Subgroups — #35152875

Order 20224.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776792	C₂	1	1	yes	maximal, characteristic
2	#23772406	C₂	1	2	yes	maximal, complemented
3	#23772403	C₂	1	2	yes	maximal, complemented
4	#23772393	C₂	1	2	yes	maximal, complemented
5	#23772393	C₂	1	2	yes	maximal, complemented
6	#23772384	C₂	1	2	yes	maximal, complemented
7	#23772384	C₂	1	2	yes	maximal, complemented
8	#23772377	C₂	1	2	yes	maximal, complemented
9	#23772374	C₂	1	2	yes	maximal, complemented
10	#23772349	C₂	1	1	yes	maximal, characteristic, complemented
11	#23772146	C₂	1	1	yes	maximal, characteristic, complemented
12	#23772143	C₂	1	1	yes	maximal, characteristic, complemented
13	#23772128	C₂	1	1	yes	maximal, characteristic, complemented
14	#23772128	C₂	1	1	yes	maximal, characteristic, complemented
15	#23772124	C₂	1	1	yes	maximal, characteristic, complemented
16	#23772124	C₂	1	1	yes	maximal, characteristic, complemented
17	#23772050	C₂	1	1	yes	maximal, characteristic, complemented
18	#23772043	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#19098623	C₂	1	1	yes	maximal, characteristic, complemented
20	#23771827	C₂	1	1	yes	maximal, characteristic, complemented
21	#23771822	C₂	1	1	yes	maximal, characteristic, complemented
22	#23771817	C₂	1	1	yes	maximal, characteristic, complemented
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	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
29	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
30	#19099187	C₄	1	1	yes	characteristic
31	#19099187	C₄	1	1	yes	characteristic
32	#19099187	C₄	1	1	yes	characteristic
33	#19099187	C₄	1	1	yes	characteristic
34	#19099176	C₄	1	1	yes	characteristic
35	#19099176	C₄	1	1	yes	characteristic
36	#19099169	C₄	1	1	yes	characteristic
37	#19099169	C₄	1	1	yes	characteristic
38	#19099162	C₄	1	2	yes	—
39	#19099162	C₄	1	2	yes	—
40	#19099153	C₄	1	2	yes	—
41	#19099153	C₄	1	2	yes	—
42	#19099113	C₂²	1	1	yes	characteristic
43	#19099100	C₂²	1	2	yes	—
44	#19099100	C₂²	1	2	yes	—
45	#19099100	C₂²	1	2	yes	—
46	#19099100	C₂²	1	2	yes	—
47	#19099075	C₂²	1	1	yes	characteristic
48	#19099075	C₂²	1	1	yes	characteristic
49	#19099031	C₂²	1	1	yes	characteristic
50	#19099031	C₂²	1	1	yes	characteristic
51	C₂×#14579118	C₂²	1	1	yes	characteristic
52	#19098694	C₂²	1	2	yes	complemented
53	#19098694	C₂²	1	2	yes	complemented
54	#19098694	C₂²	1	2	yes	complemented
55	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
56	#19098642	C₂²	1	2	yes	—
57	#19098642	C₂²	1	2	yes	—
58	#19098642	C₂²	1	2	yes	complemented
59	#19098640	C₂²	1	2	yes	—
60	#19098640	C₂²	1	2	yes	—
61	#19098640	C₂²	1	2	yes	complemented
62	#19098636	C₂²	1	2	yes	—
63	#19098636	C₂²	1	2	yes	—
64	#19098636	C₂²	1	2	yes	—
65	#19098636	C₂²	1	2	yes	—
66	#19098636	C₂²	1	2	yes	complemented
67	#19098636	C₂²	1	2	yes	complemented
68	#19098633	C₂²	1	2	yes	—
69	#19098633	C₂²	1	2	yes	—
70	#19098633	C₂²	1	2	yes	—
71	#19098633	C₂²	1	2	yes	—
72	#19098633	C₂²	1	2	yes	complemented
73	#19098633	C₂²	1	2	yes	complemented
74	C₈×D₃₁₆	C₂²	1	2	yes	—
75	C₈×D₃₁₆	C₂²	1	2	yes	—
76	C₈×D₃₁₆	C₂²	1	2	yes	complemented
77	#19098628	C₂²	1	2	yes	—
78	#19098628	C₂²	1	2	yes	—
79	#19098628	C₂²	1	2	yes	complemented
80	#19098623	C₂²	1	1	yes	characteristic
81	#19098623	C₂²	1	1	yes	characteristic
82	#19098623	C₂²	1	1	yes	characteristic
83	#19098623	C₂²	1	1	yes	characteristic
84	#19098623	C₂²	1	1	yes	characteristic
85	#19098623	C₂²	1	1	yes	characteristic
86	#19098623	C₂²	1	1	yes	characteristic
87	#19098623	C₂²	1	1	yes	characteristic
88	#19098623	C₂²	1	2	yes	complemented
89	#19098623	C₂²	1	2	yes	complemented
90	#19098623	C₂²	1	2	yes	complemented
91	#19098623	C₂²	1	2	yes	complemented
92	#19098619	C₂²	1	2	yes	complemented
93	#19098619	C₂²	1	2	yes	complemented
94	#19098615	C₂²	1	2	yes	complemented
95	#19098615	C₂²	1	2	yes	complemented
96	#19098590	C₂²	1	1	yes	characteristic
97	#19098590	C₂²	1	1	yes	characteristic
98	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
99	#19098531	C₂²	1	1	yes	characteristic
100	#19098531	C₂²	1	1	yes	characteristic
101	#19098529	C₂²	1	1	yes	characteristic
102	#19098529	C₂²	1	1	yes	characteristic
103	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic
104	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic
105	#19098520	C₂²	1	2	yes	—
106	#19098520	C₂²	1	2	yes	—
107	#19098520	C₂²	1	2	yes	complemented
108	#19098520	C₂²	1	2	yes	complemented
109	#19098519	C₂²	1	1	yes	characteristic
110	#19098519	C₂²	1	1	yes	characteristic
111	#19098517	C₂²	1	2	yes	—
112	#19098517	C₂²	1	2	yes	—
113	#19098517	C₂²	1	2	yes	complemented
114	#19098517	C₂²	1	2	yes	complemented
115	C₄×#11929608	C₂²	1	1	yes	characteristic
