	1	no	—
244	C₄×D₄×C₇₉	—	2	1	no	—
245	C₄×D₄×C₇₉	—	2	1	no	—
246	C₄×D₄×C₇₉	—	2	1	no	—
247	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₉	C₂³	1	2	yes	—
253	C₄×D₄×C₇₉	C₂³	1	2	yes	—
254	C₄×D₄×C₇₉	C₂³	1	2	yes	—
255	#117×C₇₉	—	2	1	no	—
256	#117×C₇₉	—	2	2	no	—
257	#117×C₇₉	—	2	1	no	—
258	#117×C₇₉	—	2	1	no	—
259	#117×C₇₉	—	2	2	no	—
260	#117×C₇₉	—	2	1	no	—
261	#117×C₇₉	—	2	1	no	—
262	#117×C₇₉	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
264	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
267	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
268	#107×C₇₉	C₂³	1	1	yes	characteristic
269	#107×C₇₉	C₂³	1	1	yes	characteristic
270	#106×C₇₉	C₂³	1	1	yes	characteristic
271	#106×C₇₉	C₂³	1	2	yes	—
272	#106×C₇₉	C₂³	1	1	yes	characteristic
273	#106×C₇₉	C₂³	1	2	yes	—
274	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
279	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
282	#103×C₇₉	C₂³	1	1	yes	characteristic
283	#103×C₇₉	C₂³	1	2	yes	—
284	#103×C₇₉	C₂³	1	2	yes	—
285	#103×C₇₉	C₂³	1	1	yes	characteristic
286	#103×C₇₉	C₂³	1	2	yes	—
287	#103×C₇₉	C₂³	1	2	yes	—
288	#103×C₇₉	C₂³	1	2	yes	—
289	#103×C₇₉	C₂³	1	2	yes	—
290	#102×C₇₉	C₂³	1	1	yes	characteristic
291	#102×C₇₉	C₂³	1	1	yes	characteristic
292	#102×C₇₉	C₂³	1	1	yes	characteristic
293	#102×C₇₉	C₂³	1	1	yes	characteristic
294	#102×C₇₉	C₂³	1	1	yes	characteristic
295	#102×C₇₉	C₂³	1	1	yes	characteristic
296	#102×C₇₉	C₂³	1	2	yes	—
297	#102×C₇₉	C₂³	1	2	yes	—
298	#102×C₇₉	C₂³	1	2	yes	—
299	#102×C₇₉	C₂³	1	2	yes	—
300	#102×C₇₉	C₂³	1	2	yes	—
301	#102×C₇₉	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
305	#97×C₇₉	C₂³	1	2	yes	—
306	#97×C₇₉	C₂³	1	2	yes	—
307	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₇₉	C₂³	1	2	yes	—
310	C₄×C₈×C₇₉	C₂³	1	2	yes	—
311	C₄×C₈×C₇₉	C₂³	1	2	yes	—
312	C₂⁴×C₇₉	—	2	1	no	—
313	#41×C₇₉	—	4	2	no	—
314	#41×C₇₉	—	4	2	no	—
315	#41×C₇₉	—	8	2	no	—
316	#41×C₇₉	—	8	2	no	—
317	C₂×Q₈×C₇₉	—	2	1	no	—
318	C₂×Q₈×C₇₉	—	2	2	no	—
319	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
325	C₂×D₄×C₇₉	—	2	2	no	—
326	C₂×D₄×C₇₉	—	2	1	no	—
327	C₂×D₄×C₇₉	—	2	1	no	—
328	C₂×D₄×C₇₉	—	2	1	no	—
329	C₂×D₄×C₇₉	—	2	2	no	—
330	C₂×D₄×C₇₉	—	2	2	no	—
331	C₂×D₄×C₇₉	—	2	1	no	—
332	C₂×D₄×C₇₉	—	2	2	no	—
333	C₂×D₄×C₇₉	—	2	2	no	—
334	C₂×D₄×C₇₉	—	4	1	no	—
335	C₂×D₄×C₇₉	—	4	1	no	—
336	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
339	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₇₉	—	2	1	no	—
341	C₂²×C₄×C₇₉	—	2	1	no	—
342	C₂²×C₄×C₇₉	—	2	2	no	—
343	C₂²×C₄×C₇₉	—	2	1	no	—
344	C₂²×C₄×C₇₉	—	2	1	no	—
345	C₂²×C₄×C₇₉	—	2	2	no	—
346	C₂²×C₄×C₇₉	—	2	2	no	—
347	C₂²×C₄×C₇₉	—	2	2	no	—
348	C₂²×C₄×C₇₉	—	2	1	no	—
349	C₂²×C₄×C₇₉	—	2	1	no	—
350	C₂²×C₄×C₇₉	—	8	2	no	—
