Subgroups — #35197318

Order 20224.

7390 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777456	C₂	1	8	yes	maximal, complemented
2	#23777422	C₂	1	8	yes	maximal, complemented
3	#23777351	C₂	1	8	yes	maximal, complemented
4	#23777328	C₂	1	8	yes	maximal, complemented
5	#23777252	C₂	1	2	yes	maximal, complemented
6	#23777239	C₂	1	4	yes	maximal, complemented
7	#23777203	C₂	1	1	yes	maximal, characteristic, complemented
8	#23777164	C₂	1	1	yes	maximal, characteristic, complemented
9	#23777120	C₂	1	2	yes	maximal, complemented
10	#23777089	C₂	1	4	yes	maximal, complemented
11	#23777035	C₂	1	2	yes	maximal, complemented
12	#23776822	C₂	1	2	yes	maximal, complemented
13	#23776809	C₂	1	4	yes	maximal, complemented
14	#23776790	C₂	1	2	yes	maximal, complemented
15	C₂×#19099151	C₂	1	4	yes	maximal, complemented
16	C₄×#14579206	C₂	1	2	yes	maximal, complemented
17	C₂×#518×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14579206	C₂²	1	2	yes	—
19	#19099296	C₂²	1	8	yes	complemented
20	#19099283	C₂²	1	4	yes	complemented
21	#19099281	C₂²	1	8	yes	complemented
22	#19099278	C₂²	1	4	yes	complemented
23	#19099276	C₂²	1	8	yes	complemented
24	#19099272	C₂²	1	8	yes	complemented
25	#19099270	C₂²	1	4	yes	complemented
26	#19099263	C₂²	1	8	yes	complemented
27	#19099262	C₂²	1	16	yes	complemented
28	#19099259	C₂²	1	8	yes	complemented
29	#19099257	C₂²	1	8	yes	complemented
30	#19099253	C₂²	1	8	yes	complemented
31	#19099252	C₂²	1	8	yes	complemented
32	#19099242	C₂²	1	16	yes	complemented
33	#19099239	C₂²	1	16	yes	complemented
34	#19099239	C₂²	1	16	yes	complemented
35	#19099234	C₂²	1	4	yes	complemented
36	D₄×Dic₁₅₈	C₂²	1	4	yes	complemented
37	#19099222	C₂²	1	8	yes	complemented
38	#19099218	C₂²	1	4	yes	complemented
39	#19099217	C₂²	1	4	yes	complemented
40	#19099209	C₂²	1	8	yes	complemented
41	#19099208	C₂²	1	8	yes	complemented
42	#19099207	C₂²	1	8	yes	complemented
43	#19099207	C₂²	1	8	yes	complemented
44	#19099203	C₂²	1	16	yes	complemented
45	#19099203	C₂²	1	16	yes	complemented
46	D₄×D₃₁₆	C₂²	1	4	yes	complemented
47	D₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
48	D₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
49	#19099194	C₂²	1	2	yes	complemented
50	#19099189	C₂²	1	4	yes	complemented
51	#19099184	C₂²	1	4	yes	complemented
52	#19099184	C₂²	1	4	yes	complemented
53	#19099178	C₂²	1	8	yes	complemented
54	#19099175	C₂²	1	4	yes	complemented
55	#19099168	C₂²	1	4	yes	complemented
56	#19099164	C₂²	1	8	yes	complemented
57	#19099160	C₂²	1	4	yes	complemented
58	#19099160	C₂²	1	4	yes	complemented
59	#19099155	C₂²	1	16	yes	complemented
60	#19099151	C₂²	1	4	yes	complemented
61	#19099151	C₂²	1	4	yes	complemented
62	#19099151	C₂²	1	8	yes	complemented
63	#19099151	C₂²	1	8	yes	complemented
64	#19099151	C₂²	1	8	yes	complemented
65	#19099151	C₂²	1	16	yes	complemented
66	#19099151	C₂²	1	16	yes	complemented
67	#19099146	C₂²	1	16	yes	complemented
68	#19099144	C₂²	1	2	yes	complemented
69	#19099130	C₂²	1	4	yes	complemented
70	#19099125	C₂²	1	4	yes	complemented
71	#19099122	C₂²	1	8	yes	complemented
72	#19099120	C₂²	1	2	yes	complemented
73	#19099113	C₂²	1	2	yes	complemented
74	#19099110	C₂²	1	8	yes	complemented
75	#19099097	C₂²	1	8	yes	complemented
76	#19099095	C₂²	1	8	yes	complemented
77	#19099093	C₂²	1	16	yes	complemented
78	#19099091	C₂²	1	8	yes	complemented
