Subgroups — #35197147

Order 20224.

8650 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777732	C₂	1	8	yes	maximal, complemented
2	#23777727	C₂	1	8	yes	maximal, complemented
3	#23777725	C₂	1	8	yes	maximal, complemented
4	#23777275	C₂	1	2	yes	maximal, complemented
5	#23777271	C₂	1	2	yes	maximal, complemented
6	#23777268	C₂	1	8	yes	maximal, complemented
7	#23777175	C₂	1	2	yes	maximal, complemented
8	#23777174	C₂	1	2	yes	maximal, complemented
9	#23777172	C₂	1	8	yes	maximal, complemented
10	#23777035	C₂	1	1	yes	maximal, characteristic, complemented
11	#23777033	C₂	1	2	yes	maximal, complemented
12	#23777029	C₂	1	8	yes	maximal, complemented
13	#23776692	C₂	1	2	yes	maximal, complemented
14	C₂²×#14579157	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3484	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579207	C₂²	1	2	yes	complemented
17	C₂×#14579206	C₂²	1	8	yes	complemented
18	C₂×#14579206	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
21	#19099303	C₂²	1	8	yes	complemented
22	#19099302	C₂²	1	8	yes	complemented
23	#19099301	C₂²	1	16	yes	complemented
24	#19099297	C₂²	1	8	yes	complemented
25	#19099296	C₂²	1	8	yes	complemented
26	#19099295	C₂²	1	8	yes	complemented
27	#19099234	C₂²	1	8	yes	complemented
28	#19099233	C₂²	1	8	yes	complemented
29	#19099232	C₂²	1	8	yes	complemented
30	#19099231	C₂²	1	16	yes	complemented
31	#19099231	C₂²	1	8	yes	complemented
32	#19099209	C₂²	1	8	yes	complemented
33	#19099207	C₂²	1	8	yes	complemented
34	#19099204	C₂²	1	8	yes	complemented
35	#19099203	C₂²	1	16	yes	complemented
36	#19099203	C₂²	1	16	yes	complemented
37	#19099200	C₂²	1	16	yes	complemented
38	#19099200	C₂²	1	16	yes	complemented
39	D₄×D₃₁₆	C₂²	1	8	yes	complemented
40	#19099197	C₂²	1	8	yes	complemented
41	#19099197	C₂²	1	8	yes	complemented
42	D₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
43	D₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
44	D₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
45	D₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
46	#19099195	C₂²	1	16	yes	complemented
47	#19099195	C₂²	1	16	yes	complemented
48	#19099195	C₂²	1	8	yes	complemented
49	#19099166	C₂²	1	8	yes	complemented
50	#19099165	C₂²	1	16	yes	complemented
51	#19099164	C₂²	1	8	yes	complemented
52	#19099163	C₂²	1	16	yes	complemented
53	#19099132	C₂²	1	2	yes	complemented
54	#19099131	C₂²	1	4	yes	complemented
55	#19099130	C₂²	1	2	yes	complemented
56	#19099130	C₂²	1	4	yes	complemented
57	#19099129	C₂²	1	16	yes	complemented
58	#19099128	C₂²	1	16	yes	complemented
59	#19099128	C₂²	1	16	yes	complemented
60	#19099127	C₂²	1	2	yes	complemented
61	#19099127	C₂²	1	4	yes	complemented
62	#19099126	C₂²	1	4	yes	complemented
63	#19099125	C₂²	1	8	yes	complemented
64	#19099124	C₂²	1	8	yes	complemented
65	#19099123	C₂²	1	16	yes	complemented
66	#19099122	C₂²	1	8	yes	complemented
67	#19099122	C₂²	1	4	yes	complemented
68	#19099116	C₂²	1	2	yes	complemented
69	#19099115	C₂²	1	4	yes	complemented
70	#19099112	C₂²	1	4	yes	complemented
71	#19099110	C₂²	1	8	yes	complemented
72	#19099109	C₂²	1	2	yes	complemented
73	#19099109	C₂²	1	4	yes	complemented
74	#19099108	C₂²	1	4	yes	complemented
75	#19099108	C₂²	1	8	yes	complemented
76	C₂×#14579157	C₂²	1	8	yes	complemented
77	C₂×#14579157	C₂²	1	2	yes	complemented
78	C₂×#14579157	C₂²	1	2	yes	complemented
79	C₂×#14579157	C₂²	1	8	yes	complemented
80	C₂×#14579157	C₂²	1	4	yes	complemented
81	C₂×#14579157	C₂²	1	4	yes	complemented
82	#127×D₇₉	C₂²	1	4	yes	complemented
83	#19099099	C₂²	1	4	yes	complemented
84	#19099094	C₂²	1	4	yes	complemented
85	#19099093	C₂²	1	8	yes	complemented
86	#19099090	C₂²	1	8	yes	complemented
87	#19099074	C₂²	1	2	yes	complemented
88	#19099069	C₂²	1	8	yes	complemented
89	C₂×#14579130	C₂²	1	4	yes	complemented
90	#120×D₇₉	C₂²	1	8	yes	complemented
91	#19099038	C₂²	1	1	yes	characteristic, complemented
92	#19099037	C₂²	1	2	yes	complemented
93	#19099036	C₂²	1	8	yes	complemented
94	#41×Dic₇₉	C₂²	1	2	yes	complemented
95	#19099031	C₂²	1	2	yes	complemented
96	C₄×#11929623	C₂²	1	8	yes	complemented
97	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
98	C₂×H(5,𝔽₂)×C₇₉	C₂²	1	1	yes	characteristic, complemented
99	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
100	#546×C₇₉	C₂²	1	8	yes	complemented
101	D₄²×C₇₉	C₂²	1	8	yes	complemented
102	#535×C₇₉	C₂²	1	2	yes	complemented
103	#534×C₇₉	C₂²	1	4	yes	complemented
104	#525×C₇₉	C₂²	1	2	yes	complemented
105	C₂×#120×C₇₉	C₂²	1	4	yes	complemented
106	#518×C₇₉	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×D₇₉	C₂³	1	2	yes	—
108	#14579207	—	4	8	no	—
109	#14579206	—	4	32	no	—
110	#14579206	—	4	4	no	—
111	C₂×#11929625	C₂³	1	4	yes	complemented
112	C₂×#11929624	C₂³	1	2	yes	—
113	C₂×#11929624	C₂³	1	16	yes	complemented
114	C₂×#11929624	C₂³	1	4	yes	complemented
115	C₂×#11929623	C₂³	1	8	yes	—
116	C₂×#11929623	C₂³	1	16	yes	complemented
117	C₂×#11929623	C₂³	1	4	yes	complemented
118	C₂²×D₃₁₆	—	4	4	no	—
119	C₂²×D₃₁₆	C₂³	1	2	yes	—
120	C₂²×D₃₁₆	C₂³	1	8	yes	—
121	C₂²×D₃₁₆	C₂³	1	2	yes	—
122	C₂²×D₃₁₆	C₂³	1	4	yes	complemented
123	C₂²×C₂²⋊D₇₉	—	4	16	no	—
124	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
