Subgroups — C₇₉×#62054 #34173743

Order 20224.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#3316	C₂	1	2	yes	maximal, complemented
9	C₇₉×#3299	C₂	1	2	yes	maximal, complemented
10	C₇₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#3282	C₂	1	2	yes	maximal, complemented
13	C₇₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₇₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₇₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₉×#3225	C₂	1	2	yes	maximal, complemented
18	C₇₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₉×#3120	C₂	1	2	yes	maximal, complemented
20	C₇₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇₉×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×#461×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₇₉	C₂²	1	2	yes	—
25	C₂×#135×C₇₉	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
27	#563×C₇₉	—	2	2	no	—
28	#557×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	#556×C₇₉	C₂²	1	1	yes	characteristic
30	#556×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	#554×C₇₉	—	2	1	no	—
32	#554×C₇₉	C₂²	1	2	yes	—
33	#553×C₇₉	—	2	1	no	—
34	#552×C₇₉	—	2	1	no	—
35	#551×C₇₉	—	2	2	no	—
36	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
37	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#548×C₇₉	—	2	1	no	—
40	#548×C₇₉	C₂²	1	2	yes	—
41	#547×C₇₉	C₂²	1	1	yes	characteristic
42	#547×C₇₉	C₂²	1	1	yes	characteristic
43	#547×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#546×C₇₉	C₂²	1	2	yes	—
45	#544×C₇₉	—	2	1	no	—
46	#542×C₇₉	—	2	1	no	—
47	#542×C₇₉	C₂²	1	2	yes	—
48	#541×C₇₉	C₂²	1	2	yes	complemented
49	#539×C₇₉	—	2	2	no	—
50	#539×C₇₉	—	2	2	no	—
51	#536×C₇₉	C₂²	1	2	yes	complemented
52	#533×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
54	#529×C₇₉	C₂²	1	1	yes	characteristic
55	#529×C₇₉	C₂²	1	1	yes	characteristic
56	#525×C₇₉	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
58	#520×C₇₉	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
60	#497×C₇₉	C₂²	1	2	yes	—
61	#495×C₇₉	C₂²	1	2	yes	—
62	#494×C₇₉	C₂²	1	1	yes	characteristic, complemented
63	#494×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	#489×C₇₉	C₂²	1	2	yes	complemented
65	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
66	#487×C₇₉	C₂²	1	2	yes	complemented
67	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
68	#484×C₇₉	C₂²	1	1	yes	characteristic
69	#484×C₇₉	C₂²	1	2	yes	complemented
70	#483×C₇₉	C₂²	1	2	yes	complemented
71	#481×C₇₉	C₂²	1	1	yes	characteristic
72	#479×C₇₉	C₂²	1	2	yes	complemented
73	#478×C₇₉	C₂²	1	1	yes	characteristic
74	#478×C₇₉	C₂²	1	1	yes	characteristic
75	#477×C₇₉	C₂²	1	2	yes	complemented
76	#475×C₇₉	C₂²	1	1	yes	characteristic, complemented
77	#475×C₇₉	C₂²	1	2	yes	complemented
78	#474×C₇₉	C₂²	1	1	yes	characteristic, complemented
79	#470×C₇₉	C₂²	1	2	yes	complemented
80	#468×C₇₉	C₂²	1	2	yes	—
81	#467×C₇₉	C₂²	1	2	yes	—
82	#467×C₇₉	C₂²	1	2	yes	complemented
83	#465×C₇₉	C₂²	1	2	yes	—
84	#465×C₇₉	C₂²	1	2	yes	—
85	#464×C₇₉	C₂²	1	2	yes	—
86	#464×C₇₉	C₂²	1	2	yes	—
87	#464×C₇₉	C₂²	1	2	yes	complemented
88	#464×C₇₉	C₂²	1	2	yes	complemented
89	#463×C₇₉	C₂²	1	2	yes	—
90	#463×C₇₉	C₂²	1	1	yes	characteristic
91	#463×C₇₉	C₂²	1	1	yes	characteristic
92	#462×C₇₉	C₂²	1	1	yes	characteristic, complemented
93	#462×C₇₉	C₂²	1	2	yes	complemented
94	#462×C₇₉	C₂²	1	2	yes	complemented
95	#462×C₇₉	C₂²	1	2	yes	complemented
96	#461×C₇₉	C₂²	1	1	yes	characteristic
97	#461×C₇₉	C₂²	1	1	yes	characteristic
98	#461×C₇₉	C₂²	1	1	yes	characteristic
99	#461×C₇₉	C₂²	1	2	yes	—
100	#461×C₇₉	C₂²	1	1	yes	characteristic
101	#461×C₇₉	C₂²	1	2	yes	—