79	#19099091	C₂²	1	8	yes	complemented
80	C₂×#14579154	C₂²	1	8	yes	complemented
81	C₂×#14579147	C₂²	1	8	yes	complemented
82	#19099074	C₂²	1	4	yes	complemented
83	#19099074	C₂²	1	8	yes	complemented
84	#19099074	C₂²	1	8	yes	complemented
85	#19099072	C₂²	1	16	yes	complemented
86	C₂×#14579143	C₂²	1	8	yes	complemented
87	C₂×#14579140	C₂²	1	4	yes	complemented
88	C₂×#14579135	C₂²	1	4	yes	complemented
89	C₂×#14579134	C₂²	1	8	yes	complemented
90	C₂×#14579130	C₂²	1	8	yes	complemented
91	#19099044	C₂²	1	4	yes	complemented
92	#19099042	C₂²	1	8	yes	complemented
93	#19099038	C₂²	1	2	yes	—
94	#19099036	C₂²	1	8	yes	complemented
95	#19099035	C₂²	1	8	yes	complemented
96	C₄×#11929624	C₂²	1	4	yes	complemented
97	C₄×#11929623	C₂²	1	8	yes	complemented
98	C₂×C₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
99	C₄×D₄×D₇₉	C₂²	1	8	yes	complemented
100	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
101	#518×C₇₉	C₂²	1	8	yes	complemented
102	#518×C₇₉	C₂²	1	8	yes	complemented
103	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
112	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
113	#14579206	—	2	16	no	—
114	C₂×#11929624	C₂³	1	4	yes	—
115	C₂×#11929624	C₂³	1	8	yes	complemented
116	C₂×#11929624	C₂³	1	8	yes	complemented
117	C₂×#11929623	C₂³	1	8	yes	—
118	C₂²×Dic₁₅₈	C₂³	1	4	yes	complemented
119	C₂²×D₃₁₆	C₂³	1	4	yes	complemented
120	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
121	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
122	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
123	C₂×D₄×D₇₉	C₂³	1	8	yes	—
124	C₂²×C₄×D₇₉	C₂³	1	8	yes	complemented
125	#14579161	C₂³	1	2	yes	complemented
126	#14579161	C₂³	1	2	yes	complemented
127	#14579161	C₂³	1	2	yes	complemented
128	#14579160	C₂³	1	8	yes	complemented
129	#14579158	C₂³	1	2	yes	complemented
130	#14579157	C₂³	1	8	yes	—
131	#14579156	C₂³	1	8	yes	complemented
132	#14579156	C₂³	1	8	yes	complemented
133	#14579155	C₂³	1	16	yes	complemented
134	#14579154	C₂³	1	8	yes	—
135	#14579154	C₂³	1	16	yes	—
136	#14579154	C₂³	1	8	yes	—
137	#14579154	C₂³	1	16	yes	complemented
138	#14579154	C₂³	1	16	yes	complemented
139	#14579153	C₂³	1	8	yes	complemented
140	#14579153	C₂³	1	4	yes	complemented
141	#14579152	C₂³	1	8	yes	complemented
142	#14579151	C₂³	1	8	yes	complemented
143	#14579151	C₂³	1	8	yes	complemented
144	#14579149	C₂³	1	8	yes	complemented
145	#14579149	C₂³	1	4	yes	complemented
146	#14579148	C₂³	1	8	yes	—
147	#14579147	C₂³	1	8	yes	—
148	#14579147	C₂³	1	16	yes	—
149	#14579147	C₂³	1	8	yes	—
150	#14579147	C₂³	1	16	yes	complemented
151	#14579147	C₂³	1	16	yes	complemented
152	#14579146	C₂³	1	8	yes	complemented
153	#14579146	C₂³	1	8	yes	complemented
154	#14579145	C₂³	1	16	yes	complemented
155	#14579144	C₂³	1	8	yes	—
156	#14579144	C₂³	1	16	yes	complemented
157	#14579144	C₂³	1	16	yes	complemented
158	#14579143	C₂³	1	8	yes	—
159	#14579143	C₂³	1	16	yes	—
160	#14579143	C₂³	1	8	yes	—
161	#14579143	C₂³	1	16	yes	complemented
162	#14579143	C₂³	1	16	yes	complemented
163	#14579142	C₂³	1	16	yes	—
164	#14579141	C₂³	1	8	yes	complemented
165	#14579140	C₂³	1	4	yes	—
166	#14579140	C₂³	1	8	yes	—
167	#14579140	C₂³	1	4	yes	—
168	#14579140	C₂³	1	4	yes	—
169	#14579140	C₂³	1	4	yes	—
170	#14579140	C₂³	1	8	yes	complemented
171	#14579140	C₂³	1	8	yes	complemented
172	#14579140	C₂³	1	8	yes	complemented