125	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
126	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
127	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
128	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
129	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
130	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
131	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
132	C₂×D₄×D₇₉	C₂³	1	16	yes	—
133	C₂×D₄×D₇₉	C₂³	1	8	yes	—
134	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
135	C₂×D₄×D₇₉	C₂³	1	4	yes	complemented
136	C₂×D₄×D₇₉	C₂³	1	4	yes	complemented
137	C₂³×Dic₇₉	C₂³	1	2	yes	—
138	#14579160	C₂³	1	4	yes	complemented
139	#14579159	C₂³	1	2	yes	complemented
140	#14579158	C₂³	1	4	yes	complemented
141	#14579157	C₂³	1	16	yes	—
142	#14579157	C₂³	1	4	yes	—
143	#14579157	C₂³	1	4	yes	—
144	#14579157	C₂³	1	8	yes	—
145	#14579157	C₂³	1	8	yes	—
146	#14579157	C₂³	1	8	yes	—
147	#14579157	C₂³	1	8	yes	—
148	#14579157	C₂³	1	4	yes	—
149	#14579157	C₂³	1	4	yes	—
150	#14579157	C₂³	1	16	yes	complemented
151	#14579157	C₂³	1	16	yes	complemented
152	#14579157	C₂³	1	4	yes	complemented
153	#14579157	C₂³	1	4	yes	complemented
154	#14579157	C₂³	1	2	yes	complemented
155	#14579156	C₂³	1	8	yes	complemented
156	#14579154	C₂³	1	8	yes	complemented
157	#14579152	C₂³	1	4	yes	complemented
158	#14579151	C₂³	1	8	yes	complemented
159	#14579150	C₂³	1	4	yes	complemented
160	#14579150	C₂³	1	2	yes	complemented
161	#14579149	C₂³	1	4	yes	complemented
162	#14579148	C₂³	1	4	yes	complemented
163	#14579148	C₂³	1	2	yes	complemented
164	#14579147	C₂³	1	16	yes	complemented
165	#14579147	C₂³	1	16	yes	complemented
166	#14579147	C₂³	1	8	yes	complemented
167	#14579146	C₂³	1	16	yes	complemented
168	#14579145	C₂³	1	8	yes	—
169	#14579145	C₂³	1	16	yes	complemented
170	#14579144	C₂³	1	4	yes	—
171	#14579144	C₂³	1	16	yes	complemented
172	#14579143	C₂³	1	16	yes	complemented
173	#14579143	C₂³	1	16	yes	complemented
174	#14579142	C₂³	1	8	yes	—
175	#14579142	C₂³	1	8	yes	complemented
176	#14579140	C₂³	1	4	yes	—
177	#14579138	C₂³	1	8	yes	—
178	#14579138	C₂³	1	8	yes	—
179	#14579136	C₂³	1	8	yes	complemented
180	#14579136	C₂³	1	16	yes	complemented
181	#14579135	C₂³	1	4	yes	—
182	#14579135	C₂³	1	16	yes	complemented
183	#14579135	C₂³	1	16	yes	complemented
184	#14579135	C₂³	1	8	yes	complemented
185	#14579134	C₂³	1	16	yes	complemented
186	#14579134	C₂³	1	16	yes	complemented
187	#14579134	C₂³	1	16	yes	complemented
188	#14579134	C₂³	1	16	yes	complemented
189	#14579134	C₂³	1	16	yes	complemented
190	#14579133	C₂³	1	8	yes	—
191	#14579133	C₂³	1	8	yes	—
192	#14579133	C₂³	1	16	yes	complemented
193	#14579133	C₂³	1	16	yes	complemented
194	#14579133	C₂³	1	16	yes	complemented
195	#14579133	C₂³	1	16	yes	complemented
196	#14579133	C₂³	1	16	yes	complemented
197	#14579132	C₂³	1	16	yes	complemented
198	#14579132	C₂³	1	8	yes	complemented
199	#14579132	C₂³	1	16	yes	complemented
200	#14579131	C₂³	1	8	yes	—
201	#14579131	C₂³	1	16	yes	—
202	#14579131	C₂³	1	16	yes	complemented
203	#14579131	C₂³	1	16	yes	complemented
204	#14579130	C₂³	1	8	yes	—
205	#14579130	C₂³	1	16	yes	—
206	#14579130	C₂³	1	4	yes	—
207	#14579130	C₂³	1	16	yes	complemented
208	#14579129	C₂³	1	8	yes	—
209	#14579129	C₂³	1	16	yes	—
210	#14579129	C₂³	1	16	yes	complemented
211	#14579129	C₂³	1	8	yes	complemented
212	#14579129	C₂³	1	16	yes	complemented
213	Q₈×Dic₇₉	C₂³	1	4	yes	complemented
214	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
215	#14579126	C₂³	1	8	yes	complemented
216	#14579126	C₂³	1	4	yes	complemented
217	C₄×D₃₁₆	C₂³	1	8	yes	complemented
218	D₄×Dic₇₉	C₂³	1	8	yes	—
219	D₄×Dic₇₉	C₂³	1	8	yes	—
220	D₄×Dic₇₉	C₂³	1	8	yes	complemented
221	D₄×Dic₇₉	C₂³	1	4	yes	complemented
222	#14579123	C₂³	1	8	yes	complemented
223	#14579123	C₂³	1	4	yes	complemented
224	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
225	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
226	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
227	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	complemented
228	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	—
229	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	—
230	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
231	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
232	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	complemented
233	#14579120	C₂³	1	2	yes	—
234	#14579120	C₂³	1	4	yes	complemented
235	#14579119	C₂³	1	8	yes	complemented
236	#14579118	C₂³	1	4	yes	complemented
237	#14579117	C₂³	1	8	yes	—
238	#14579117	C₂³	1	8	yes	complemented
239	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
240	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
241	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	—
242	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
243	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
244	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
245	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
246	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
247	C₂×C₄×Dic₇₉	C₂³	1	4	yes	complemented
248	C₄²×D₇₉	C₂³	1	4	yes	complemented
249	C₂⁵×C₇₉	C₂³	1	2	yes	—
250	H(5,𝔽₂)×C₇₉	—	4	4	no	—
