Subgroups — C₇₉×#36516 #34148205

Order 20224.

2514 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2855	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2561	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2534	C₂	1	2	yes	maximal
7	C₇₉×#2503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2477	C₂	1	4	yes	maximal, complemented
10	C₇₉×#2475	C₂	1	4	yes	maximal, complemented
11	C₇₉×#2439	C₂	1	2	yes	maximal, complemented
12	C₇₉×#2415	C₂	1	2	yes	maximal, complemented
13	C₇₉×#2362	C₂	1	2	yes	maximal, complemented
14	C₇₉×#2352	C₂	1	2	yes	maximal, complemented
15	C₇₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₇₉	C₂	1	2	yes	maximal, complemented
17	C₄×#120×C₇₉	C₂	1	1	yes	maximal, characteristic
18	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
19	#554×C₇₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#125×C₇₉	C₂²	1	2	yes	complemented
22	C₂×#123×C₇₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
28	C₂×#120×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₉	—	2	8	no	—
34	C₂×#117×C₇₉	C₂²	1	2	yes	—
35	C₂×#117×C₇₉	C₂²	1	2	yes	—
36	C₂×#117×C₇₉	C₂²	1	4	yes	—
37	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
42	#400×C₇₉	C₂²	1	4	yes	complemented
43	#398×C₇₉	C₂²	1	2	yes	complemented
44	#397×C₇₉	C₂²	1	4	yes	—
45	#397×C₇₉	C₂²	1	2	yes	complemented
46	#396×C₇₉	C₂²	1	4	yes	—
47	#394×C₇₉	C₂²	1	4	yes	—
48	#393×C₇₉	C₂²	1	4	yes	—
49	#391×C₇₉	C₂²	1	4	yes	complemented
50	#391×C₇₉	C₂²	1	2	yes	complemented
51	#389×C₇₉	C₂²	1	4	yes	complemented
52	#389×C₇₉	C₂²	1	2	yes	complemented
53	#389×C₇₉	C₂²	1	2	yes	complemented
54	#388×C₇₉	C₂²	1	4	yes	—
55	#388×C₇₉	C₂²	1	4	yes	—
56	#388×C₇₉	C₂²	1	4	yes	—
57	#388×C₇₉	C₂²	1	4	yes	complemented
58	#387×C₇₉	C₂²	1	4	yes	complemented
59	#387×C₇₉	C₂²	1	4	yes	complemented
60	#387×C₇₉	C₂²	1	4	yes	complemented
61	#387×C₇₉	C₂²	1	4	yes	complemented
62	#386×C₇₉	C₂²	1	4	yes	—
63	#386×C₇₉	C₂²	1	1	yes	characteristic
64	#386×C₇₉	C₂²	1	2	yes	—
65	#385×C₇₉	C₂²	1	1	yes	characteristic
66	#385×C₇₉	C₂²	1	2	yes	—
67	#385×C₇₉	C₂²	1	2	yes	—
68	#385×C₇₉	C₂²	1	4	yes	—
69	#382×C₇₉	C₂²	1	2	yes	complemented
70	#381×C₇₉	C₂²	1	2	yes	—
71	#381×C₇₉	C₂²	1	2	yes	—
72	#381×C₇₉	C₂²	1	2	yes	—
73	#380×C₇₉	C₂²	1	2	yes	—
74	#380×C₇₉	C₂²	1	1	yes	characteristic
75	#380×C₇₉	C₂²	1	2	yes	—
76	#380×C₇₉	C₂²	1	2	yes	complemented
77	#379×C₇₉	C₂²	1	2	yes	—
78	#379×C₇₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₇₉	C₂²	1	4	yes	complemented
80	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	complemented
85	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇₉	—	2	4	no	—
91	C₂³×C₄×C₇₉	—	2	8	no	—
92	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₇₉	—	2	4	no	—
101	#125×C₇₉	—	2	8	no	—
