Subgroups — #35168901

Order 20224.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777199	C₂	1	2	yes	maximal, complemented
2	#23776358	C₂	1	2	yes	maximal, complemented
3	#23776354	C₂	1	2	yes	maximal, complemented
4	#23776302	C₂	1	2	yes	maximal, complemented
5	#23776294	C₂	1	2	yes	maximal, complemented
6	#23776268	C₂	1	1	yes	maximal, characteristic, complemented
7	#23776267	C₂	1	1	yes	maximal, characteristic, complemented
8	#23776267	C₂	1	1	yes	maximal, characteristic, complemented
9	#23776264	C₂	1	1	yes	maximal, characteristic, complemented
10	#23776264	C₂	1	1	yes	maximal, characteristic, complemented
11	D₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#23776252	C₂	1	1	yes	maximal, characteristic, complemented
13	#23773937	C₂	1	1	yes	maximal, characteristic, complemented
14	#23773933	C₂	1	1	yes	maximal, characteristic, complemented
15	#23773913	C₂	1	1	yes	maximal, characteristic, complemented
16	#23773230	C₂	1	2	yes	maximal, complemented
17	#23773226	C₂	1	2	yes	maximal, complemented
18	#23773195	C₂	1	2	yes	maximal, complemented
19	#23772329	C₂	1	1	yes	maximal, characteristic, complemented
20	#23772247	C₂	1	1	yes	maximal, characteristic
21	#23772247	C₂	1	1	yes	maximal, characteristic
22	C₄×D₈×D₇₉	C₂	1	1	yes	maximal, characteristic
23	C₇₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₇₉	C₂²	1	1	yes	characteristic
25	#19099273	C₂²	1	2	yes	complemented
26	#19099272	C₂²	1	2	yes	complemented
27	#19099272	C₂²	1	2	yes	complemented
28	#19099269	C₂²	1	2	yes	complemented
29	#19099269	C₂²	1	2	yes	complemented
30	#19099268	—	2	2	no	—
31	#19099267	—	2	2	no	—
32	#19099267	—	2	2	no	—
33	D₄×Dic₁₅₈	C₂²	1	2	yes	complemented
34	#19099228	C₂²	1	2	yes	complemented
35	#19099226	—	2	2	no	—
36	#19099193	C₂²	1	2	yes	—
37	#19099190	C₂²	1	2	yes	—
38	#19099188	—	2	2	no	—
39	#19099188	—	2	2	no	—
40	#19099119	C₂²	1	2	yes	—
41	#19099117	C₂²	1	1	yes	characteristic
42	C₂×#14579139	—	2	2	no	—
43	C₂²⋊Q₈×D₇₉	—	2	2	no	—
44	#19099035	C₂²	1	2	yes	—
45	#19099035	C₂²	1	2	yes	—
46	C₄×D₄×D₇₉	C₂²	1	2	yes	—
47	#19098973	C₂²	1	2	yes	complemented
48	#19098971	C₂²	1	2	yes	complemented
49	#19098970	C₂²	1	2	yes	complemented
50	#19098969	C₂²	1	2	yes	complemented
51	#19098968	C₂²	1	1	yes	characteristic, complemented
52	#19098967	C₂²	1	1	yes	characteristic, complemented
53	#19098967	C₂²	1	1	yes	characteristic, complemented
54	#19098967	C₂²	1	1	yes	characteristic, complemented
55	#19098967	C₂²	1	1	yes	characteristic, complemented
56	#19098965	C₂²	1	1	yes	characteristic, complemented
57	#19098965	C₂²	1	1	yes	characteristic, complemented
58	#19098964	C₂²	1	1	yes	characteristic, complemented
59	#19098964	C₂²	1	1	yes	characteristic, complemented
60	#19098962	C₂²	1	2	yes	complemented
61	#19098960	C₂²	1	2	yes	complemented
62	#19098865	C₂²	1	2	yes	complemented
63	#19098865	C₂²	1	2	yes	complemented
64	#19098864	C₂²	1	2	yes	complemented
65	#19098864	C₂²	1	2	yes	complemented
66	#19098863	C₂²	1	2	yes	complemented
67	#19098863	C₂²	1	2	yes	complemented
68	#19098862	C₂²	1	2	yes	complemented
69	#19098862	C₂²	1	2	yes	complemented
70	#19098860	C₂²	1	2	yes	complemented
71	#19098860	C₂²	1	2	yes	complemented
72	#19098854	C₂²	1	2	yes	complemented
73	#19098852	C₂²	1	2	yes	complemented
74	#19098852	C₂²	1	2	yes	complemented
75	#19098851	C₂²	1	2	yes	complemented
76	#19098851	C₂²	1	2	yes	complemented
77	#19098843	C₂²	1	2	yes	complemented
78	#19098842	C₂²	1	2	yes	complemented
79	#19098842	C₂²	1	2	yes	complemented
80	#19098841	C₂²	1	2	yes	complemented
81	#19098841	C₂²	1	2	yes	complemented
82	#19098840	C₂²	1	2	yes	complemented
83	#19098694	C₂²	1	1	yes	characteristic, complemented
84	#19098692	C₂²	1	1	yes	characteristic, complemented
85	#19098692	C₂²	1	1	yes	characteristic, complemented
86	#19098690	C₂²	1	1	yes	characteristic, complemented
87	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
88	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
89	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
90	#19098673	C₂²	1	2	yes	—
91	#19098673	C₂²	1	2	yes	—
92	#19098672	C₂²	1	2	yes	—
93	#19098672	C₂²	1	2	yes	—
94	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