351	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
354	Q₁₆×C₇₉	—	4	2	no	—
355	Q₁₆×C₇₉	—	4	2	no	—
356	Q₁₆×C₇₉	—	4	2	no	—
357	SD₁₆×C₇₉	—	4	2	no	—
358	SD₁₆×C₇₉	—	4	1	no	—
359	SD₁₆×C₇₉	—	4	1	no	—
360	SD₁₆×C₇₉	—	4	2	no	—
361	SD₁₆×C₇₉	—	4	2	no	—
362	SD₁₆×C₇₉	—	4	2	no	—
363	SD₁₆×C₇₉	—	4	2	no	—
364	SD₁₆×C₇₉	—	4	2	no	—
365	D₈×C₇₉	—	4	1	no	—
366	D₈×C₇₉	—	4	2	no	—
367	D₈×C₇₉	—	4	1	no	—
368	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
371	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
373	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₇₉	—	2	1	no	—
375	C₄⋊C₄×C₇₉	—	2	1	no	—
376	C₄⋊C₄×C₇₉	—	2	2	no	—
377	C₄⋊C₄×C₇₉	—	2	2	no	—
378	C₄⋊C₄×C₇₉	—	2	2	no	—
379	C₄⋊C₄×C₇₉	—	2	1	no	—
380	C₄⋊C₄×C₇₉	—	2	1	no	—
381	C₄⋊C₄×C₇₉	—	2	2	no	—
382	C₄⋊C₄×C₇₉	—	2	1	no	—
383	C₄⋊C₄×C₇₉	—	2	1	no	—
384	C₄⋊C₄×C₇₉	—	2	1	no	—
385	C₄⋊C₄×C₇₉	—	2	1	no	—
386	C₄⋊C₄×C₇₉	—	2	2	no	—
387	C₄⋊C₄×C₇₉	—	2	2	no	—
388	C₄⋊C₄×C₇₉	—	2	1	no	—
389	C₄⋊C₄×C₇₉	—	2	2	no	—
390	C₄⋊C₄×C₇₉	—	2	2	no	—
391	C₄⋊C₄×C₇₉	—	2	2	no	—
392	C₄⋊C₄×C₇₉	—	2	2	no	—
393	C₄⋊C₄×C₇₉	—	2	2	no	—
394	C₄⋊C₄×C₇₉	—	2	2	no	—
395	C₄⋊C₄×C₇₉	—	2	1	no	—
396	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₇₉	—	2	2	no	—
411	C₂²⋊C₄×C₇₉	—	2	1	no	—
412	C₂²⋊C₄×C₇₉	—	2	1	no	—
413	C₂²⋊C₄×C₇₉	—	2	1	no	—
414	C₂²⋊C₄×C₇₉	—	2	1	no	—
415	C₂²⋊C₄×C₇₉	—	2	1	no	—
416	C₂²⋊C₄×C₇₉	—	2	1	no	—
417	C₂²⋊C₄×C₇₉	—	2	2	no	—
418	C₂²⋊C₄×C₇₉	—	2	2	no	—
419	C₂²⋊C₄×C₇₉	—	2	2	no	—
420	C₂²⋊C₄×C₇₉	—	2	2	no	—
421	C₂²⋊C₄×C₇₉	—	2	1	no	—
422	C₂²⋊C₄×C₇₉	—	2	1	no	—
423	C₂²⋊C₄×C₇₉	—	2	2	no	—
424	C₂²⋊C₄×C₇₉	—	2	2	no	—
425	C₂²⋊C₄×C₇₉	—	2	2	no	—
426	C₂²⋊C₄×C₇₉	—	2	2	no	—
427	C₂²⋊C₄×C₇₉	—	2	2	no	—
428	C₂²⋊C₄×C₇₉	—	2	2	no	—
429	C₂²⋊C₄×C₇₉	—	2	1	no	—
430	C₂²⋊C₄×C₇₉	—	2	2	no	—
431	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
433	C₄²×C₇₉	—	2	2	no	—
434	C₄²×C₇₉	—	2	2	no	—
435	C₄²×C₇₉	—	2	2	no	—
436	C₄²×C₇₉	—	2	1	no	—
437	C₄²×C₇₉	—	2	2	no	—
438	C₄²×C₇₉	—	2	2	no	—
439	C₄²×C₇₉	—	2	2	no	—
440	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
443	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
444	C₄²×C₇₉	C₂⁴	1	2	yes	—
445	C₄²×C₇₉	C₂⁴	1	2	yes	—
446	C₂³×C₇₉	—	2	1	no	—
447	C₂³×C₇₉	—	2	1	no	—
448	C₂³×C₇₉	—	2	1	no	—
449	C₂³×C₇₉	—	2	2	no	—
450	C₂³×C₇₉	—	4	2	no	—
451	C₂³×C₇₉	—	8	1	no	—
452	C₂³×C₇₉	—	8	1	no	—
453	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₇₉	—	2	2	no	—
455	Q₈×C₇₉	—	2	2	no	—
456	Q₈×C₇₉	—	2	1	no	—
457	Q₈×C₇₉	—	2	2	no	—
458	Q₈×C₇₉	—	2	2	no	—
459	Q₈×C₇₉	—	2	1	no	—
460	Q₈×C₇₉	—	2	2	no	—
461	Q₈×C₇₉	—	2	2	no	—
462	Q₈×C₇₉	—	4	2	no	—
463	Q₈×C₇₉	—	8	1	no	—
464	Q₈×C₇₉	—	8	2	no	—
465	D₄×C₇₉	—	2	1	no	—
466	D₄×C₇₉	—	2	1	no	—
467	D₄×C₇₉	—	2	1	no	—
468	D₄×C₇₉	—	2	1	no	—
469	D₄×C₇₉	—	2	2	no	—
470	D₄×C₇₉	—	2	1	no	—