102	#123×C₇₉	—	2	8	no	—
103	C₂²⋊Q₈×C₇₉	—	2	8	no	—
104	C₂²⋊Q₈×C₇₉	—	2	4	no	—
105	C₂²⋊Q₈×C₇₉	—	2	8	no	—
106	C₂²⋊Q₈×C₇₉	—	2	8	no	—
107	C₂²⋊Q₈×C₇₉	—	2	4	no	—
108	#120×C₇₉	—	2	4	no	—
109	C₄×Q₈×C₇₉	—	2	4	no	—
110	C₄×D₄×C₇₉	—	2	8	no	—
111	C₄×D₄×C₇₉	—	2	4	no	—
112	C₄×D₄×C₇₉	—	2	8	no	—
113	#117×C₇₉	—	2	8	no	—
114	#117×C₇₉	—	2	16	no	—
115	#117×C₇₉	—	2	8	no	—
116	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₇₉	D₄	1	8	yes	complemented
119	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
137	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₇₉	—	2	8	no	—
154	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
155	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
160	#95×C₇₉	C₂³	1	2	yes	—
161	#95×C₇₉	C₂³	1	2	yes	—
162	#95×C₇₉	C₂³	1	2	yes	—
163	#95×C₇₉	C₂³	1	4	yes	—
164	#95×C₇₉	C₂³	1	4	yes	—
165	#95×C₇₉	C₂³	1	4	yes	—
166	#95×C₇₉	C₂³	1	4	yes	—
167	#95×C₇₉	C₂³	1	4	yes	—
168	#95×C₇₉	C₂³	1	2	yes	—
169	#95×C₇₉	C₂³	1	4	yes	—
170	#95×C₇₉	C₂³	1	4	yes	—
171	#95×C₇₉	C₂³	1	4	yes	—
172	#95×C₇₉	C₂³	1	4	yes	—
173	C₂⁴×C₇₉	—	2	2	no	—
174	C₂⁴×C₇₉	—	2	4	no	—
175	C₂⁴×C₇₉	—	2	2	no	—
176	C₂⁴×C₇₉	—	2	2	no	—
177	C₂⁴×C₇₉	—	4	2	no	—
178	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
180	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
181	C₂×Q₈×C₇₉	—	2	2	no	—
182	C₂×Q₈×C₇₉	—	2	4	no	—
183	C₂×Q₈×C₇₉	—	2	4	no	—
184	C₂×Q₈×C₇₉	—	4	4	no	—
185	C₂×D₄×C₇₉	—	2	2	no	—
186	C₂×D₄×C₇₉	—	2	2	no	—
187	C₂×D₄×C₇₉	—	2	4	no	—
188	C₂×D₄×C₇₉	—	2	4	no	—
189	C₂×D₄×C₇₉	—	4	2	no	—
190	C₂×D₄×C₇₉	#41	1	4	yes	—
191	C₂²×C₄×C₇₉	—	2	32	no	—
192	C₂²×C₄×C₇₉	—	2	2	no	—
193	C₂²×C₄×C₇₉	—	2	4	no	—
194	C₂²×C₄×C₇₉	—	2	4	no	—
195	C₂²×C₄×C₇₉	—	2	4	no	—
196	C₂²×C₄×C₇₉	—	2	4	no	—
197	C₂²×C₄×C₇₉	—	2	4	no	—
198	C₂²×C₄×C₇₉	—	2	4	no	—
199	C₂²×C₄×C₇₉	—	2	4	no	—
200	C₂²×C₄×C₇₉	—	2	4	no	—
201	C₂²×C₄×C₇₉	—	2	4	no	—
202	C₂²×C₄×C₇₉	—	2	4	no	—
203	C₂²×C₄×C₇₉	—	2	2	no	—
204	C₂²×C₄×C₇₉	—	2	4	no	—
205	C₂²×C₄×C₇₉	—	2	4	no	—
206	C₂²×C₄×C₇₉	—	4	4	no	—
207	C₂²×C₄×C₇₉	—	4	4	no	—
208	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
210	C₂²×C₄×C₇₉	#41	1	8	yes	—
211	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
225	C₄⋊C₄×C₇₉	—	2	4	no	—
226	C₄⋊C₄×C₇₉	—	2	4	no	—
227	C₄⋊C₄×C₇₉	—	2	4	no	—
228	C₄⋊C₄×C₇₉	—	2	2	no	—
229	C₄⋊C₄×C₇₉	—	2	2	no	—
230	C₄⋊C₄×C₇₉	—	2	4	no	—
231	C₄⋊C₄×C₇₉	—	2	4	no	—
232	C₄⋊C₄×C₇₉	—	2	4	no	—
233	C₄⋊C₄×C₇₉	—	2	4	no	—
234	C₄⋊C₄×C₇₉	—	2	4	no	—
235	C₄⋊C₄×C₇₉	—	2	4	no	—
236	C₄⋊C₄×C₇₉	—	2	8	no	—
237	C₄⋊C₄×C₇₉	—	2	8	no	—
238	C₄⋊C₄×C₇₉	—	4	4	no	—
239	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
240	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
241	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
242	C₂²⋊C₄×C₇₉	—	2	4	no	—
243	C₂²⋊C₄×C₇₉	—	2	2	no	—