251	C₂×#41×C₇₉	C₂³	1	2	yes	—
252	C₂×#41×C₇₉	C₂³	1	4	yes	complemented
253	C₂²×D₄×C₇₉	—	4	4	no	—
254	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
255	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
256	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
257	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
258	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
259	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
260	C₂²×D₄×C₇₉	C₂³	1	4	yes	complemented
261	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
262	#127×C₇₉	C₂³	1	4	yes	complemented
263	#124×C₇₉	C₂³	1	4	yes	complemented
264	#123×C₇₉	C₂³	1	4	yes	—
265	#123×C₇₉	C₂³	1	8	yes	complemented
266	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
267	#121×C₇₉	C₂³	1	4	yes	—
268	#121×C₇₉	C₂³	1	16	yes	complemented
269	#121×C₇₉	C₂³	1	8	yes	complemented
270	#120×C₇₉	C₂³	1	8	yes	—
271	#120×C₇₉	C₂³	1	16	yes	—
272	#120×C₇₉	C₂³	1	4	yes	—
273	#120×C₇₉	C₂³	1	8	yes	complemented
274	C₄×D₄×C₇₉	C₂³	1	8	yes	—
275	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
276	#117×C₇₉	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
278	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
279	C₂³×D₇₉	—	4	8	no	—
280	C₂³×D₇₉	—	4	4	no	—
281	C₂³×D₇₉	C₂⁴	1	8	yes	—
282	C₂³×D₇₉	C₂⁴	1	4	yes	—
283	C₂³×D₇₉	C₂⁴	1	8	yes	—
284	C₂³×D₇₉	C₂⁴	1	4	yes	—
285	#11929625	—	4	8	no	—
286	#11929624	—	2	8	no	—
287	#11929624	—	4	32	no	—
288	#11929624	—	4	8	no	—
289	#11929623	—	2	32	no	—
290	#11929623	—	4	32	no	—
291	#11929623	—	4	8	no	—
292	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
293	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
294	C₂×D₃₁₆	—	2	8	no	—
295	C₂×D₃₁₆	—	4	4	no	—
296	C₂×D₃₁₆	—	4	8	no	—
297	C₂×D₃₁₆	—	4	16	no	—
298	C₂×D₃₁₆	C₂⁴	1	2	yes	—
299	C₂×D₃₁₆	C₂⁴	1	4	yes	—
300	C₂×D₃₁₆	C₂⁴	1	4	yes	—
301	C₂×D₃₁₆	C₂⁴	1	16	yes	—
302	C₂×D₃₁₆	C₂⁴	1	8	yes	—
303	C₂×D₃₁₆	C₂⁴	1	8	yes	—
304	C₂×C₂²⋊D₇₉	—	2	32	no	—
305	C₂×C₂²⋊D₇₉	—	4	16	no	—
306	C₂×C₂²⋊D₇₉	—	4	8	no	—
307	C₂×C₂²⋊D₇₉	—	4	32	no	—
308	C₂×C₂²⋊D₇₉	—	4	16	no	—
309	C₂×C₂²⋊D₇₉	—	4	32	no	—
310	C₂×C₂²⋊D₇₉	—	4	16	no	—
311	C₂×C₂²⋊D₇₉	—	4	16	no	—
312	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
313	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
314	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
315	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
316	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
317	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
318	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
319	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
320	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
321	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
322	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
323	D₄×D₇₉	—	4	32	no	—
324	D₄×D₇₉	—	4	32	no	—
325	D₄×D₇₉	—	4	16	no	—
326	D₄×D₇₉	—	4	8	no	—
327	D₄×D₇₉	—	4	8	no	—
328	C₂²×Dic₇₉	—	2	8	no	—
329	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
330	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
331	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
332	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
333	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
334	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
335	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
336	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
337	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
338	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
339	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
340	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
341	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
342	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
343	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
344	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
345	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
346	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
347	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
348	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
349	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
350	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
351	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
352	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
353	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
354	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
355	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
356	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
357	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
358	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
359	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
360	C₄×Dic₇₉	C₂⁴	1	2	yes	—
361	C₄×Dic₇₉	C₂⁴	1	8	yes	—
362	C₄×Dic₇₉	C₂⁴	1	4	yes	—
363	C₄×Dic₇₉	C₂⁴	1	2	yes	—
364	C₄×Dic₇₉	C₂⁴	1	2	yes	—
365	C₄×Dic₇₉	C₂⁴	1	4	yes	—
366	C₄×Dic₇₉	C₂⁴	1	2	yes	—
367	C₄×Dic₇₉	C₂⁴	1	8	yes	—
368	C₄×Dic₇₉	C₂⁴	1	4	yes	—
369	C₂⁴×C₇₉	—	4	4	no	—
370	C₂⁴×C₇₉	—	4	8	no	—
371	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
373	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