95	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
96	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
97	D₈×Dic₇₉	C₂²	1	1	yes	characteristic
98	D₈×Dic₇₉	C₂²	1	1	yes	characteristic
99	D₈×Dic₇₉	C₂²	1	1	yes	characteristic
100	#19098645	C₂²	1	1	yes	characteristic
101	#19098645	C₂²	1	1	yes	characteristic
102	#19098645	C₂²	1	1	yes	characteristic
103	C₄×#11929609	C₂²	1	2	yes	—
104	#19098643	C₂²	1	2	yes	—
105	#19098604	C₂²	1	2	yes	—
106	#19098602	C₂²	1	2	yes	—
107	#19098600	C₂²	1	1	yes	characteristic
108	#19098600	C₂²	1	1	yes	characteristic
109	#19098598	C₂²	1	2	yes	—
110	#107×D₇₉	C₂²	1	1	yes	characteristic
111	#19098588	C₂²	1	1	yes	characteristic
112	#19098588	C₂²	1	1	yes	characteristic
113	#19098585	C₂²	1	1	yes	characteristic
114	#19098566	C₂²	1	2	yes	—
115	#19098566	C₂²	1	2	yes	—
116	#102×D₇₉	C₂²	1	2	yes	—
117	#19098517	C₂²	1	1	yes	characteristic
118	#19098517	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
120	#554×C₇₉	C₂²	1	2	yes	complemented
121	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
122	#499×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	#499×C₇₉	C₂²	1	1	yes	characteristic, complemented
124	#478×C₇₉	C₂²	1	2	yes	complemented
125	#478×C₇₉	C₂²	1	2	yes	complemented
126	#476×C₇₉	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
131	C₂²×Dic₁₅₈	—	2	2	no	—
132	C₂×Q₈×D₇₉	—	2	2	no	—
133	C₂×D₄×D₇₉	C₂³	1	2	yes	—
134	C₂²×C₄×D₇₉	—	2	2	no	—
135	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
136	C₂×#11929609	C₂³	1	2	yes	—
137	D₈×D₇₉	Q₈	1	8	yes	complemented
138	C₂×#11929607	C₂³	1	1	yes	characteristic
139	C₂×#11929607	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
142	#14579161	C₂³	1	2	yes	—
143	#14579160	—	2	2	no	—
144	#14579160	D₄	1	1	yes	characteristic
145	#14579160	C₂³	1	2	yes	—
146	#14579160	C₂³	1	2	yes	—
147	#14579160	C₂³	1	2	yes	—
148	#14579160	C₂³	1	2	yes	—
149	#14579159	—	2	2	no	—
150	#14579159	D₄	1	1	yes	characteristic
151	#14579153	C₂³	1	2	yes	—
152	#14579153	C₂³	1	2	yes	—
153	#14579152	C₂³	1	2	yes	—
154	#14579152	C₂³	1	2	yes	—
155	#14579151	—	2	2	no	—
156	#14579151	—	2	2	no	—
157	#14579151	D₄	1	1	yes	characteristic
158	#14579151	D₄	1	1	yes	characteristic
159	#14579141	—	2	2	no	—
160	#14579141	—	2	2	no	—
161	#14579141	—	2	2	no	—
162	#14579141	D₄	1	1	yes	characteristic
163	#14579140	—	2	2	no	—
164	#14579140	—	2	2	no	—
165	#14579140	—	2	2	no	—
166	#14579139	—	2	2	no	—
167	#14579139	—	2	2	no	—
168	#14579139	—	2	2	no	—
169	#14579139	—	2	2	no	—
170	#14579139	—	2	2	no	—
171	#14579139	—	2	2	no	—
172	#14579139	—	2	2	no	—
173	#14579139	—	2	2	no	—
174	#14579139	—	2	2	no	—
175	#14579139	—	2	2	no	—
176	#14579139	—	2	2	no	—
177	#14579139	—	2	2	no	—
178	#14579139	D₄	1	1	yes	characteristic
179	#14579139	D₄	1	1	yes	characteristic
180	#14579138	—	2	2	no	—
181	#14579138	—	2	2	no	—
182	#14579138	—	2	2	no	—
183	#14579138	—	2	2	no	—
184	#14579138	—	2	2	no	—
185	#14579138	—	2	2	no	—
186	#14579137	—	2	2	no	—
187	#14579137	—	2	2	no	—
188	#14579137	—	2	2	no	—
189	#14579137	D₄	1	1	yes	characteristic
190	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
193	#14579126	—	2	2	no	—
194	#14579126	—	2	2	no	—
195	C₄×D₃₁₆	C₂³	1	2	yes	—
196	C₄×D₃₁₆	C₂³	1	2	yes	—
197	C₄×D₃₁₆	C₂³	1	2	yes	—
198	D₄×Dic₇₉	C₂³	1	2	yes	—
199	D₄×Dic₇₉	C₂³	1	2	yes	—
200	D₄×Dic₇₉	C₂³	1	2	yes	—
201	#14579123	C₂³	1	2	yes	—
202	#14579123	C₂³	1	2	yes	—
203	#14579123	C₂³	1	2	yes	—
204	C₄×C₂²⋊D₇₉	—	2	2	no	—
205	C₄×C₂²⋊D₇₉	—	2	2	no	—
206	C₄×C₂²⋊D₇₉	—	2	2	no	—
207	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
208	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
210	#14579119	C₂³	1	2	yes	—
211	#14579119	C₂³	1	2	yes	—
212	#14579118	C₂³	1	1	yes	characteristic
213	#14579118	C₂³	1	1	yes	characteristic
214	C₂×Dic₇₉⋊C₄	—	2	2	no	—
215	C₂×Dic₇₉⋊C₄	—	2	2	no	—
216	C₄⋊C₄×D₇₉	—	2	2	no	—
217	C₄⋊C₄×D₇₉	—	2	2	no	—
218	C₄⋊C₄×D₇₉	—	2	2	no	—
219	C₄⋊C₄×D₇₉	C₂³	1	2	yes	—
220	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
221	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
222	C₂²⋊C₄×D₇₉	—	2	2	no	—
223	C₂²⋊C₄×D₇₉	—	2	2	no	—
224	C₂²⋊C₄×D₇₉	—	2	2	no	—
225	C₄²×D₇₉	C₂³	1	1	yes	characteristic
226	#14579095	C₂³	1	1	yes	characteristic
227	#14579095	C₂³	1	1	yes	characteristic