244	C₂²⋊C₄×C₇₉	—	2	4	no	—
245	C₂²⋊C₄×C₇₉	—	2	2	no	—
246	C₂²⋊C₄×C₇₉	—	2	8	no	—
247	C₂²⋊C₄×C₇₉	—	2	4	no	—
248	C₂²⋊C₄×C₇₉	—	2	8	no	—
249	C₂²⋊C₄×C₇₉	—	2	2	no	—
250	C₂²⋊C₄×C₇₉	—	2	8	no	—
251	C₂²⋊C₄×C₇₉	—	2	8	no	—
252	C₂²⋊C₄×C₇₉	—	2	4	no	—
253	C₂²⋊C₄×C₇₉	—	2	2	no	—
254	C₂²⋊C₄×C₇₉	—	2	4	no	—
255	C₂²⋊C₄×C₇₉	—	2	4	no	—
256	C₂²⋊C₄×C₇₉	—	4	2	no	—
257	C₂²⋊C₄×C₇₉	—	4	4	no	—
258	C₄²×C₇₉	—	2	8	no	—
259	C₄²×C₇₉	—	2	8	no	—
260	C₄²×C₇₉	—	2	4	no	—
261	C₄²×C₇₉	—	2	2	no	—
262	C₄²×C₇₉	—	2	4	no	—
263	C₄²×C₇₉	—	4	4	no	—
264	C₂³×C₇₉	—	2	2	no	—
265	C₂³×C₇₉	—	2	2	no	—
266	C₂³×C₇₉	—	2	8	no	—
267	C₂³×C₇₉	—	2	2	no	—
268	C₂³×C₇₉	—	2	1	no	—
269	C₂³×C₇₉	—	2	2	no	—
270	C₂³×C₇₉	—	2	2	no	—
271	C₂³×C₇₉	—	2	2	no	—
272	C₂³×C₇₉	—	2	1	no	—
273	C₂³×C₇₉	—	2	2	no	—
274	C₂³×C₇₉	—	2	2	no	—
275	C₂³×C₇₉	—	2	2	no	—
276	C₂³×C₇₉	—	2	2	no	—
277	C₂³×C₇₉	—	4	8	no	—
278	C₂³×C₇₉	—	4	8	no	—
279	C₂³×C₇₉	—	4	4	no	—
280	C₂³×C₇₉	—	4	4	no	—
281	C₂³×C₇₉	C₂²×D₄	1	2	yes	—
282	C₂³×C₇₉	C₂×#41	1	2	yes	—
283	C₂³×C₇₉	C₂×#41	1	4	yes	—
284	C₂³×C₇₉	C₂×#41	1	2	yes	—
285	C₂³×C₇₉	2₋¹⁺⁴	1	2	yes	—
286	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
287	Q₈×C₇₉	—	4	4	no	—
288	Q₈×C₇₉	—	8	4	no	—
289	D₄×C₇₉	—	2	8	no	—
290	D₄×C₇₉	—	4	8	no	—
291	C₂×C₄×C₇₉	—	2	16	no	—
292	C₂×C₄×C₇₉	—	2	8	no	—
293	C₂×C₄×C₇₉	—	2	2	no	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	2	no	—
296	C₂×C₄×C₇₉	—	2	2	no	—
297	C₂×C₄×C₇₉	—	2	1	no	—
298	C₂×C₄×C₇₉	—	2	4	no	—
299	C₂×C₄×C₇₉	—	2	4	no	—
300	C₂×C₄×C₇₉	—	2	8	no	—
301	C₂×C₄×C₇₉	—	2	16	no	—
302	C₂×C₄×C₇₉	—	2	4	no	—
303	C₂×C₄×C₇₉	—	2	2	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	2	1	no	—
306	C₂×C₄×C₇₉	—	2	2	no	—
307	C₂×C₄×C₇₉	—	2	2	no	—
308	C₂×C₄×C₇₉	—	2	2	no	—
309	C₂×C₄×C₇₉	—	2	4	no	—
310	C₂×C₄×C₇₉	—	2	2	no	—
311	C₂×C₄×C₇₉	—	2	4	no	—
312	C₂×C₄×C₇₉	—	2	2	no	—
313	C₂×C₄×C₇₉	—	2	4	no	—
314	C₂×C₄×C₇₉	—	2	4	no	—
315	C₂×C₄×C₇₉	—	2	2	no	—
316	C₂×C₄×C₇₉	—	2	4	no	—
317	C₂×C₄×C₇₉	—	2	2	no	—
318	C₂×C₄×C₇₉	—	2	4	no	—
319	C₂×C₄×C₇₉	—	2	4	no	—
320	C₂×C₄×C₇₉	—	2	2	no	—
321	C₂×C₄×C₇₉	—	2	2	no	—
322	C₂×C₄×C₇₉	—	4	8	no	—
323	C₂×C₄×C₇₉	—	4	8	no	—
324	C₂×C₄×C₇₉	—	4	4	no	—
325	C₂×C₄×C₇₉	—	8	4	no	—
326	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
331	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
332	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
333	C₂²×C₇₉	—	2	2	no	—
334	C₂²×C₇₉	—	2	4	no	—
335	C₂²×C₇₉	—	2	2	no	—
336	C₂²×C₇₉	—	2	4	no	—
337	C₂²×C₇₉	—	2	4	no	—
338	C₂²×C₇₉	—	2	2	no	—
339	C₂²×C₇₉	—	2	4	no	—
340	C₂²×C₇₉	—	2	4	no	—
341	C₂²×C₇₉	—	2	4	no	—
342	C₂²×C₇₉	—	4	16	no	—
343	C₂²×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	4	2	no	—
345	C₂²×C₇₉	—	4	2	no	—
346	C₂²×C₇₉	—	4	1	no	—
347	C₂²×C₇₉	—	4	2	no	—
348	C₂²×C₇₉	—	4	2	no	—