116	#19098515	C₂²	1	2	yes	complemented
117	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
118	M₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
119	C₄×#11929607	C₂²	1	2	yes	complemented
120	C₂×#14579071	C₂²	1	1	yes	characteristic
121	#97×D₇₉	C₂²	1	2	yes	complemented
122	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₇₉	C₂²	1	2	yes	complemented
124	#533×C₇₉	C₂²	1	1	yes	characteristic
125	#446×C₇₉	C₂²	1	2	yes	complemented
126	#446×C₇₉	C₂²	1	2	yes	complemented
127	#446×C₇₉	C₂²	1	2	yes	complemented
128	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
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	C₂×#11929624	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
138	#14579169	—	2	4	no	—
139	#14579169	—	2	4	no	—
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	C₂×#11929607	C₂³	1	2	yes	—
149	C₂×#11929607	C₂³	1	2	yes	—
150	M₁₆×D₇₉	—	2	4	no	—
151	M₁₆×D₇₉	—	2	4	no	—
152	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₇₉	C₂³	1	2	yes	—
155	C₂×C₈×D₇₉	C₂³	1	2	yes	—
156	C₂×C₈×D₇₉	C₂³	1	2	yes	—
157	C₂×C₈×D₇₉	C₂³	1	2	yes	—
158	C₂×C₈×D₇₉	C₂³	1	2	yes	—
159	C₂×C₈×D₇₉	C₂³	1	2	yes	—
160	#14579161	C₂×C₄	1	1	yes	characteristic
161	#14579158	C₂×C₄	1	1	yes	characteristic
162	#14579156	C₂×C₄	1	2	yes	—
163	#14579156	C₂×C₄	1	2	yes	—
164	#14579156	C₂×C₄	1	2	yes	—
165	#14579156	C₂×C₄	1	2	yes	—
166	#14579156	C₂×C₄	1	2	yes	—
167	#14579156	C₂×C₄	1	2	yes	—
168	#14579156	C₂×C₄	1	2	yes	—
169	#14579156	C₂×C₄	1	2	yes	—
170	#14579152	C₂×C₄	1	2	yes	—
171	#14579152	C₂×C₄	1	2	yes	—
172	#14579152	C₂×C₄	1	2	yes	—
173	#14579152	C₂×C₄	1	2	yes	—
174	#14579150	C₂×C₄	1	2	yes	—
175	#14579150	C₂×C₄	1	2	yes	—
176	#14579150	C₂×C₄	1	2	yes	—
177	#14579150	C₂×C₄	1	2	yes	—
178	#14579149	C₂×C₄	1	1	yes	characteristic
179	#14579149	C₂×C₄	1	1	yes	characteristic
180	#14579146	C₂×C₄	1	2	yes	—
181	#14579146	C₂×C₄	1	2	yes	—
182	#14579146	C₂×C₄	1	2	yes	—
183	#14579146	C₂×C₄	1	2	yes	—
184	#14579146	C₂×C₄	1	2	yes	—
185	#14579146	C₂×C₄	1	2	yes	—
186	#14579146	C₂×C₄	1	2	yes	—
187	#14579146	C₂×C₄	1	2	yes	—
188	#14579145	C₂×C₄	1	2	yes	—
189	#14579145	C₂×C₄	1	2	yes	—
190	#14579141	C₂×C₄	1	1	yes	characteristic
191	#14579141	C₂×C₄	1	1	yes	characteristic
192	#14579141	C₂×C₄	1	1	yes	characteristic
193	#14579141	C₂×C₄	1	1	yes	characteristic
194	#14579137	C₂×C₄	1	2	yes	—
195	#14579137	C₂×C₄	1	2	yes	—
196	#14579137	C₂×C₄	1	2	yes	—
197	#14579137	C₂×C₄	1	2	yes	—
198	#14579136	C₂×C₄	1	2	yes	—
199	#14579136	C₂×C₄	1	2	yes	—
200	#14579136	C₂×C₄	1	2	yes	—
201	#14579136	C₂×C₄	1	2	yes	—
202	#14579136	C₂×C₄	1	1	yes	characteristic
203	#14579136	C₂×C₄	1	1	yes	characteristic
204	#14579136	C₂×C₄	1	1	yes	characteristic
205	#14579136	C₂×C₄	1	1	yes	characteristic
206	#14579135	C₂×C₄	1	2	yes	—
207	#14579135	C₂×C₄	1	2	yes	—
208	#14579131	C₂×C₄	1	2	yes	—
209	#14579131	C₂×C₄	1	2	yes	—
210	#14579126	C₂×C₄	1	1	yes	characteristic
211	#14579126	C₂×C₄	1	1	yes	characteristic
212	#14579126	C₂×C₄	1	1	yes	characteristic
213	#14579126	C₂×C₄	1	1	yes	characteristic
214	C₄×D₃₁₆	C₂³	1	2	yes	—
215	C₄×D₃₁₆	C₂³	1	2	yes	—
216	C₄×D₃₁₆	C₂³	1	2	yes	—
217	C₄×D₃₁₆	C₂³	1	2	yes	—
218	C₄×D₃₁₆	C₂³	1	2	yes	—
219	C₄×D₃₁₆	C₂³	1	2	yes	—
220	#14579123	C₂×C₄	1	1	yes	characteristic
221	#14579123	C₂×C₄	1	1	yes	characteristic
222	#14579123	C₂×C₄	1	1	yes	characteristic
223	#14579123	C₂×C₄	1	1	yes	characteristic
224	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
225	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
226	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
227	(C₂²⋊D₇₉)⋊C₄	C₂×C₄	1	2	yes	—
228	#14579118	C₂×C₄	1	1	yes	characteristic
229	#14579118	C₂×C₄	1	1	yes	characteristic
230	#14579118	C₂×C₄	1	1	yes	characteristic
231	#14579118	C₂×C₄	1	1	yes	characteristic
232	#14579118	C₂³	1	1	yes	characteristic
233	#14579118	C₂³	1	1	yes	characteristic
234	#14579118	C₂³	1	1	yes	characteristic
235	#14579118	C₂³	1	1	yes	characteristic
236	#14579118	C₂³	1	2	yes	—
237	#14579118	C₂³	1	2	yes	—
238	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
239	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×(C₂×D₇₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×(C₂×D₇₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
242	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
243	C₄²×D₇₉	C₂³	1	2	yes	—
244	C₄²×D₇₉	C₂³	1	2	yes	—
245	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
246	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
247	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
248	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
249	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