173	#14579140	C₂³	1	8	yes	complemented
174	#14579139	C₂³	1	8	yes	complemented
175	#14579139	C₂³	1	8	yes	complemented
176	#14579138	C₂³	1	16	yes	complemented
177	#14579138	C₂³	1	16	yes	complemented
178	#14579136	C₂³	1	8	yes	complemented
179	#14579135	C₂³	1	8	yes	—
180	#14579135	C₂³	1	4	yes	—
181	#14579135	C₂³	1	4	yes	—
182	#14579135	C₂³	1	4	yes	—
183	#14579135	C₂³	1	4	yes	—
184	#14579135	C₂³	1	8	yes	complemented
185	#14579135	C₂³	1	8	yes	complemented
186	#14579135	C₂³	1	8	yes	complemented
187	#14579135	C₂³	1	8	yes	complemented
188	#14579134	C₂³	1	8	yes	—
189	#14579134	C₂³	1	16	yes	—
190	#14579134	C₂³	1	8	yes	—
191	#14579134	C₂³	1	16	yes	complemented
192	#14579134	C₂³	1	16	yes	complemented
193	#14579133	C₂³	1	16	yes	—
194	#14579133	C₂³	1	16	yes	—
195	#14579132	C₂³	1	8	yes	—
196	#14579132	C₂³	1	8	yes	—
197	#14579131	C₂³	1	16	yes	complemented
198	#14579130	C₂³	1	8	yes	—
199	#14579130	C₂³	1	16	yes	—
200	#14579130	C₂³	1	16	yes	—
201	#14579130	C₂³	1	16	yes	—
202	#14579129	C₂³	1	16	yes	—
203	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
204	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
205	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
206	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
207	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
208	#14579126	C₂³	1	8	yes	complemented
209	C₄×D₃₁₆	C₂³	1	4	yes	complemented
210	C₄×D₃₁₆	C₂³	1	4	yes	complemented
211	C₄×D₃₁₆	C₂³	1	4	yes	complemented
212	C₄×D₃₁₆	C₂³	1	4	yes	complemented
213	C₄×D₃₁₆	C₂³	1	8	yes	complemented
214	D₄×Dic₇₉	C₂³	1	8	yes	—
215	D₄×Dic₇₉	C₂³	1	8	yes	—
216	#14579123	C₂³	1	8	yes	complemented
217	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
218	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
219	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
220	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
221	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
222	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
223	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
224	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
225	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
226	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
227	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
228	#14579120	C₂³	1	4	yes	—
229	#14579120	C₂³	1	8	yes	complemented
230	#14579120	C₂³	1	8	yes	complemented
231	#14579119	C₂³	1	8	yes	complemented
232	#14579118	C₂³	1	8	yes	complemented
233	#14579118	C₂³	1	16	yes	complemented
234	#14579117	C₂³	1	16	yes	complemented
235	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
236	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
237	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
238	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
239	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
240	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
241	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
242	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
243	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
244	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
245	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
246	C₂×C₄×Dic₇₉	C₂³	1	8	yes	complemented
247	C₄²×D₇₉	C₂³	1	8	yes	complemented
248	C₂⁵×C₇₉	C₂³	1	2	yes	—
