Subgroups — #35152693

Order 20224.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776978	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772352	C₂	1	2	yes	maximal, complemented
4	#23772345	C₂	1	2	yes	maximal, complemented
5	#23772345	C₂	1	2	yes	maximal, complemented
6	#23772344	C₂	1	1	yes	maximal, characteristic, complemented
7	#23772344	C₂	1	1	yes	maximal, characteristic, complemented
8	#23772342	C₂	1	2	yes	maximal, complemented
9	#23772341	C₂	1	1	yes	maximal, characteristic, complemented
10	#23772339	C₂	1	1	yes	maximal, characteristic, complemented
11	#23772336	C₂	1	2	yes	maximal, complemented
12	#23772336	C₂	1	2	yes	maximal, complemented
13	#23772333	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772329	C₂	1	2	yes	maximal, complemented
15	C₂×#19098692	C₂	1	1	yes	maximal, characteristic, complemented
16	#446×D₇₉	C₂	1	2	yes	maximal, complemented
17	#23771967	C₂	1	1	yes	maximal, characteristic
18	#23771967	C₂	1	1	yes	maximal, characteristic
19	#23771965	C₂	1	1	yes	maximal, characteristic
20	#23771829	C₂	1	1	yes	maximal, characteristic
21	#23771827	C₂	1	1	yes	maximal, characteristic
22	#23771822	C₂	1	1	yes	maximal, characteristic
23	C₇₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14579169	C₂²	1	1	yes	characteristic
25	C₂×#14579169	C₂²	1	1	yes	characteristic
26	C₂×#14579167	C₂²	1	1	yes	characteristic
27	C₂×#14579167	C₂²	1	1	yes	characteristic
28	#19099293	C₄	1	1	yes	characteristic
29	#19099290	C₄	1	1	yes	characteristic
30	#19099290	C₄	1	1	yes	characteristic
31	#19099288	C₄	1	1	yes	characteristic
32	#19099274	C₄	1	1	yes	characteristic
33	#19099271	C₄	1	2	yes	—
34	#19099269	C₄	1	1	yes	characteristic
35	#19099269	C₄	1	1	yes	characteristic
36	#19099267	C₄	1	2	yes	—
37	#19099267	C₄	1	2	yes	—
38	#19099228	C₄	1	1	yes	characteristic
39	#19099226	C₄	1	2	yes	—
40	#19099117	C₂²	1	2	yes	—
41	#19099117	C₂²	1	2	yes	—
42	#19099117	C₂²	1	2	yes	—
43	#19099116	C₂²	1	1	yes	characteristic
44	#19099116	C₂²	1	1	yes	characteristic
45	C₄×#11929624	C₂²	1	1	yes	characteristic
46	#19099031	C₂²	1	1	yes	characteristic
47	#19099031	C₂²	1	1	yes	characteristic
48	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
49	C₄×Q₈×D₇₉	C₂²	1	2	yes	—
50	#19098694	C₂²	1	2	yes	—
51	#19098694	C₂²	1	2	yes	—
52	#19098694	C₂²	1	2	yes	—
53	#19098694	C₂²	1	2	yes	—
54	#19098693	C₂²	1	2	yes	—
55	#19098693	C₂²	1	2	yes	—
56	#19098693	C₂²	1	2	yes	—
57	#19098692	C₂²	1	1	yes	characteristic
58	#19098692	C₂²	1	2	yes	—
59	#19098692	C₂²	1	1	yes	characteristic
60	#19098692	C₂²	1	1	yes	characteristic
61	#19098692	C₂²	1	1	yes	characteristic
62	#19098692	C₂²	1	1	yes	characteristic
63	#19098692	C₂²	1	1	yes	characteristic
64	#19098692	C₂²	1	1	yes	characteristic
65	#19098692	C₂²	1	1	yes	characteristic
66	#19098692	C₂²	1	2	yes	—
67	#19098692	C₂²	1	2	yes	—
68	#19098692	C₂²	1	2	yes	—
69	#19098691	C₂²	1	2	yes	—
70	#19098691	C₂²	1	2	yes	—
71	#19098691	C₂²	1	2	yes	—
72	#19098691	C₂²	1	2	yes	—
73	#19098691	C₂²	1	2	yes	—
74	#19098691	C₂²	1	2	yes	—
75	#19098690	C₂²	1	2	yes	—
76	#19098690	C₂²	1	2	yes	—
77	C₈×Dic₁₅₈	C₂²	1	2	yes	—
78	C₈×Dic₁₅₈	C₂²	1	2	yes	—
79	C₈×Dic₁₅₈	C₂²	1	2	yes	—
80	#19098687	C₂²	1	2	yes	—
81	#19098687	C₂²	1	2	yes	—
82	#19098590	C₂²	1	1	yes	characteristic
83	#19098590	C₂²	1	1	yes	characteristic
84	#19098589	C₂²	1	1	yes	characteristic
85	#19098589	C₂²	1	1	yes	characteristic
86	#19098588	C₂²	1	2	yes	—
87	#19098588	C₂²	1	2	yes	—
88	#19098588	C₂²	1	2	yes	—
89	#19098588	C₂²	1	2	yes	—
90	#19098588	C₂²	1	2	yes	—
91	#19098588	C₂²	1	2	yes	—
92	#19098587	C₂²	1	1	yes	characteristic
93	#19098586	C₂²	1	1	yes	characteristic
94	#19098586	C₂²	1	1	yes	characteristic
95	#19098585	C₂²	1	2	yes	—
96	#19098585	C₂²	1	2	yes	—
97	#19098585	C₂²	1	2	yes	—
98	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
99	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
100	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
101	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
102	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
103	#19098521	C₂²	1	1	yes	characteristic
104	#19098521	C₂²	1	1	yes	characteristic
105	#19098520	C₂²	1	2	yes	—
106	#19098520	C₂²	1	2	yes	—
107	#19098519	C₂²	1	1	yes	characteristic
108	#19098519	C₂²	1	1	yes	characteristic
109	#19098517	C₂²	1	2	yes	—
110	#19098517	C₂²	1	2	yes	—
111	#19098517	C₂²	1	2	yes	—
112	#19098517	C₂²	1	2	yes	—
113	#19098515	C₂²	1	2	yes	—
114	#19098515	C₂²	1	2	yes	—
115	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
116	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