374	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
375	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
376	#41×C₇₉	—	2	8	no	—
377	#41×C₇₉	—	4	8	no	—
378	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
379	C₂×D₄×C₇₉	—	2	4	no	—
380	C₂×D₄×C₇₉	—	2	4	no	—
381	C₂×D₄×C₇₉	—	4	16	no	—
382	C₂×D₄×C₇₉	—	4	8	no	—
383	C₂×D₄×C₇₉	—	4	4	no	—
384	C₂×D₄×C₇₉	—	4	16	no	—
385	C₂×D₄×C₇₉	—	4	8	no	—
386	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
387	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
388	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
389	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
390	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
391	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
392	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
393	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
394	C₂²×C₄×C₇₉	—	2	4	no	—
395	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
396	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
397	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
399	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
400	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
402	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
403	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
404	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
407	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
408	C₄²×C₇₉	C₂⁴	1	4	yes	—
409	C₂³×C₇₉	—	2	4	no	—
410	C₂³×C₇₉	—	2	2	no	—
411	C₂³×C₇₉	—	2	16	no	—
412	C₂³×C₇₉	—	2	4	no	—
413	C₂³×C₇₉	—	2	4	no	—
414	C₂³×C₇₉	—	4	4	no	—
415	C₂³×C₇₉	—	4	8	no	—
416	C₂³×C₇₉	—	4	4	no	—
417	C₂³×C₇₉	—	4	8	no	—
418	C₂³×C₇₉	—	4	8	no	—
419	C₂³×C₇₉	—	4	4	no	—
420	C₂³×C₇₉	—	8	16	no	—
421	C₂³×C₇₉	C₂⁵	1	4	yes	—
422	C₂³×C₇₉	C₂⁵	1	4	yes	—
423	C₂³×C₇₉	C₂⁵	1	4	yes	—
424	C₂³×C₇₉	C₂⁵	1	2	yes	—
425	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
426	C₂²×D₇₉	—	2	16	no	—
427	C₂²×D₇₉	—	2	8	no	—
428	C₂²×D₇₉	—	4	8	no	—
429	C₂²×D₇₉	—	4	8	no	—
430	C₂²×D₇₉	—	4	8	no	—
431	C₂²×D₇₉	—	4	16	no	—
432	C₂²×D₇₉	—	4	8	no	—
433	C₂²×D₇₉	—	4	4	no	—
434	C₂²×D₇₉	—	4	8	no	—
435	C₂²×D₇₉	—	8	16	no	—
436	C₂²×D₇₉	C₂⁵	1	8	yes	—
437	C₂²×D₇₉	C₂⁵	1	4	yes	—
438	Q₈×C₇₉	—	2	4	no	—
439	D₄×C₇₉	—	2	16	no	—
440	D₄×C₇₉	—	2	8	no	—
441	D₄×C₇₉	—	2	4	no	—
442	D₄×C₇₉	—	2	8	no	—
443	D₄×C₇₉	—	2	8	no	—
444	D₄×C₇₉	—	4	16	no	—
445	D₄×C₇₉	—	4	8	no	—
446	D₄×C₇₉	—	4	8	no	—
447	C₂×C₄×C₇₉	—	2	2	no	—
448	C₂×C₄×C₇₉	—	2	8	no	—
449	C₂×C₄×C₇₉	—	2	8	no	—
450	C₂×C₄×C₇₉	—	4	8	no	—
451	C₂×C₄×C₇₉	—	4	4	no	—
452	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	complemented
453	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
454	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
455	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
456	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
457	C₂²⋊D₇₉	—	2	16	no	—
458	C₂²⋊D₇₉	—	2	8	no	—
459	C₂²⋊D₇₉	—	2	16	no	—
460	C₂²⋊D₇₉	—	2	32	no	—
461	C₂²⋊D₇₉	—	2	32	no	—
462	C₂²⋊D₇₉	—	4	8	no	—
463	C₂²⋊D₇₉	—	4	8	no	—
464	C₂²⋊D₇₉	—	4	16	no	—
465	C₂²⋊D₇₉	—	4	16	no	—
466	C₂²⋊D₇₉	—	4	16	no	—
467	C₂²⋊D₇₉	—	4	16	no	—
468	C₂×Dic₇₉	—	2	4	no	—
469	C₂×Dic₇₉	—	2	8	no	—
470	C₂×Dic₇₉	—	2	8	no	—
471	C₂×Dic₇₉	—	2	16	no	—
472	C₂×Dic₇₉	—	4	4	no	—
473	C₂×Dic₇₉	—	4	8	no	—
474	C₂×Dic₇₉	H(5,𝔽₂)	1	8	yes	complemented
475	C₂×Dic₇₉	C₂⁵	1	4	yes	—
476	C₂×Dic₇₉	C₂⁵	1	8	yes	—
477	C₂×Dic₇₉	C₂⁵	1	4	yes	—
478	C₂×Dic₇₉	C₂⁵	1	4	yes	—
479	D₃₁₆	—	2	4	no	—
480	D₃₁₆	—	2	8	no	—
481	D₃₁₆	—	2	8	no	—
482	D₃₁₆	—	4	16	no	—
483	D₃₁₆	—	4	8	no	—
484	D₃₁₆	—	4	8	no	—
485	C₄×D₇₉	—	2	8	no	—
486	C₄×D₇₉	—	2	16	no	—
487	C₄×D₇₉	—	4	16	no	—
488	C₄×D₇₉	—	4	8	no	—
489	Dic₁₅₈	—	2	4	no	—
490	Dic₁₅₈	—	2	16	no	—
491	C₂²×C₇₉	—	2	8	no	—
492	C₂²×C₇₉	—	2	2	no	—
493	C₂²×C₇₉	—	2	2	no	—
494	C₂²×C₇₉	—	2	2	no	—
495	C₂²×C₇₉	—	2	8	no	—
496	C₂²×C₇₉	—	2	8	no	—
497	C₂²×C₇₉	—	2	8	no	—
498	C₂²×C₇₉	—	2	4	no	—
499	C₂²×C₇₉	—	2	4	no	—
500	C₂²×C₇₉	—	2	4	no	—
501	C₂²×C₇₉	—	8	4	no	—
502	C₂²×C₇₉	—	8	16	no	—
503	C₂²×C₇₉	—	8	4	no	—
504	C₂²×C₇₉	—	16	4	no	—
505	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
506	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
507	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
508	C₂×D₇₉	—	2	16	no	—
509	C₂×D₇₉	—	2	8	no	—
510	C₂×D₇₉	—	2	4	no	—
511	C₂×D₇₉	—	2	8	no	—
512	C₂×D₇₉	—	8	16	no	—
513	C₂×D₇₉	—	8	8	no	—
514	C₂×D₇₉	—	16	8	no	—
515	C₂×D₇₉	—	16	4	no	—
516	C₄×C₇₉	—	2	2	no	—
517	C₄×C₇₉	—	2	4	no	—
518	C₄×C₇₉	—	2	8	no	—
519	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
520	Dic₇₉	—	2	4	no	—
521	Dic₇₉	—	2	8	no	—
522	Dic₇₉	—	2	4	no	—
523	Dic₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
524	#62832	—	79	1	no	maximal, Sylow
525	C₂×C₇₉	—	2	4	no	—
526	C₂×C₇₉	—	2	2	no	—
527	C₂×C₇₉	—	4	4	no	—
528	C₂×C₇₉	—	4	4	no	—
529	C₂×C₇₉	—	4	4	no	—
530	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
531	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
532	D₇₉	—	4	8	no	—
533	D₇₉	—	4	4	no	—
534	#3543	—	79	8	no	—
535	#3543	—	79	8	no	—
536	#3543	—	79	8	no	—
537	#3508	—	79	8	no	—
538	#3508	—	79	2	no	—
539	#3508	—	79	2	no	—
540	#3498	—	79	2	no	—
541	#3498	—	79	8	no	—
542	#3498	—	79	2	no	—
543	#3484	—	79	1	no	—
544	#3484	—	79	2	no	—
545	#3484	—	79	8	no	—