471	D₄×C₇₉	—	2	1	no	—
472	D₄×C₇₉	—	2	2	no	—
473	D₄×C₇₉	—	4	2	no	—
474	D₄×C₇₉	—	4	4	no	—
475	D₄×C₇₉	—	4	2	no	—
476	D₄×C₇₉	—	8	1	no	—
477	D₄×C₇₉	—	8	2	no	—
478	D₄×C₇₉	—	8	2	no	—
479	D₄×C₇₉	—	8	2	no	—
480	D₄×C₇₉	—	8	2	no	—
481	D₄×C₇₉	—	8	1	no	—
482	C₂×C₄×C₇₉	—	2	2	no	—
483	C₂×C₄×C₇₉	—	2	1	no	—
484	C₂×C₄×C₇₉	—	2	1	no	—
485	C₂×C₄×C₇₉	—	2	2	no	—
486	C₂×C₄×C₇₉	—	2	1	no	—
487	C₂×C₄×C₇₉	—	2	1	no	—
488	C₂×C₄×C₇₉	—	2	2	no	—
489	C₂×C₄×C₇₉	—	2	1	no	—
490	C₂×C₄×C₇₉	—	2	1	no	—
491	C₂×C₄×C₇₉	—	2	1	no	—
492	C₂×C₄×C₇₉	—	2	2	no	—
493	C₂×C₄×C₇₉	—	4	1	no	—
494	C₂×C₄×C₇₉	—	4	4	no	—
495	C₂×C₄×C₇₉	—	4	2	no	—
496	C₂×C₄×C₇₉	—	4	2	no	—
497	C₂×C₄×C₇₉	—	4	2	no	—
498	C₂×C₄×C₇₉	—	8	2	no	—
499	C₂×C₄×C₇₉	—	8	1	no	—
500	C₂×C₄×C₇₉	—	8	1	no	—
501	C₂×C₄×C₇₉	—	8	2	no	—
502	C₂×C₄×C₇₉	—	8	2	no	—
503	C₂×C₄×C₇₉	—	8	1	no	—
504	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
514	C₈×C₇₉	—	2	1	no	—
515	C₈×C₇₉	—	2	2	no	—
516	C₈×C₇₉	—	2	1	no	—
517	C₈×C₇₉	—	2	1	no	—
518	C₈×C₇₉	—	2	2	no	—
519	C₈×C₇₉	—	2	1	no	—
520	C₂²×C₇₉	—	2	1	no	—
521	C₂²×C₇₉	—	2	1	no	—
522	C₂²×C₇₉	—	2	1	no	—
523	C₂²×C₇₉	—	4	1	no	—
524	C₂²×C₇₉	—	4	2	no	—
525	C₂²×C₇₉	—	4	1	no	—
526	C₂²×C₇₉	—	4	1	no	—
527	C₂²×C₇₉	—	4	2	no	—
528	C₂²×C₇₉	—	4	1	no	—
529	C₂²×C₇₉	—	4	1	no	—
530	C₂²×C₇₉	—	4	1	no	—
531	C₂²×C₇₉	—	4	1	no	—
532	C₂²×C₇₉	—	4	1	no	—
533	C₂²×C₇₉	—	4	1	no	—
534	C₂²×C₇₉	—	4	2	no	—
535	C₂²×C₇₉	—	8	4	no	—
536	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₇₉	—	2	1	no	—
538	C₄×C₇₉	—	2	1	no	—
539	C₄×C₇₉	—	2	2	no	—
540	C₄×C₇₉	—	2	2	no	—
541	C₄×C₇₉	—	2	1	no	—
542	C₄×C₇₉	—	2	1	no	—
543	C₄×C₇₉	—	2	2	no	—
544	C₄×C₇₉	—	2	2	no	—
545	C₄×C₇₉	—	4	2	no	—
546	C₄×C₇₉	—	4	1	no	—
547	C₄×C₇₉	—	4	2	no	—
548	C₄×C₇₉	—	4	1	no	—
549	C₄×C₇₉	—	4	2	no	—
550	C₄×C₇₉	—	4	1	no	—
551	C₄×C₇₉	—	4	1	no	—
552	C₄×C₇₉	—	4	1	no	—
553	C₄×C₇₉	#577	1	2	yes	—
554	C₄×C₇₉	#585	1	1	yes	characteristic
555	C₄×C₇₉	#585	1	1	yes	characteristic
556	#61927	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
557	C₂×C₇₉	—	4	1	no	—
558	C₂×C₇₉	—	8	1	no	—
559	C₂×C₇₉	—	8	2	no	—
560	C₂×C₇₉	—	8	1	no	—
561	C₂×C₇₉	—	8	1	no	—
562	C₂×C₇₉	#3487	1	1	yes	characteristic
563	C₂×C₇₉	C₂×#577	1	1	yes	characteristic
564	C₂×C₇₉	#3584	1	1	yes	characteristic
565	#3555	C₂×C₇₉	1	1	yes	characteristic, complemented
566	#3506	C₂×C₇₉	1	1	yes	characteristic, complemented
567	#3401	C₂×C₇₉	1	2	yes	complemented
568	#3398	C₂×C₇₉	1	1	yes	characteristic, complemented
569	#3397	C₂×C₇₉	1	1	yes	characteristic, complemented
570	#3394	C₂×C₇₉	1	2	yes	complemented
571	#3393	C₂×C₇₉	1	1	yes	characteristic, complemented
572	#3392	C₂×C₇₉	1	1	yes	characteristic, complemented
573	#3371	C₂×C₇₉	1	2	yes	complemented
574	#3369	C₂×C₇₉	1	1	yes	characteristic, complemented