117	C₄×#11929607	C₂²	1	2	yes	—
118	C₂×#14579072	C₂²	1	1	yes	characteristic
119	C₂×#14579071	C₂²	1	1	yes	characteristic
120	#97×D₇₉	C₂²	1	2	yes	—
121	#97×D₇₉	C₂²	1	2	yes	—
122	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₇₉	C₂²	1	2	yes	—
124	#533×C₇₉	C₂²	1	1	yes	characteristic
125	#446×C₇₉	C₂²	1	2	yes	—
126	#446×C₇₉	C₂²	1	2	yes	—
127	#446×C₇₉	C₂²	1	2	yes	—
128	C₈×Q₈×C₇₉	C₂²	1	2	yes	—
129	#424×C₇₉	C₂²	1	1	yes	characteristic
130	#424×C₇₉	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
132	#405×C₇₉	C₂²	1	1	yes	characteristic
133	#405×C₇₉	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
135	C₂×#11929624	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
137	C₂×Q₈×D₇₉	C₂×C₄	1	2	yes	—
138	#14579169	—	2	4	no	—
139	#14579169	Q₈	1	8	yes	complemented
140	#14579167	—	2	4	no	—
141	#14579167	—	2	4	no	—
142	C₂×#11929608	C₂³	1	1	yes	characteristic
143	C₂×#11929608	C₂³	1	1	yes	characteristic
144	C₂×#11929607	C₂³	1	2	yes	—
145	C₂×#11929607	C₂³	1	2	yes	—
146	C₂×#11929607	C₂³	1	2	yes	—
147	C₂×#11929607	C₂³	1	2	yes	—
148	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₇₉	C₂³	1	2	yes	—
151	C₂×C₈×D₇₉	C₂³	1	2	yes	—
152	C₂×C₈×D₇₉	C₂³	1	2	yes	—
153	C₂×C₈×D₇₉	C₂³	1	2	yes	—
154	#14579160	C₂×C₄	1	2	yes	—
155	#14579160	C₂×C₄	1	2	yes	—
156	#14579160	C₂×C₄	1	1	yes	characteristic
157	#14579160	C₂×C₄	1	1	yes	characteristic
158	#14579160	C₂×C₄	1	1	yes	characteristic
159	#14579160	C₂×C₄	1	1	yes	characteristic
160	#14579160	C₂×C₄	1	2	yes	—
161	#14579159	C₂×C₄	1	2	yes	—
162	#14579159	C₂×C₄	1	2	yes	—
163	#14579159	C₂×C₄	1	2	yes	—
164	#14579152	C₂×C₄	1	1	yes	characteristic
165	#14579152	C₂×C₄	1	1	yes	characteristic
166	#14579152	C₂×C₄	1	1	yes	characteristic
167	#14579152	C₂×C₄	1	1	yes	characteristic
168	#14579151	C₂×C₄	1	2	yes	—
169	#14579151	C₂×C₄	1	2	yes	—
170	#14579151	C₂×C₄	1	2	yes	—
171	#14579151	C₂×C₄	1	2	yes	—
172	#14579151	C₂×C₄	1	2	yes	—
173	#14579151	C₂×C₄	1	2	yes	—
174	#14579141	C₂×C₄	1	2	yes	—
175	#14579141	C₂×C₄	1	2	yes	—
176	#14579141	C₂×C₄	1	2	yes	—
177	#14579139	C₂×C₄	1	2	yes	—
178	#14579139	C₂×C₄	1	2	yes	—
179	#14579139	C₂×C₄	1	2	yes	—
180	#14579139	C₂×C₄	1	2	yes	—
181	#14579139	C₂×C₄	1	2	yes	—
182	#14579139	C₂×C₄	1	2	yes	—
183	#14579138	C₂×C₄	1	2	yes	—
184	#14579138	C₂×C₄	1	2	yes	—
185	#14579138	C₂×C₄	1	2	yes	—
186	#14579138	C₂×C₄	1	2	yes	—
187	#14579137	C₂×C₄	1	2	yes	—
188	#14579137	C₂×C₄	1	2	yes	—
189	#14579137	C₂×C₄	1	2	yes	—
190	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
191	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
192	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
193	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
194	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
195	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
196	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
197	C₄×Dic₁₅₈	C₂³	1	2	yes	—
198	C₄×Dic₁₅₈	C₂³	1	2	yes	—
199	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₅₈	C₂³	1	2	yes	—
201	C₄×Dic₁₅₈	C₂³	1	2	yes	—
202	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
205	#14579126	C₂×C₄	1	2	yes	—
206	#14579126	C₂×C₄	1	2	yes	—
207	#14579126	C₂×C₄	1	2	yes	—
208	#14579126	C₂×C₄	1	1	yes	characteristic
209	#14579126	C₂×C₄	1	1	yes	characteristic
210	#14579126	C₂×C₄	1	1	yes	characteristic
211	#14579126	C₂×C₄	1	1	yes	characteristic
212	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
213	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
214	#14579123	C₂×C₄	1	1	yes	characteristic
215	#14579123	C₂×C₄	1	1	yes	characteristic
216	#14579123	C₂×C₄	1	1	yes	characteristic
217	#14579123	C₂×C₄	1	1	yes	characteristic
218	C₄×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
219	C₄×C₂²⋊D₇₉	C₂×C₄	1	2	yes	—
220	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
221	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
222	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
223	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
224	#14579120	C₂³	1	1	yes	characteristic
225	#14579118	C₂³	1	2	yes	—
226	#14579118	C₂³	1	2	yes	—
227	#14579118	C₂³	1	2	yes	—
228	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
229	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
230	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
231	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
232	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
233	C₄⋊C₄×D₇₉	C₂×C₄	1	2	yes	—
234	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
235	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
236	C₄²×D₇₉	C₂³	1	2	yes	—