102	#461×C₇₉	C₂²	1	2	yes	—
103	#461×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	complemented
107	#451×C₇₉	C₂²	1	2	yes	—
108	#451×C₇₉	C₂²	1	2	yes	—
109	#451×C₇₉	C₂²	1	2	yes	complemented
110	#450×C₇₉	C₂²	1	1	yes	characteristic
111	#449×C₇₉	C₂²	1	2	yes	—
112	#448×C₇₉	C₂²	1	2	yes	—
113	#447×C₇₉	C₂²	1	1	yes	characteristic
114	#446×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
116	#441×C₇₉	C₂²	1	2	yes	complemented
117	#440×C₇₉	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₇₉	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
124	#436×C₇₉	C₂²	1	1	yes	characteristic, complemented
125	#435×C₇₉	C₂²	1	2	yes	—
126	C₈×D₄×C₇₉	C₂²	1	2	yes	—
127	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
128	#433×C₇₉	C₂²	1	2	yes	complemented
129	#431×C₇₉	C₂²	1	1	yes	characteristic
130	#424×C₇₉	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
132	#417×C₇₉	C₂²	1	2	yes	complemented
133	C₂×#103×C₇₉	C₂²	1	2	yes	—
134	C₂×#103×C₇₉	C₂²	1	2	yes	complemented
135	C₂×#41×C₇₉	—	2	1	no	—
136	C₂×#41×C₇₉	C₂³	1	2	yes	—
137	C₂×#41×C₇₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₇₉	—	2	1	no	—
139	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
140	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇₉	—	2	1	no	—
143	#137×C₇₉	—	4	4	no	—
144	#135×C₇₉	—	4	4	no	—
145	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₇₉	—	4	4	no	—
151	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₇₉	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₇₉	C₂³	1	2	yes	—
158	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₇₉	—	2	2	no	—
164	C₄⋊Q₈×C₇₉	—	2	1	no	—
165	C₄⋊Q₈×C₇₉	—	2	1	no	—
166	C₄⋊Q₈×C₇₉	—	2	1	no	—
167	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
171	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
174	#126×C₇₉	—	2	2	no	—
175	#126×C₇₉	—	2	2	no	—
176	#126×C₇₉	—	2	2	no	—
177	#126×C₇₉	—	2	2	no	—
178	#126×C₇₉	—	2	2	no	—
179	#126×C₇₉	—	2	1	no	—
180	#126×C₇₉	D₄	1	2	yes	—
181	#125×C₇₉	—	2	2	no	—
182	#125×C₇₉	—	2	2	no	—
183	#125×C₇₉	—	2	2	no	—
184	#125×C₇₉	—	2	2	no	—
185	#125×C₇₉	—	2	1	no	—
186	#125×C₇₉	—	2	1	no	—
187	#125×C₇₉	D₄	1	1	yes	characteristic
188	#125×C₇₉	C₂³	1	1	yes	characteristic
189	#124×C₇₉	—	2	2	no	—
190	#124×C₇₉	—	2	2	no	—
191	#124×C₇₉	D₄	1	1	yes	characteristic
192	#124×C₇₉	C₂³	1	1	yes	characteristic
193	#124×C₇₉	C₂³	1	2	yes	—
194	#124×C₇₉	C₂³	1	2	yes	—
195	#123×C₇₉	—	2	1	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	#123×C₇₉	—	2	2	no	—
201	#123×C₇₉	—	2	2	no	—
202	#123×C₇₉	—	2	2	no	—
203	#123×C₇₉	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₇₉	—	2	1	no	—
205	C₂²⋊Q₈×C₇₉	—	2	1	no	—
206	C₂²⋊Q₈×C₇₉	—	2	1	no	—
207	C₂²⋊Q₈×C₇₉	—	2	2	no	—
208	C₂²⋊Q₈×C₇₉	—	2	1	no	—
209	C₂²⋊Q₈×C₇₉	—	2	1	no	—
210	C₂²⋊Q₈×C₇₉	—	2	2	no	—
211	C₂²⋊Q₈×C₇₉	—	2	2	no	—
212	C₂²⋊Q₈×C₇₉	—	2	2	no	—
213	C₂²⋊Q₈×C₇₉	—	2	2	no	—
214	C₂²⋊Q₈×C₇₉	—	2	2	no	—
215	C₂²⋊Q₈×C₇₉	—	2	2	no	—
216	C₂²⋊Q₈×C₇₉	—	2	2	no	—
217	C₂²⋊Q₈×C₇₉	—	2	2	no	—
218	C₂²⋊Q₈×C₇₉	—	2	2	no	—
219	C₂²⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
225	#121×C₇₉	—	2	1	no	—
226	#121×C₇₉	—	2	2	no	—
227	#121×C₇₉	—	2	1	no	—
228	#121×C₇₉	—	2	2	no	—
229	#121×C₇₉	D₄	1	1	yes	characteristic
230	#121×C₇₉	C₂³	1	1	yes	characteristic
231	#121×C₇₉	C₂³	1	2	yes	—
232	#120×C₇₉	—	2	2	no	—
233	C₄×Q₈×C₇₉	—	2	1	no	—
234	C₄×Q₈×C₇₉	—	2	1	no	—
235	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
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	2	no	—
246	C₄×D₄×C₇₉	—	2	2	no	—
247	C₄×D₄×C₇₉	—	2	2	no	—
248	C₄×D₄×C₇₉	—	2	1	no	—
249	C₄×D₄×C₇₉	—	2	1	no	—
250	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₇₉	C₂³	1	2	yes	—