575	#3366	C₂×C₇₉	1	1	yes	characteristic, complemented
576	#3365	C₂×C₇₉	1	2	yes	complemented
577	#3362	C₂×C₇₉	1	1	yes	characteristic, complemented
578	#3360	C₂×C₇₉	1	1	yes	characteristic, complemented
579	#3224	C₂×C₇₉	1	2	yes	complemented
580	#3222	C₂×C₇₉	1	2	yes	complemented
581	#3212	C₂×C₇₉	1	1	yes	characteristic, complemented
582	#3210	C₂×C₇₉	1	1	yes	characteristic, complemented
583	#3125	C₂×C₇₉	1	2	yes	complemented
584	#3120	C₂×C₇₉	1	2	yes	complemented
585	#3105	C₂×C₇₉	1	1	yes	characteristic, complemented
586	#3101	C₂×C₇₉	1	1	yes	characteristic, complemented
587	#2986	C₂×C₇₉	1	1	yes	characteristic, complemented
588	C₇₉	#61927	1	1	yes	characteristic, direct product factor, Sylow
589	#563	—	2	2	no	—
590	#559	C₂²×C₇₉	1	2	yes	—
591	#559	C₂²×C₇₉	1	2	yes	—
592	Q₈²	C₂²×C₇₉	1	1	yes	characteristic, complemented
593	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
594	#557	C₂²×C₇₉	1	2	yes	complemented
595	#556	—	2	1	no	—
596	#556	C₂²×C₇₉	1	1	yes	characteristic
597	#556	C₂²×C₇₉	1	1	yes	characteristic
598	#556	C₂²×C₇₉	1	1	yes	characteristic, complemented
599	#556	C₂²×C₇₉	1	2	yes	complemented
600	#555	—	2	1	no	—
601	#554	C₂²×C₇₉	1	1	yes	characteristic, complemented
602	#553	—	2	2	no	—
603	#552	—	2	1	no	—
604	#550	C₂²×C₇₉	1	1	yes	characteristic
605	#550	C₂²×C₇₉	1	1	yes	characteristic
606	#547	—	2	1	no	—
607	#544	—	2	1	no	—
608	#542	C₂²×C₇₉	1	2	yes	—
609	#541	—	2	1	no	—
610	#541	—	2	2	no	—
611	#541	C₂²×C₇₉	1	2	yes	—
612	#538	—	2	2	no	—
613	#535	C₂²×C₇₉	1	2	yes	—
614	#533	C₂²×C₇₉	1	1	yes	characteristic
615	#533	C₂²×C₇₉	1	1	yes	characteristic
616	#532	C₂²×C₇₉	1	1	yes	characteristic
617	#529	C₂²×C₇₉	1	1	yes	characteristic
618	#525	—	2	1	no	—
619	#525	—	2	1	no	—
620	#520	C₂²×C₇₉	1	2	yes	—
621	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
622	#497	C₂²×C₇₉	1	2	yes	—
623	#496	C₂²×C₇₉	1	2	yes	—
624	#495	C₂²×C₇₉	1	2	yes	—
625	#495	C₂²×C₇₉	1	2	yes	complemented
626	#494	C₂²×C₇₉	1	1	yes	characteristic, complemented
627	#492	C₂²×C₇₉	1	2	yes	—
628	#492	C₂²×C₇₉	1	1	yes	characteristic, complemented
629	#490	C₂²×C₇₉	1	2	yes	—
630	#489	C₂²×C₇₉	1	2	yes	—
631	#488	C₂²×C₇₉	1	2	yes	—
632	#488	C₂²×C₇₉	1	2	yes	complemented
633	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
634	#486	C₂²×C₇₉	1	2	yes	—
635	#486	C₂²×C₇₉	1	1	yes	characteristic, complemented
636	#484	C₂²×C₇₉	1	1	yes	characteristic
637	#483	C₂²×C₇₉	1	2	yes	—
638	#481	C₂²×C₇₉	1	1	yes	characteristic
639	#479	C₂²×C₇₉	1	2	yes	complemented
640	#478	C₂²×C₇₉	1	1	yes	characteristic
641	#478	C₂²×C₇₉	1	1	yes	characteristic
642	#478	C₂²×C₇₉	1	2	yes	complemented
643	#476	C₂²×C₇₉	1	1	yes	characteristic
644	#476	C₂²×C₇₉	1	1	yes	characteristic
645	#476	C₂²×C₇₉	1	2	yes	complemented