546	#3484	D₇₉	1	1	yes	characteristic, complemented
547	#3444	—	79	2	no	—
548	C₂²×#127	—	79	1	no	—
549	C₇₉	#62832	1	1	yes	characteristic, complemented, Sylow
550	C₂×H(5,𝔽₂)	—	79	2	no	—
551	C₂×H(5,𝔽₂)	—	79	1	no	—
552	C₂×H(5,𝔽₂)	—	79	8	no	—
553	C₂×H(5,𝔽₂)	C₂×D₇₉	1	1	yes	characteristic, complemented
554	C₂³×D₄	—	79	4	no	—
555	C₂³×D₄	—	79	1	no	—
556	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
557	#560	—	79	8	no	—
558	#560	—	79	16	no	—
559	#560	—	79	8	no	—
560	#559	—	79	8	no	—
561	#559	—	79	8	no	—
562	#559	—	79	8	no	—
563	#550	—	79	8	no	—
564	#550	—	79	8	no	—
565	#550	—	79	8	no	—
566	#550	—	79	16	no	—
567	#550	—	79	8	no	—
568	#546	—	79	8	no	—
569	#546	—	79	8	no	—
570	#546	—	79	16	no	—
571	#546	—	79	16	no	—
572	#546	—	79	8	no	—
573	#546	—	79	16	no	—
574	#546	—	79	16	no	—
575	#546	C₂×D₇₉	1	8	yes	complemented
576	D₄²	—	79	16	no	—
577	D₄²	—	79	16	no	—
578	D₄²	—	79	8	no	—
579	D₄²	—	79	8	no	—
580	D₄²	—	79	8	no	—
581	D₄²	—	79	8	no	—
582	D₄²	—	79	16	no	—
583	D₄²	—	79	16	no	—
584	D₄²	—	79	8	no	—
585	D₄²	—	79	8	no	—
586	D₄²	C₂×D₇₉	1	8	yes	complemented
587	#540	—	79	16	no	—
588	#540	—	79	16	no	—
589	#540	—	79	8	no	—
590	#540	—	79	8	no	—
591	#535	—	79	2	no	—
592	#535	—	79	4	no	—
593	#535	—	79	2	no	—
594	#535	—	79	4	no	—
595	#535	—	79	4	no	—
596	#535	—	79	4	no	—
597	#535	—	79	16	no	—
598	#535	—	79	16	no	—
599	#535	—	79	16	no	—
600	#535	—	79	2	no	—
601	#535	C₂×D₇₉	1	2	yes	complemented
602	#534	—	79	4	no	—
603	#534	—	79	8	no	—
604	#534	—	79	8	no	—
605	#534	—	79	16	no	—
606	#534	—	79	8	no	—
607	#534	C₂×D₇₉	1	4	yes	complemented
608	#533	—	79	4	no	—
609	#533	—	79	2	no	—
610	#532	—	79	2	no	—
611	#532	—	79	4	no	—
612	#532	—	79	4	no	—
613	#532	—	79	4	no	—
614	#532	—	79	8	no	—
615	#532	—	79	8	no	—
616	C₂×#127	—	79	2	no	—
617	C₂×#127	—	79	2	no	—
618	C₂×#127	—	79	8	no	—
619	C₂×#127	—	79	8	no	—
620	C₂×#127	—	79	4	no	—
621	C₂×#127	—	79	4	no	—
622	C₂×#127	—	79	4	no	—
623	#529	—	79	8	no	—
624	#529	—	79	4	no	—
625	#529	—	79	4	no	—
626	#529	—	79	8	no	—
627	#525	—	79	2	no	—
628	#525	—	79	8	no	—
629	#525	C₂×D₇₉	1	2	yes	complemented
630	C₂×#120	—	79	4	no	—
631	C₂×#120	—	79	8	no	—
632	C₂×#120	C₂×D₇₉	1	4	yes	complemented
633	#518	—	79	1	no	—
634	#518	—	79	2	no	—
635	#518	—	79	8	no	—
636	#518	C₂×D₇₉	1	1	yes	characteristic, complemented
637	C₄×#41	—	79	2	no	—
638	C₄×#41	—	79	8	no	—
639	C₄×#41	—	79	2	no	—
640	C₂²×C₄²	—	79	1	no	—
641	C₂⁵	—	79	2	no	—
642	C₂⁵	C₂²×D₇₉	1	2	yes	—
643	H(5,𝔽₂)	—	4	4	no	—
644	H(5,𝔽₂)	—	316	4	no	—
645	H(5,𝔽₂)	—	316	32	no	—
646	H(5,𝔽₂)	—	316	8	no	—
647	C₂×#41	—	79	4	no	—
648	C₂×#41	—	79	4	no	—
649	C₂×#41	—	79	16	no	—
650	C₂×#41	—	79	8	no	—
651	C₂×#41	—	79	4	no	—
652	C₂×#41	—	79	16	no	—
653	C₂×#41	—	79	2	no	—
654	C₂×#41	C₂²×D₇₉	1	2	yes	—
655	C₂×#41	C₂²×D₇₉	1	4	yes	complemented
656	C₂²×D₄	—	4	4	no	—
657	C₂²×D₄	—	316	4	no	—
658	C₂²×D₄	—	316	16	no	—
659	C₂²×D₄	—	79	4	no	—
660	C₂²×D₄	—	79	8	no	—
661	C₂²×D₄	—	79	8	no	—
662	C₂²×D₄	—	79	8	no	—
663	C₂²×D₄	—	79	16	no	—
664	C₂²×D₄	—	79	8	no	—
665	C₂²×D₄	—	79	16	no	—
666	C₂²×D₄	—	79	8	no	—
667	C₂²×D₄	—	79	16	no	—
668	C₂²×D₄	—	79	4	no	—
669	C₂²×D₄	—	79	4	no	—
670	C₂²×D₄	—	79	16	no	—
671	C₂²×D₄	—	79	8	no	—
672	C₂²×D₄	—	79	2	no	—
673	C₂²×D₄	—	79	8	no	—
674	C₂²×D₄	—	79	4	no	—
675	C₂²×D₄	—	79	2	no	—
676	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
677	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
678	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
679	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
680	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
681	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
682	C₂²×D₄	C₂²×D₇₉	1	4	yes	complemented
683	C₂³×C₄	—	79	2	no	—
684	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
685	C₄⋊Q₈	—	79	2	no	—
686	C₄⋊Q₈	—	79	4	no	—
687	#127	—	79	4	no	—
688	#127	—	79	4	no	—
689	#127	—	79	2	no	—
690	#127	—	79	4	no	—
691	#127	—	79	4	no	—
692	#127	—	79	16	no	—
693	#127	—	79	8	no	—
694	#127	—	79	8	no	—
695	#127	—	79	8	no	—
696	#127	—	79	8	no	—
697	#127	—	79	4	no	—
698	#127	—	79	4	no	—
699	#127	—	79	16	no	—
700	#127	—	79	16	no	—
701	#127	—	79	4	no	—
702	#127	C₂²×D₇₉	1	4	yes	complemented
703	#126	—	79	8	no	—
704	#126	—	79	8	no	—
705	#125	—	79	8	no	—
706	#125	—	79	4	no	—
707	#124	—	79	2	no	—
708	#124	—	79	4	no	—
709	#124	—	79	2	no	—
710	#124	—	79	4	no	—
711	#124	—	79	8	no	—
712	#124	—	79	16	no	—
713	#124	—	79	16	no	—
714	#124	—	79	4	no	—
715	#124	C₂²×D₇₉	1	4	yes	complemented
716	#123	—	79	8	no	—
717	#123	—	79	8	no	—
718	#123	—	79	4	no	—
719	#123	—	79	16	no	—
720	#123	—	79	16	no	—
721	#123	—	79	8	no	—
722	#123	—	79	16	no	—
723	#123	—	79	16	no	—
724	#123	—	79	16	no	—
725	#123	C₂²×D₇₉	1	4	yes	—
726	#123	C₂²×D₇₉	1	8	yes	complemented
727	C₂²⋊Q₈	—	79	4	no	—
728	C₂²⋊Q₈	—	79	8	no	—
729	C₂²⋊Q₈	—	79	8	no	—
730	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
731	#121	—	79	8	no	—
732	#121	—	79	8	no	—
733	#121	—	79	8	no	—
734	#121	—	79	16	no	—
735	#121	—	79	16	no	—
736	#121	—	79	16	no	—
737	#121	—	79	16	no	—
738	#121	—	79	16	no	—
739	#121	—	79	16	no	—
740	#121	—	79	16	no	—
741	#121	—	79	4	no	—
742	#121	—	79	8	no	—
743	#121	—	79	16	no	—
744	#121	—	79	16	no	—
745	#121	—	79	8	no	—
746	#121	—	79	16	no	—