254	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₇₉	C₂³	1	2	yes	—
257	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
263	#117×C₇₉	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
273	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
274	#107×C₇₉	C₂³	1	1	yes	characteristic
275	#107×C₇₉	C₂³	1	1	yes	characteristic
276	#107×C₇₉	C₂³	1	2	yes	—
277	#106×C₇₉	C₂³	1	1	yes	characteristic
278	#106×C₇₉	C₂³	1	2	yes	—
279	#106×C₇₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
285	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
287	#103×C₇₉	C₂³	1	2	yes	—
288	#103×C₇₉	C₂³	1	2	yes	—
289	#103×C₇₉	C₂³	1	2	yes	—
290	#103×C₇₉	C₂³	1	1	yes	characteristic
291	#103×C₇₉	C₂³	1	1	yes	characteristic
292	#103×C₇₉	C₂³	1	2	yes	—
293	#103×C₇₉	C₂³	1	2	yes	—
294	#103×C₇₉	C₂³	1	2	yes	—
295	#103×C₇₉	C₂³	1	2	yes	—
296	#103×C₇₉	C₂³	1	2	yes	—
297	#103×C₇₉	C₂³	1	2	yes	—
298	#103×C₇₉	C₂³	1	2	yes	—
299	#103×C₇₉	C₂³	1	2	yes	—
300	#102×C₇₉	C₂³	1	1	yes	characteristic
301	#102×C₇₉	C₂³	1	2	yes	—
302	#102×C₇₉	C₂³	1	1	yes	characteristic
303	#102×C₇₉	C₂³	1	1	yes	characteristic
304	#102×C₇₉	C₂³	1	1	yes	characteristic
305	#102×C₇₉	C₂³	1	1	yes	characteristic
306	#102×C₇₉	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₇₉	C₂³	1	2	yes	—
311	#97×C₇₉	C₂³	1	2	yes	—
312	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₉	C₂³	1	2	yes	—
315	C₂⁴×C₇₉	—	2	1	no	—
316	#41×C₇₉	—	2	4	no	—
317	#41×C₇₉	—	4	2	no	—
318	#41×C₇₉	—	4	2	no	—
319	#41×C₇₉	—	4	2	no	—
320	#41×C₇₉	—	8	2	no	—
321	C₂×Q₈×C₇₉	—	2	1	no	—
322	C₂×Q₈×C₇₉	—	2	2	no	—
323	C₂×Q₈×C₇₉	—	2	2	no	—
324	C₂×Q₈×C₇₉	—	2	2	no	—
325	C₂×Q₈×C₇₉	—	4	2	no	—
326	C₂×Q₈×C₇₉	—	4	2	no	—
327	C₂×Q₈×C₇₉	—	4	2	no	—
328	C₂×Q₈×C₇₉	—	4	2	no	—
329	C₂×Q₈×C₇₉	—	8	2	no	—
330	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₇₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
335	C₂×D₄×C₇₉	—	2	2	no	—
336	C₂×D₄×C₇₉	—	2	1	no	—
337	C₂×D₄×C₇₉	—	2	2	no	—
338	C₂×D₄×C₇₉	—	2	2	no	—
339	C₂×D₄×C₇₉	—	2	2	no	—
340	C₂×D₄×C₇₉	—	2	1	no	—
341	C₂×D₄×C₇₉	—	4	1	no	—
342	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₇₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₇₉	—	2	1	no	—
348	C₂²×C₄×C₇₉	—	2	2	no	—
349	C₂²×C₄×C₇₉	—	2	2	no	—
350	C₂²×C₄×C₇₉	—	2	2	no	—
351	C₂²×C₄×C₇₉	—	2	2	no	—
352	C₂²×C₄×C₇₉	—	2	1	no	—
353	C₂²×C₄×C₇₉	—	2	1	no	—
354	C₂²×C₄×C₇₉	—	2	1	no	—
355	C₂²×C₄×C₇₉	—	2	2	no	—
356	C₂²×C₄×C₇₉	—	2	1	no	—
357	C₂²×C₄×C₇₉	—	2	2	no	—
358	C₂²×C₄×C₇₉	—	2	1	no	—
359	C₂²×C₄×C₇₉	—	8	2	no	—
360	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
364	Q₁₆×C₇₉	—	4	2	no	—
365	Q₁₆×C₇₉	—	4	2	no	—
366	Q₁₆×C₇₉	—	4	2	no	—
367	Q₁₆×C₇₉	—	4	2	no	—
368	Q₁₆×C₇₉	—	4	2	no	—
369	SD₁₆×C₇₉	—	2	4	no	—
370	SD₁₆×C₇₉	—	2	4	no	—
371	SD₁₆×C₇₉	—	2	2	no	—
372	SD₁₆×C₇₉	—	4	2	no	—
373	SD₁₆×C₇₉	—	4	2	no	—
374	SD₁₆×C₇₉	—	4	1	no	—
375	SD₁₆×C₇₉	—	4	2	no	—
376	D₈×C₇₉	—	2	2	no	—
377	D₈×C₇₉	—	4	1	no	—
378	M₁₆×C₇₉	—	4	2	no	—
379	C₂×C₈×C₇₉	—	4	2	no	—
380	C₂×C₈×C₇₉	—	4	2	no	—
381	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
386	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₇₉	—	2	1	no	—
388	C₄⋊C₄×C₇₉	—	2	2	no	—
389	C₄⋊C₄×C₇₉	—	2	1	no	—
390	C₄⋊C₄×C₇₉	—	2	1	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	1	no	—
395	C₄⋊C₄×C₇₉	—	2	2	no	—
396	C₄⋊C₄×C₇₉	—	2	2	no	—
397	C₄⋊C₄×C₇₉	—	2	2	no	—
398	C₄⋊C₄×C₇₉	—	2	1	no	—
399	C₄⋊C₄×C₇₉	—	2	1	no	—
400	C₄⋊C₄×C₇₉	—	2	1	no	—
401	C₄⋊C₄×C₇₉	—	2	1	no	—
402	C₄⋊C₄×C₇₉	—	2	1	no	—
403	C₄⋊C₄×C₇₉	—	2	1	no	—
404	C₄⋊C₄×C₇₉	—	2	2	no	—
405	C₄⋊C₄×C₇₉	—	2	2	no	—
406	C₄⋊C₄×C₇₉	—	2	2	no	—
407	C₄⋊C₄×C₇₉	—	2	1	no	—
408	C₄⋊C₄×C₇₉	—	2	2	no	—
409	C₄⋊C₄×C₇₉	—	2	2	no	—