237	C₄²×D₇₉	C₂³	1	2	yes	—
238	C₄²×D₇₉	C₂³	1	2	yes	—
239	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
240	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
241	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
242	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
243	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
244	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
245	Dic₇₉⋊C₈	C₂³	1	2	yes	—
246	Dic₇₉⋊C₈	C₂³	1	2	yes	—
247	Dic₇₉⋊C₈	C₂³	1	2	yes	—
248	Dic₇₉⋊C₈	C₂³	1	2	yes	—
249	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
250	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
251	Dic₇₉⋊C₈	C₂³	1	2	yes	—
252	Dic₇₉⋊C₈	C₂³	1	2	yes	—
253	Dic₇₉⋊C₈	C₂³	1	2	yes	—
254	Dic₇₉⋊C₈	C₂³	1	2	yes	—
255	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
256	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
257	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
258	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
259	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
260	Dic₇₉⋊C₈	C₂³	1	1	yes	characteristic
261	#14579072	C₂³	1	1	yes	characteristic
262	#14579072	C₂³	1	2	yes	—
263	#14579072	C₂³	1	1	yes	characteristic
264	#14579072	C₂³	1	1	yes	characteristic
265	#14579072	C₂³	1	1	yes	characteristic
266	#14579072	C₂³	1	2	yes	—
267	#14579071	C₂³	1	1	yes	characteristic
268	#14579071	C₂³	1	2	yes	—
269	#14579071	C₂³	1	1	yes	characteristic
270	#14579071	C₂³	1	2	yes	—
271	#14579071	C₂³	1	2	yes	—
272	#14579071	C₂³	1	2	yes	—
273	#14579071	C₂³	1	1	yes	characteristic
274	#14579071	C₂³	1	1	yes	characteristic
275	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
276	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
277	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
278	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
279	C₈×Dic₇₉	C₂³	1	2	yes	—
280	C₈×Dic₇₉	C₂³	1	2	yes	—
281	C₈×Dic₇₉	C₂³	1	2	yes	—
282	C₈×Dic₇₉	C₂³	1	2	yes	—
283	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
284	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
290	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
291	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
292	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
293	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
294	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
295	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
296	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
297	#117×C₇₉	C₂³	1	1	yes	characteristic
298	#117×C₇₉	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
305	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
306	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
307	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
308	#97×C₇₉	C₂³	1	2	yes	—
309	#97×C₇₉	C₂³	1	2	yes	—
310	#97×C₇₉	C₂³	1	2	yes	—
311	C₄×C₈×C₇₉	C₂³	1	2	yes	—
312	C₄×C₈×C₇₉	C₂³	1	2	yes	—
313	C₄×C₈×C₇₉	C₂³	1	2	yes	—
314	#11929624	C₂×Q₈	1	4	yes	—
315	#11929624	#41	1	4	yes	—
316	C₂×Dic₁₅₈	—	4	2	no	—
317	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
318	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
319	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
320	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
321	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
322	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
323	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
324	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
325	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
326	Q₈×D₇₉	—	4	4	no	—
327	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
328	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
329	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
330	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
331	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
332	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
333	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
334	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
335	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
336	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
337	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
338	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
339	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
340	#11929608	—	2	2	no	—
341	#11929608	—	2	2	no	—
342	#11929607	—	2	4	no	—
343	#11929607	—	2	4	no	—
344	#11929607	—	2	4	no	—
345	#11929607	C₂×Q₈	1	8	yes	complemented
346	C₂×C₇₉⋊C₈	—	2	2	no	—