747	#121	—	79	16	no	—
748	#121	—	79	16	no	—
749	#121	—	79	16	no	—
750	#121	—	79	16	no	—
751	#121	—	79	16	no	—
752	#121	C₂²×D₇₉	1	4	yes	—
753	#121	C₂²×D₇₉	1	8	yes	complemented
754	#121	C₂²×D₇₉	1	16	yes	complemented
755	#120	—	79	4	no	—
756	#120	—	79	16	no	—
757	#120	—	79	8	no	—
758	#120	—	79	16	no	—
759	#120	—	79	8	no	—
760	#120	—	79	16	no	—
761	#120	—	79	8	no	—
762	#120	—	79	16	no	—
763	#120	—	79	16	no	—
764	#120	—	79	16	no	—
765	#120	—	79	8	no	—
766	#120	—	79	16	no	—
767	#120	—	79	16	no	—
768	#120	C₂²×D₇₉	1	4	yes	—
769	#120	C₂²×D₇₉	1	16	yes	—
770	#120	C₂²×D₇₉	1	8	yes	—
771	#120	C₂²×D₇₉	1	8	yes	complemented
772	C₄×Q₈	—	79	4	no	—
773	C₄×Q₈	—	79	8	no	—
774	C₄×Q₈	—	79	4	no	—
775	C₄×Q₈	—	79	8	no	—
776	C₄×D₄	—	79	8	no	—
777	C₄×D₄	—	79	8	no	—
778	C₄×D₄	—	79	4	no	—
779	C₄×D₄	—	79	8	no	—
780	C₄×D₄	—	79	8	no	—
781	C₄×D₄	—	79	8	no	—
782	C₄×D₄	—	79	16	no	—
783	C₄×D₄	—	79	16	no	—
784	C₄×D₄	—	79	4	no	—
785	C₄×D₄	—	79	8	no	—
786	C₄×D₄	—	79	8	no	—
787	C₄×D₄	—	79	8	no	—
788	C₄×D₄	—	79	8	no	—
789	C₄×D₄	—	79	16	no	—
790	C₄×D₄	—	79	16	no	—
791	C₄×D₄	—	79	8	no	—
792	C₄×D₄	C₂²×D₇₉	1	8	yes	—
793	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
794	#117	—	79	2	no	—
795	#117	—	79	4	no	—
796	#117	—	79	8	no	—
797	#117	—	79	8	no	—
798	#117	—	79	8	no	—
799	#117	—	79	4	no	—
800	#117	C₂²×D₇₉	1	2	yes	—
801	C₂×C₂²⋊C₄	—	79	4	no	—
802	C₂×C₂²⋊C₄	—	79	8	no	—
803	C₂×C₂²⋊C₄	—	79	16	no	—
804	C₂×C₂²⋊C₄	—	79	8	no	—
805	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
806	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
807	C₂×C₄²	—	79	4	no	—
808	C₂×C₄²	—	79	4	no	—
809	C₂×C₄²	—	79	2	no	—
810	C₂×C₄²	—	79	2	no	—
811	C₂×C₄²	—	79	4	no	—
812	C₂×C₄²	—	79	4	no	—
813	C₂⁴	—	4	4	no	—
814	C₂⁴	—	4	8	no	—
815	C₂⁴	—	316	8	no	—
816	C₂⁴	—	316	4	no	—
817	C₂⁴	—	79	8	no	—
818	C₂⁴	—	79	4	no	—
819	C₂⁴	—	79	8	no	—
820	C₂⁴	—	79	4	no	—
821	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
822	C₂⁴	C₂³×D₇₉	1	2	yes	—
823	C₂⁴	C₂³×D₇₉	1	8	yes	—
824	C₂⁴	C₂³×D₇₉	1	2	yes	—
825	C₂⁴	C₂³×D₇₉	1	4	yes	—
826	#41	—	2	8	no	—
827	#41	—	4	8	no	—
828	#41	—	316	8	no	—
829	#41	—	316	32	no	—
830	#41	—	316	8	no	—
831	#41	—	316	32	no	—
832	#41	—	316	8	no	—
833	#41	—	158	32	no	—
834	#41	—	158	8	no	—
835	C₂×Q₈	—	79	8	no	—
836	C₂×Q₈	—	79	2	no	—
837	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	4	no	—
840	C₂×D₄	—	4	16	no	—
841	C₂×D₄	—	4	8	no	—
842	C₂×D₄	—	4	4	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	16	no	—
845	C₂×D₄	—	316	4	no	—
846	C₂×D₄	—	316	16	no	—
847	C₂×D₄	—	316	8	no	—
848	C₂×D₄	—	316	32	no	—
849	C₂×D₄	—	316	16	no	—
850	C₂×D₄	—	316	16	no	—
851	C₂×D₄	—	316	8	no	—
852	C₂×D₄	—	316	8	no	—
853	C₂×D₄	—	316	8	no	—
854	C₂×D₄	—	316	32	no	—
855	C₂×D₄	—	316	16	no	—
856	C₂×D₄	—	316	16	no	—
857	C₂×D₄	—	316	32	no	—
858	C₂×D₄	—	316	16	no	—
859	C₂×D₄	—	316	32	no	—
860	C₂×D₄	—	79	16	no	—
861	C₂×D₄	—	79	8	no	—
862	C₂×D₄	—	79	16	no	—
863	C₂×D₄	—	79	8	no	—
864	C₂×D₄	—	79	16	no	—
865	C₂×D₄	—	79	16	no	—
866	C₂×D₄	—	79	8	no	—
867	C₂×D₄	—	79	4	no	—
868	C₂×D₄	—	79	8	no	—
869	C₂×D₄	—	79	16	no	—
870	C₂×D₄	—	79	16	no	—
871	C₂×D₄	—	79	8	no	—
872	C₂×D₄	—	79	16	no	—
873	C₂×D₄	—	79	8	no	—
874	C₂×D₄	—	79	2	no	—
875	C₂×D₄	—	79	4	no	—
876	C₂×D₄	—	79	4	no	—
877	C₂×D₄	—	158	32	no	—
878	C₂×D₄	—	158	8	no	—
879	C₂×D₄	C₂³×D₇₉	1	4	yes	—
880	C₂×D₄	C₂³×D₇₉	1	2	yes	—
881	C₂×D₄	C₂³×D₇₉	1	4	yes	—
882	C₂×D₄	C₂³×D₇₉	1	8	yes	—
883	C₂×D₄	C₂³×D₇₉	1	4	yes	—
884	C₂×D₄	C₂³×D₇₉	1	8	yes	—
885	C₂×D₄	C₂³×D₇₉	1	16	yes	—
886	C₂×D₄	C₂³×D₇₉	1	8	yes	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	79	4	no	—
889	C₂²×C₄	—	79	8	no	—
890	C₂²×C₄	—	79	8	no	—
891	C₂²×C₄	—	79	16	no	—
892	C₂²×C₄	—	79	2	no	—
893	C₂²×C₄	—	79	4	no	—
894	C₂²×C₄	—	79	4	no	—
895	C₂²×C₄	—	79	2	no	—
896	C₂²×C₄	—	79	8	no	—
897	C₂²×C₄	—	79	8	no	—
898	C₂²×C₄	—	79	4	no	—
899	C₂²×C₄	—	158	8	no	—
900	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
901	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
902	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
903	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
904	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
905	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
906	C₄⋊C₄	—	79	8	no	—
907	C₄⋊C₄	—	79	8	no	—
908	C₄⋊C₄	—	79	8	no	—
909	C₄⋊C₄	—	79	8	no	—
910	C₄⋊C₄	—	79	8	no	—
911	C₄⋊C₄	—	79	4	no	—
912	C₄⋊C₄	—	79	8	no	—
913	C₄⋊C₄	—	79	8	no	—
914	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
915	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
916	C₂²⋊C₄	—	79	8	no	—
917	C₂²⋊C₄	—	79	4	no	—
918	C₂²⋊C₄	—	79	16	no	—
919	C₂²⋊C₄	—	79	8	no	—
920	C₂²⋊C₄	—	79	8	no	—
921	C₂²⋊C₄	—	79	8	no	—
922	C₂²⋊C₄	—	79	16	no	—
923	C₂²⋊C₄	—	79	16	no	—
924	C₂²⋊C₄	—	79	16	no	—
925	C₂²⋊C₄	—	79	8	no	—
926	C₂²⋊C₄	—	79	8	no	—
927	C₂²⋊C₄	—	79	8	no	—
928	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
929	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
930	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
931	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
932	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
933	C₄²	—	79	2	no	—
934	C₄²	—	79	4	no	—
935	C₄²	—	79	2	no	—
936	C₄²	—	79	2	no	—
937	C₄²	—	79	4	no	—
938	C₄²	—	79	2	no	—
939	C₄²	—	79	8	no	—
940	C₄²	—	79	8	no	—