249	C₂²×D₄×C₇₉	—	2	8	no	—
250	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
251	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
252	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
253	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
254	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
255	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
256	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
257	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
258	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
259	C₄×D₄×C₇₉	C₂³	1	16	yes	—
260	C₄×D₄×C₇₉	C₂³	1	8	yes	—
261	C₄×D₄×C₇₉	C₂³	1	4	yes	—
262	C₄×D₄×C₇₉	C₂³	1	4	yes	—
263	C₄×D₄×C₇₉	C₂³	1	8	yes	—
264	C₄×D₄×C₇₉	C₂³	1	4	yes	—
265	C₄×D₄×C₇₉	C₂³	1	8	yes	—
266	C₄×D₄×C₇₉	C₂³	1	8	yes	—
267	C₄×D₄×C₇₉	C₂³	1	4	yes	—
268	#117×C₇₉	C₂³	1	4	yes	—
269	#117×C₇₉	C₂³	1	4	yes	—
270	#117×C₇₉	C₂³	1	8	yes	—
271	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
278	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
281	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
282	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
284	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
285	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
288	C₂³×D₇₉	C₂⁴	1	8	yes	—
289	#11929624	—	2	16	no	—
290	#11929624	—	8	8	no	—
291	#11929624	—	8	8	no	—
292	#11929623	—	2	32	no	—
293	C₂×Dic₁₅₈	—	8	4	no	—
294	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
295	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
296	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
297	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
298	C₂×D₃₁₆	—	8	4	no	—
299	C₂×D₃₁₆	C₂⁴	1	4	yes	—
300	C₂×D₃₁₆	C₂⁴	1	4	yes	—
301	C₂×D₃₁₆	C₂⁴	1	8	yes	—
302	C₂×D₃₁₆	C₂⁴	1	4	yes	—
303	C₂×C₂²⋊D₇₉	—	2	32	no	—
304	C₂×C₂²⋊D₇₉	—	8	8	no	—
305	C₂×C₂²⋊D₇₉	—	8	8	no	—
306	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
307	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
308	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
309	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
310	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
311	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
312	D₄×D₇₉	—	2	32	no	—
313	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
314	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
315	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
316	C₂×C₄×D₇₉	—	8	8	no	—
317	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
318	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
319	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
320	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
321	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
322	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
323	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
324	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
325	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
326	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
327	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
328	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
329	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
330	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
331	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