347	C₂×C₇₉⋊C₈	C₂×Q₈	1	4	yes	complemented
348	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
350	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
351	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
354	C₈×D₇₉	—	2	4	no	—
355	C₈×D₇₉	—	2	4	no	—
356	C₈×D₇₉	—	2	4	no	—
357	C₈×D₇₉	C₂×Q₈	1	8	yes	complemented
358	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
359	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
360	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
361	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
363	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
366	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
367	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
368	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
369	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
370	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
371	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
372	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
373	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
374	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
375	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
379	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
381	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
382	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
383	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
384	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
385	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
386	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
387	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
388	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
389	Dic₇₉⋊C₄	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₇₉	C₂²×C₄	1	2	yes	—
391	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
392	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
393	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
394	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
397	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
398	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
399	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
400	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
401	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
402	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
403	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
404	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
405	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
406	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
407	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
408	C₄×Dic₇₉	C₂⁴	1	2	yes	—
409	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
410	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
411	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
412	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
413	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
414	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
415	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
416	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
417	M₁₆×C₇₉	—	2	2	no	—
418	M₁₆×C₇₉	C₂×Q₈	1	4	yes	complemented
419	C₂×C₈×C₇₉	—	2	2	no	—
420	C₂×C₈×C₇₉	—	2	2	no	—
421	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
424	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
428	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
429	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
430	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
431	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
432	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
433	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
434	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
435	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
436	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
439	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
440	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
441	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
442	C₄²×C₇₉	C₂⁴	1	2	yes	—
443	C₄²×C₇₉	C₂⁴	1	2	yes	—
444	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
445	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
446	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
447	Q₈×C₇₉	—	4	2	no	—
448	Q₈×C₇₉	—	4	2	no	—
449	C₂×C₄×C₇₉	—	4	1	no	—
450	C₂×C₄×C₇₉	—	4	1	no	—
451	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