228	#14579095	C₂³	1	1	yes	characteristic
229	#14579095	C₂³	1	2	yes	—
230	#14579094	C₂³	1	2	yes	—
231	#14579094	C₂³	1	2	yes	—
232	#14579094	C₂³	1	2	yes	—
233	#14579094	C₂³	1	2	yes	—
234	#14579094	C₂³	1	2	yes	—
235	#14579093	C₂³	1	2	yes	—
236	#14579093	C₂³	1	2	yes	—
237	#14579092	C₂³	1	2	yes	—
238	#14579092	C₂³	1	2	yes	—
239	#14579092	C₂³	1	2	yes	—
240	#14579092	C₂³	1	2	yes	—
241	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
244	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
247	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
250	#14579083	C₂³	1	2	yes	—
251	#14579083	C₂³	1	2	yes	—
252	#14579083	C₂³	1	2	yes	—
253	#14579082	C₂³	1	2	yes	—
254	#14579082	C₂³	1	2	yes	—
255	#14579082	C₂³	1	2	yes	—
256	#14579081	C₂³	1	2	yes	—
257	#14579081	C₂³	1	2	yes	—
258	#14579081	C₂³	1	2	yes	—
259	#14579072	C₂³	1	1	yes	characteristic
260	#14579072	C₂³	1	1	yes	characteristic
261	#14579071	C₂³	1	1	yes	characteristic
262	#14579071	C₂³	1	1	yes	characteristic
263	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
265	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
266	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
267	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
268	C₂×D₈×C₇₉	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
270	#125×C₇₉	C₂³	1	2	yes	—
271	#125×C₇₉	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₇₉	—	2	2	no	—
273	C₂²⋊Q₈×C₇₉	—	2	2	no	—
274	C₂²⋊Q₈×C₇₉	—	2	2	no	—
275	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₇₉	C₂³	1	2	yes	—
277	C₄×D₄×C₇₉	C₂³	1	2	yes	—
278	C₄×D₄×C₇₉	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
280	#107×C₇₉	C₂³	1	1	yes	characteristic
281	#107×C₇₉	C₂³	1	1	yes	characteristic
282	#107×C₇₉	C₂³	1	1	yes	characteristic
283	#107×C₇₉	C₂³	1	2	yes	—
284	#106×C₇₉	C₂³	1	2	yes	—
285	#106×C₇₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
289	#102×C₇₉	C₂³	1	2	yes	—
290	#102×C₇₉	C₂³	1	2	yes	—
291	#102×C₇₉	C₂³	1	2	yes	—
292	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
295	C₂³×D₇₉	—	2	2	no	—
296	C₂×Dic₁₅₈	—	2	2	no	—
297	C₂×Dic₁₅₈	—	2	2	no	—
298	C₂×Dic₁₅₈	—	2	2	no	—
299	C₂×Dic₁₅₈	—	2	2	no	—
300	C₂×Dic₁₅₈	—	2	2	no	—
301	C₂×Dic₁₅₈	—	8	4	no	—
302	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
303	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
305	Q₈×D₇₉	—	8	4	no	—
306	C₂×D₃₁₆	C₂⁴	1	2	yes	—
307	C₂×C₂²⋊D₇₉	—	2	2	no	—
308	D₄×D₇₉	—	2	4	no	—
309	D₄×D₇₉	C₂×Q₈	1	8	yes	complemented
310	C₂²×Dic₇₉	—	2	2	no	—
311	C₂²×Dic₇₉	—	2	2	no	—
312	C₂²×Dic₇₉	—	2	2	no	—
313	C₂×C₄×D₇₉	—	2	2	no	—
314	C₂×C₄×D₇₉	—	2	2	no	—
315	C₂×C₄×D₇₉	—	2	2	no	—
316	C₂×C₄×D₇₉	—	2	2	no	—
317	C₂×C₄×D₇₉	—	2	2	no	—
318	C₂×C₄×D₇₉	—	2	2	no	—
319	C₂×C₄×D₇₉	—	2	2	no	—
320	C₂×C₄×D₇₉	—	8	4	no	—
321	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
322	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
323	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
324	D₆₃₂	C₂×Q₈	1	4	yes	complemented
325	#11929609	C₂×Q₈	1	8	yes	complemented
326	#11929607	—	2	2	no	—
327	#11929607	—	2	2	no	—
328	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
331	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
332	C₈×D₇₉	—	2	2	no	—
333	C₈×D₇₉	C₂×Q₈	1	4	yes	complemented
334	C₄⋊Dic₇₉	—	2	2	no	—
335	C₄⋊Dic₇₉	—	2	2	no	—
336	C₄⋊Dic₇₉	—	2	2	no	—
337	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
338	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
339	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
340	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
341	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
342	C₄⋊Dic₇₉	C₂⁴	1	2	yes	—
343	Dic₇₉⋊C₄	—	2	2	no	—
344	Dic₇₉⋊C₄	—	2	2	no	—
345	Dic₇₉⋊C₄	—	2	2	no	—
346	Dic₇₉⋊C₄	—	2	2	no	—
347	Dic₇₉⋊C₄	—	2	2	no	—
348	Dic₇₉⋊C₄	—	2	2	no	—
349	Dic₇₉⋊C₄	—	2	2	no	—
350	Dic₇₉⋊C₄	—	2	2	no	—
351	Dic₇₉⋊C₄	—	2	2	no	—
352	Dic₇₉⋊C₄	—	2	2	no	—
353	Dic₇₉⋊C₄	—	2	2	no	—
354	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
355	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
356	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
357	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
358	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