349	C₂²×C₇₉	—	4	2	no	—
350	C₂²×C₇₉	#548	1	4	yes	—
351	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
352	C₂²×C₇₉	C₂²×#41	1	2	yes	—
353	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂²×C₇₉	#585	1	2	yes	—
356	C₄×C₇₉	—	2	2	no	—
357	C₄×C₇₉	—	2	4	no	—
358	C₄×C₇₉	—	2	2	no	—
359	C₄×C₇₉	—	2	4	no	—
360	C₄×C₇₉	—	2	4	no	—
361	C₄×C₇₉	—	4	1	no	—
362	C₄×C₇₉	—	4	2	no	—
363	C₄×C₇₉	—	4	4	no	—
364	C₄×C₇₉	—	4	4	no	—
365	C₄×C₇₉	—	4	2	no	—
366	C₄×C₇₉	—	4	2	no	—
367	C₄×C₇₉	—	4	1	no	—
368	C₄×C₇₉	—	4	2	no	—
369	C₄×C₇₉	#525	1	4	yes	—
370	#36516	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₇₉	—	2	4	no	—
372	C₂×C₇₉	—	4	2	no	—
373	C₂×C₇₉	—	4	4	no	—
374	C₂×C₇₉	C₂×#525	1	1	yes	characteristic
375	C₂×C₇₉	C₂×#548	1	1	yes	characteristic
376	C₂×C₇₉	#3475	1	2	yes	—
377	C₂×C₇₉	#3485	1	1	yes	characteristic
378	C₂×C₇₉	#3495	1	2	yes	—
379	C₂×#554	C₂×C₇₉	1	1	yes	characteristic, complemented
380	C₂²×#117	C₂×C₇₉	1	1	yes	characteristic, complemented
381	#2855	C₂×C₇₉	1	2	yes	complemented
382	#2848	C₂×C₇₉	1	1	yes	characteristic, complemented
383	#2561	C₂×C₇₉	1	2	yes	complemented
384	#2534	C₂×C₇₉	1	2	yes	—
385	#2503	C₂×C₇₉	1	1	yes	characteristic, complemented
386	#2486	C₂×C₇₉	1	1	yes	characteristic, complemented
387	#2477	C₂×C₇₉	1	4	yes	complemented
388	#2475	C₂×C₇₉	1	4	yes	complemented
389	#2439	C₂×C₇₉	1	2	yes	complemented
390	#2415	C₂×C₇₉	1	2	yes	complemented
391	#2362	C₂×C₇₉	1	2	yes	complemented
392	#2352	C₂×C₇₉	1	2	yes	complemented
393	#2345	C₂×C₇₉	1	1	yes	characteristic, complemented
394	C₄×#123	C₂×C₇₉	1	2	yes	complemented
395	C₄×#120	C₂×C₇₉	1	1	yes	characteristic
396	C₇₉	#36516	1	1	yes	characteristic, direct product factor, Sylow
397	C₂⁴×C₄	C₂²×C₇₉	1	1	yes	characteristic
398	#554	—	2	8	no	—
399	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
400	C₂×#125	C₂²×C₇₉	1	2	yes	complemented
401	C₂×#123	C₂²×C₇₉	1	2	yes	—
402	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
403	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
406	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	complemented
407	C₂×#120	C₂²×C₇₉	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
409	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
412	C₂×#117	—	2	8	no	—
413	C₂×#117	C₂²×C₇₉	1	2	yes	—
414	C₂×#117	C₂²×C₇₉	1	2	yes	—
415	C₂×#117	C₂²×C₇₉	1	4	yes	—
416	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
417	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
419	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
420	C₂²×C₄²	C₂²×C₇₉	1	2	yes	—
421	#400	C₂²×C₇₉	1	4	yes	complemented
422	#398	C₂²×C₇₉	1	2	yes	complemented
423	#397	C₂²×C₇₉	1	4	yes	—
424	#397	C₂²×C₇₉	1	2	yes	complemented
425	#396	C₂²×C₇₉	1	4	yes	—
426	#394	C₂²×C₇₉	1	4	yes	—