452	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
454	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
461	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
462	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
463	C₂²⋊D₇₉	C₄×Q₈	1	8	yes	—
464	C₂×Dic₇₉	—	2	2	no	—
465	C₂×Dic₇₉	—	4	1	no	—
466	C₂×Dic₇₉	—	4	1	no	—
467	C₂×Dic₇₉	—	4	1	no	—
468	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
469	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
470	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
471	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
472	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
473	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
474	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
475	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
476	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
477	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
478	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
479	D₃₁₆	C₄×Q₈	1	4	yes	—
480	C₄×D₇₉	—	2	4	no	—
481	C₄×D₇₉	—	4	2	no	—
482	C₄×D₇₉	—	4	2	no	—
483	C₄×D₇₉	—	4	2	no	—
484	C₄×D₇₉	—	4	2	no	—
485	C₄×D₇₉	—	4	2	no	—
486	C₄×D₇₉	C₂²×Q₈	1	4	yes	—
487	C₄×D₇₉	C₂×#41	1	4	yes	—
488	Dic₁₅₈	—	2	2	no	—
489	Dic₁₅₈	—	2	4	no	—
490	Dic₁₅₈	—	2	2	no	—
491	Dic₁₅₈	—	4	2	no	—
492	Dic₁₅₈	—	4	1	no	—
493	Dic₁₅₈	—	4	1	no	—
494	Dic₁₅₈	—	4	2	no	—
495	Dic₁₅₈	—	4	2	no	—
496	Dic₁₅₈	C₄×Q₈	1	4	yes	—
497	C₈×C₇₉	—	2	1	no	—
498	C₈×C₇₉	—	2	1	no	—
499	C₈×C₇₉	—	2	2	no	—
500	C₈×C₇₉	—	2	1	no	—
501	C₈×C₇₉	—	2	1	no	—
502	C₈×C₇₉	C₂²×Q₈	1	4	yes	—
503	C₇₉⋊C₈	—	2	1	no	—
504	C₇₉⋊C₈	—	2	2	no	—
505	C₇₉⋊C₈	—	2	2	no	—
506	C₇₉⋊C₈	—	2	1	no	—
507	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
508	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
509	C₂²×C₇₉	—	2	1	no	—
510	C₂²×C₇₉	—	2	1	no	—
511	C₂²×C₇₉	C₂×C₄×Q₈	1	2	yes	—
512	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
513	C₂×D₇₉	—	2	2	no	—
514	C₂×D₇₉	—	2	2	no	—
515	C₂×D₇₉	C₂×C₄×Q₈	1	4	yes	—
516	C₄×C₇₉	—	2	1	no	—
517	C₄×C₇₉	—	2	1	no	—
518	C₄×C₇₉	—	2	2	no	—
519	C₄×C₇₉	—	2	2	no	—
520	C₄×C₇₉	—	2	1	no	—
521	C₄×C₇₉	—	2	1	no	—
522	C₄×C₇₉	—	2	2	no	—
523	C₄×C₇₉	—	2	2	no	—
524	C₄×C₇₉	C₂×C₄×Q₈	1	2	yes	—
525	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
526	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
527	Dic₇₉	—	2	1	no	—
528	Dic₇₉	—	2	2	no	—
529	Dic₇₉	—	2	1	no	—
530	Dic₇₉	—	2	1	no	—
531	Dic₇₉	—	2	2	no	—
532	Dic₇₉	—	2	1	no	—
533	Dic₇₉	—	2	1	no	—
534	Dic₇₉	—	2	1	no	—
535	Dic₇₉	—	2	1	no	—
536	Dic₇₉	C₂×C₄×Q₈	1	4	yes	—
537	Dic₇₉	#568	1	2	yes	—
538	#60195	—	79	1	no	maximal, Sylow
539	C₂×C₇₉	—	2	2	no	—
540	C₂×C₇₉	C₂²×C₄×Q₈	1	1	yes	characteristic
541	C₂×C₇₉	C₂×#568	1	1	yes	characteristic
542	C₂×C₇₉	#3573	1	1	yes	characteristic
543	D₇₉	—	2	4	no	—
544	Q₈×#41	—	79	1	no	—
545	Q₈×M₁₆	—	79	2	no	—
546	Q₈×M₁₆	—	79	1	no	—
547	#2962	—	79	2	no	—
548	#2962	—	79	2	no	—
549	#2962	—	79	2	no	—
550	#2962	—	79	1	no	—
551	#2962	—	79	1	no	—
552	#2962	D₇₉	1	1	yes	characteristic, complemented
553	#2961	—	79	2	no	—
554	#2961	—	79	2	no	—
555	#2961	—	79	1	no	—
556	#2961	—	79	1	no	—
557	#2960	—	79	2	no	—
558	#2960	—	79	1	no	—
559	C₂×#446	—	79	2	no	—
560	C₂×#446	—	79	1	no	—
561	#2906	—	79	1	no	—
562	#2906	—	79	1	no	—
563	#2906	—	79	1	no	—
564	#2875	—	79	1	no	—
565	#2875	—	79	1	no	—
566	C₄×#131	—	79	1	no	—
567	C₇₉	#60195	1	1	yes	characteristic, complemented, Sylow
568	C₂×#131	—	79	1	no	—
569	C₂×#131	—	79	1	no	—
570	C₂×#131	—	79	1	no	—
571	C₂×#131	—	79	1	no	—
572	Q₈²	—	79	1	no	—
573	#557	—	79	1	no	—
574	#557	—	79	1	no	—
575	#557	—	79	1	no	—
576	#554	—	79	1	no	—
577	#554	—	79	1	no	—
578	#554	—	79	1	no	—
579	#554	—	79	2	no	—
580	#554	—	79	2	no	—
581	#554	—	79	2	no	—
582	D₄×Q₈	—	79	1	no	—
583	D₄×Q₈	—	79	2	no	—
584	#533	—	79	2	no	—
585	#533	—	79	2	no	—
586	#533	—	79	2	no	—
587	#533	—	79	1	no	—
588	#533	—	79	1	no	—
589	#533	C₂×D₇₉	1	1	yes	characteristic
590	C₄×#41	—	79	1	no	—
591	C₄×#41	—	79	1	no	—
592	C₄×#41	—	79	1	no	—
593	C₂×C₄×Q₈	—	79	2	no	—
594	C₂×C₄×Q₈	—	79	1	no	—
595	#446	—	79	2	no	—
596	#446	—	79	2	no	—
597	#446	—	79	2	no	—
598	#446	—	79	2	no	—
599	#446	—	79	2	no	—
600	#446	—	79	2	no	—
601	#446	—	79	1	no	—
602	#446	—	79	2	no	—
603	#446	—	79	1	no	—
604	#446	—	79	1	no	—
605	#446	—	79	1	no	—
606	#446	—	79	1	no	—
607	#446	—	79	1	no	—
608	#446	—	79	1	no	—
609	#446	—	79	1	no	—
610	#446	—	79	2	no	—
611	#446	—	79	2	no	—
612	#446	—	79	2	no	—
613	#446	—	79	2	no	—
614	#446	—	79	2	no	—
615	#446	—	79	2	no	—
616	#446	—	79	2	no	—
617	#446	—	79	2	no	—
618	#446	—	79	2	no	—
619	#446	—	79	2	no	—