359	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
360	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
361	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
362	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
363	Dic₇₉⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊Dic₇₉	—	2	2	no	—
365	C₂²⋊Dic₇₉	—	2	2	no	—
366	C₂²⋊Dic₇₉	—	2	2	no	—
367	(C₂×D₇₉)⋊C₄	—	2	2	no	—
368	(C₂×D₇₉)⋊C₄	—	2	2	no	—
369	(C₂×D₇₉)⋊C₄	—	2	2	no	—
370	(C₂×D₇₉)⋊C₄	—	2	2	no	—
371	(C₂×D₇₉)⋊C₄	—	2	2	no	—
372	(C₂×D₇₉)⋊C₄	—	2	2	no	—
373	(C₂×D₇₉)⋊C₄	—	2	2	no	—
374	(C₂×D₇₉)⋊C₄	—	2	2	no	—
375	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
376	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
377	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
378	(C₂×D₇₉)⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₄×Dic₇₉	—	2	2	no	—
380	C₄×Dic₇₉	—	2	2	no	—
381	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
382	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
383	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
384	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
385	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
386	C₂×Q₈×C₇₉	—	2	2	no	—
387	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
388	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₇₉	—	2	2	no	—
390	C₂²×C₄×C₇₉	—	2	2	no	—
391	C₂²×C₄×C₇₉	—	2	2	no	—
392	D₈×C₇₉	C₂×Q₈	1	4	yes	complemented
393	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₇₉	—	2	2	no	—
398	C₄⋊C₄×C₇₉	—	2	2	no	—
399	C₄⋊C₄×C₇₉	—	2	2	no	—
400	C₄⋊C₄×C₇₉	—	2	2	no	—
401	C₄⋊C₄×C₇₉	—	2	2	no	—
402	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
408	C₂²⋊C₄×C₇₉	—	2	2	no	—
409	C₂²⋊C₄×C₇₉	—	2	2	no	—
410	C₂²⋊C₄×C₇₉	—	2	2	no	—
411	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
412	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
413	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
414	C₂³×C₇₉	—	2	2	no	—
415	C₂²×D₇₉	—	2	2	no	—
416	C₂²×D₇₉	—	2	8	no	—
417	C₂²×D₇₉	—	8	2	no	—
418	C₂²×D₇₉	—	8	2	no	—
419	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₇₉	—	4	1	no	—
421	Q₈×C₇₉	—	8	2	no	—
422	D₄×C₇₉	—	2	2	no	—
423	D₄×C₇₉	C₂²×Q₈	1	4	yes	—
424	C₂×C₄×C₇₉	—	2	2	no	—
425	C₂×C₄×C₇₉	—	2	2	no	—
426	C₂×C₄×C₇₉	—	2	2	no	—
427	C₂×C₄×C₇₉	—	8	2	no	—
428	C₂×C₄×C₇₉	—	8	2	no	—
429	C₂×C₄×C₇₉	—	8	2	no	—
430	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
437	C₂²⋊D₇₉	—	2	8	no	—
438	C₂×Dic₇₉	—	2	2	no	—
439	C₂×Dic₇₉	—	2	2	no	—
440	C₂×Dic₇₉	—	2	2	no	—
441	C₂×Dic₇₉	—	4	4	no	—
442	C₂×Dic₇₉	—	8	2	no	—
443	C₂×Dic₇₉	—	8	2	no	—
444	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
445	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
446	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
447	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
448	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
449	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
450	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
451	D₃₁₆	—	2	2	no	—
452	D₃₁₆	C₂²×Q₈	1	4	yes	—
453	C₄×D₇₉	—	2	2	no	—
454	C₄×D₇₉	—	4	1	no	—
455	C₄×D₇₉	—	4	4	no	—
456	C₄×D₇₉	—	8	2	no	—
457	C₄×D₇₉	—	8	2	no	—
458	C₄×D₇₉	—	8	2	no	—
459	C₄×D₇₉	—	8	2	no	—
460	C₄×D₇₉	—	8	2	no	—
461	C₄×D₇₉	—	8	2	no	—
462	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
463	C₄×D₇₉	2₋¹⁺⁴	1	2	yes	—
464	Dic₁₅₈	—	2	2	no	—
465	Dic₁₅₈	—	2	2	no	—
466	Dic₁₅₈	—	4	1	no	—
467	Dic₁₅₈	—	4	4	no	—
468	Dic₁₅₈	—	8	2	no	—
469	Dic₁₅₈	—	8	2	no	—
470	Dic₁₅₈	—	8	2	no	—
471	Dic₁₅₈	—	8	2	no	—
472	C₈×C₇₉	—	2	1	no	—
473	C₈×C₇₉	—	2	1	no	—
474	C₈×C₇₉	—	2	1	no	—
475	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
476	C₇₉⋊C₈	—	2	1	no	—
477	C₇₉⋊C₈	—	2	1	no	—
478	C₇₉⋊C₈	—	2	1	no	—
479	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
480	C₂²×C₇₉	—	2	4	no	—
481	C₂²×C₇₉	—	4	2	no	—
482	C₂²×C₇₉	—	4	2	no	—
483	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
484	C₂×D₇₉	—	2	1	no	—
485	C₂×D₇₉	—	2	1	no	—
486	C₂×D₇₉	—	2	4	no	—
487	C₂×D₇₉	—	4	2	no	—
488	C₂×D₇₉	—	4	2	no	—
489	C₂×D₇₉	—	8	8	no	—
490	C₂×D₇₉	D₄×Q₈	1	2	yes	—
491	C₄×C₇₉	—	2	1	no	—
492	C₄×C₇₉	—	2	1	no	—
493	C₄×C₇₉	—	2	1	no	—
494	C₄×C₇₉	—	2	1	no	—
495	C₄×C₇₉	—	2	1	no	—
496	C₄×C₇₉	—	2	1	no	—