250	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
251	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
253	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
254	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
255	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
256	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
257	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
258	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
259	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
265	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
267	(C₂×D₇₉)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₇₉)⋊C₈	C₂³	1	1	yes	characteristic
269	#14579072	C₂³	1	2	yes	—
270	#14579072	C₂³	1	2	yes	—
271	#14579072	C₂³	1	2	yes	—
272	#14579071	C₂³	1	1	yes	characteristic
273	#14579071	C₂³	1	2	yes	—
274	#14579071	C₂³	1	1	yes	characteristic
275	#14579071	C₂³	1	1	yes	characteristic
276	#14579071	C₂³	1	1	yes	characteristic
277	#14579071	C₂³	1	2	yes	—
278	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
279	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
280	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
281	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
282	C₈×Dic₇₉	C₂³	1	2	yes	—
283	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
284	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
285	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
286	C₈×Dic₇₉	C₂³	1	2	yes	—
287	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
291	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
292	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
293	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
294	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
295	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
296	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
297	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
298	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
299	#117×C₇₉	C₂³	1	1	yes	characteristic
300	#117×C₇₉	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
303	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
304	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
309	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
310	#97×C₇₉	C₂³	1	2	yes	—
311	#97×C₇₉	C₂³	1	2	yes	—
312	#97×C₇₉	C₂³	1	2	yes	—
313	C₄×C₈×C₇₉	C₂³	1	2	yes	—
314	C₄×C₈×C₇₉	C₂³	1	2	yes	—
315	C₄×C₈×C₇₉	C₂³	1	2	yes	—
316	C₂³×D₇₉	C₂²×C₄	1	1	yes	characteristic
317	#11929624	—	2	2	no	—
318	#11929624	—	2	2	no	—
319	#11929624	—	2	2	no	—
320	#11929624	—	2	2	no	—
321	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
322	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
326	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
327	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
328	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
329	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
330	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
331	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₇₉	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
334	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
335	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₄×D₇₉	—	2	2	no	—
337	C₂×C₄×D₇₉	—	2	2	no	—
338	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
341	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
342	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
343	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
344	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
345	C₂×C₄×D₇₉	C₂⁴	1	2	yes	—
346	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
347	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
348	#11929608	—	2	2	no	—
349	#11929608	#41	1	4	yes	—
350	#11929607	—	2	4	no	—
351	#11929607	—	2	4	no	—
352	#11929607	—	2	4	no	—
353	#11929607	—	2	4	no	—
354	#11929607	—	2	4	no	—
355	#11929607	—	2	4	no	—
356	C₂×C₇₉⋊C₈	—	2	2	no	—
357	C₂×C₇₉⋊C₈	—	2	2	no	—
358	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
361	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
364	C₈×D₇₉	—	2	4	no	—
365	C₈×D₇₉	—	2	4	no	—
366	C₈×D₇₉	—	2	4	no	—
367	C₈×D₇₉	—	2	4	no	—
368	C₈×D₇₉	—	2	4	no	—
369	C₈×D₇₉	—	2	4	no	—
370	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
371	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
372	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
373	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
374	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
375	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