620	#446	—	79	2	no	—
621	#446	—	79	2	no	—
622	#446	C₂×D₇₉	1	2	yes	—
623	#446	C₂×D₇₉	1	2	yes	—
624	#446	C₂×D₇₉	1	2	yes	—
625	C₈×Q₈	—	79	2	no	—
626	C₈×Q₈	—	79	2	no	—
627	C₈×Q₈	—	79	2	no	—
628	C₈×Q₈	—	79	2	no	—
629	C₈×Q₈	—	79	2	no	—
630	C₈×Q₈	C₂×D₇₉	1	2	yes	—
631	#424	—	79	1	no	—
632	#424	—	79	1	no	—
633	#424	—	79	1	no	—
634	#424	—	79	1	no	—
635	#424	—	79	2	no	—
636	#424	—	79	2	no	—
637	#424	—	79	2	no	—
638	#424	—	79	2	no	—
639	#424	—	79	2	no	—
640	#424	—	79	2	no	—
641	#424	C₂×D₇₉	1	1	yes	characteristic
642	#424	C₂×D₇₉	1	1	yes	characteristic
643	#423	—	79	1	no	—
644	#423	—	79	1	no	—
645	#423	—	79	1	no	—
646	#423	—	79	2	no	—
647	#423	—	79	2	no	—
648	#423	—	79	2	no	—
649	C₂×C₄⋊C₈	—	79	1	no	—
650	C₂×C₄⋊C₈	—	79	1	no	—
651	C₂×C₄⋊C₈	—	79	2	no	—
652	C₂×C₄⋊C₈	—	79	2	no	—
653	C₂×C₄⋊C₈	—	79	2	no	—
654	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
655	#405	—	79	1	no	—
656	#405	—	79	1	no	—
657	#405	—	79	1	no	—
658	#405	—	79	1	no	—
659	#405	—	79	2	no	—
660	#405	—	79	2	no	—
661	#405	—	79	2	no	—
662	#405	—	79	2	no	—
663	#405	—	79	2	no	—
664	#405	—	79	2	no	—
665	#405	C₂×D₇₉	1	1	yes	characteristic
666	#405	C₂×D₇₉	1	1	yes	characteristic
667	C₄×M₁₆	—	79	1	no	—
668	C₄×M₁₆	—	79	1	no	—
669	C₄×M₁₆	—	79	2	no	—
670	C₄×M₁₆	—	79	2	no	—
671	C₄×M₁₆	—	79	2	no	—
672	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
673	C₂×#97	—	79	1	no	—
674	C₂×#97	—	79	1	no	—
675	C₂×#97	—	79	2	no	—
676	C₂×#97	—	79	2	no	—
677	C₂×C₄×C₈	—	79	1	no	—
678	C₂×C₄×C₈	—	79	2	no	—
679	C₂×#41	—	79	1	no	—
680	C₂²×Q₈	—	79	2	no	—
681	C₂²×Q₈	—	79	1	no	—
682	#131	—	79	8	no	—
683	#131	—	158	4	no	—
684	#131	—	158	4	no	—
685	#131	—	158	4	no	—
686	C₂×M₁₆	—	79	1	no	—
687	C₂×M₁₆	—	79	1	no	—
688	C₂×M₁₆	—	79	2	no	—
689	C₂×M₁₆	—	79	2	no	—
690	C₂×M₁₆	—	79	2	no	—
691	C₂×M₁₆	—	79	2	no	—
692	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
693	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
694	C₂²×C₈	—	79	1	no	—
695	C₂²×C₈	—	79	2	no	—
696	C₂²×C₈	—	79	1	no	—
697	C₂²×C₈	—	79	2	no	—
698	C₂²×C₈	—	79	2	no	—
699	C₂²×C₈	—	79	2	no	—
700	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
701	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
702	C₄⋊Q₈	—	79	2	no	—
703	C₄⋊Q₈	—	79	2	no	—
704	C₄⋊Q₈	—	79	2	no	—
705	C₄⋊Q₈	—	79	2	no	—
706	C₄⋊Q₈	—	79	2	no	—
707	C₄⋊Q₈	—	79	1	no	—
708	C₄⋊Q₈	—	79	1	no	—
709	C₄⋊Q₈	—	79	1	no	—
710	C₄⋊Q₈	—	79	1	no	—
711	C₄⋊Q₈	—	79	2	no	—
712	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
713	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
714	#125	—	79	2	no	—
715	#125	—	79	2	no	—
716	#125	—	79	2	no	—
717	#125	—	79	2	no	—
718	#125	—	79	2	no	—
719	#125	—	79	2	no	—
720	#125	—	79	1	no	—
721	#125	—	79	1	no	—
722	#125	—	79	1	no	—
723	#125	—	79	1	no	—
724	#125	C₄×D₇₉	1	1	yes	characteristic
725	#125	C₄×D₇₉	1	1	yes	characteristic
726	C₂²⋊Q₈	—	79	2	no	—
727	C₂²⋊Q₈	—	79	2	no	—
728	C₂²⋊Q₈	—	79	2	no	—
729	C₂²⋊Q₈	—	79	2	no	—
730	C₂²⋊Q₈	—	79	2	no	—
731	C₂²⋊Q₈	—	79	2	no	—
732	C₂²⋊Q₈	—	79	2	no	—
733	C₂²⋊Q₈	—	79	2	no	—
734	C₂²⋊Q₈	—	79	2	no	—
735	C₂²⋊Q₈	—	79	2	no	—
736	C₂²⋊Q₈	—	79	2	no	—
737	C₂²⋊Q₈	—	79	2	no	—
738	C₂²⋊Q₈	—	79	2	no	—
739	C₂²⋊Q₈	—	79	2	no	—
740	C₂²⋊Q₈	—	79	2	no	—
741	C₂²⋊Q₈	—	79	2	no	—
742	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
743	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
744	C₄×Q₈	—	79	2	no	—
745	C₄×Q₈	—	79	2	no	—
746	C₄×Q₈	—	79	2	no	—
747	C₄×Q₈	—	79	2	no	—
748	C₄×Q₈	—	79	1	no	—
749	C₄×Q₈	—	79	1	no	—
750	C₄×Q₈	—	79	1	no	—
751	C₄×Q₈	—	79	1	no	—
752	C₄×Q₈	—	79	1	no	—
753	C₄×Q₈	—	79	1	no	—
754	C₄×Q₈	—	79	1	no	—
755	C₄×Q₈	—	79	1	no	—
756	C₄×Q₈	—	79	1	no	—
757	C₄×Q₈	—	79	1	no	—
758	C₄×Q₈	—	79	1	no	—
759	C₄×Q₈	—	79	2	no	—
760	C₄×Q₈	—	79	1	no	—
761	C₄×Q₈	—	79	1	no	—
762	C₄×Q₈	—	79	2	no	—
763	C₄×Q₈	—	79	1	no	—
764	C₄×Q₈	—	79	2	no	—
765	C₄×Q₈	—	79	2	no	—
766	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
767	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
768	C₄×D₄	—	79	2	no	—
769	C₄×D₄	—	79	2	no	—
770	C₄×D₄	—	79	1	no	—
771	C₄×D₄	—	79	1	no	—
772	C₄×D₄	—	79	1	no	—
773	C₄×D₄	—	79	1	no	—
774	C₄×D₄	—	79	2	no	—
775	C₄×D₄	—	79	2	no	—
776	C₄×D₄	—	79	2	no	—
777	C₄×D₄	—	79	2	no	—
778	C₄×D₄	—	79	1	no	—
779	C₄×D₄	—	79	1	no	—
780	#117	—	79	1	no	—
781	#117	—	79	2	no	—
782	#117	—	79	2	no	—
783	#117	—	79	2	no	—
784	#117	C₂²×D₇₉	1	1	yes	characteristic
785	#117	C₂²×D₇₉	1	1	yes	characteristic
786	C₂×C₄⋊C₄	—	79	1	no	—
787	C₂×C₄⋊C₄	—	79	1	no	—
788	C₂×C₄⋊C₄	—	79	1	no	—
789	C₂×C₄⋊C₄	—	79	2	no	—
790	C₂×C₄⋊C₄	—	79	2	no	—
791	C₂×C₄⋊C₄	—	79	2	no	—
792	C₂×C₄²	—	79	1	no	—
793	C₂×C₄²	—	79	1	no	—