497	C₄×C₇₉	—	4	2	no	—
498	C₄×C₇₉	—	4	2	no	—
499	C₄×C₇₉	—	4	2	no	—
500	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
501	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
502	Dic₇₉	—	2	1	no	—
503	Dic₇₉	—	2	1	no	—
504	Dic₇₉	—	2	1	no	—
505	Dic₇₉	—	2	1	no	—
506	Dic₇₉	—	2	1	no	—
507	Dic₇₉	—	4	2	no	—
508	Dic₇₉	—	4	2	no	—
509	Dic₇₉	—	4	2	no	—
510	Dic₇₉	D₄×Q₈	1	2	yes	—
511	Dic₇₉	#576	1	2	yes	—
512	#61370	—	79	1	no	maximal, Sylow
513	C₂×C₇₉	—	4	4	no	—
514	C₂×C₇₉	C₂×D₄×Q₈	1	1	yes	characteristic
515	C₂×C₇₉	C₂×#576	1	1	yes	characteristic
516	C₂×C₇₉	#3584	1	1	yes	characteristic
517	D₇₉	—	2	2	no	—
518	D₇₉	—	4	4	no	—
519	#3501	—	79	2	no	—
520	#3389	—	79	2	no	—
521	#3389	—	79	2	no	—
522	#3384	—	79	2	no	—
523	#3384	—	79	2	no	—
524	#3380	—	79	1	no	—
525	#3380	—	79	1	no	—
526	#3380	—	79	1	no	—
527	#3380	—	79	1	no	—
528	#3380	—	79	1	no	—
529	#3380	D₇₉	1	1	yes	characteristic, complemented
530	Q₈×D₈	—	79	1	no	—
531	Q₈×D₈	—	79	1	no	—
532	#3164	—	79	1	no	—
533	#3164	—	79	1	no	—
534	#3160	—	79	1	no	—
535	#3081	—	79	2	no	—
536	#3081	—	79	2	no	—
537	#3077	—	79	2	no	—
538	#2960	—	79	1	no	—
539	#2948	—	79	1	no	—
540	#2948	—	79	1	no	—
541	C₂×C₄×D₈	—	79	1	no	—
542	C₇₉	#61370	1	1	yes	characteristic, complemented, Sylow
543	C₂²×D₈	—	79	1	no	—
544	#554	—	79	2	no	—
545	#554	—	79	2	no	—
546	#554	—	79	2	no	—
547	#554	—	79	2	no	—
548	#554	—	79	2	no	—
549	#554	—	158	2	no	—
550	#554	—	158	2	no	—
551	#554	—	158	2	no	—
552	#554	C₂×D₇₉	1	2	yes	complemented
553	D₄×Q₈	—	79	2	no	—
554	D₄×Q₈	—	79	2	no	—
555	D₄×Q₈	—	158	2	no	—
556	#544	—	79	2	no	—
557	#544	—	79	2	no	—
558	#543	—	158	2	no	—
559	#543	—	158	2	no	—
560	#533	—	79	1	no	—
561	#533	—	79	2	no	—
562	C₂×C₂²⋊Q₈	—	158	2	no	—
563	C₂×C₂²⋊Q₈	—	158	2	no	—
564	#518	—	79	2	no	—
565	#518	—	79	2	no	—
566	C₂×C₄×D₄	—	79	2	no	—
567	#501	—	79	2	no	—
568	#501	—	79	2	no	—
569	#501	—	79	2	no	—
570	#501	—	79	2	no	—
571	#500	—	79	1	no	—
572	#500	—	79	1	no	—
573	#500	—	79	1	no	—
574	#500	—	79	1	no	—
575	#500	—	79	1	no	—
576	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
577	#499	—	79	2	no	—
578	#499	—	79	1	no	—
579	#499	—	79	1	no	—
580	#499	—	79	1	no	—
581	#499	—	79	1	no	—
582	#499	C₂×D₇₉	1	1	yes	characteristic, complemented
583	#499	C₂×D₇₉	1	1	yes	characteristic, complemented
584	#498	—	79	2	no	—
585	#478	—	79	2	no	—
586	#478	—	79	2	no	—
587	#478	—	79	2	no	—
588	#478	—	79	2	no	—
589	#478	—	79	2	no	—
590	#478	—	79	2	no	—
591	#478	—	79	2	no	—
592	#478	—	79	2	no	—
593	#478	—	79	2	no	—
594	#478	—	79	2	no	—
595	#478	C₂×D₇₉	1	2	yes	complemented
596	#478	C₂×D₇₉	1	2	yes	complemented
597	#476	—	79	2	no	—
598	#476	—	79	2	no	—
599	#476	—	79	2	no	—
600	#476	—	79	2	no	—
601	#476	—	79	2	no	—
602	#476	C₂×D₇₉	1	2	yes	complemented
603	#474	—	79	2	no	—
604	#474	—	79	2	no	—
605	#474	—	79	2	no	—
606	#474	—	79	2	no	—
607	#474	—	79	2	no	—
608	#474	—	79	2	no	—
609	#446	—	79	1	no	—
610	#446	—	79	1	no	—
611	#446	—	79	1	no	—
612	#446	—	79	1	no	—
613	C₈×Q₈	—	79	1	no	—
614	C₈×Q₈	—	79	1	no	—
615	C₈×Q₈	—	79	1	no	—
616	C₈×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
617	#442	—	79	2	no	—
618	#442	—	79	2	no	—
619	#442	—	79	2	no	—
620	#442	—	79	2	no	—
621	C₄×D₈	—	79	1	no	—
622	C₄×D₈	—	79	1	no	—
623	C₄×D₈	—	79	1	no	—
624	C₄×D₈	—	79	2	no	—
625	C₄×D₈	—	79	1	no	—
626	C₄×D₈	—	79	1	no	—
627	C₄×D₈	—	79	1	no	—
628	C₄×D₈	—	79	2	no	—
629	C₄×D₈	—	79	1	no	—
630	C₄×D₈	—	79	1	no	—
631	C₄×D₈	—	79	1	no	—
632	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
633	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
634	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
635	#428	—	79	2	no	—
636	#428	—	79	2	no	—
637	#427	—	79	1	no	—
638	#427	—	79	1	no	—
639	#427	—	79	2	no	—
640	C₂×#107	—	79	1	no	—
641	#424	—	79	1	no	—
642	#424	—	79	1	no	—
643	#423	—	79	1	no	—
644	#418	—	79	2	no	—
645	#418	—	79	2	no	—
646	C₂×#102	—	79	2	no	—
647	#405	—	79	1	no	—
648	#405	—	79	1	no	—
649	C₂×C₄×C₈	—	79	1	no	—
650	C₂²×Q₈	—	158	2	no	—
651	C₂²×Q₈	—	158	2	no	—
652	C₂²×D₄	—	79	2	no	—
653	C₂³×C₄	—	158	2	no	—
654	C₂×D₈	—	79	2	no	—
655	C₂×D₈	—	79	8	no	—
656	C₂×D₈	—	79	1	no	—
657	C₂×D₈	C₂²×D₇₉	1	1	yes	characteristic
658	C₂×M₁₆	—	79	1	no	—
659	C₂×M₁₆	—	79	1	no	—