646	#475	C₂²×C₇₉	1	2	yes	complemented
647	#464	C₂²×C₇₉	1	2	yes	—
648	#464	C₂²×C₇₉	1	2	yes	—
649	#464	C₂²×C₇₉	1	2	yes	—
650	#464	C₂²×C₇₉	1	2	yes	complemented
651	#464	C₂²×C₇₉	1	2	yes	complemented
652	#464	C₂²×C₇₉	1	2	yes	complemented
653	#463	C₂²×C₇₉	1	2	yes	—
654	#463	C₂²×C₇₉	1	1	yes	characteristic
655	#463	C₂²×C₇₉	1	1	yes	characteristic
656	#463	C₂²×C₇₉	1	2	yes	complemented
657	#462	C₂²×C₇₉	1	1	yes	characteristic, complemented
658	#462	C₂²×C₇₉	1	2	yes	complemented
659	#461	C₂²×C₇₉	1	1	yes	characteristic
660	#461	C₂²×C₇₉	1	1	yes	characteristic
661	#461	C₂²×C₇₉	1	1	yes	characteristic, complemented
662	#461	C₂²×C₇₉	1	2	yes	complemented
663	#460	C₂²×C₇₉	1	2	yes	—
664	#460	C₂²×C₇₉	1	2	yes	—
665	#460	C₂²×C₇₉	1	2	yes	—
666	#460	C₂²×C₇₉	1	1	yes	characteristic, complemented
667	#459	C₂²×C₇₉	1	2	yes	—
668	#459	C₂²×C₇₉	1	1	yes	characteristic, complemented
669	#452	C₂²×C₇₉	1	2	yes	—
670	#452	C₂²×C₇₉	1	2	yes	—
671	#452	C₂²×C₇₉	1	2	yes	—
672	#450	C₂²×C₇₉	1	2	yes	—
673	#450	C₂²×C₇₉	1	1	yes	characteristic
674	#449	C₂²×C₇₉	1	2	yes	—
675	#447	C₂²×C₇₉	1	1	yes	characteristic
676	#446	C₂²×C₇₉	1	1	yes	characteristic, complemented
677	#446	C₂²×C₇₉	1	1	yes	characteristic, complemented
678	#446	C₂²×C₇₉	1	2	yes	complemented
679	C₈×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
680	C₈×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
681	C₈×Q₈	C₂²×C₇₉	1	2	yes	complemented
682	#442	C₂²×C₇₉	1	2	yes	complemented
683	#441	C₂²×C₇₉	1	2	yes	complemented
684	#441	C₂²×C₇₉	1	2	yes	complemented
685	#440	C₂²×C₇₉	1	2	yes	complemented
686	C₄×Q₁₆	C₂²×C₇₉	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	complemented
694	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
695	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
696	#433	C₂²×C₇₉	1	2	yes	—
697	#433	C₂²×C₇₉	1	2	yes	—
698	#431	C₂²×C₇₉	1	1	yes	characteristic
699	#431	C₂²×C₇₉	1	1	yes	characteristic
700	C₂×#41	—	2	1	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₇₉	1	2	yes	—
703	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₇₉	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₇₉	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
716	C₂×D₈	C₂³×C₇₉	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₇₉	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₇₉	1	2	yes	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
723	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
729	#127	C₂³×C₇₉	1	1	yes	characteristic
730	#127	C₂³×C₇₉	1	2	yes	—
731	#127	C₂³×C₇₉	1	2	yes	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	D₄×C₇₉	1	2	yes	—
749	#125	C₂³×C₇₉	1	1	yes	characteristic
750	#125	C₂³×C₇₉	1	2	yes	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	C₂³×C₇₉	1	1	yes	characteristic