794	C₂×C₄²	—	79	2	no	—
795	C₂×C₄²	—	79	2	no	—
796	C₂×C₄²	—	79	2	no	—
797	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
798	C₄⋊C₈	—	79	1	no	—
799	C₄⋊C₈	—	79	1	no	—
800	C₄⋊C₈	—	79	2	no	—
801	C₄⋊C₈	—	79	1	no	—
802	C₄⋊C₈	—	79	1	no	—
803	C₄⋊C₈	—	79	2	no	—
804	C₄⋊C₈	—	79	2	no	—
805	C₄⋊C₈	—	79	1	no	—
806	C₄⋊C₈	—	79	2	no	—
807	C₄⋊C₈	—	79	1	no	—
808	C₄⋊C₈	—	79	1	no	—
809	C₄⋊C₈	—	79	1	no	—
810	C₄⋊C₈	—	79	2	no	—
811	C₄⋊C₈	—	79	2	no	—
812	C₄⋊C₈	—	79	2	no	—
813	C₄⋊C₈	—	79	2	no	—
814	C₄⋊C₈	—	79	2	no	—
815	C₄⋊C₈	—	79	2	no	—
816	C₄⋊C₈	—	79	2	no	—
817	C₄⋊C₈	—	79	2	no	—
818	C₄⋊C₈	—	79	2	no	—
819	C₄⋊C₈	—	79	2	no	—
820	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
821	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
822	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
823	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
824	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
825	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
826	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
827	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
828	#97	—	79	1	no	—
829	#97	—	79	1	no	—
830	#97	—	79	2	no	—
831	#97	—	79	1	no	—
832	#97	—	79	2	no	—
833	#97	—	79	1	no	—
834	#97	—	79	2	no	—
835	#97	—	79	2	no	—
836	#97	—	79	1	no	—
837	#97	—	79	1	no	—
838	#97	—	79	2	no	—
839	#97	—	79	1	no	—
840	#97	—	79	1	no	—
841	#97	—	79	2	no	—
842	#97	C₂²×D₇₉	1	2	yes	—
843	#97	C₂²×D₇₉	1	2	yes	—
844	#97	C₂²×D₇₉	1	2	yes	—
845	C₄×C₈	—	79	1	no	—
846	C₄×C₈	—	79	1	no	—
847	C₄×C₈	—	79	2	no	—
848	C₄×C₈	—	79	1	no	—
849	C₄×C₈	—	79	1	no	—
850	C₄×C₈	—	79	2	no	—
851	C₄×C₈	—	79	2	no	—
852	C₄×C₈	—	79	2	no	—
853	C₄×C₈	—	79	2	no	—
854	C₄×C₈	—	79	2	no	—
855	C₄×C₈	C₂²×D₇₉	1	2	yes	—
856	C₄×C₈	C₂²×D₇₉	1	2	yes	—
857	C₄×C₈	C₂²×D₇₉	1	2	yes	—
858	#41	—	79	4	no	—
859	#41	—	79	4	no	—
860	C₂×Q₈	—	316	2	no	—
861	C₂×Q₈	—	316	4	no	—
862	C₂×Q₈	—	79	2	no	—
863	C₂×Q₈	—	79	1	no	—
864	C₂×Q₈	—	79	1	no	—
865	C₂×Q₈	—	79	2	no	—
866	C₂×Q₈	—	79	2	no	—
867	C₂×Q₈	—	79	1	no	—
868	C₂×Q₈	—	79	1	no	—
869	C₂×Q₈	—	79	2	no	—
870	C₂×Q₈	—	79	1	no	—
871	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
872	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
873	C₂×D₄	—	79	2	no	—
874	C₂×D₄	—	79	1	no	—
875	C₂²×C₄	—	79	1	no	—
876	C₂²×C₄	—	79	1	no	—
877	C₂²×C₄	—	79	1	no	—
878	C₂²×C₄	—	79	2	no	—
879	C₂²×C₄	—	79	2	no	—
880	C₂²×C₄	—	79	2	no	—
881	C₂²×C₄	—	79	2	no	—
882	C₂²×C₄	—	79	2	no	—
883	C₂²×C₄	—	79	2	no	—
884	C₂²×C₄	—	79	1	no	—
885	C₂²×C₄	—	79	2	no	—
886	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
887	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
888	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
889	M₁₆	—	2	2	no	—
890	M₁₆	—	79	8	no	—
891	M₁₆	—	158	4	no	—
892	M₁₆	—	158	4	no	—
893	M₁₆	—	158	4	no	—
894	M₁₆	—	158	2	no	—
895	M₁₆	—	158	2	no	—
896	M₁₆	Q₈×D₇₉	1	4	yes	complemented
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	79	4	no	—
900	C₂×C₈	—	79	1	no	—
901	C₂×C₈	—	79	1	no	—
902	C₂×C₈	—	79	8	no	—
903	C₂×C₈	—	79	1	no	—
904	C₂×C₈	—	79	2	no	—
905	C₂×C₈	—	79	2	no	—
906	C₂×C₈	—	79	1	no	—
907	C₂×C₈	—	158	4	no	—
908	C₂×C₈	—	158	4	no	—
909	C₂×C₈	—	158	4	no	—
910	C₂×C₈	—	158	2	no	—
911	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
912	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₇₉	1	2	yes	—
914	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
916	C₂×C₈	C₂³×D₇₉	1	2	yes	—
917	C₄⋊C₄	—	79	1	no	—
918	C₄⋊C₄	—	79	1	no	—
919	C₄⋊C₄	—	79	2	no	—
920	C₄⋊C₄	—	79	2	no	—
921	C₄⋊C₄	—	79	1	no	—
922	C₄⋊C₄	—	79	1	no	—
923	C₄⋊C₄	—	79	1	no	—
924	C₄⋊C₄	—	79	1	no	—
925	C₄⋊C₄	—	79	2	no	—
926	C₄⋊C₄	—	79	1	no	—
927	C₄⋊C₄	—	79	2	no	—
928	C₄⋊C₄	—	79	1	no	—
929	C₄⋊C₄	—	79	2	no	—
930	C₄⋊C₄	—	79	2	no	—
931	C₄⋊C₄	—	79	2	no	—
932	C₄⋊C₄	—	79	2	no	—
933	C₄⋊C₄	—	79	2	no	—
934	C₄⋊C₄	—	79	2	no	—
935	C₄⋊C₄	—	79	2	no	—
936	C₄⋊C₄	—	79	2	no	—
937	C₄⋊C₄	—	79	2	no	—
938	C₄⋊C₄	—	79	2	no	—
939	C₄⋊C₄	—	79	1	no	—
940	C₄⋊C₄	—	79	2	no	—
941	C₄⋊C₄	—	79	2	no	—
942	C₄⋊C₄	—	79	1	no	—
943	C₄⋊C₄	—	79	1	no	—
944	C₄⋊C₄	—	79	1	no	—
945	C₄⋊C₄	—	79	1	no	—
946	C₄⋊C₄	—	79	1	no	—
947	C₄⋊C₄	—	79	2	no	—
948	C₄⋊C₄	—	79	2	no	—
949	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
950	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
951	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
952	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
954	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
956	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
957	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
958	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