660	C₂²×C₈	—	79	1	no	—
661	C₂²×C₈	—	79	1	no	—
662	C₄⋊Q₈	—	79	1	no	—
663	C₄⋊Q₈	—	79	1	no	—
664	C₄⋊Q₈	—	79	2	no	—
665	C₄⋊Q₈	—	79	2	no	—
666	C₄⋊Q₈	—	79	2	no	—
667	C₄⋊Q₈	—	79	2	no	—
668	C₄⋊Q₈	—	79	2	no	—
669	C₄⋊Q₈	—	158	2	no	—
670	C₄⋊Q₈	—	158	2	no	—
671	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
672	#125	—	79	1	no	—
673	#125	—	79	1	no	—
674	#125	—	79	2	no	—
675	#125	—	79	2	no	—
676	#125	—	79	2	no	—
677	#125	—	79	2	no	—
678	#125	—	158	2	no	—
679	#125	—	158	2	no	—
680	#125	C₂²×D₇₉	1	2	yes	—
681	#125	C₂²×D₇₉	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	79	1	no	—
686	C₂²⋊Q₈	—	79	1	no	—
687	C₂²⋊Q₈	—	79	1	no	—
688	C₂²⋊Q₈	—	79	1	no	—
689	C₂²⋊Q₈	—	158	2	no	—
690	C₂²⋊Q₈	—	158	2	no	—
691	C₂²⋊Q₈	—	158	2	no	—
692	C₂²⋊Q₈	—	158	2	no	—
693	C₂²⋊Q₈	—	158	2	no	—
694	C₂²⋊Q₈	—	158	2	no	—
695	C₂²⋊Q₈	—	158	2	no	—
696	C₂²⋊Q₈	—	158	2	no	—
697	C₂²⋊Q₈	—	158	2	no	—
698	C₂²⋊Q₈	—	158	2	no	—
699	C₂²⋊Q₈	—	158	2	no	—
700	C₂²⋊Q₈	—	158	2	no	—
701	C₂²⋊Q₈	—	158	2	no	—
702	C₂²⋊Q₈	—	158	2	no	—
703	C₂²⋊Q₈	—	158	2	no	—
704	C₂²⋊Q₈	—	158	2	no	—
705	C₂²⋊Q₈	—	158	2	no	—
706	C₂²⋊Q₈	—	158	2	no	—
707	C₂²⋊Q₈	—	158	2	no	—
708	C₂²⋊Q₈	—	158	2	no	—
709	C₂²⋊Q₈	—	158	2	no	—
710	C₂²⋊Q₈	—	158	2	no	—
711	C₂²⋊Q₈	—	158	2	no	—
712	C₂²⋊Q₈	—	158	2	no	—
713	C₂²⋊Q₈	—	158	2	no	—
714	C₂²⋊Q₈	—	158	2	no	—
715	C₂²⋊Q₈	—	158	2	no	—
716	C₄×Q₈	—	79	1	no	—
717	C₄×Q₈	—	79	1	no	—
718	C₄×Q₈	—	79	1	no	—
719	C₄×Q₈	—	158	2	no	—
720	C₄×Q₈	—	158	2	no	—
721	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
722	C₄×D₄	—	79	2	no	—
723	C₄×D₄	—	79	2	no	—
724	C₄×D₄	—	79	2	no	—
725	C₄×D₄	—	79	2	no	—
726	C₄×D₄	—	79	2	no	—
727	C₄×D₄	—	79	2	no	—
728	C₄×D₄	—	79	2	no	—
729	C₄×D₄	—	79	2	no	—
730	C₄×D₄	—	79	2	no	—
731	C₄×D₄	—	158	2	no	—
732	C₄×D₄	—	158	2	no	—
733	C₄×D₄	—	158	2	no	—
734	C₄×D₄	—	158	2	no	—
735	C₄×D₄	—	158	2	no	—
736	C₄×D₄	—	158	2	no	—
737	C₄×D₄	C₂²×D₇₉	1	2	yes	—
738	C₄×D₄	C₂²×D₇₉	1	2	yes	—
739	C₄×D₄	C₂²×D₇₉	1	2	yes	—
740	#117	—	79	1	no	—
741	#117	—	79	1	no	—
742	#117	—	79	2	no	—
743	#117	—	79	2	no	—
744	C₂×C₄⋊C₄	—	2	2	no	—
745	C₂×C₄⋊C₄	—	79	2	no	—
746	C₂×C₄⋊C₄	—	158	2	no	—
747	C₂×C₄⋊C₄	—	158	2	no	—
748	C₂×C₄⋊C₄	—	158	2	no	—
749	C₂×C₄⋊C₄	—	158	2	no	—
750	C₂×C₄⋊C₄	—	158	2	no	—
751	C₂×C₂²⋊C₄	—	158	2	no	—
752	C₂×C₂²⋊C₄	—	158	2	no	—
753	C₂×C₂²⋊C₄	—	158	2	no	—
754	C₂×C₂²⋊C₄	—	158	2	no	—
755	C₂×C₂²⋊C₄	—	158	2	no	—
756	C₂×C₄²	—	79	1	no	—
757	#107	—	79	1	no	—
758	#107	—	79	1	no	—
759	#107	—	79	1	no	—
760	#107	—	79	2	no	—
761	#107	—	79	2	no	—
762	#107	—	79	2	no	—
763	#107	—	79	2	no	—
764	#107	—	79	2	no	—
765	#107	—	79	2	no	—
766	#107	C₂²×D₇₉	1	1	yes	characteristic
767	#107	C₂²×D₇₉	1	1	yes	characteristic
768	#107	C₂²×D₇₉	1	1	yes	characteristic
769	#107	C₂²×D₇₉	1	2	yes	—
770	#106	—	79	2	no	—
771	#106	—	79	2	no	—
772	#106	—	79	2	no	—
773	#106	—	79	2	no	—
774	#106	—	79	2	no	—
775	#106	—	79	2	no	—
776	#106	C₂²×D₇₉	1	2	yes	—
777	#106	C₂²×D₇₉	1	2	yes	—
778	C₄⋊C₈	—	79	1	no	—
779	C₄⋊C₈	—	79	1	no	—
780	C₄⋊C₈	—	79	1	no	—
781	C₄⋊C₈	—	79	1	no	—
782	C₄⋊C₈	—	79	1	no	—
783	C₄⋊C₈	—	79	1	no	—
784	C₄⋊C₈	—	79	1	no	—
785	C₄⋊C₈	—	79	1	no	—
786	C₄⋊C₈	—	79	1	no	—
787	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
788	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
789	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
790	#102	—	79	2	no	—
791	#102	—	79	2	no	—
792	#102	—	79	2	no	—
793	#102	—	79	2	no	—
794	#102	—	79	2	no	—
795	#102	—	79	2	no	—
796	#102	—	79	2	no	—
797	#102	—	79	2	no	—
798	#102	—	79	2	no	—
799	#102	C₂²×D₇₉	1	2	yes	—
800	#102	C₂²×D₇₉	1	2	yes	—
801	#102	C₂²×D₇₉	1	2	yes	—
802	#97	—	79	1	no	—
803	#97	—	79	1	no	—
804	#97	—	79	1	no	—
805	#97	—	79	1	no	—
806	C₄×C₈	—	79	1	no	—
807	C₄×C₈	—	79	1	no	—
808	C₄×C₈	—	79	1	no	—
809	C₄×C₈	—	79	1	no	—
810	C₄×C₈	—	79	1	no	—
811	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
812	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
813	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
814	C₂⁴	—	158	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	79	1	no	—
817	C₂×Q₈	—	79	1	no	—
818	C₂×Q₈	—	79	1	no	—
819	C₂×Q₈	—	632	4	no	—
820	C₂×Q₈	—	632	4	no	—
821	C₂×Q₈	—	158	2	no	—
822	C₂×Q₈	—	158	2	no	—
823	C₂×Q₈	—	158	2	no	—
824	C₂×Q₈	—	158	2	no	—