755	#124	C₂³×C₇₉	1	2	yes	—
756	#124	C₂³×C₇₉	1	2	yes	—
757	#124	C₂³×C₇₉	1	2	yes	—
758	#124	C₂³×C₇₉	1	2	yes	—
759	#123	—	2	1	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
774	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
775	C₂²⋊Q₈	D₄×C₇₉	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	C₂³×C₇₉	1	1	yes	characteristic
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
794	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
795	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
797	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
798	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
799	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
800	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₇₉	1	2	yes	—
817	C₄×D₄	C₂³×C₇₉	1	2	yes	—
818	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₇₉	1	2	yes	—
820	#117	—	2	1	no	—
821	#117	—	2	2	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₇₉	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	2	no	—
829	C₂×C₄⋊C₄	—	2	1	no	—
830	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	—	2	1	no	—
832	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
833	#107	C₂³×C₇₉	1	1	yes	characteristic
834	#107	C₂³×C₇₉	1	1	yes	characteristic
835	#106	C₂³×C₇₉	1	1	yes	characteristic
836	#106	C₂³×C₇₉	1	2	yes	—
837	#106	C₂³×C₇₉	1	1	yes	characteristic
838	#106	C₂³×C₇₉	1	2	yes	—
839	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
844	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
845	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
846	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
847	#103	C₂³×C₇₉	1	1	yes	characteristic
848	#103	C₂³×C₇₉	1	2	yes	—
849	#103	C₂³×C₇₉	1	2	yes	—
850	#103	C₂³×C₇₉	1	1	yes	characteristic
851	#103	C₂³×C₇₉	1	2	yes	—
852	#103	C₂³×C₇₉	1	2	yes	—
853	#103	C₂³×C₇₉	1	2	yes	—
854	#103	C₂³×C₇₉	1	2	yes	—
855	#102	C₂³×C₇₉	1	1	yes	characteristic
856	#102	C₂³×C₇₉	1	1	yes	characteristic
857	#102	C₂³×C₇₉	1	1	yes	characteristic
858	#102	C₂³×C₇₉	1	1	yes	characteristic
859	#102	C₂³×C₇₉	1	1	yes	characteristic
860	#102	C₂³×C₇₉	1	1	yes	characteristic
861	#102	C₂³×C₇₉	1	2	yes	—
862	#102	C₂³×C₇₉	1	2	yes	—
863	#102	C₂³×C₇₉	1	2	yes	—
864	#102	C₂³×C₇₉	1	2	yes	—
865	#102	C₂³×C₇₉	1	2	yes	—
866	#102	C₂³×C₇₉	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
870	#97	C₂³×C₇₉	1	2	yes	—
871	#97	C₂³×C₇₉	1	2	yes	—
872	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₇₉	1	2	yes	—
875	C₄×C₈	C₂³×C₇₉	1	2	yes	—
876	C₄×C₈	C₂³×C₇₉	1	2	yes	—
877	C₂⁴	—	2	1	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	8	2	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