332	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
333	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
334	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
335	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
336	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
337	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
338	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
339	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
340	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
341	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
342	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
343	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
344	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
345	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
346	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
347	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
348	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
349	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
350	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
351	C₄×Dic₇₉	C₂⁴	1	8	yes	—
352	C₄×Dic₇₉	C₂⁴	1	8	yes	—
353	C₄×Dic₇₉	C₂⁴	1	8	yes	—
354	C₄×Dic₇₉	C₂⁴	1	16	yes	—
355	C₂⁴×C₇₉	—	2	8	no	—
356	C₂⁴×C₇₉	—	8	2	no	—
357	C₂⁴×C₇₉	—	8	2	no	—
358	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
360	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
361	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
362	C₂×D₄×C₇₉	—	2	8	no	—
363	C₂×D₄×C₇₉	—	2	32	no	—
364	C₂×D₄×C₇₉	—	2	4	no	—
365	C₂×D₄×C₇₉	#41	1	8	yes	complemented
366	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
367	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
368	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₇₉	—	2	4	no	—
370	C₂²×C₄×C₇₉	—	8	2	no	—
371	C₂²×C₄×C₇₉	—	8	2	no	—
372	C₂²×C₄×C₇₉	—	8	2	no	—
373	C₂²×C₄×C₇₉	—	8	2	no	—
374	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
376	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
377	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
378	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
379	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
390	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
391	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
393	C₂²⋊C₄×C₇₉	C₂⁴	1	2	yes	—
394	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
396	C₂²⋊C₄×C₇₉	C₂⁴	1	2	yes	—
397	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
400	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
402	C₄²×C₇₉	C₂⁴	1	4	yes	—
403	C₄²×C₇₉	C₂⁴	1	8	yes	—
404	C₄²×C₇₉	C₂⁴	1	2	yes	—
405	C₄²×C₇₉	C₂⁴	1	2	yes	—
406	C₂³×C₇₉	—	2	2	no	—
407	C₂³×C₇₉	—	2	4	no	—
408	C₂³×C₇₉	—	2	16	no	—
409	C₂³×C₇₉	—	4	2	no	—
410	C₂³×C₇₉	—	4	2	no	—
411	C₂³×C₇₉	—	4	2	no	—
412	C₂³×C₇₉	—	4	2	no	—
413	C₂³×C₇₉	—	4	1	no	—
414	C₂³×C₇₉	—	4	1	no	—
415	C₂³×C₇₉	—	4	8	no	—
416	C₂³×C₇₉	—	4	8	no	—
417	C₂³×C₇₉	—	8	16	no	—
418	C₂³×C₇₉	C₂×#41	1	8	yes	—
419	C₂³×C₇₉	C₂⁵	1	2	yes	—
420	C₂³×C₇₉	C₂⁵	1	4	yes	—
421	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
422	C₂³×C₇₉	C₂⁵	1	4	yes	—
423	C₂²×D₇₉	—	2	16	no	—
424	C₂²×D₇₉	—	4	8	no	—
425	C₂²×D₇₉	—	4	8	no	—
426	C₂²×D₇₉	C₂⁵	1	8	yes	—
427	D₄×C₇₉	—	2	16	no	—
428	D₄×C₇₉	—	2	8	no	—
429	D₄×C₇₉	C₂×#41	1	16	yes	—
430	C₂×C₄×C₇₉	—	2	2	no	—
431	C₂×C₄×C₇₉	—	2	8	no	—