941	C₄²	—	79	4	no	—
942	C₄²	C₂³×D₇₉	1	4	yes	—
943	C₂³	—	2	4	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	16	no	—
946	C₂³	—	2	4	no	—
947	C₂³	—	2	4	no	—
948	C₂³	—	4	8	no	—
949	C₂³	—	4	4	no	—
950	C₂³	—	4	8	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	8	no	—
954	C₂³	—	8	16	no	—
955	C₂³	—	316	8	no	—
956	C₂³	—	316	8	no	—
957	C₂³	—	316	8	no	—
958	C₂³	—	316	8	no	—
959	C₂³	—	316	16	no	—
960	C₂³	—	316	8	no	—
961	C₂³	—	316	4	no	—
962	C₂³	—	79	8	no	—
963	C₂³	—	79	4	no	—
964	C₂³	—	632	16	no	—
965	C₂³	—	158	16	no	—
966	C₂³	—	158	8	no	—
967	C₂³	C₂⁴×D₇₉	1	4	yes	—
968	C₂³	C₂⁴×D₇₉	1	4	yes	—
969	C₂³	C₂⁴×D₇₉	1	4	yes	—
970	C₂³	C₂⁴×D₇₉	1	2	yes	—
971	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
972	Q₈	—	2	4	no	—
973	Q₈	—	158	16	no	—
974	Q₈	—	158	4	no	—
975	D₄	—	2	16	no	—
976	D₄	—	2	8	no	—
977	D₄	—	2	8	no	—
978	D₄	—	2	8	no	—
979	D₄	—	2	4	no	—
980	D₄	—	4	8	no	—
981	D₄	—	4	8	no	—
982	D₄	—	4	16	no	—
983	D₄	—	316	8	no	—
984	D₄	—	316	16	no	—
985	D₄	—	316	8	no	—
986	D₄	—	316	16	no	—
987	D₄	—	316	16	no	—
988	D₄	—	316	16	no	—
989	D₄	—	316	16	no	—
990	D₄	—	316	8	no	—
991	D₄	—	316	8	no	—
992	D₄	—	158	16	no	—
993	D₄	—	158	32	no	—
994	D₄	—	158	32	no	—
995	D₄	—	158	16	no	—
996	D₄	—	158	8	no	—
997	D₄	—	158	4	no	—
998	D₄	—	158	8	no	—
999	D₄	—	158	8	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	8	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	8	no	—
1005	C₂×C₄	—	316	16	no	—
1006	C₂×C₄	—	316	8	no	—
1007	C₂×C₄	—	316	8	no	—
1008	C₂×C₄	—	316	4	no	—
1009	C₂×C₄	—	79	8	no	—
1010	C₂×C₄	—	79	4	no	—
1011	C₂×C₄	—	79	4	no	—
1012	C₂×C₄	—	79	8	no	—
1013	C₂×C₄	—	79	4	no	—
1014	C₂×C₄	—	158	16	no	—
1015	C₂×C₄	—	158	8	no	—
1016	C₂×C₄	—	158	8	no	—
1017	C₂×C₄	—	158	16	no	—
1018	C₂×C₄	—	158	4	no	—
1019	C₂×C₄	—	158	8	no	—
1020	C₂×C₄	#14579206	1	4	yes	complemented
1021	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1022	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1023	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
1024	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1025	C₂²	—	2	8	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	8	no	—
1030	C₂²	—	2	8	no	—
1031	C₂²	—	2	8	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	4	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	8	16	no	—
1036	C₂²	—	8	4	no	—
1037	C₂²	—	8	4	no	—
1038	C₂²	—	16	4	no	—
1039	C₂²	—	632	16	no	—
1040	C₂²	—	632	8	no	—
1041	C₂²	—	158	16	no	—
1042	C₂²	—	158	8	no	—
1043	C₂²	—	158	8	no	—
1044	C₂²	—	158	4	no	—
1045	C₂²	—	1264	4	no	—
1046	C₂²	—	1264	8	no	—
1047	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
1048	C₂²	C₂×#14579206	1	2	yes	—
1049	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
1050	C₄	—	2	8	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	2	4	no	—
1053	C₄	—	79	8	no	—
1054	C₄	—	158	8	no	—
1055	C₄	—	158	4	no	—
1056	C₄	—	158	4	no	—
1057	C₄	C₂×#14579206	1	4	yes	—
1058	C₂	—	2	4	no	—
1059	C₂	—	2	2	no	—
1060	C₂	—	4	4	no	—
1061	C₂	—	4	4	no	—
1062	C₂	—	4	4	no	—
1063	C₂	—	316	8	no	—
1064	C₂	—	316	4	no	—
1065	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—
1066	C₂	C₂²×#14579206	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3484	C₂
hypercenter	#3484	D₇₉
hypocenter	C₇₉	#62832
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3484

Complements

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

N	H ≅ G/N	type
1. #23777732	C₂	semidirect
2. #23777727	C₂	semidirect
3. #23777725	C₂	semidirect
4. #23777275	C₂	semidirect
5. #23777271	C₂	semidirect
6. #23777268	C₂	semidirect
7. #23777175	C₂	semidirect
8. #23777174	C₂	semidirect
9. #23777172	C₂	semidirect
10. #23777035	C₂	semidirect
11. #23777033	C₂	semidirect
12. #23777029	C₂	semidirect
13. #23776692	C₂	semidirect
14. C₂²×#14579157	C₂	semidirect
15. C₇₉×#3484	C₂	semidirect
16. C₂×#14579207	C₂²	semidirect
17. C₂×#14579206	C₂²	semidirect
18. C₂×#14579206	C₂²	semidirect
19. C₂³×D₃₁₆	C₂²	semidirect
20. C₂³×C₂²⋊D₇₉	C₂²	semidirect
21. #19099303	C₂²	semidirect
22. #19099302	C₂²	semidirect
23. #19099301	C₂²	semidirect
24. #19099297	C₂²	semidirect
25. #19099296	C₂²	semidirect
26. #19099295	C₂²	semidirect
27. #19099234	C₂²	semidirect
28. #19099233	C₂²	semidirect
29. #19099232	C₂²	semidirect
30. #19099231	C₂²	semidirect
31. #19099231	C₂²	semidirect
32. #19099209	C₂²	semidirect
33. #19099207	C₂²	semidirect
34. #19099204	C₂²	semidirect
35. #19099203	C₂²	semidirect
36. #19099203	C₂²	semidirect
37. #19099200	C₂²	semidirect
38. #19099200	C₂²	semidirect
39. D₄×D₃₁₆	C₂²	semidirect
40. #19099197	C₂²	semidirect
41. #19099197	C₂²	semidirect
42. D₄×C₂²⋊D₇₉	C₂²	semidirect
43. D₄×C₂²⋊D₇₉	C₂²	semidirect
44. D₄×C₂²⋊D₇₉	C₂²	semidirect
45. D₄×C₂²⋊D₇₉	C₂²	semidirect
46. #19099195	C₂²	semidirect
47. #19099195	C₂²	semidirect
48. #19099195	C₂²	semidirect
49. #19099166	C₂²	semidirect
50. #19099165	C₂²	semidirect
51. #19099164	C₂²	semidirect
52. #19099163	C₂²	semidirect
53. #19099132	C₂²	semidirect
54. #19099131	C₂²	semidirect
55. #19099130	C₂²	semidirect
56. #19099130	C₂²	semidirect
57. #19099129	C₂²	semidirect
58. #19099128	C₂²	semidirect
59. #19099128	C₂²	semidirect
60. #19099127	C₂²	semidirect
61. #19099127	C₂²	semidirect
62. #19099126	C₂²	semidirect