886	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
888	C₂×Q₈	C₂⁴×C₇₉	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	4	1	no	—
900	C₂×D₄	—	4	1	no	—
901	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₇₉	1	2	yes	—
904	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	8	2	no	—
916	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	Q₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	D₈	—	4	2	no	—
932	D₈	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
936	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
938	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
1006	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₇₉	1	2	yes	—
1010	C₄²	C₂⁴×C₇₉	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	1	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	8	4	no	—
1101	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	#577×C₇₉	1	2	yes	—
1119	C₄	#585×C₇₉	1	1	yes	characteristic
1120	C₄	#585×C₇₉	1	1	yes	characteristic
1121	C₂	—	4	1	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	C₇₉×#3487	1	1	yes	characteristic
1127	C₂	C₂×#577×C₇₉	1	1	yes	characteristic
1128	C₂	C₇₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ #533×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3555	C₂	semidirect
2. C₇₉×#3506	C₂	semidirect
3. C₇₉×#3401	C₂	semidirect
4. C₇₉×#3398	C₂	semidirect
5. C₇₉×#3397	C₂	semidirect
6. C₇₉×#3394	C₂	semidirect
7. C₇₉×#3393	C₂	semidirect
8. C₇₉×#3392	C₂	semidirect
9. C₇₉×#3371	C₂	semidirect
10. C₇₉×#3369	C₂	semidirect
11. C₇₉×#3366	C₂	semidirect
12. C₇₉×#3365	C₂	semidirect
13. C₇₉×#3362	C₂	semidirect
14. C₇₉×#3360	C₂	semidirect
15. C₇₉×#3224	C₂	semidirect
16. C₇₉×#3222	C₂	semidirect
17. C₇₉×#3212	C₂	semidirect
18. C₇₉×#3210	C₂	semidirect
19. C₇₉×#3125	C₂	semidirect
20. C₇₉×#3120	C₂	semidirect
21. C₇₉×#3105	C₂	semidirect
22. C₇₉×#3101	C₂	semidirect
23. C₇₉×#2986	C₂	semidirect
27. Q₈²×C₇₉	C₂²	semidirect
28. #557×C₇₉	C₂²	semidirect
29. #557×C₇₉	C₂²	semidirect
33. #556×C₇₉	C₂²	semidirect
34. #556×C₇₉	C₂²	semidirect
36. #554×C₇₉	C₂²	semidirect
60. #495×C₇₉	C₂²	semidirect
61. #494×C₇₉	C₂²	semidirect
63. #492×C₇₉	C₂²	semidirect
67. #488×C₇₉	C₂²	semidirect
68. #487×C₇₉	C₂²	semidirect
70. #486×C₇₉	C₂²	semidirect
74. #479×C₇₉	C₂²	semidirect
77. #478×C₇₉	C₂²	semidirect
80. #476×C₇₉	C₂²	semidirect
81. #475×C₇₉	C₂²	semidirect
85. #464×C₇₉	C₂²	semidirect
86. #464×C₇₉	C₂²	semidirect
87. #464×C₇₉	C₂²	semidirect
91. #463×C₇₉	C₂²	semidirect
92. #462×C₇₉	C₂²	semidirect
93. #462×C₇₉	C₂²	semidirect
96. #461×C₇₉	C₂²	semidirect
97. #461×C₇₉	C₂²	semidirect
101. #460×C₇₉	C₂²	semidirect
103. #459×C₇₉	C₂²	semidirect
111. #446×C₇₉	C₂²	semidirect
112. #446×C₇₉	C₂²	semidirect
113. #446×C₇₉	C₂²	semidirect