410	C₄⋊C₄×C₇₉	—	2	2	no	—
411	C₄⋊C₄×C₇₉	—	2	2	no	—
412	C₄⋊C₄×C₇₉	—	2	1	no	—
413	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₇₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₇₉	—	2	2	no	—
425	C₂²⋊C₄×C₇₉	—	2	1	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	1	no	—
431	C₂²⋊C₄×C₇₉	—	2	1	no	—
432	C₂²⋊C₄×C₇₉	—	2	1	no	—
433	C₂²⋊C₄×C₇₉	—	2	2	no	—
434	C₂²⋊C₄×C₇₉	—	2	2	no	—
435	C₂²⋊C₄×C₇₉	—	2	2	no	—
436	C₂²⋊C₄×C₇₉	—	2	2	no	—
437	C₂²⋊C₄×C₇₉	—	2	2	no	—
438	C₂²⋊C₄×C₇₉	—	2	1	no	—
439	C₂²⋊C₄×C₇₉	—	2	1	no	—
440	C₂²⋊C₄×C₇₉	—	2	1	no	—
441	C₂²⋊C₄×C₇₉	—	2	2	no	—
442	C₂²⋊C₄×C₇₉	—	2	1	no	—
443	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
448	C₄²×C₇₉	—	2	2	no	—
449	C₄²×C₇₉	—	2	2	no	—
450	C₄²×C₇₉	—	2	1	no	—
451	C₄²×C₇₉	—	2	2	no	—
452	C₄²×C₇₉	—	2	2	no	—
453	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₇₉	C₂⁴	1	2	yes	—
457	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
458	C₂³×C₇₉	—	2	1	no	—
459	C₂³×C₇₉	—	2	1	no	—
460	C₂³×C₇₉	—	2	1	no	—
461	C₂³×C₇₉	—	4	2	no	—
462	C₂³×C₇₉	—	4	2	no	—
463	C₂³×C₇₉	—	8	1	no	—
464	C₂³×C₇₉	C₂²×D₄	1	2	yes	—
465	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₇₉	—	2	2	no	—
467	Q₈×C₇₉	—	2	2	no	—
468	Q₈×C₇₉	—	2	2	no	—
469	Q₈×C₇₉	—	2	1	no	—
470	Q₈×C₇₉	—	2	2	no	—
471	Q₈×C₇₉	—	2	1	no	—
472	Q₈×C₇₉	—	2	2	no	—
473	Q₈×C₇₉	—	2	2	no	—
474	Q₈×C₇₉	—	2	2	no	—
475	Q₈×C₇₉	—	4	2	no	—
476	Q₈×C₇₉	—	8	2	no	—
477	Q₈×C₇₉	—	8	2	no	—
478	Q₈×C₇₉	—	8	2	no	—
479	D₄×C₇₉	—	2	4	no	—
480	D₄×C₇₉	—	2	2	no	—
481	D₄×C₇₉	—	2	1	no	—
482	D₄×C₇₉	—	2	1	no	—
483	D₄×C₇₉	—	2	1	no	—
484	D₄×C₇₉	—	2	1	no	—
485	D₄×C₇₉	—	2	1	no	—
486	D₄×C₇₉	—	4	2	no	—
487	D₄×C₇₉	—	4	4	no	—
488	D₄×C₇₉	—	4	2	no	—
489	D₄×C₇₉	—	8	2	no	—
490	D₄×C₇₉	—	8	2	no	—
491	D₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
492	C₂×C₄×C₇₉	—	2	2	no	—
493	C₂×C₄×C₇₉	—	2	2	no	—
494	C₂×C₄×C₇₉	—	2	1	no	—
495	C₂×C₄×C₇₉	—	2	2	no	—
496	C₂×C₄×C₇₉	—	2	1	no	—
497	C₂×C₄×C₇₉	—	2	2	no	—
498	C₂×C₄×C₇₉	—	2	1	no	—
499	C₂×C₄×C₇₉	—	2	1	no	—
500	C₂×C₄×C₇₉	—	2	2	no	—
501	C₂×C₄×C₇₉	—	2	1	no	—
502	C₂×C₄×C₇₉	—	2	1	no	—
503	C₂×C₄×C₇₉	—	2	2	no	—
504	C₂×C₄×C₇₉	—	2	2	no	—
505	C₂×C₄×C₇₉	—	2	2	no	—
506	C₂×C₄×C₇₉	—	2	1	no	—
507	C₂×C₄×C₇₉	—	4	4	no	—
508	C₂×C₄×C₇₉	—	4	2	no	—
509	C₂×C₄×C₇₉	—	4	2	no	—
510	C₂×C₄×C₇₉	—	4	2	no	—
511	C₂×C₄×C₇₉	—	8	1	no	—
512	C₂×C₄×C₇₉	—	8	1	no	—
513	C₂×C₄×C₇₉	—	8	2	no	—
514	C₂×C₄×C₇₉	—	8	2	no	—
515	C₂×C₄×C₇₉	—	8	1	no	—
516	C₂×C₄×C₇₉	—	8	2	no	—
517	C₂×C₄×C₇₉	—	8	2	no	—
518	C₂×C₄×C₇₉	—	8	2	no	—
519	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
528	C₈×C₇₉	—	2	1	no	—
529	C₈×C₇₉	—	2	2	no	—
530	C₈×C₇₉	—	2	2	no	—
531	C₈×C₇₉	—	2	1	no	—
532	C₈×C₇₉	—	2	1	no	—
533	C₈×C₇₉	—	2	1	no	—
534	C₂²×C₇₉	—	2	1	no	—
535	C₂²×C₇₉	—	2	1	no	—
536	C₂²×C₇₉	—	2	2	no	—
537	C₂²×C₇₉	—	2	2	no	—
538	C₂²×C₇₉	—	2	2	no	—
539	C₂²×C₇₉	—	2	2	no	—
540	C₂²×C₇₉	—	4	1	no	—
541	C₂²×C₇₉	—	4	1	no	—
542	C₂²×C₇₉	—	4	1	no	—
543	C₂²×C₇₉	—	4	1	no	—
544	C₂²×C₇₉	—	4	1	no	—
545	C₂²×C₇₉	—	4	1	no	—
546	C₂²×C₇₉	—	4	1	no	—
547	C₂²×C₇₉	—	4	1	no	—
548	C₂²×C₇₉	—	8	4	no	—
549	C₂²×C₇₉	#578	1	2	yes	—
550	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₇₉	—	2	2	no	—
552	C₄×C₇₉	—	2	1	no	—
553	C₄×C₇₉	—	2	1	no	—
554	C₄×C₇₉	—	2	2	no	—
555	C₄×C₇₉	—	2	1	no	—
556	C₄×C₇₉	—	2	1	no	—
557	C₄×C₇₉	—	2	2	no	—
558	C₄×C₇₉	—	4	2	no	—
559	C₄×C₇₉	—	4	2	no	—
560	C₄×C₇₉	—	4	2	no	—
561	C₄×C₇₉	—	4	1	no	—
562	C₄×C₇₉	—	4	1	no	—
563	C₄×C₇₉	—	4	1	no	—
564	C₄×C₇₉	—	4	1	no	—
565	C₄×C₇₉	—	4	2	no	—
566	C₄×C₇₉	—	4	1	no	—
567	C₄×C₇₉	#577	1	2	yes	—
568	C₄×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₄×C₇₉	#585	1	1	yes	characteristic
570	#62054	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