381	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	Dic₇₉⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
391	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
393	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
394	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
395	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
397	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
398	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
399	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
400	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
401	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
402	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
403	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
404	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
405	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
406	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
407	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
408	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
409	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
410	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
411	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	2	yes	—
412	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
413	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
414	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
415	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
416	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
420	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
421	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
422	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
423	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
424	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
425	M₁₆×C₇₉	—	2	2	no	—
426	M₁₆×C₇₉	#41	1	4	yes	—
427	C₂×C₈×C₇₉	—	2	2	no	—
428	C₂×C₈×C₇₉	—	2	2	no	—
429	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
432	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
436	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
437	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
438	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
439	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
440	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
441	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
442	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
443	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
444	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
446	C₂²⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
447	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₇₉	C₂⁴	1	2	yes	—
451	C₄²×C₇₉	C₂⁴	1	2	yes	—
452	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
453	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
454	C₂²×D₇₉	—	2	2	no	—
455	C₂²×D₇₉	—	4	1	no	—
456	C₂²×D₇₉	—	4	1	no	—
457	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
458	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
459	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
460	C₂²×D₇₉	C₂³×C₄	1	2	yes	—
461	Q₈×C₇₉	—	4	2	no	—
462	Q₈×C₇₉	—	4	2	no	—
463	C₂×C₄×C₇₉	—	4	1	no	—
464	C₂×C₄×C₇₉	—	4	1	no	—
465	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
470	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
471	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
472	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
475	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
476	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
477	C₂²⋊D₇₉	—	2	4	no	—
478	C₂²⋊D₇₉	—	2	4	no	—
479	C₂×Dic₇₉	—	2	2	no	—
480	C₂×Dic₇₉	—	4	1	no	—
481	C₂×Dic₇₉	—	4	1	no	—
482	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
483	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
484	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
485	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
486	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
487	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
488	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
489	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
490	D₃₁₆	—	2	2	no	—
491	D₃₁₆	—	2	2	no	—
492	D₃₁₆	—	4	2	no	—
493	D₃₁₆	—	4	2	no	—
494	D₃₁₆	—	4	2	no	—
495	D₃₁₆	—	4	2	no	—
496	D₃₁₆	—	4	2	no	—
497	D₃₁₆	—	4	2	no	—
498	C₄×D₇₉	—	2	2	no	—
499	C₄×D₇₉	—	2	2	no	—
500	C₄×D₇₉	—	2	1	no	—
501	C₄×D₇₉	—	2	1	no	—
502	C₄×D₇₉	—	2	2	no	—
503	C₄×D₇₉	—	2	2	no	—
504	C₄×D₇₉	—	2	2	no	—
505	C₄×D₇₉	—	2	2	no	—
506	C₄×D₇₉	—	2	1	no	—
507	C₄×D₇₉	—	2	1	no	—
508	C₄×D₇₉	—	4	2	no	—
509	C₄×D₇₉	—	4	2	no	—
510	C₄×D₇₉	—	4	2	no	—
511	C₄×D₇₉	—	4	2	no	—
512	Dic₁₅₈	—	2	2	no	—