825	C₂×Q₈	—	158	2	no	—
826	C₂×Q₈	D₄×D₇₉	1	1	yes	characteristic
827	C₂×D₄	—	79	8	no	—
828	C₂×D₄	—	79	2	no	—
829	C₂×D₄	—	158	4	no	—
830	C₂×D₄	—	158	2	no	—
831	C₂×D₄	C₂³×D₇₉	1	2	yes	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	79	1	no	—
836	C₂²×C₄	—	79	1	no	—
837	C₂²×C₄	—	79	1	no	—
838	C₂²×C₄	—	632	4	no	—
839	C₂²×C₄	—	158	2	no	—
840	C₂²×C₄	—	158	2	no	—
841	C₂²×C₄	—	158	2	no	—
842	C₂²×C₄	—	158	2	no	—
843	C₂²×C₄	—	158	2	no	—
844	C₂²×C₄	—	158	2	no	—
845	C₂²×C₄	—	158	2	no	—
846	C₂²×C₄	—	158	2	no	—
847	C₂²×C₄	—	158	2	no	—
848	C₂²×C₄	—	158	2	no	—
849	D₈	—	79	8	no	—
850	D₈	—	79	4	no	—
851	D₈	Q₈×D₇₉	1	4	yes	complemented
852	M₁₆	—	158	2	no	—
853	M₁₆	—	158	2	no	—
854	C₂×C₈	—	79	1	no	—
855	C₂×C₈	—	79	4	no	—
856	C₂×C₈	—	79	1	no	—
857	C₂×C₈	—	79	1	no	—
858	C₂×C₈	—	79	1	no	—
859	C₂×C₈	—	158	2	no	—
860	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
861	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
862	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
863	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	79	1	no	—
870	C₄⋊C₄	—	79	1	no	—
871	C₄⋊C₄	—	79	1	no	—
872	C₄⋊C₄	—	79	1	no	—
873	C₄⋊C₄	—	79	1	no	—
874	C₄⋊C₄	—	79	1	no	—
875	C₄⋊C₄	—	79	1	no	—
876	C₄⋊C₄	—	79	1	no	—
877	C₄⋊C₄	—	79	1	no	—
878	C₄⋊C₄	—	79	1	no	—
879	C₄⋊C₄	—	79	1	no	—
880	C₄⋊C₄	—	79	1	no	—
881	C₄⋊C₄	—	79	1	no	—
882	C₄⋊C₄	—	79	2	no	—
883	C₄⋊C₄	—	79	2	no	—
884	C₄⋊C₄	—	79	2	no	—
885	C₄⋊C₄	—	158	2	no	—
886	C₄⋊C₄	—	158	2	no	—
887	C₄⋊C₄	—	158	2	no	—
888	C₄⋊C₄	—	158	2	no	—
889	C₄⋊C₄	—	158	2	no	—
890	C₄⋊C₄	—	158	2	no	—
891	C₄⋊C₄	—	158	2	no	—
892	C₄⋊C₄	—	158	2	no	—
893	C₄⋊C₄	—	158	2	no	—
894	C₄⋊C₄	—	158	2	no	—
895	C₄⋊C₄	—	158	2	no	—
896	C₄⋊C₄	—	158	2	no	—
897	C₄⋊C₄	—	158	2	no	—
898	C₄⋊C₄	—	158	2	no	—
899	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
900	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
901	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
902	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
903	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
904	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	79	1	no	—
909	C₂²⋊C₄	—	79	1	no	—
910	C₂²⋊C₄	—	79	1	no	—
911	C₂²⋊C₄	—	79	1	no	—
912	C₂²⋊C₄	—	158	2	no	—
913	C₂²⋊C₄	—	158	2	no	—
914	C₂²⋊C₄	—	158	2	no	—
915	C₂²⋊C₄	—	158	2	no	—
916	C₂²⋊C₄	—	158	2	no	—
917	C₂²⋊C₄	—	158	2	no	—
918	C₂²⋊C₄	—	158	2	no	—
919	C₂²⋊C₄	—	158	2	no	—
920	C₂²⋊C₄	—	158	2	no	—
921	C₂²⋊C₄	—	158	2	no	—
922	C₂²⋊C₄	—	158	2	no	—
923	C₄²	—	79	1	no	—
924	C₄²	—	79	1	no	—
925	C₄²	—	79	1	no	—
926	C₄²	—	79	1	no	—
927	C₄²	—	79	1	no	—
928	C₄²	—	158	2	no	—
929	C₄²	—	158	2	no	—
930	C₄²	C₂³×D₇₉	1	1	yes	characteristic
931	C₄²	C₂³×D₇₉	1	1	yes	characteristic
932	C₄²	C₂³×D₇₉	1	1	yes	characteristic
933	C₂³	—	2	2	no	—
934	C₂³	—	79	1	no	—
935	C₂³	—	632	2	no	—
936	C₂³	—	632	2	no	—
937	C₂³	—	158	8	no	—
938	C₂³	—	158	2	no	—
939	Q₈	—	4	1	no	—
940	Q₈	—	8	2	no	—
941	Q₈	—	316	1	no	—
942	Q₈	—	316	4	no	—
943	Q₈	—	632	2	no	—
944	Q₈	—	632	2	no	—
945	Q₈	—	632	2	no	—
946	Q₈	—	632	2	no	—
947	Q₈	—	158	2	no	—
948	Q₈	—	158	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	79	4	no	—
951	D₄	—	158	8	no	—
952	D₄	—	158	2	no	—
953	D₄	C₂×Q₈×D₇₉	1	4	yes	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	316	1	no	—
961	C₂×C₄	—	316	4	no	—
962	C₂×C₄	—	316	4	no	—
963	C₂×C₄	—	79	1	no	—
964	C₂×C₄	—	79	1	no	—
965	C₂×C₄	—	79	2	no	—
966	C₂×C₄	—	79	2	no	—
967	C₂×C₄	—	79	1	no	—
968	C₂×C₄	—	79	1	no	—
969	C₂×C₄	—	79	1	no	—
970	C₂×C₄	—	79	1	no	—
971	C₂×C₄	—	79	1	no	—
972	C₂×C₄	—	632	2	no	—
973	C₂×C₄	—	632	2	no	—
974	C₂×C₄	—	632	2	no	—
975	C₂×C₄	—	632	2	no	—
976	C₂×C₄	—	632	2	no	—
977	C₂×C₄	—	632	2	no	—
978	C₂×C₄	—	632	2	no	—
979	C₂×C₄	—	632	2	no	—
980	C₂×C₄	—	158	2	no	—
981	C₂×C₄	—	158	2	no	—
982	C₂×C₄	—	158	2	no	—
983	C₂×C₄	—	158	2	no	—
984	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
985	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
986	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
987	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
988	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
989	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
990	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	1	no	—
994	C₈	—	79	2	no	—