571	C₂×C₇₉	—	2	2	no	—
572	C₂×C₇₉	—	4	2	no	—
573	C₂×C₇₉	—	4	2	no	—
574	C₂×C₇₉	—	8	1	no	—
575	C₂×C₇₉	—	8	1	no	—
576	C₂×C₇₉	#3488	1	1	yes	characteristic
577	C₂×C₇₉	C₂×#577	1	1	yes	characteristic
578	C₂×C₇₉	C₂×#578	1	1	yes	characteristic
579	#3552	C₂×C₇₉	1	1	yes	characteristic, complemented
580	#3520	C₂×C₇₉	1	1	yes	characteristic, complemented
581	#3398	C₂×C₇₉	1	1	yes	characteristic, complemented
582	#3393	C₂×C₇₉	1	1	yes	characteristic, complemented
583	#3367	C₂×C₇₉	1	1	yes	characteristic, complemented
584	#3359	C₂×C₇₉	1	1	yes	characteristic, complemented
585	#3330	C₂×C₇₉	1	1	yes	characteristic, complemented
586	#3316	C₂×C₇₉	1	2	yes	complemented
587	#3299	C₂×C₇₉	1	2	yes	complemented
588	#3298	C₂×C₇₉	1	1	yes	characteristic, complemented
589	#3283	C₂×C₇₉	1	1	yes	characteristic, complemented
590	#3282	C₂×C₇₉	1	2	yes	complemented
591	#3276	C₂×C₇₉	1	1	yes	characteristic, complemented
592	#3266	C₂×C₇₉	1	2	yes	complemented
593	#3258	C₂×C₇₉	1	2	yes	complemented
594	#3248	C₂×C₇₉	1	1	yes	characteristic, complemented
595	#3225	C₂×C₇₉	1	2	yes	complemented
596	#3209	C₂×C₇₉	1	1	yes	characteristic, complemented
597	#3120	C₂×C₇₉	1	2	yes	complemented
598	#3105	C₂×C₇₉	1	1	yes	characteristic, complemented
599	#3046	C₂×C₇₉	1	2	yes	complemented
600	C₂×#461	C₂×C₇₉	1	1	yes	characteristic, complemented
601	#2994	C₂×C₇₉	1	1	yes	characteristic, complemented
602	C₇₉	#62054	1	1	yes	characteristic, direct product factor, Sylow
603	C₂×#137	C₂²×C₇₉	1	2	yes	—
604	C₂×#135	C₂²×C₇₉	1	2	yes	—
605	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
606	#563	—	2	2	no	—
607	#557	C₂²×C₇₉	1	1	yes	characteristic, complemented
608	#556	C₂²×C₇₉	1	1	yes	characteristic
609	#556	C₂²×C₇₉	1	1	yes	characteristic, complemented
610	#554	—	2	1	no	—
611	#554	C₂²×C₇₉	1	2	yes	—
612	#553	—	2	1	no	—
613	#552	—	2	1	no	—
614	#551	—	2	2	no	—
615	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
616	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
618	#548	—	2	1	no	—
619	#548	C₂²×C₇₉	1	2	yes	—
620	#547	C₂²×C₇₉	1	1	yes	characteristic
621	#547	C₂²×C₇₉	1	1	yes	characteristic
622	#547	C₂²×C₇₉	1	1	yes	characteristic, complemented
623	#546	C₂²×C₇₉	1	2	yes	—
624	#544	—	2	1	no	—
625	#542	—	2	1	no	—
626	#542	C₂²×C₇₉	1	2	yes	—
627	#541	C₂²×C₇₉	1	2	yes	complemented
628	#539	—	2	2	no	—
629	#539	—	2	2	no	—
630	#536	C₂²×C₇₉	1	2	yes	complemented
631	#533	C₂²×C₇₉	1	1	yes	characteristic
632	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
633	#529	C₂²×C₇₉	1	1	yes	characteristic
634	#529	C₂²×C₇₉	1	1	yes	characteristic
635	#525	—	2	1	no	—
636	C₂×C₂²⋊Q₈	—	2	1	no	—
637	#520	C₂²×C₇₉	1	2	yes	—
638	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
639	#497	C₂²×C₇₉	1	2	yes	—
640	#495	C₂²×C₇₉	1	2	yes	—
641	#494	C₂²×C₇₉	1	1	yes	characteristic, complemented
642	#494	C₂²×C₇₉	1	1	yes	characteristic, complemented
643	#489	C₂²×C₇₉	1	2	yes	complemented
644	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
645	#487	C₂²×C₇₉	1	2	yes	complemented
646	#487	C₂²×C₇₉	1	1	yes	characteristic, complemented
647	#484	C₂²×C₇₉	1	1	yes	characteristic
648	#484	C₂²×C₇₉	1	2	yes	complemented
649	#483	C₂²×C₇₉	1	2	yes	complemented
650	#481	C₂²×C₇₉	1	1	yes	characteristic
651	#479	C₂²×C₇₉	1	2	yes	complemented
652	#478	C₂²×C₇₉	1	1	yes	characteristic
653	#478	C₂²×C₇₉	1	1	yes	characteristic
654	#477	C₂²×C₇₉	1	2	yes	complemented
655	#475	C₂²×C₇₉	1	1	yes	characteristic, complemented
656	#475	C₂²×C₇₉	1	2	yes	complemented
657	#474	C₂²×C₇₉	1	1	yes	characteristic, complemented
658	#470	C₂²×C₇₉	1	2	yes	complemented
659	#468	C₂²×C₇₉	1	2	yes	—
660	#467	C₂²×C₇₉	1	2	yes	—