513	Dic₁₅₈	—	2	2	no	—
514	C₈×C₇₉	—	2	1	no	—
515	C₈×C₇₉	—	2	1	no	—
516	C₈×C₇₉	—	2	2	no	—
517	C₈×C₇₉	—	2	1	no	—
518	C₈×C₇₉	—	2	1	no	—
519	C₈×C₇₉	C₂×#41	1	4	yes	—
520	C₇₉⋊C₈	—	2	1	no	—
521	C₇₉⋊C₈	—	2	1	no	—
522	C₇₉⋊C₈	—	2	2	no	—
523	C₇₉⋊C₈	—	2	1	no	—
524	C₇₉⋊C₈	—	2	1	no	—
525	C₇₉⋊C₈	C₂×#41	1	4	yes	—
526	C₂²×C₇₉	—	2	1	no	—
527	C₂²×C₇₉	—	2	1	no	—
528	C₂²×C₇₉	C₄×#41	1	2	yes	—
529	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
530	C₂×D₇₉	—	2	2	no	—
531	C₂×D₇₉	—	2	2	no	—
532	C₂×D₇₉	—	2	1	no	—
533	C₂×D₇₉	—	2	1	no	—
534	C₂×D₇₉	—	2	1	no	—
535	C₂×D₇₉	—	2	1	no	—
536	C₂×D₇₉	—	2	1	no	—
537	C₂×D₇₉	—	2	1	no	—
538	C₂×D₇₉	—	2	2	no	—
539	C₂×D₇₉	—	2	2	no	—
540	C₂×D₇₉	—	2	2	no	—
541	C₂×D₇₉	—	2	2	no	—
542	C₂×D₇₉	—	8	2	no	—
543	C₄×C₇₉	—	2	1	no	—
544	C₄×C₇₉	—	2	1	no	—
545	C₄×C₇₉	—	2	1	no	—
546	C₄×C₇₉	—	2	1	no	—
547	C₄×C₇₉	—	2	2	no	—
548	C₄×C₇₉	—	2	2	no	—
549	C₄×C₇₉	—	2	2	no	—
550	C₄×C₇₉	—	2	2	no	—
551	C₄×C₇₉	C₄×#41	1	2	yes	—
552	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
553	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
554	Dic₇₉	—	2	2	no	—
555	Dic₇₉	—	2	2	no	—
556	Dic₇₉	—	2	1	no	—
557	Dic₇₉	—	2	1	no	—
558	Dic₇₉	—	2	1	no	—
559	Dic₇₉	—	2	1	no	—
560	Dic₇₉	—	2	1	no	—
561	Dic₇₉	—	2	1	no	—
562	#60212	—	79	1	no	maximal, Sylow
563	C₂×C₇₉	—	2	2	no	—
564	C₂×C₇₉	C₂×C₄×#41	1	1	yes	characteristic
565	C₂×C₇₉	#3573	1	1	yes	characteristic
566	C₂×C₇₉	#3573	1	1	yes	characteristic
567	D₇₉	—	4	2	no	—
568	D₇₉	—	4	2	no	—
569	D₇₉	—	4	1	no	—
570	D₇₉	—	4	1	no	—
571	#3455	—	79	1	no	—
572	#2969	—	79	2	no	—
573	#2969	—	79	2	no	—
574	#2968	—	79	2	no	—
575	#2968	—	79	2	no	—
576	#2967	—	79	2	no	—
577	#2967	—	79	2	no	—
578	#2966	—	79	2	no	—
579	#2966	—	79	2	no	—
580	#2962	—	79	1	no	—
581	#2962	D₇₉	1	1	yes	characteristic, complemented
582	#2935	—	79	1	no	—
583	#2935	—	79	1	no	—
584	#2933	—	79	1	no	—
585	#2933	—	79	1	no	—
586	#2933	—	79	1	no	—
587	#2933	—	79	1	no	—
588	#2923	—	79	1	no	—
589	#2922	—	79	1	no	—
590	C₂×#433	—	79	1	no	—
591	#2875	—	79	1	no	—
592	C₄×#131	—	79	1	no	—
593	#2873	—	79	1	no	—
594	C₇₉	#60212	1	1	yes	characteristic, complemented, Sylow
595	C₂×#131	—	79	1	no	—
596	C₂×#131	—	79	1	no	—
597	C₂×#131	—	79	1	no	—
598	C₂×#131	—	79	1	no	—
599	C₂²×M₁₆	—	79	1	no	—
600	C₂²×M₁₆	—	79	1	no	—
601	#542	—	79	1	no	—
602	#542	—	79	1	no	—
603	#542	—	79	1	no	—
604	#542	—	79	1	no	—
605	#541	—	79	1	no	—
606	#541	—	79	1	no	—
607	#540	—	79	1	no	—
608	#540	—	79	1	no	—
609	#539	—	79	2	no	—
610	#539	—	79	2	no	—
611	#538	—	79	2	no	—
612	#538	—	79	2	no	—
613	#533	C₂×D₇₉	1	1	yes	characteristic
614	#532	—	79	1	no	—
615	#529	—	79	2	no	—
616	#529	—	79	2	no	—
617	#529	—	79	2	no	—
618	#529	—	79	2	no	—
619	#525	—	79	1	no	—
620	#525	—	79	1	no	—
621	C₄×#41	—	79	1	no	—
622	C₄×#41	—	79	1	no	—
623	C₂×#117	—	79	1	no	—
624	#446	—	79	2	no	—
625	#446	—	79	2	no	—
626	#446	—	79	2	no	—
627	#446	C₂×D₇₉	1	2	yes	complemented
628	#446	C₂×D₇₉	1	2	yes	complemented
629	#446	C₂×D₇₉	1	2	yes	complemented
630	C₈×Q₈	—	79	2	no	—
631	C₈×Q₈	C₂×D₇₉	1	2	yes	complemented
632	#436	—	79	2	no	—
633	#436	—	79	2	no	—
634	#436	—	79	2	no	—
635	#436	—	79	2	no	—
636	#436	—	79	2	no	—
637	#436	—	79	2	no	—
638	#435	—	79	2	no	—
639	#435	—	79	2	no	—
640	#435	—	79	2	no	—
641	#435	—	79	2	no	—
642	#435	—	79	2	no	—
643	#435	—	79	2	no	—
644	#435	—	79	2	no	—
645	#435	—	79	2	no	—
646	#435	—	79	2	no	—
647	#435	—	79	2	no	—
648	#435	—	79	2	no	—
649	#435	—	79	2	no	—
650	C₈×D₄	—	79	2	no	—
651	C₈×D₄	—	79	2	no	—
652	C₈×D₄	—	79	2	no	—
653	C₈×D₄	—	79	2	no	—
654	C₈×D₄	—	79	2	no	—
655	C₈×D₄	—	79	2	no	—
656	#433	—	79	1	no	—
657	#433	—	79	1	no	—
658	#433	—	79	1	no	—
659	#433	—	79	1	no	—
660	#433	—	79	1	no	—
661	#433	—	79	1	no	—
662	#433	—	79	1	no	—
663	#433	—	79	1	no	—
664	#433	—	79	2	no	—
665	#433	—	79	2	no	—
666	#433	—	79	2	no	—
667	#433	—	79	2	no	—
668	#432	—	79	2	no	—
669	#432	—	79	2	no	—
670	#431	—	79	2	no	—
671	#431	—	79	2	no	—
672	#424	—	79	1	no	—
673	#424	—	79	1	no	—
674	#424	C₂×D₇₉	1	1	yes	characteristic
675	#424	C₂×D₇₉	1	1	yes	characteristic
676	C₂×C₄⋊C₈	—	79	1	no	—
677	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
678	#408	—	79	1	no	—
679	#408	—	79	1	no	—
680	#408	—	79	1	no	—
681	#408	—	79	1	no	—
682	C₂×C₂²⋊C₈	—	79	1	no	—
683	C₂×C₂²⋊C₈	—	79	1	no	—
684	#405	—	79	1	no	—
685	#405	—	79	1	no	—
686	#405	—	79	2	no	—
687	#405	—	79	2	no	—
688	#405	—	79	2	no	—
689	#405	—	79	2	no	—
690	#405	—	79	2	no	—
691	#405	—	79	2	no	—
692	#405	—	79	2	no	—
693	#405	—	79	2	no	—
694	#405	C₂×D₇₉	1	1	yes	characteristic
695	#405	C₂×D₇₉	1	1	yes	characteristic
696	C₄×M₁₆	—	79	1	no	—
697	C₄×M₁₆	—	79	1	no	—
698	C₄×M₁₆	—	79	1	no	—
699	C₄×M₁₆	—	79	2	no	—
700	C₄×M₁₆	—	79	2	no	—