432	C₂×C₄×C₇₉	—	4	8	no	—
433	C₂×C₄×C₇₉	—	4	4	no	—
434	C₂×C₄×C₇₉	—	4	4	no	—
435	C₂×C₄×C₇₉	—	4	8	no	—
436	C₂×C₄×C₇₉	—	4	8	no	—
437	C₂×C₄×C₇₉	—	4	1	no	—
438	C₂×C₄×C₇₉	—	4	2	no	—
439	C₂×C₄×C₇₉	—	4	1	no	—
440	C₂×C₄×C₇₉	—	4	1	no	—
441	C₂×C₄×C₇₉	—	4	2	no	—
442	C₂×C₄×C₇₉	—	4	1	no	—
443	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
444	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
445	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
446	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
447	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
448	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
449	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
450	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
451	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
452	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
453	C₂²⋊D₇₉	—	2	32	no	—
454	C₂²⋊D₇₉	—	2	16	no	—
455	C₂²⋊D₇₉	—	4	8	no	—
456	C₂²⋊D₇₉	—	4	8	no	—
457	C₂²⋊D₇₉	—	4	16	no	—
458	C₂²⋊D₇₉	—	4	16	no	—
459	C₂×Dic₇₉	—	2	16	no	—
460	C₂×Dic₇₉	—	4	8	no	—
461	C₂×Dic₇₉	—	4	8	no	—
462	C₂×Dic₇₉	C₂⁵	1	8	yes	—
463	C₂×Dic₇₉	C₂⁵	1	8	yes	—
464	C₂×Dic₇₉	C₂⁵	1	8	yes	—
465	D₃₁₆	—	2	8	no	—
466	D₃₁₆	—	4	4	no	—
467	D₃₁₆	—	4	8	no	—
468	D₃₁₆	—	4	4	no	—
469	C₄×D₇₉	—	2	16	no	—
470	C₄×D₇₉	—	4	8	no	—
471	C₄×D₇₉	—	4	16	no	—
472	C₄×D₇₉	—	4	8	no	—
473	Dic₁₅₈	—	2	8	no	—
474	Dic₁₅₈	—	4	4	no	—
475	Dic₁₅₈	—	4	8	no	—
476	Dic₁₅₈	—	4	4	no	—
477	C₂²×C₇₉	—	2	1	no	—
478	C₂²×C₇₉	—	2	1	no	—
479	C₂²×C₇₉	—	2	4	no	—
480	C₂²×C₇₉	—	2	4	no	—
481	C₂²×C₇₉	—	2	2	no	—
482	C₂²×C₇₉	—	2	4	no	—
483	C₂²×C₇₉	—	2	4	no	—
484	C₂²×C₇₉	—	2	4	no	—
485	C₂²×C₇₉	—	2	2	no	—
486	C₂²×C₇₉	—	2	2	no	—
487	C₂²×C₇₉	—	4	8	no	—
488	C₂²×C₇₉	—	4	8	no	—
489	C₂²×C₇₉	—	4	4	no	—
490	C₂²×C₇₉	—	8	16	no	—
491	C₂²×C₇₉	C₂²×#41	1	2	yes	—
492	C₂²×C₇₉	C₂²×#41	1	8	yes	—
493	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
494	C₂×D₇₉	—	2	8	no	—
495	C₂×D₇₉	—	2	8	no	—
496	C₂×D₇₉	—	2	8	no	—
497	C₂×D₇₉	—	8	16	no	—
498	C₄×C₇₉	—	2	2	no	—
499	C₄×C₇₉	—	2	1	no	—
500	C₄×C₇₉	—	2	4	no	—
501	C₄×C₇₉	—	2	2	no	—
502	C₄×C₇₉	—	2	2	no	—
503	C₄×C₇₉	—	2	4	no	—
504	C₄×C₇₉	—	2	2	no	—
505	C₄×C₇₉	—	2	1	no	—
506	C₄×C₇₉	C₂²×#41	1	4	yes	—
507	Dic₇₉	—	2	8	no	—
508	Dic₇₉	—	2	8	no	—
509	Dic₇₉	—	2	8	no	—
510	#62846	—	79	1	no	maximal, Sylow
511	C₂×C₇₉	—	2	8	no	—
512	C₂×C₇₉	—	2	2	no	—
513	C₂×C₇₉	—	4	4	no	—
514	C₂×C₇₉	—	4	2	no	—
515	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
516	C₂×C₇₉	H(7,𝔽₂)	1	1	yes	characteristic
517	C₂×C₇₉	H(7,𝔽₂)	1	1	yes	characteristic
518	D₇₉	—	4	8	no	—
519	#3521	—	79	8	no	—
520	#3519	—	79	8	no	—
521	#3514	—	79	8	no	—
522	#3513	—	79	8	no	—
523	#3506	—	79	2	no	—
524	#3505	—	79	4	no	—
525	#3501	—	79	1	no	—
526	#3496	—	79	1	no	—
527	#3493	—	79	2	no	—
528	#3490	—	79	4	no	—
529	#3484	—	79	2	no	—
530	#3460	—	79	2	no	—
531	#3459	—	79	4	no	—
532	#3455	—	79	2	no	—
533	C₂×#538	—	79	4	no	—
534	C₄×H(5,𝔽₂)	—	79	2	no	—
535	C₂×#518	D₇₉	1	1	yes	characteristic, complemented
536	C₇₉	#62846	1	1	yes	characteristic, complemented, Sylow
537	C₂×H(5,𝔽₂)	—	79	2	no	—
538	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
539	#559	—	79	8	no	—
540	#556	—	79	4	no	—
541	#556	—	79	8	no	—
542	#555	—	79	4	no	—
543	#555	—	79	8	no	—
544	#554	—	79	4	no	—
545	#554	—	79	8	no	—
546	#553	—	79	8	no	—
547	#553	—	79	16	no	—
548	#553	—	79	8	no	—