661	#467	C₂²×C₇₉	1	2	yes	complemented
662	#465	C₂²×C₇₉	1	2	yes	—
663	#465	C₂²×C₇₉	1	2	yes	—
664	#464	C₂²×C₇₉	1	2	yes	—
665	#464	C₂²×C₇₉	1	2	yes	—
666	#464	C₂²×C₇₉	1	2	yes	complemented
667	#464	C₂²×C₇₉	1	2	yes	complemented
668	#463	C₂²×C₇₉	1	1	yes	characteristic
669	#463	C₂²×C₇₉	1	1	yes	characteristic
670	#463	C₂²×C₇₉	1	2	yes	—
671	#462	C₂²×C₇₉	1	2	yes	complemented
672	#462	C₂²×C₇₉	1	1	yes	characteristic, complemented
673	#462	C₂²×C₇₉	1	2	yes	complemented
674	#462	C₂²×C₇₉	1	2	yes	complemented
675	#461	C₂²×C₇₉	1	1	yes	characteristic
676	#461	C₂²×C₇₉	1	2	yes	—
677	#461	C₂²×C₇₉	1	1	yes	characteristic
678	#461	C₂²×C₇₉	1	1	yes	characteristic
679	#461	C₂²×C₇₉	1	2	yes	—
680	#461	C₂²×C₇₉	1	1	yes	characteristic
681	#461	C₂²×C₇₉	1	2	yes	—
682	#461	C₂²×C₇₉	1	1	yes	characteristic, complemented
683	#452	C₂²×C₇₉	1	2	yes	—
684	#452	C₂²×C₇₉	1	2	yes	—
685	#452	C₂²×C₇₉	1	2	yes	complemented
686	#451	C₂²×C₇₉	1	2	yes	—
687	#451	C₂²×C₇₉	1	2	yes	—
688	#451	C₂²×C₇₉	1	2	yes	complemented
689	#450	C₂²×C₇₉	1	1	yes	characteristic
690	#449	C₂²×C₇₉	1	2	yes	—
691	#448	C₂²×C₇₉	1	2	yes	—
692	#447	C₂²×C₇₉	1	1	yes	characteristic
693	#446	C₂²×C₇₉	1	1	yes	characteristic, complemented
694	C₈×Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
695	#441	C₂²×C₇₉	1	2	yes	complemented
696	#440	C₂²×C₇₉	1	2	yes	—
697	C₄×Q₁₆	C₂²×C₇₉	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₇₉	1	2	yes	—
700	C₄×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
701	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
702	C₄×D₈	C₂²×C₇₉	1	1	yes	characteristic
703	#436	C₂²×C₇₉	1	1	yes	characteristic, complemented
704	#435	C₂²×C₇₉	1	2	yes	—
705	C₈×D₄	C₂²×C₇₉	1	2	yes	—
706	C₈×D₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
707	#433	C₂²×C₇₉	1	2	yes	complemented
708	#431	C₂²×C₇₉	1	1	yes	characteristic
709	#424	C₂²×C₇₉	1	2	yes	complemented
710	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
711	#417	C₂²×C₇₉	1	2	yes	complemented
712	C₂×#103	C₂²×C₇₉	1	2	yes	—
713	C₂×#103	C₂²×C₇₉	1	2	yes	complemented
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₇₉	1	2	yes	—
716	C₂×#41	C₂³×C₇₉	1	2	yes	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
719	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
720	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
721	C₂³×C₄	—	2	1	no	—
722	#137	—	4	4	no	—
723	#135	—	4	4	no	—
724	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
729	C₂×SD₁₆	—	4	4	no	—
730	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₇₉	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₇₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₇₉	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₇₉	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₇₉	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
740	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
741	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
747	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	D₄×C₇₉	1	2	yes	—
760	#125	—	2	2	no	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	—	2	1	no	—
766	#125	D₄×C₇₉	1	1	yes	characteristic
767	#125	C₂³×C₇₉	1	1	yes	characteristic
768	#124	—	2	2	no	—
769	#124	—	2	2	no	—
770	#124	D₄×C₇₉	1	1	yes	characteristic
771	#124	C₂³×C₇₉	1	1	yes	characteristic
772	#124	C₂³×C₇₉	1	2	yes	—
773	#124	C₂³×C₇₉	1	2	yes	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	D₄×C₇₉	1	2	yes	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₇₉	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₇₉	1	2	yes	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	D₄×C₇₉	1	1	yes	characteristic