114. C₈×Q₈×C₇₉	C₂²	semidirect
115. C₈×Q₈×C₇₉	C₂²	semidirect
116. C₈×Q₈×C₇₉	C₂²	semidirect
117. #442×C₇₉	C₂²	semidirect
118. #441×C₇₉	C₂²	semidirect
119. #441×C₇₉	C₂²	semidirect
120. #440×C₇₉	C₂²	semidirect
121. C₄×Q₁₆×C₇₉	C₂²	semidirect
126. C₄×SD₁₆×C₇₉	C₂²	semidirect
127. C₄×SD₁₆×C₇₉	C₂²	semidirect
128. C₄×SD₁₆×C₇₉	C₂²	semidirect
556. #61927	C₇₉	direct (N × H)
565. #3555	C₂×C₇₉	semidirect
566. #3506	C₂×C₇₉	semidirect
567. #3401	C₂×C₇₉	semidirect
568. #3398	C₂×C₇₉	semidirect
569. #3397	C₂×C₇₉	semidirect
570. #3394	C₂×C₇₉	semidirect
571. #3393	C₂×C₇₉	semidirect
572. #3392	C₂×C₇₉	semidirect
573. #3371	C₂×C₇₉	semidirect
574. #3369	C₂×C₇₉	semidirect
575. #3366	C₂×C₇₉	semidirect
576. #3365	C₂×C₇₉	semidirect
577. #3362	C₂×C₇₉	semidirect
578. #3360	C₂×C₇₉	semidirect
579. #3224	C₂×C₇₉	semidirect
580. #3222	C₂×C₇₉	semidirect
581. #3212	C₂×C₇₉	semidirect
582. #3210	C₂×C₇₉	semidirect
583. #3125	C₂×C₇₉	semidirect
584. #3120	C₂×C₇₉	semidirect
585. #3105	C₂×C₇₉	semidirect
586. #3101	C₂×C₇₉	semidirect
587. #2986	C₂×C₇₉	semidirect
588. C₇₉	#61927	direct (N × H)
592. Q₈²	C₂²×C₇₉	semidirect
593. #557	C₂²×C₇₉	semidirect
594. #557	C₂²×C₇₉	semidirect
598. #556	C₂²×C₇₉	semidirect
599. #556	C₂²×C₇₉	semidirect
601. #554	C₂²×C₇₉	semidirect
625. #495	C₂²×C₇₉	semidirect
626. #494	C₂²×C₇₉	semidirect
628. #492	C₂²×C₇₉	semidirect
632. #488	C₂²×C₇₉	semidirect
633. #487	C₂²×C₇₉	semidirect
635. #486	C₂²×C₇₉	semidirect
639. #479	C₂²×C₇₉	semidirect
642. #478	C₂²×C₇₉	semidirect
645. #476	C₂²×C₇₉	semidirect
646. #475	C₂²×C₇₉	semidirect
650. #464	C₂²×C₇₉	semidirect
651. #464	C₂²×C₇₉	semidirect
652. #464	C₂²×C₇₉	semidirect
656. #463	C₂²×C₇₉	semidirect
657. #462	C₂²×C₇₉	semidirect
658. #462	C₂²×C₇₉	semidirect
661. #461	C₂²×C₇₉	semidirect
662. #461	C₂²×C₇₉	semidirect
666. #460	C₂²×C₇₉	semidirect
668. #459	C₂²×C₇₉	semidirect
676. #446	C₂²×C₇₉	semidirect
677. #446	C₂²×C₇₉	semidirect
678. #446	C₂²×C₇₉	semidirect
679. C₈×Q₈	C₂²×C₇₉	semidirect
680. C₈×Q₈	C₂²×C₇₉	semidirect
681. C₈×Q₈	C₂²×C₇₉	semidirect
682. #442	C₂²×C₇₉	semidirect
683. #441	C₂²×C₇₉	semidirect
684. #441	C₂²×C₇₉	semidirect
685. #440	C₂²×C₇₉	semidirect
686. C₄×Q₁₆	C₂²×C₇₉	semidirect
691. C₄×SD₁₆	C₂²×C₇₉	semidirect
692. C₄×SD₁₆	C₂²×C₇₉	semidirect
693. C₄×SD₁₆	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×#3555	2
C₇₉×#3506	2
C₇₉×#3401	2
C₇₉×#3398	2
C₇₉×#3397	2
C₇₉×#3394	2
C₇₉×#3393	2
C₇₉×#3392	2
C₇₉×#3371	2
C₇₉×#3369	2
C₇₉×#3366	2
C₇₉×#3365	2
C₇₉×#3362	2
C₇₉×#3360	2
C₇₉×#3224	2
C₇₉×#3222	2
C₇₉×#3212	2
C₇₉×#3210	2
C₇₉×#3125	2
C₇₉×#3120	2
C₇₉×#3105	2
C₇₉×#3101	2
C₇₉×#2986	2
#61927	79

Subgroups — C79×#61927 #34173616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#61927 #34173616