63. #19099125	C₂²	semidirect
64. #19099124	C₂²	semidirect
65. #19099123	C₂²	semidirect
66. #19099122	C₂²	semidirect
67. #19099122	C₂²	semidirect
68. #19099116	C₂²	semidirect
69. #19099115	C₂²	semidirect
70. #19099112	C₂²	semidirect
71. #19099110	C₂²	semidirect
72. #19099109	C₂²	semidirect
73. #19099109	C₂²	semidirect
74. #19099108	C₂²	semidirect
75. #19099108	C₂²	semidirect
76. C₂×#14579157	C₂²	semidirect
77. C₂×#14579157	C₂²	semidirect
78. C₂×#14579157	C₂²	semidirect
79. C₂×#14579157	C₂²	semidirect
80. C₂×#14579157	C₂²	semidirect
81. C₂×#14579157	C₂²	semidirect
82. #127×D₇₉	C₂²	semidirect
83. #19099099	C₂²	semidirect
84. #19099094	C₂²	semidirect
85. #19099093	C₂²	semidirect
86. #19099090	C₂²	semidirect
87. #19099074	C₂²	semidirect
88. #19099069	C₂²	semidirect
89. C₂×#14579130	C₂²	semidirect
90. #120×D₇₉	C₂²	semidirect
91. #19099038	C₂²	semidirect
92. #19099037	C₂²	semidirect
93. #19099036	C₂²	semidirect
94. #41×Dic₇₉	C₂²	semidirect
95. #19099031	C₂²	semidirect
96. C₄×#11929623	C₂²	semidirect
97. C₂²×C₄×Dic₇₉	C₂²	semidirect
98. C₂×H(5,𝔽₂)×C₇₉	C₂²	semidirect
99. C₂³×D₄×C₇₉	C₂²	semidirect
100. #546×C₇₉	C₂²	semidirect
101. D₄²×C₇₉	C₂²	semidirect
102. #535×C₇₉	C₂²	semidirect
103. #534×C₇₉	C₂²	semidirect
104. #525×C₇₉	C₂²	semidirect
105. C₂×#120×C₇₉	C₂²	semidirect
106. #518×C₇₉	C₂²	semidirect
111. C₂×#11929625	C₂³	semidirect
113. C₂×#11929624	C₂³	semidirect
114. C₂×#11929624	C₂³	semidirect
116. C₂×#11929623	C₂³	semidirect
117. C₂×#11929623	C₂³	semidirect
122. C₂²×D₃₁₆	C₂³	semidirect
131. C₂²×C₂²⋊D₇₉	C₂³	semidirect
134. C₂×D₄×D₇₉	C₂³	semidirect
135. C₂×D₄×D₇₉	C₂³	semidirect
136. C₂×D₄×D₇₉	C₂³	semidirect
138. #14579160	C₂³	semidirect
139. #14579159	C₂³	semidirect
140. #14579158	C₂³	semidirect
150. #14579157	C₂³	semidirect
151. #14579157	C₂³	semidirect
152. #14579157	C₂³	semidirect
153. #14579157	C₂³	semidirect
154. #14579157	C₂³	semidirect
155. #14579156	C₂³	semidirect
156. #14579154	C₂³	semidirect
157. #14579152	C₂³	semidirect
158. #14579151	C₂³	semidirect
159. #14579150	C₂³	semidirect
160. #14579150	C₂³	semidirect
161. #14579149	C₂³	semidirect
162. #14579148	C₂³	semidirect
163. #14579148	C₂³	semidirect
164. #14579147	C₂³	semidirect
165. #14579147	C₂³	semidirect
166. #14579147	C₂³	semidirect
167. #14579146	C₂³	semidirect
169. #14579145	C₂³	semidirect
171. #14579144	C₂³	semidirect
172. #14579143	C₂³	semidirect
173. #14579143	C₂³	semidirect
175. #14579142	C₂³	semidirect
179. #14579136	C₂³	semidirect
180. #14579136	C₂³	semidirect
182. #14579135	C₂³	semidirect
183. #14579135	C₂³	semidirect
184. #14579135	C₂³	semidirect
185. #14579134	C₂³	semidirect
186. #14579134	C₂³	semidirect
187. #14579134	C₂³	semidirect
188. #14579134	C₂³	semidirect
189. #14579134	C₂³	semidirect
192. #14579133	C₂³	semidirect
193. #14579133	C₂³	semidirect
194. #14579133	C₂³	semidirect
195. #14579133	C₂³	semidirect
196. #14579133	C₂³	semidirect
197. #14579132	C₂³	semidirect
198. #14579132	C₂³	semidirect
199. #14579132	C₂³	semidirect
202. #14579131	C₂³	semidirect
203. #14579131	C₂³	semidirect
207. #14579130	C₂³	semidirect
210. #14579129	C₂³	semidirect
211. #14579129	C₂³	semidirect
212. #14579129	C₂³	semidirect
213. Q₈×Dic₇₉	C₂³	semidirect
214. C₄×Dic₁₅₈	C₂³	semidirect
215. #14579126	C₂³	semidirect
216. #14579126	C₂³	semidirect
217. C₄×D₃₁₆	C₂³	semidirect
220. D₄×Dic₇₉	C₂³	semidirect
221. D₄×Dic₇₉	C₂³	semidirect
222. #14579123	C₂³	semidirect
223. #14579123	C₂³	semidirect
225. C₄×C₂²⋊D₇₉	C₂³	semidirect
226. C₄×C₂²⋊D₇₉	C₂³	semidirect
227. C₄×C₂²⋊D₇₉	C₂³	semidirect
230. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
231. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
232. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
234. #14579120	C₂³	semidirect
235. #14579119	C₂³	semidirect
236. #14579118	C₂³	semidirect
238. #14579117	C₂³	semidirect
247. C₂×C₄×Dic₇₉	C₂³	semidirect
248. C₄²×D₇₉	C₂³	semidirect
252. C₂×#41×C₇₉	C₂³	semidirect
260. C₂²×D₄×C₇₉	C₂³	semidirect
262. #127×C₇₉	C₂³	semidirect
263. #124×C₇₉	C₂³	semidirect
265. #123×C₇₉	C₂³	semidirect
268. #121×C₇₉	C₂³	semidirect
269. #121×C₇₉	C₂³	semidirect
273. #120×C₇₉	C₂³	semidirect
275. C₄×D₄×C₇₉	C₂³	semidirect
452. C₂×C₄×C₇₉	H(5,𝔽₂)	semidirect
474. C₂×Dic₇₉	H(5,𝔽₂)	semidirect
546. #3484	D₇₉	semidirect
549. C₇₉	#62832	semidirect
553. C₂×H(5,𝔽₂)	C₂×D₇₉	semidirect
556. C₂³×D₄	C₂×D₇₉	semidirect
575. #546	C₂×D₇₉	semidirect
586. D₄²	C₂×D₇₉	semidirect
601. #535	C₂×D₇₉	semidirect
607. #534	C₂×D₇₉	semidirect
629. #525	C₂×D₇₉	semidirect
632. C₂×#120	C₂×D₇₉	semidirect
636. #518	C₂×D₇₉	semidirect
655. C₂×#41	C₂²×D₇₉	semidirect
682. C₂²×D₄	C₂²×D₇₉	semidirect
702. #127	C₂²×D₇₉	semidirect
715. #124	C₂²×D₇₉	semidirect
726. #123	C₂²×D₇₉	semidirect
753. #121	C₂²×D₇₉	semidirect
754. #121	C₂²×D₇₉	semidirect
771. #120	C₂²×D₇₉	semidirect
793. C₄×D₄	C₂²×D₇₉	semidirect
1020. C₂×C₄	#14579206	semidirect

Maximal subgroups

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

subgroup	index
#23777732	2
#23777727	2
#23777725	2
#23777275	2
#23777271	2
#23777268	2
#23777175	2
#23777174	2
#23777172	2
#23777035	2
#23777033	2
#23777029	2
#23776692	2
C₂²×#14579157	2
C₇₉×#3484	2
#62832	79