809	#121	C₂³×C₇₉	1	1	yes	characteristic
810	#121	C₂³×C₇₉	1	2	yes	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
816	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
818	C₄×Q₈	C₂³×C₇₉	1	2	yes	—
819	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₇₉	1	2	yes	—
834	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₇₉	1	2	yes	—
836	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₇₉	1	2	yes	—
843	C₂×C₄⋊C₄	—	2	1	no	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
853	#107	C₂³×C₇₉	1	1	yes	characteristic
854	#107	C₂³×C₇₉	1	1	yes	characteristic
855	#107	C₂³×C₇₉	1	2	yes	—
856	#106	C₂³×C₇₉	1	1	yes	characteristic
857	#106	C₂³×C₇₉	1	2	yes	—
858	#106	C₂³×C₇₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
860	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
866	#103	C₂³×C₇₉	1	2	yes	—
867	#103	C₂³×C₇₉	1	2	yes	—
868	#103	C₂³×C₇₉	1	2	yes	—
869	#103	C₂³×C₇₉	1	2	yes	—
870	#103	C₂³×C₇₉	1	1	yes	characteristic
871	#103	C₂³×C₇₉	1	2	yes	—
872	#103	C₂³×C₇₉	1	2	yes	—
873	#103	C₂³×C₇₉	1	2	yes	—
874	#103	C₂³×C₇₉	1	2	yes	—
875	#103	C₂³×C₇₉	1	1	yes	characteristic
876	#103	C₂³×C₇₉	1	2	yes	—
877	#103	C₂³×C₇₉	1	2	yes	—
878	#103	C₂³×C₇₉	1	2	yes	—
879	#102	C₂³×C₇₉	1	1	yes	characteristic
880	#102	C₂³×C₇₉	1	2	yes	—
881	#102	C₂³×C₇₉	1	1	yes	characteristic
882	#102	C₂³×C₇₉	1	1	yes	characteristic
883	#102	C₂³×C₇₉	1	1	yes	characteristic
884	#102	C₂³×C₇₉	1	1	yes	characteristic
885	#102	C₂³×C₇₉	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₇₉	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₇₉	1	2	yes	—
890	#97	C₂³×C₇₉	1	2	yes	—
891	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₇₉	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₇₉	1	2	yes	—
894	C₂⁴	—	2	1	no	—
895	#41	—	2	4	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
911	C₂×Q₈	C₂⁴×C₇₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₇₉	1	1	yes	characteristic
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	8	2	no	—
939	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
943	Q₁₆	—	4	2	no	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	D₈	—	2	2	no	—
956	D₈	—	4	1	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
965	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
995	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₇₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₇₉	1	2	yes	—
1036	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	C₂²×D₄×C₇₉	1	2	yes	—
1044	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	8	4	no	—
1128	C₂²	#578×C₇₉	1	2	yes	—
1129	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	#577×C₇₉	1	2	yes	—
1147	C₄	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
1148	C₄	#585×C₇₉	1	1	yes	characteristic
1149	C₂	—	2	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	C₇₉×#3488	1	1	yes	characteristic
1155	C₂	C₂×#577×C₇₉	1	1	yes	characteristic
1156	C₂	C₂×#578×C₇₉	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 ◁ #529×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3552	C₂	semidirect
2. C₇₉×#3520	C₂	semidirect
3. C₇₉×#3398	C₂	semidirect
4. C₇₉×#3393	C₂	semidirect
5. C₇₉×#3367	C₂	semidirect
6. C₇₉×#3359	C₂	semidirect
7. C₇₉×#3330	C₂	semidirect
8. C₇₉×#3316	C₂	semidirect
9. C₇₉×#3299	C₂	semidirect
10. C₇₉×#3298	C₂	semidirect
11. C₇₉×#3283	C₂	semidirect
12. C₇₉×#3282	C₂	semidirect
13. C₇₉×#3276	C₂	semidirect
14. C₇₉×#3266	C₂	semidirect
15. C₇₉×#3258	C₂	semidirect
16. C₇₉×#3248	C₂	semidirect
17. C₇₉×#3225	C₂	semidirect
18. C₇₉×#3209	C₂	semidirect
19. C₇₉×#3120	C₂	semidirect
20. C₇₉×#3105	C₂	semidirect