427	#393	C₂²×C₇₉	1	4	yes	—
428	#391	C₂²×C₇₉	1	4	yes	complemented
429	#391	C₂²×C₇₉	1	2	yes	complemented
430	#389	C₂²×C₇₉	1	4	yes	complemented
431	#389	C₂²×C₇₉	1	2	yes	complemented
432	#389	C₂²×C₇₉	1	2	yes	complemented
433	#388	C₂²×C₇₉	1	4	yes	—
434	#388	C₂²×C₇₉	1	4	yes	—
435	#388	C₂²×C₇₉	1	4	yes	—
436	#388	C₂²×C₇₉	1	4	yes	complemented
437	#387	C₂²×C₇₉	1	4	yes	complemented
438	#387	C₂²×C₇₉	1	4	yes	complemented
439	#387	C₂²×C₇₉	1	4	yes	complemented
440	#387	C₂²×C₇₉	1	4	yes	complemented
441	#386	C₂²×C₇₉	1	4	yes	—
442	#386	C₂²×C₇₉	1	2	yes	—
443	#386	C₂²×C₇₉	1	1	yes	characteristic
444	#385	C₂²×C₇₉	1	2	yes	—
445	#385	C₂²×C₇₉	1	4	yes	—
446	#385	C₂²×C₇₉	1	1	yes	characteristic
447	#385	C₂²×C₇₉	1	2	yes	—
448	#382	C₂²×C₇₉	1	2	yes	complemented
449	#381	C₂²×C₇₉	1	2	yes	—
450	#381	C₂²×C₇₉	1	2	yes	—
451	#381	C₂²×C₇₉	1	2	yes	—
452	#380	C₂²×C₇₉	1	1	yes	characteristic
453	#380	C₂²×C₇₉	1	2	yes	—
454	#380	C₂²×C₇₉	1	2	yes	—
455	#380	C₂²×C₇₉	1	2	yes	complemented
456	#379	C₂²×C₇₉	1	1	yes	characteristic
457	#379	C₂²×C₇₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	complemented
459	C₄×C₄⋊C₄	C₂²×C₇₉	1	4	yes	complemented
460	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₇₉	1	4	yes	complemented
464	C₂⁵	C₂³×C₇₉	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
467	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
468	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
469	C₂³×C₄	—	2	4	no	—
470	C₂³×C₄	—	2	8	no	—
471	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
472	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
474	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
477	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
478	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
479	C₄⋊Q₈	—	2	4	no	—
480	#125	—	2	8	no	—
481	#123	—	2	8	no	—
482	C₂²⋊Q₈	—	2	8	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	8	no	—
485	C₂²⋊Q₈	—	2	8	no	—
486	C₂²⋊Q₈	—	2	4	no	—
487	#120	—	2	4	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	8	no	—
492	#117	—	2	8	no	—
493	#117	—	2	16	no	—
494	#117	—	2	8	no	—
495	C₂×C₄⋊C₄	—	2	4	no	—
496	C₂×C₄⋊C₄	—	2	4	no	—
497	C₂×C₄⋊C₄	D₄×C₇₉	1	8	yes	complemented
498	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	—	2	8	no	—
516	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₇₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₇₉	1	4	yes	—
532	C₂×C₄²	—	2	8	no	—
533	C₂×C₄²	C₂³×C₇₉	1	4	yes	—
534	C₂×C₄²	C₂³×C₇₉	1	4	yes	—
535	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
536	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
538	C₂×C₄²	C₂³×C₇₉	1	4	yes	—
539	#95	C₂³×C₇₉	1	2	yes	—
540	#95	C₂³×C₇₉	1	2	yes	—
541	#95	C₂³×C₇₉	1	2	yes	—
542	#95	C₂³×C₇₉	1	4	yes	—