701	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
702	C₂×#97	—	79	1	no	—
703	C₂×#97	—	79	2	no	—
704	C₂×C₄×C₈	—	79	1	no	—
705	C₂×C₄×C₈	—	79	2	no	—
706	C₂×#41	—	79	1	no	—
707	C₂×#41	—	79	1	no	—
708	C₂³×C₄	—	79	1	no	—
709	#131	—	158	4	no	—
710	#131	—	158	4	no	—
711	#131	—	158	4	no	—
712	#131	—	158	4	no	—
713	C₂×M₁₆	—	79	1	no	—
714	C₂×M₁₆	—	79	1	no	—
715	C₂×M₁₆	—	79	2	no	—
716	C₂×M₁₆	—	79	2	no	—
717	C₂×M₁₆	—	79	2	no	—
718	C₂×M₁₆	—	79	2	no	—
719	C₂×M₁₆	—	79	2	no	—
720	C₂×M₁₆	—	79	2	no	—
721	C₂×M₁₆	—	158	4	no	—
722	C₂×M₁₆	—	158	4	no	—
723	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
724	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
725	C₂²×C₈	—	79	1	no	—
726	C₂²×C₈	—	79	1	no	—
727	C₂²×C₈	—	79	2	no	—
728	C₂²×C₈	—	79	2	no	—
729	C₂²×C₈	—	79	2	no	—
730	C₂²×C₈	—	79	2	no	—
731	C₂²×C₈	—	79	2	no	—
732	C₂²×C₈	—	79	2	no	—
733	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
734	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
735	C₄⋊Q₈	—	79	1	no	—
736	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
737	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
738	#127	—	79	1	no	—
739	#126	—	79	2	no	—
740	#126	—	79	2	no	—
741	#126	—	79	2	no	—
742	#126	—	79	2	no	—
743	#126	—	79	2	no	—
744	#126	—	79	2	no	—
745	#126	—	79	2	no	—
746	#126	—	79	2	no	—
747	#125	—	79	2	no	—
748	#125	—	79	2	no	—
749	#125	—	79	2	no	—
750	#125	—	79	2	no	—
751	#125	C₄×D₇₉	1	1	yes	characteristic
752	#125	C₄×D₇₉	1	1	yes	characteristic
753	#124	—	79	2	no	—
754	#124	—	79	2	no	—
755	#124	—	79	2	no	—
756	#124	—	79	2	no	—
757	#124	—	79	1	no	—
758	#124	—	79	1	no	—
759	#123	—	79	2	no	—
760	#123	—	79	2	no	—
761	#123	—	79	2	no	—
762	#123	—	79	2	no	—
763	#123	—	79	2	no	—
764	#123	—	79	2	no	—
765	#123	—	79	2	no	—
766	#123	—	79	2	no	—
767	#123	—	79	2	no	—
768	#123	—	79	2	no	—
769	C₂²⋊Q₈	—	79	2	no	—
770	C₂²⋊Q₈	—	79	2	no	—
771	C₂²⋊Q₈	—	79	2	no	—
772	C₂²⋊Q₈	—	79	2	no	—
773	C₂²⋊Q₈	—	79	1	no	—
774	C₂²⋊Q₈	—	79	1	no	—
775	C₂²⋊Q₈	—	79	1	no	—
776	C₂²⋊Q₈	—	79	1	no	—
777	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
778	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
779	#121	—	79	2	no	—
780	#121	—	79	2	no	—
781	#121	—	79	1	no	—
782	#121	—	79	1	no	—
783	#121	—	79	1	no	—
784	#121	—	79	1	no	—
785	#121	—	79	2	no	—
786	#121	—	79	2	no	—
787	#121	—	79	2	no	—
788	#121	—	79	2	no	—
789	#120	—	79	2	no	—
790	#120	—	79	2	no	—
791	C₄×Q₈	—	79	1	no	—
792	C₄×Q₈	—	79	1	no	—
793	C₄×Q₈	—	79	1	no	—
794	C₄×Q₈	—	79	1	no	—
795	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
796	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
797	C₄×D₄	—	79	1	no	—
798	C₄×D₄	—	79	1	no	—
799	C₄×D₄	—	79	1	no	—
800	C₄×D₄	—	79	1	no	—
801	C₄×D₄	—	79	2	no	—
802	C₄×D₄	—	79	2	no	—
803	C₄×D₄	—	79	2	no	—
804	C₄×D₄	—	79	2	no	—
805	C₄×D₄	—	79	2	no	—
806	C₄×D₄	—	79	2	no	—
807	C₄×D₄	—	79	2	no	—
808	C₄×D₄	—	79	2	no	—
809	C₄×D₄	—	79	2	no	—
810	C₄×D₄	—	79	2	no	—
811	#117	—	79	1	no	—
812	#117	—	79	1	no	—
813	#117	—	79	1	no	—
814	#117	—	79	1	no	—
815	#117	—	79	1	no	—
816	#117	—	79	1	no	—
817	#117	—	79	1	no	—
818	#117	—	79	1	no	—
819	#117	—	79	2	no	—
820	#117	—	79	2	no	—
821	#117	C₂²×D₇₉	1	1	yes	characteristic
822	#117	C₂²×D₇₉	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	79	1	no	—
824	C₂×C₄⋊C₄	—	79	1	no	—
825	C₂×C₂²⋊C₄	—	79	1	no	—
826	C₂×C₂²⋊C₄	—	79	1	no	—
827	C₂×C₄²	—	79	1	no	—
828	C₂×C₄²	—	79	2	no	—
829	C₂×C₄²	—	79	2	no	—
830	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
831	C₄⋊C₈	—	79	1	no	—
832	C₄⋊C₈	—	79	1	no	—
833	C₄⋊C₈	—	79	1	no	—
834	C₄⋊C₈	—	79	1	no	—
835	C₄⋊C₈	—	79	2	no	—
836	C₄⋊C₈	—	79	2	no	—
837	C₄⋊C₈	—	79	2	no	—
838	C₄⋊C₈	—	79	2	no	—
839	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
840	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
841	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
842	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
844	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
845	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
846	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
847	C₂²⋊C₈	—	79	1	no	—
848	C₂²⋊C₈	—	79	1	no	—
849	C₂²⋊C₈	—	79	1	no	—
850	C₂²⋊C₈	—	79	1	no	—
851	C₂²⋊C₈	—	79	1	no	—
852	C₂²⋊C₈	—	79	1	no	—
853	C₂²⋊C₈	—	79	1	no	—
854	C₂²⋊C₈	—	79	1	no	—
855	C₂²⋊C₈	—	79	2	no	—
856	C₂²⋊C₈	—	79	2	no	—
857	C₂²⋊C₈	—	79	2	no	—
858	C₂²⋊C₈	—	79	2	no	—
859	C₂²⋊C₈	—	79	2	no	—
860	C₂²⋊C₈	—	79	2	no	—
861	C₂²⋊C₈	—	79	2	no	—
862	C₂²⋊C₈	—	79	2	no	—
863	#97	—	79	1	no	—
864	#97	—	79	2	no	—
865	#97	—	79	1	no	—
866	#97	—	79	1	no	—
867	#97	—	79	1	no	—
868	#97	—	79	2	no	—
869	#97	—	79	2	no	—
870	#97	—	79	2	no	—
871	#97	—	79	2	no	—
872	#97	C₂²×D₇₉	1	2	yes	—
873	#97	C₂²×D₇₉	1	2	yes	—