21. C₇₉×#3046	C₂	semidirect
22. C₂×#461×C₇₉	C₂	semidirect
23. C₇₉×#2994	C₂	semidirect
28. #557×C₇₉	C₂²	semidirect
30. #556×C₇₉	C₂²	semidirect
38. D₄×Q₈×C₇₉	C₂²	semidirect
43. #547×C₇₉	C₂²	semidirect
48. #541×C₇₉	C₂²	semidirect
51. #536×C₇₉	C₂²	semidirect
62. #494×C₇₉	C₂²	semidirect
63. #494×C₇₉	C₂²	semidirect
64. #489×C₇₉	C₂²	semidirect
65. #487×C₇₉	C₂²	semidirect
66. #487×C₇₉	C₂²	semidirect
67. #487×C₇₉	C₂²	semidirect
69. #484×C₇₉	C₂²	semidirect
70. #483×C₇₉	C₂²	semidirect
72. #479×C₇₉	C₂²	semidirect
75. #477×C₇₉	C₂²	semidirect
76. #475×C₇₉	C₂²	semidirect
77. #475×C₇₉	C₂²	semidirect
78. #474×C₇₉	C₂²	semidirect
79. #470×C₇₉	C₂²	semidirect
82. #467×C₇₉	C₂²	semidirect
87. #464×C₇₉	C₂²	semidirect
88. #464×C₇₉	C₂²	semidirect
92. #462×C₇₉	C₂²	semidirect
93. #462×C₇₉	C₂²	semidirect
94. #462×C₇₉	C₂²	semidirect
95. #462×C₇₉	C₂²	semidirect
103. #461×C₇₉	C₂²	semidirect
106. #452×C₇₉	C₂²	semidirect
109. #451×C₇₉	C₂²	semidirect
114. #446×C₇₉	C₂²	semidirect
115. C₈×Q₈×C₇₉	C₂²	semidirect
116. #441×C₇₉	C₂²	semidirect
118. C₄×Q₁₆×C₇₉	C₂²	semidirect
124. #436×C₇₉	C₂²	semidirect
127. C₈×D₄×C₇₉	C₂²	semidirect
128. #433×C₇₉	C₂²	semidirect
130. #424×C₇₉	C₂²	semidirect
132. #417×C₇₉	C₂²	semidirect
134. C₂×#103×C₇₉	C₂²	semidirect
570. #62054	C₇₉	direct (N × H)
579. #3552	C₂×C₇₉	semidirect
580. #3520	C₂×C₇₉	semidirect
581. #3398	C₂×C₇₉	semidirect
582. #3393	C₂×C₇₉	semidirect
583. #3367	C₂×C₇₉	semidirect
584. #3359	C₂×C₇₉	semidirect
585. #3330	C₂×C₇₉	semidirect
586. #3316	C₂×C₇₉	semidirect
587. #3299	C₂×C₇₉	semidirect
588. #3298	C₂×C₇₉	semidirect
589. #3283	C₂×C₇₉	semidirect
590. #3282	C₂×C₇₉	semidirect
591. #3276	C₂×C₇₉	semidirect
592. #3266	C₂×C₇₉	semidirect
593. #3258	C₂×C₇₉	semidirect
594. #3248	C₂×C₇₉	semidirect
595. #3225	C₂×C₇₉	semidirect
596. #3209	C₂×C₇₉	semidirect
597. #3120	C₂×C₇₉	semidirect
598. #3105	C₂×C₇₉	semidirect
599. #3046	C₂×C₇₉	semidirect
600. C₂×#461	C₂×C₇₉	semidirect
601. #2994	C₂×C₇₉	semidirect
602. C₇₉	#62054	direct (N × H)
607. #557	C₂²×C₇₉	semidirect
609. #556	C₂²×C₇₉	semidirect
617. D₄×Q₈	C₂²×C₇₉	semidirect
622. #547	C₂²×C₇₉	semidirect
627. #541	C₂²×C₇₉	semidirect
630. #536	C₂²×C₇₉	semidirect
641. #494	C₂²×C₇₉	semidirect
642. #494	C₂²×C₇₉	semidirect
643. #489	C₂²×C₇₉	semidirect
644. #487	C₂²×C₇₉	semidirect
645. #487	C₂²×C₇₉	semidirect
646. #487	C₂²×C₇₉	semidirect
648. #484	C₂²×C₇₉	semidirect
649. #483	C₂²×C₇₉	semidirect
651. #479	C₂²×C₇₉	semidirect
654. #477	C₂²×C₇₉	semidirect
655. #475	C₂²×C₇₉	semidirect
656. #475	C₂²×C₇₉	semidirect
657. #474	C₂²×C₇₉	semidirect
658. #470	C₂²×C₇₉	semidirect
661. #467	C₂²×C₇₉	semidirect
666. #464	C₂²×C₇₉	semidirect
667. #464	C₂²×C₇₉	semidirect
671. #462	C₂²×C₇₉	semidirect
672. #462	C₂²×C₇₉	semidirect
673. #462	C₂²×C₇₉	semidirect
674. #462	C₂²×C₇₉	semidirect
682. #461	C₂²×C₇₉	semidirect
685. #452	C₂²×C₇₉	semidirect
688. #451	C₂²×C₇₉	semidirect
693. #446	C₂²×C₇₉	semidirect
694. C₈×Q₈	C₂²×C₇₉	semidirect
695. #441	C₂²×C₇₉	semidirect
697. C₄×Q₁₆	C₂²×C₇₉	semidirect
703. #436	C₂²×C₇₉	semidirect
706. C₈×D₄	C₂²×C₇₉	semidirect
707. #433	C₂²×C₇₉	semidirect
709. #424	C₂²×C₇₉	semidirect
711. #417	C₂²×C₇₉	semidirect
713. 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×#3552	2
C₇₉×#3520	2
C₇₉×#3398	2
C₇₉×#3393	2
C₇₉×#3367	2
C₇₉×#3359	2
C₇₉×#3330	2
C₇₉×#3316	2
C₇₉×#3299	2
C₇₉×#3298	2
C₇₉×#3283	2
C₇₉×#3282	2
C₇₉×#3276	2
C₇₉×#3266	2
C₇₉×#3258	2
C₇₉×#3248	2
C₇₉×#3225	2
C₇₉×#3209	2
C₇₉×#3120	2
C₇₉×#3105	2
C₇₉×#3046	2
C₂×#461×C₇₉	2
C₇₉×#2994	2
#62054	79

Subgroups — C79×#62054 #34173743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#62054 #34173743