543	#95	C₂³×C₇₉	1	4	yes	—
544	#95	C₂³×C₇₉	1	4	yes	—
545	#95	C₂³×C₇₉	1	4	yes	—
546	#95	C₂³×C₇₉	1	4	yes	—
547	#95	C₂³×C₇₉	1	2	yes	—
548	#95	C₂³×C₇₉	1	4	yes	—
549	#95	C₂³×C₇₉	1	4	yes	—
550	#95	C₂³×C₇₉	1	4	yes	—
551	#95	C₂³×C₇₉	1	4	yes	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
558	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
559	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	4	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	#41×C₇₉	1	4	yes	—
570	C₂²×C₄	—	2	32	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
588	C₂²×C₄	C₂×D₄×C₇₉	1	8	yes	—
589	C₂²×C₄	#41×C₇₉	1	8	yes	—
590	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	8	no	—
616	C₄⋊C₄	—	2	8	no	—
617	C₄⋊C₄	—	4	4	no	—
618	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
619	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
620	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	8	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	4	2	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₄²	—	2	8	no	—
638	C₄²	—	2	8	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	4	4	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	8	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	8	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	C₂²×D₄×C₇₉	1	2	yes	—
661	C₂³	C₂×#41×C₇₉	1	2	yes	—
662	C₂³	C₂×#41×C₇₉	1	4	yes	—
663	C₂³	C₂×#41×C₇₉	1	2	yes	—
664	C₂³	2₋¹⁺⁴×C₇₉	1	2	yes	—
665	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
666	Q₈	—	4	4	no	—
667	Q₈	—	8	4	no	—
668	D₄	—	2	8	no	—
669	D₄	—	4	8	no	—
670	C₂×C₄	—	2	16	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	16	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
711	C₂×C₄	C₂×#41×C₇₉	1	4	yes	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	4	16	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	#548×C₇₉	1	4	yes	—
730	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
731	C₂²	C₂²×#41×C₇₉	1	2	yes	—
732	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
733	C₂²	C₂×2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
734	C₂²	#585×C₇₉	1	2	yes	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	4	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	4	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	#525×C₇₉	1	4	yes	—
749	C₂	—	2	4	no	—
750	C₂	—	4	4	no	—
751	C₂	—	4	2	no	—
752	C₂	C₂×#525×C₇₉	1	1	yes	characteristic
753	C₂	C₂×#548×C₇₉	1	1	yes	characteristic
754	C₂	C₇₉×#3475	1	2	yes	—
755	C₂	C₇₉×#3485	1	1	yes	characteristic
756	C₂	C₇₉×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
prime radical	C₂×#120×C₇₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₇₉	C₂	semidirect
2. C₂²×#117×C₇₉	C₂	semidirect
3. C₇₉×#2855	C₂	semidirect