874	#97	C₂²×D₇₉	1	2	yes	—
875	C₄×C₈	—	79	1	no	—
876	C₄×C₈	—	79	2	no	—
877	C₄×C₈	—	79	1	no	—
878	C₄×C₈	—	79	1	no	—
879	C₄×C₈	—	79	1	no	—
880	C₄×C₈	—	79	2	no	—
881	C₄×C₈	—	79	2	no	—
882	C₄×C₈	—	79	2	no	—
883	C₄×C₈	—	79	2	no	—
884	C₄×C₈	C₂²×D₇₉	1	2	yes	—
885	C₄×C₈	C₂²×D₇₉	1	2	yes	—
886	C₄×C₈	C₂²×D₇₉	1	2	yes	—
887	C₂⁴	—	79	1	no	—
888	#41	—	158	2	no	—
889	#41	—	158	2	no	—
890	#41	—	158	2	no	—
891	#41	—	158	2	no	—
892	C₂×Q₈	—	79	1	no	—
893	C₂×Q₈	—	79	1	no	—
894	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
895	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
896	C₂×D₄	—	79	2	no	—
897	C₂×D₄	—	79	2	no	—
898	C₂×D₄	—	79	2	no	—
899	C₂×D₄	—	79	2	no	—
900	C₂×D₄	—	79	2	no	—
901	C₂×D₄	—	79	2	no	—
902	C₂×D₄	—	79	2	no	—
903	C₂×D₄	—	79	2	no	—
904	C₂×D₄	—	79	1	no	—
905	C₂×D₄	—	79	1	no	—
906	C₂²×C₄	—	79	1	no	—
907	C₂²×C₄	—	79	1	no	—
908	C₂²×C₄	—	79	2	no	—
909	C₂²×C₄	—	79	2	no	—
910	C₂²×C₄	—	79	2	no	—
911	C₂²×C₄	—	79	2	no	—
912	C₂²×C₄	—	79	1	no	—
913	C₂²×C₄	—	79	2	no	—
914	C₂²×C₄	—	79	2	no	—
915	C₂²×C₄	—	79	1	no	—
916	C₂²×C₄	—	79	1	no	—
917	C₂²×C₄	—	79	1	no	—
918	C₂²×C₄	—	79	1	no	—
919	C₂²×C₄	—	158	2	no	—
920	C₂²×C₄	—	158	2	no	—
921	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
922	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
923	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
924	M₁₆	—	2	2	no	—
925	M₁₆	—	79	4	no	—
926	M₁₆	—	158	4	no	—
927	M₁₆	—	158	4	no	—
928	M₁₆	—	158	4	no	—
929	M₁₆	—	158	2	no	—
930	M₁₆	—	158	4	no	—
931	M₁₆	—	158	4	no	—
932	M₁₆	—	158	4	no	—
933	M₁₆	#11929625	1	4	yes	—
934	C₂×C₈	—	2	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	79	2	no	—
937	C₂×C₈	—	79	1	no	—
938	C₂×C₈	—	79	1	no	—
939	C₂×C₈	—	79	2	no	—
940	C₂×C₈	—	79	1	no	—
941	C₂×C₈	—	79	1	no	—
942	C₂×C₈	—	158	4	no	—
943	C₂×C₈	—	158	4	no	—
944	C₂×C₈	—	158	4	no	—
945	C₂×C₈	—	158	2	no	—
946	C₂×C₈	—	158	2	no	—
947	C₂×C₈	—	158	4	no	—
948	C₂×C₈	—	158	4	no	—
949	C₂×C₈	—	158	4	no	—
950	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₇₉	1	2	yes	—
953	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
954	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
955	C₂×C₈	C₂³×D₇₉	1	2	yes	—
956	C₄⋊C₄	—	79	1	no	—
957	C₄⋊C₄	—	79	1	no	—
958	C₄⋊C₄	—	79	1	no	—
959	C₄⋊C₄	—	79	1	no	—
960	C₄⋊C₄	—	79	1	no	—
961	C₄⋊C₄	—	79	1	no	—
962	C₄⋊C₄	—	79	1	no	—
963	C₄⋊C₄	—	79	1	no	—
964	C₄⋊C₄	—	79	2	no	—
965	C₄⋊C₄	—	79	2	no	—
966	C₄⋊C₄	—	79	2	no	—
967	C₄⋊C₄	—	79	2	no	—
968	C₄⋊C₄	—	79	2	no	—
969	C₄⋊C₄	—	79	2	no	—
970	C₄⋊C₄	—	79	2	no	—
971	C₄⋊C₄	—	79	2	no	—
972	C₄⋊C₄	—	79	2	no	—
973	C₄⋊C₄	—	79	2	no	—
974	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
975	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
976	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
978	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
979	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
980	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
981	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
982	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
983	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
984	C₂²⋊C₄	—	79	1	no	—
985	C₂²⋊C₄	—	79	1	no	—
986	C₂²⋊C₄	—	79	1	no	—
987	C₂²⋊C₄	—	79	1	no	—
988	C₂²⋊C₄	—	79	1	no	—
989	C₂²⋊C₄	—	79	1	no	—
990	C₂²⋊C₄	—	79	1	no	—
991	C₂²⋊C₄	—	79	1	no	—
992	C₂²⋊C₄	—	79	2	no	—
993	C₂²⋊C₄	—	79	2	no	—
994	C₂²⋊C₄	—	79	2	no	—
995	C₂²⋊C₄	—	79	2	no	—
996	C₂²⋊C₄	—	79	2	no	—
997	C₂²⋊C₄	—	79	2	no	—
998	C₂²⋊C₄	—	79	2	no	—
999	C₂²⋊C₄	—	79	2	no	—
1000	C₂²⋊C₄	—	79	2	no	—
1001	C₂²⋊C₄	—	79	2	no	—
1002	C₂²⋊C₄	—	79	2	no	—
1003	C₂²⋊C₄	—	79	2	no	—
1004	C₂²⋊C₄	—	79	2	no	—
1005	C₂²⋊C₄	—	79	2	no	—
1006	C₂²⋊C₄	—	79	2	no	—
1007	C₂²⋊C₄	—	79	2	no	—
1008	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
1010	C₄²	—	79	1	no	—
1011	C₄²	—	79	1	no	—
1012	C₄²	—	79	1	no	—
1013	C₄²	—	79	1	no	—
1014	C₄²	—	79	2	no	—
1015	C₄²	—	79	2	no	—
1016	C₄²	—	79	2	no	—
1017	C₄²	—	79	2	no	—
1018	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
1019	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
1020	C₄²	C₂³×D₇₉	1	1	yes	characteristic
1021	C₄²	C₂³×D₇₉	1	2	yes	—
1022	C₄²	C₂³×D₇₉	1	2	yes	—
1023	C₄²	C₂³×D₇₉	1	1	yes	characteristic
1024	C₂³	—	316	1	no	—
1025	C₂³	—	316	1	no	—
1026	C₂³	—	79	1	no	—
1027	C₂³	—	79	1	no	—
1028	C₂³	—	79	2	no	—
1029	C₂³	—	79	2	no	—
1030	C₂³	—	158	2	no	—
1031	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
1032	Q₈	—	4	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	158	2	no	—
1035	Q₈	—	158	2	no	—
1036	D₄	—	316	2	no	—
1037	D₄	—	316	2	no	—
1038	D₄	—	316	2	no	—
1039	D₄	—	316	2	no	—
1040	D₄	—	316	2	no	—
1041	D₄	—	316	2	no	—
1042	D₄	—	158	4	no	—
1043	D₄	—	158	4	no	—