549	#553	—	79	8	no	—
550	#552	—	79	8	no	—
551	#552	—	79	8	no	—
552	#551	—	79	16	no	—
553	#551	—	79	16	no	—
554	#551	—	79	16	no	—
555	#550	—	79	4	no	—
556	D₄×Q₈	—	79	4	no	—
557	#548	—	79	8	no	—
558	#547	—	79	4	no	—
559	#547	—	79	4	no	—
560	#546	—	79	8	no	—
561	#546	—	79	8	no	—
562	#546	—	79	8	no	—
563	#546	—	79	8	no	—
564	#546	—	79	16	no	—
565	#546	—	79	16	no	—
566	D₄²	—	79	8	no	—
567	D₄²	—	79	8	no	—
568	D₄²	—	79	4	no	—
569	#544	—	79	2	no	—
570	#543	—	79	4	no	—
571	#542	—	79	8	no	—
572	#542	—	79	4	no	—
573	#542	—	79	4	no	—
574	#541	—	79	4	no	—
575	#540	—	79	8	no	—
576	#540	—	79	4	no	—
577	#539	—	79	16	no	—
578	#539	—	79	4	no	—
579	#539	—	79	4	no	—
580	#538	—	79	16	no	—
581	#538	—	79	4	no	—
582	#538	—	79	8	no	—
583	#538	—	79	8	no	—
584	#538	—	79	8	no	—
585	#538	—	79	16	no	—
586	#538	—	79	16	no	—
587	#538	—	79	4	no	—
588	#537	—	79	2	no	—
589	#535	—	79	4	no	—
590	#534	—	79	8	no	—
591	#534	—	79	4	no	—
592	#533	—	79	2	no	—
593	#532	—	79	8	no	—
594	#532	—	79	2	no	—
595	#529	—	79	16	no	—
596	#529	—	79	8	no	—
597	#529	—	79	8	no	—
598	#529	—	79	8	no	—
599	#529	—	79	8	no	—
600	C₂×#126	—	79	8	no	—
601	C₂×#124	—	79	8	no	—
602	#525	—	79	4	no	—
603	#525	—	79	8	no	—
604	#525	—	79	8	no	—
605	#525	—	79	16	no	—
606	C₂×#123	—	79	8	no	—
607	C₂×C₂²⋊Q₈	—	79	4	no	—
608	C₂×#121	—	79	4	no	—
609	C₂×#121	—	79	8	no	—
610	C₂×#120	—	79	8	no	—
611	#520	—	79	8	no	—
612	#520	—	79	4	no	—
613	#518	—	79	2	no	—
614	#518	—	79	8	no	—
615	#518	—	79	8	no	—
616	#518	C₂×D₇₉	1	8	yes	complemented
617	#518	C₂×D₇₉	1	8	yes	complemented
618	C₄×#41	—	79	8	no	—
619	C₄×#41	—	79	4	no	—
620	C₂×C₄×D₄	—	79	8	no	—
621	C₂×C₄×D₄	—	79	8	no	—
622	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
625	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
626	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
627	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
628	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
629	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
630	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
631	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
632	C₂⁵	C₂²×D₇₉	1	2	yes	—
633	H(5,𝔽₂)	—	158	16	no	—
634	C₂×#41	—	79	8	no	—
635	C₂×#41	—	79	8	no	—
636	C₂×#41	—	79	8	no	—
637	C₂×#41	—	79	4	no	—
638	C₂²×Q₈	—	79	4	no	—
639	C₂²×D₄	—	2	8	no	—
640	C₂²×D₄	—	79	8	no	—
641	C₂²×D₄	—	79	8	no	—
642	C₂²×D₄	—	79	8	no	—
643	C₂²×D₄	—	79	8	no	—
644	C₂²×D₄	—	79	4	no	—
645	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
646	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
647	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
648	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
649	C₂³×C₄	—	79	8	no	—
650	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
651	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
652	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
653	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
654	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
655	C₄⋊Q₈	—	79	8	no	—
656	C₄⋊Q₈	—	79	2	no	—
657	C₄⋊Q₈	—	79	2	no	—
658	C₄⋊Q₈	—	79	2	no	—
659	#127	—	79	8	no	—
660	#127	—	79	2	no	—
661	#126	—	79	8	no	—
662	#126	—	79	8	no	—
663	#126	—	79	8	no	—
664	#126	—	79	16	no	—
665	#126	—	79	16	no	—
666	#126	—	79	16	no	—
667	#126	—	79	8	no	—
668	#126	—	79	16	no	—
669	#125	—	79	8	no	—
670	#125	—	79	8	no	—