4. C₇₉×#2848	C₂	semidirect
5. C₇₉×#2561	C₂	semidirect
7. C₇₉×#2503	C₂	semidirect
8. C₇₉×#2486	C₂	semidirect
9. C₇₉×#2477	C₂	semidirect
10. C₇₉×#2475	C₂	semidirect
11. C₇₉×#2439	C₂	semidirect
12. C₇₉×#2415	C₂	semidirect
13. C₇₉×#2362	C₂	semidirect
14. C₇₉×#2352	C₂	semidirect
15. C₇₉×#2345	C₂	semidirect
16. C₄×#123×C₇₉	C₂	semidirect
20. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
21. C₂×#125×C₇₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
42. #400×C₇₉	C₂²	semidirect
43. #398×C₇₉	C₂²	semidirect
45. #397×C₇₉	C₂²	semidirect
49. #391×C₇₉	C₂²	semidirect
50. #391×C₇₉	C₂²	semidirect
51. #389×C₇₉	C₂²	semidirect
52. #389×C₇₉	C₂²	semidirect
53. #389×C₇₉	C₂²	semidirect
57. #388×C₇₉	C₂²	semidirect
58. #387×C₇₉	C₂²	semidirect
59. #387×C₇₉	C₂²	semidirect
60. #387×C₇₉	C₂²	semidirect
61. #387×C₇₉	C₂²	semidirect
69. #382×C₇₉	C₂²	semidirect
76. #380×C₇₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₇₉	C₂²	semidirect
118. C₂×C₄⋊C₄×C₇₉	D₄	semidirect
370. #36516	C₇₉	direct (N × H)
379. C₂×#554	C₂×C₇₉	semidirect
380. C₂²×#117	C₂×C₇₉	semidirect
381. #2855	C₂×C₇₉	semidirect
382. #2848	C₂×C₇₉	semidirect
383. #2561	C₂×C₇₉	semidirect
385. #2503	C₂×C₇₉	semidirect
386. #2486	C₂×C₇₉	semidirect
387. #2477	C₂×C₇₉	semidirect
388. #2475	C₂×C₇₉	semidirect
389. #2439	C₂×C₇₉	semidirect
390. #2415	C₂×C₇₉	semidirect
391. #2362	C₂×C₇₉	semidirect
392. #2352	C₂×C₇₉	semidirect
393. #2345	C₂×C₇₉	semidirect
394. C₄×#123	C₂×C₇₉	semidirect
396. C₇₉	#36516	direct (N × H)
399. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
400. C₂×#125	C₂²×C₇₉	semidirect
405. C₂×C₂²⋊Q₈	C₂²×C₇₉	semidirect
406. C₂×C₂²⋊Q₈	C₂²×C₇₉	semidirect
408. C₂×C₄×Q₈	C₂²×C₇₉	semidirect
418. C₂²×C₄⋊C₄	C₂²×C₇₉	semidirect
421. #400	C₂²×C₇₉	semidirect
422. #398	C₂²×C₇₉	semidirect
424. #397	C₂²×C₇₉	semidirect
428. #391	C₂²×C₇₉	semidirect
429. #391	C₂²×C₇₉	semidirect
430. #389	C₂²×C₇₉	semidirect
431. #389	C₂²×C₇₉	semidirect
432. #389	C₂²×C₇₉	semidirect
436. #388	C₂²×C₇₉	semidirect
437. #387	C₂²×C₇₉	semidirect
438. #387	C₂²×C₇₉	semidirect
439. #387	C₂²×C₇₉	semidirect
440. #387	C₂²×C₇₉	semidirect
448. #382	C₂²×C₇₉	semidirect
455. #380	C₂²×C₇₉	semidirect
458. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
459. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
463. C₄×C₂²⋊C₄	C₂²×C₇₉	semidirect
497. C₂×C₄⋊C₄	D₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₇₉	2
C₂²×#117×C₇₉	2
C₇₉×#2855	2
C₇₉×#2848	2
C₇₉×#2561	2
C₇₉×#2534	2
C₇₉×#2503	2
C₇₉×#2486	2
C₇₉×#2477	2
C₇₉×#2475	2
C₇₉×#2439	2
C₇₉×#2415	2
C₇₉×#2362	2
C₇₉×#2352	2
C₇₉×#2345	2
C₄×#123×C₇₉	2
C₄×#120×C₇₉	2
#36516	79

Subgroups — C79×#36516 #34148205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36516 #34148205