1044	D₄	—	158	2	no	—
1045	D₄	—	158	2	no	—
1046	C₂×C₄	—	4	1	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	316	2	no	—
1049	C₂×C₄	—	316	2	no	—
1050	C₂×C₄	—	316	2	no	—
1051	C₂×C₄	—	316	2	no	—
1052	C₂×C₄	—	316	1	no	—
1053	C₂×C₄	—	316	1	no	—
1054	C₂×C₄	—	79	1	no	—
1055	C₂×C₄	—	79	1	no	—
1056	C₂×C₄	—	79	1	no	—
1057	C₂×C₄	—	79	1	no	—
1058	C₂×C₄	—	79	2	no	—
1059	C₂×C₄	—	79	2	no	—
1060	C₂×C₄	—	79	1	no	—
1061	C₂×C₄	—	79	1	no	—
1062	C₂×C₄	—	158	2	no	—
1063	C₂×C₄	—	158	2	no	—
1064	C₂×C₄	—	158	2	no	—
1065	C₂×C₄	—	158	1	no	—
1066	C₂×C₄	—	158	2	no	—
1067	C₂×C₄	—	158	2	no	—
1068	C₂×C₄	—	158	1	no	—
1069	C₂×C₄	—	158	1	no	—
1070	C₂×C₄	—	158	2	no	—
1071	C₂×C₄	—	158	2	no	—
1072	C₂×C₄	—	158	1	no	—
1073	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1074	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1075	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1076	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
1077	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1079	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1080	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1081	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
1082	C₂×C₄	#41×D₇₉	1	2	yes	—
1083	C₂×C₄	C₂×#11929625	1	2	yes	—
1084	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	2	no	—
1090	C₈	—	79	4	no	—
1091	C₈	—	158	1	no	—
1092	C₈	—	158	1	no	—
1093	C₈	—	158	1	no	—
1094	C₈	—	158	1	no	—
1095	C₈	—	158	2	no	—
1096	C₈	C₂×#11929625	1	4	yes	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	632	2	no	—
1100	C₂²	—	158	2	no	—
1101	C₂²	—	158	2	no	—
1102	C₂²	—	158	1	no	—
1103	C₂²	—	158	1	no	—
1104	C₂²	—	158	2	no	—
1105	C₂²	—	158	2	no	—
1106	C₂²	—	158	1	no	—
1107	C₂²	—	158	1	no	—
1108	C₂²	—	158	1	no	—
1109	C₂²	—	158	1	no	—
1110	C₂²	—	158	2	no	—
1111	C₂²	—	158	2	no	—
1112	C₂²	C₄×#11929625	1	2	yes	—
1113	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	158	1	no	—
1123	C₄	—	158	1	no	—
1124	C₄	—	158	1	no	—
1125	C₄	—	158	1	no	—
1126	C₄	—	158	1	no	—
1127	C₄	—	158	1	no	—
1128	C₄	—	158	2	no	—
1129	C₄	—	158	2	no	—
1130	C₄	C₄×#11929625	1	2	yes	—
1131	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
1132	C₄	C₂²×#11929625	1	1	yes	characteristic
1133	C₂	—	2	2	no	—
1134	C₂	—	316	1	no	—
1135	C₂	—	316	1	no	—
1136	C₂	—	316	2	no	—
1137	C₂	—	316	2	no	—
1138	C₂	C₂×C₄×#11929625	1	1	yes	characteristic
1139	C₂	#23778111	1	1	yes	characteristic
1140	C₂	#23778113	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	#23776792	C₂
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2962	D₇₉
hypocenter	C₇₉	#60212
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. #23772406	C₂	semidirect
3. #23772403	C₂	semidirect
4. #23772393	C₂	semidirect
5. #23772393	C₂	semidirect
6. #23772384	C₂	semidirect
7. #23772384	C₂	semidirect
8. #23772377	C₂	semidirect
9. #23772374	C₂	semidirect
10. #23772349	C₂	semidirect
11. #23772146	C₂	semidirect
12. #23772143	C₂	semidirect
13. #23772128	C₂	semidirect
14. #23772128	C₂	semidirect
15. #23772124	C₂	semidirect
16. #23772124	C₂	semidirect
17. #23772050	C₂	semidirect
18. #23772043	C₂	semidirect
19. C₂×#19098623	C₂	semidirect
20. #23771827	C₂	semidirect
21. #23771822	C₂	semidirect
22. #23771817	C₂	semidirect
23. C₇₉×#2962	C₂	semidirect
52. #19098694	C₂²	semidirect
53. #19098694	C₂²	semidirect
54. #19098694	C₂²	semidirect
55. Q₈×C₇₉⋊C₈	C₂²	semidirect
58. #19098642	C₂²	semidirect
61. #19098640	C₂²	semidirect
66. #19098636	C₂²	semidirect
67. #19098636	C₂²	semidirect
72. #19098633	C₂²	semidirect
73. #19098633	C₂²	semidirect
76. C₈×D₃₁₆	C₂²	semidirect
79. #19098628	C₂²	semidirect
88. #19098623	C₂²	semidirect
89. #19098623	C₂²	semidirect
90. #19098623	C₂²	semidirect
91. #19098623	C₂²	semidirect
92. #19098619	C₂²	semidirect
93. #19098619	C₂²	semidirect
94. #19098615	C₂²	semidirect
95. #19098615	C₂²	semidirect
107. #19098520	C₂²	semidirect
108. #19098520	C₂²	semidirect
113. #19098517	C₂²	semidirect
114. #19098517	C₂²	semidirect
116. #19098515	C₂²	semidirect
119. C₄×#11929607	C₂²	semidirect
121. #97×D₇₉	C₂²	semidirect
123. C₄×C₈×D₇₉	C₂²	semidirect
125. #446×C₇₉	C₂²	semidirect
126. #446×C₇₉	C₂²	semidirect
127. #446×C₇₉	C₂²	semidirect
128. C₈×Q₈×C₇₉	C₂²	semidirect
581. #2962	D₇₉	semidirect
594. C₇₉	#60212	semidirect
627. #446	C₂×D₇₉	semidirect
628. #446	C₂×D₇₉	semidirect
629. #446	C₂×D₇₉	semidirect
631. C₈×Q₈	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776792	2
#23772406	2
#23772403	2
#23772393	2
#23772384	2
#23772377	2
#23772374	2
#23772349	2
#23772146	2
#23772143	2
#23772128	2
#23772124	2
#23772050	2
#23772043	2
C₂×#19098623	2
#23771827	2
#23771822	2
#23771817	2
C₇₉×#2962	2
#60212	79