959	C₂²⋊C₄	—	79	2	no	—
960	C₂²⋊C₄	—	79	2	no	—
961	C₂²⋊C₄	—	79	2	no	—
962	C₂²⋊C₄	—	79	2	no	—
963	C₂²⋊C₄	—	79	2	no	—
964	C₂²⋊C₄	—	79	2	no	—
965	C₂²⋊C₄	—	79	2	no	—
966	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
967	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
968	C₄²	—	79	1	no	—
969	C₄²	—	79	2	no	—
970	C₄²	—	79	1	no	—
971	C₄²	—	79	1	no	—
972	C₄²	—	79	1	no	—
973	C₄²	—	79	2	no	—
974	C₄²	—	79	2	no	—
975	C₄²	—	79	2	no	—
976	C₄²	—	79	1	no	—
977	C₄²	—	79	1	no	—
978	C₄²	—	79	2	no	—
979	C₄²	—	79	2	no	—
980	C₄²	—	79	2	no	—
981	C₄²	—	79	1	no	—
982	C₄²	—	79	1	no	—
983	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
984	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
985	C₄²	C₂³×D₇₉	1	2	yes	—
986	C₄²	C₂³×D₇₉	1	2	yes	—
987	C₄²	C₂³×D₇₉	1	1	yes	characteristic
988	C₄²	C₂³×D₇₉	1	1	yes	characteristic
989	C₂³	—	79	2	no	—
990	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
991	Q₈	—	4	2	no	—
992	Q₈	—	4	2	no	—
993	Q₈	—	316	1	no	—
994	Q₈	—	316	1	no	—
995	Q₈	—	316	2	no	—
996	Q₈	—	316	2	no	—
997	Q₈	—	316	2	no	—
998	Q₈	—	79	4	no	—
999	Q₈	—	158	2	no	—
1000	Q₈	—	158	2	no	—
1001	Q₈	—	158	4	no	—
1002	D₄	—	79	8	no	—
1003	D₄	—	79	4	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	316	2	no	—
1007	C₂×C₄	—	316	2	no	—
1008	C₂×C₄	—	316	2	no	—
1009	C₂×C₄	—	316	2	no	—
1010	C₂×C₄	—	316	2	no	—
1011	C₂×C₄	—	316	1	no	—
1012	C₂×C₄	—	316	1	no	—
1013	C₂×C₄	—	316	1	no	—
1014	C₂×C₄	—	79	2	no	—
1015	C₂×C₄	—	79	1	no	—
1016	C₂×C₄	—	79	4	no	—
1017	C₂×C₄	—	79	4	no	—
1018	C₂×C₄	—	79	1	no	—
1019	C₂×C₄	—	79	1	no	—
1020	C₂×C₄	—	79	1	no	—
1021	C₂×C₄	—	79	2	no	—
1022	C₂×C₄	—	79	1	no	—
1023	C₂×C₄	—	79	1	no	—
1024	C₂×C₄	—	79	2	no	—
1025	C₂×C₄	—	79	1	no	—
1026	C₂×C₄	—	79	1	no	—
1027	C₂×C₄	—	158	4	no	—
1028	C₂×C₄	—	158	2	no	—
1029	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1030	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1031	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1032	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1033	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1034	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1035	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1036	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1037	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1038	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
1039	C₂×C₄	#41×D₇₉	1	2	yes	—
1040	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	79	2	no	—
1047	C₈	—	79	2	no	—
1048	C₈	—	158	1	no	—
1049	C₈	—	158	2	no	—
1050	C₈	—	158	2	no	—
1051	C₈	—	158	1	no	—
1052	C₈	C₂×Q₈×D₇₉	1	4	yes	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	79	4	no	—
1056	C₂²	—	158	2	no	—
1057	C₂²	—	158	2	no	—
1058	C₂²	C₄×Q₈×D₇₉	1	2	yes	—
1059	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	79	2	no	—
1069	C₄	—	79	4	no	—
1070	C₄	—	158	1	no	—
1071	C₄	—	158	2	no	—
1072	C₄	—	158	1	no	—
1073	C₄	—	158	1	no	—
1074	C₄	—	158	1	no	—
1075	C₄	—	158	1	no	—
1076	C₄	—	158	2	no	—
1077	C₄	—	158	1	no	—
1078	C₄	—	158	1	no	—
1079	C₄	C₄×Q₈×D₇₉	1	2	yes	—
1080	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
1081	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1082	C₂	—	2	2	no	—
1083	C₂	—	158	4	no	—
1084	C₂	C₂×C₄×Q₈×D₇₉	1	1	yes	characteristic
1085	C₂	#568×D₇₉	1	1	yes	characteristic
1086	C₂	#23778111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Fitting	C₇₉×#2962	C₂
prime radical	C₂×#11929624	C₂³
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2962	D₇₉
hypocenter	C₇₉	#60195
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. M₁₆×Dic₁₅₈	C₂	semidirect
3. #23772352	C₂	semidirect
4. #23772345	C₂	semidirect
5. #23772345	C₂	semidirect
6. #23772344	C₂	semidirect
7. #23772344	C₂	semidirect
8. #23772342	C₂	semidirect
9. #23772341	C₂	semidirect
10. #23772339	C₂	semidirect
11. #23772336	C₂	semidirect
12. #23772336	C₂	semidirect
13. #23772333	C₂	semidirect
14. #23772329	C₂	semidirect
15. C₂×#19098692	C₂	semidirect
16. #446×D₇₉	C₂	semidirect
23. C₇₉×#2962	C₂	semidirect
139. #14579169	Q₈	semidirect
345. #11929607	C₂×Q₈	semidirect
347. C₂×C₇₉⋊C₈	C₂×Q₈	semidirect
357. C₈×D₇₉	C₂×Q₈	semidirect
418. M₁₆×C₇₉	C₂×Q₈	semidirect
552. #2962	D₇₉	semidirect
567. C₇₉	#60195	semidirect
896. M₁₆	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776978	2
M₁₆×Dic₁₅₈	2
#23772352	2
#23772345	2
#23772344	2
#23772342	2
#23772341	2
#23772339	2
#23772336	2
#23772333	2
#23772329	2
C₂×#19098692	2
#446×D₇₉	2
#23771967	2
#23771965	2
#23771829	2
#23771827	2
#23771822	2
C₇₉×#2962	2
#60195	79