995	C₈	—	158	1	no	—
996	C₈	—	158	1	no	—
997	C₈	—	158	1	no	—
998	C₈	C₂×Q₈×D₇₉	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	316	2	no	—
1003	C₂²	—	316	2	no	—
1004	C₂²	—	79	2	no	—
1005	C₂²	—	632	8	no	—
1006	C₂²	—	158	4	no	—
1007	C₂²	—	158	1	no	—
1008	C₂²	—	158	1	no	—
1009	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	316	2	no	—
1020	C₄	—	316	2	no	—
1021	C₄	—	316	2	no	—
1022	C₄	—	79	2	no	—
1023	C₄	—	79	2	no	—
1024	C₄	—	158	1	no	—
1025	C₄	—	158	1	no	—
1026	C₄	—	158	1	no	—
1027	C₄	—	158	1	no	—
1028	C₄	—	158	1	no	—
1029	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
1030	C₄	2₋¹⁺⁴×D₇₉	1	1	yes	characteristic
1031	C₂	—	4	4	no	—
1032	C₂	—	316	4	no	—
1033	C₂	—	158	2	no	—
1034	C₂	D₄×Q₈×D₇₉	1	1	yes	characteristic
1035	C₂	#576×D₇₉	1	1	yes	characteristic
1036	C₂	#23778169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#3380	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	C₂×D₈×D₇₉	C₂²
hypercenter	#3380	D₇₉
hypocenter	C₇₉	#61370
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3380

Complements

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

N	H ≅ G/N	type
1. #23777199	C₂	semidirect
2. #23776358	C₂	semidirect
3. #23776354	C₂	semidirect
4. #23776302	C₂	semidirect
5. #23776294	C₂	semidirect
6. #23776268	C₂	semidirect
7. #23776267	C₂	semidirect
8. #23776267	C₂	semidirect
9. #23776264	C₂	semidirect
10. #23776264	C₂	semidirect
11. D₈×Dic₁₅₈	C₂	semidirect
12. #23776252	C₂	semidirect
13. #23773937	C₂	semidirect
14. #23773933	C₂	semidirect
15. #23773913	C₂	semidirect
16. #23773230	C₂	semidirect
17. #23773226	C₂	semidirect
18. #23773195	C₂	semidirect
19. #23772329	C₂	semidirect
23. C₇₉×#3380	C₂	semidirect
25. #19099273	C₂²	semidirect
26. #19099272	C₂²	semidirect
27. #19099272	C₂²	semidirect
28. #19099269	C₂²	semidirect
29. #19099269	C₂²	semidirect
33. D₄×Dic₁₅₈	C₂²	semidirect
34. #19099228	C₂²	semidirect
47. #19098973	C₂²	semidirect
48. #19098971	C₂²	semidirect
49. #19098970	C₂²	semidirect
50. #19098969	C₂²	semidirect
51. #19098968	C₂²	semidirect
52. #19098967	C₂²	semidirect
53. #19098967	C₂²	semidirect
54. #19098967	C₂²	semidirect
55. #19098967	C₂²	semidirect
56. #19098965	C₂²	semidirect
57. #19098965	C₂²	semidirect
58. #19098964	C₂²	semidirect
59. #19098964	C₂²	semidirect
60. #19098962	C₂²	semidirect
61. #19098960	C₂²	semidirect
62. #19098865	C₂²	semidirect
63. #19098865	C₂²	semidirect
64. #19098864	C₂²	semidirect
65. #19098864	C₂²	semidirect
66. #19098863	C₂²	semidirect
67. #19098863	C₂²	semidirect
68. #19098862	C₂²	semidirect
69. #19098862	C₂²	semidirect
70. #19098860	C₂²	semidirect
71. #19098860	C₂²	semidirect
72. #19098854	C₂²	semidirect
73. #19098852	C₂²	semidirect
74. #19098852	C₂²	semidirect
75. #19098851	C₂²	semidirect
76. #19098851	C₂²	semidirect
77. #19098843	C₂²	semidirect
78. #19098842	C₂²	semidirect
79. #19098842	C₂²	semidirect
80. #19098841	C₂²	semidirect
81. #19098841	C₂²	semidirect
82. #19098840	C₂²	semidirect
83. #19098694	C₂²	semidirect
84. #19098692	C₂²	semidirect
85. #19098692	C₂²	semidirect
86. #19098690	C₂²	semidirect
87. C₈×Dic₁₅₈	C₂²	semidirect
88. C₈×Dic₁₅₈	C₂²	semidirect
89. C₈×Dic₁₅₈	C₂²	semidirect
120. #554×C₇₉	C₂²	semidirect
121. #500×C₇₉	C₂²	semidirect
122. #499×C₇₉	C₂²	semidirect
123. #499×C₇₉	C₂²	semidirect
124. #478×C₇₉	C₂²	semidirect
125. #478×C₇₉	C₂²	semidirect
126. #476×C₇₉	C₂²	semidirect
127. C₈×Q₈×C₇₉	C₂²	semidirect
137. D₈×D₇₉	Q₈	semidirect
309. D₄×D₇₉	C₂×Q₈	semidirect
324. D₆₃₂	C₂×Q₈	semidirect
325. #11929609	C₂×Q₈	semidirect
333. C₈×D₇₉	C₂×Q₈	semidirect
392. D₈×C₇₉	C₂×Q₈	semidirect
529. #3380	D₇₉	semidirect
542. C₇₉	#61370	semidirect
552. #554	C₂×D₇₉	semidirect
576. #500	C₂×D₇₉	semidirect
582. #499	C₂×D₇₉	semidirect
583. #499	C₂×D₇₉	semidirect
595. #478	C₂×D₇₉	semidirect
596. #478	C₂×D₇₉	semidirect
602. #476	C₂×D₇₉	semidirect
616. C₈×Q₈	C₂×D₇₉	semidirect
851. D₈	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777199	2
#23776358	2
#23776354	2
#23776302	2
#23776294	2
#23776268	2
#23776267	2
#23776264	2
D₈×Dic₁₅₈	2
#23776252	2
#23773937	2
#23773933	2
#23773913	2
#23773230	2
#23773226	2
#23773195	2
#23772329	2
#23772247	2
C₄×D₈×D₇₉	2
C₇₉×#3380	2
#61370	79