671	#125	—	79	8	no	—
672	#125	—	79	8	no	—
673	#125	—	79	4	no	—
674	#124	—	79	8	no	—
675	#124	—	79	8	no	—
676	#124	—	79	16	no	—
677	#124	—	79	16	no	—
678	#124	—	79	16	no	—
679	#124	—	79	8	no	—
680	#124	—	79	8	no	—
681	#124	—	79	4	no	—
682	#123	—	79	16	no	—
683	#123	—	79	8	no	—
684	#123	—	79	16	no	—
685	#123	—	79	16	no	—
686	#123	—	79	8	no	—
687	#123	—	79	8	no	—
688	#123	—	79	8	no	—
689	#123	—	79	16	no	—
690	#123	—	79	16	no	—
691	#123	—	79	16	no	—
692	#123	—	79	16	no	—
693	#123	—	79	8	no	—
694	C₂²⋊Q₈	—	79	4	no	—
695	C₂²⋊Q₈	—	79	8	no	—
696	C₂²⋊Q₈	—	79	8	no	—
697	C₂²⋊Q₈	—	79	8	no	—
698	C₂²⋊Q₈	—	79	4	no	—
699	C₂²⋊Q₈	—	79	8	no	—
700	C₂²⋊Q₈	—	79	4	no	—
701	C₂²⋊Q₈	—	79	4	no	—
702	C₂²⋊Q₈	—	79	8	no	—
703	C₂²⋊Q₈	—	79	8	no	—
704	C₂²⋊Q₈	—	79	8	no	—
705	C₂²⋊Q₈	—	79	8	no	—
706	C₂²⋊Q₈	—	79	16	no	—
707	C₂²⋊Q₈	—	79	16	no	—
708	#121	—	79	16	no	—
709	#121	—	79	16	no	—
710	#121	—	79	8	no	—
711	#121	—	79	8	no	—
712	#121	—	79	4	no	—
713	#121	—	79	8	no	—
714	#121	—	79	8	no	—
715	#121	—	79	8	no	—
716	#121	—	79	4	no	—
717	#121	—	79	8	no	—
718	#121	—	79	8	no	—
719	#121	—	79	4	no	—
720	#121	—	79	4	no	—
721	#121	—	79	8	no	—
722	#121	—	79	8	no	—
723	#121	—	79	16	no	—
724	#121	—	79	16	no	—
725	#121	—	79	16	no	—
726	#121	—	79	8	no	—
727	#120	—	79	8	no	—
728	#120	—	79	16	no	—
729	#120	—	79	16	no	—
730	#120	—	79	16	no	—
731	#120	—	79	16	no	—
732	#120	—	79	16	no	—
733	C₄×Q₈	—	79	8	no	—
734	C₄×Q₈	—	79	4	no	—
735	C₄×Q₈	—	79	4	no	—
736	C₄×Q₈	—	79	8	no	—
737	C₄×Q₈	—	79	4	no	—
738	C₄×Q₈	—	79	4	no	—
739	C₄×D₄	—	79	8	no	—
740	C₄×D₄	—	79	8	no	—
741	C₄×D₄	—	79	8	no	—
742	C₄×D₄	—	79	16	no	—
743	C₄×D₄	—	79	16	no	—
744	C₄×D₄	—	79	16	no	—
745	C₄×D₄	—	79	8	no	—
746	C₄×D₄	—	79	16	no	—
747	C₄×D₄	—	79	8	no	—
748	C₄×D₄	—	79	8	no	—
749	C₄×D₄	—	79	16	no	—
750	C₄×D₄	—	79	8	no	—
751	C₄×D₄	—	79	16	no	—
752	C₄×D₄	—	79	16	no	—
753	C₄×D₄	—	79	4	no	—
754	C₄×D₄	—	79	4	no	—
755	C₄×D₄	—	79	8	no	—
756	C₄×D₄	—	79	4	no	—
757	C₄×D₄	—	79	4	no	—
758	C₄×D₄	C₂²×D₇₉	1	8	yes	—
759	C₄×D₄	C₂²×D₇₉	1	4	yes	—
760	C₄×D₄	C₂²×D₇₉	1	4	yes	—
761	C₄×D₄	C₂²×D₇₉	1	16	yes	—
762	C₄×D₄	C₂²×D₇₉	1	8	yes	—
763	C₄×D₄	C₂²×D₇₉	1	8	yes	—
764	C₄×D₄	C₂²×D₇₉	1	4	yes	—
765	C₄×D₄	C₂²×D₇₉	1	8	yes	—
766	C₄×D₄	C₂²×D₇₉	1	4	yes	—
767	#117	—	79	4	no	—
768	#117	—	79	8	no	—
769	#117	—	79	8	no	—
770	#117	—	79	8	no	—
771	#117	—	79	16	no	—
772	#117	—	79	8	no	—
773	#117	—	79	16	no	—
774	#117	C₂²×D₇₉	1	4	yes	—
775	#117	C₂²×D₇₉	1	4	yes	—
776	#117	C₂²×D₇₉	1	8	yes	—
777	C₂×C₄⋊C₄	—	79	8	no	—
778	C₂×C₄⋊C₄	—	79	8	no	—
779	C₂×C₄⋊C₄	—	79	4	no	—
780	C₂×C₄⋊C₄	—	79	4	no	—
781	C₂×C₄⋊C₄	—	79	8	no	—
782	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
783	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	—	79	8	no	—
787	C₂×C₂²⋊C₄	—	79	8	no	—
788	C₂×C₂²⋊C₄	—	79	8	no	—
789	C₂×C₂²⋊C₄	—	79	8	no	—
790	C₂×C₂²⋊C₄	—	79	8	no	—
791	C₂×C₂²⋊C₄	—	79	16	no	—
792	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
793	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
800	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
801	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	—
802	C₂×C₄²	—	79	8	no	—
803	C₂×C₄²	—	79	8	no	—
804	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
805	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
806	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
807	C₂⁴	—	2	8	no	—
808	C₂⁴	—	8	2	no	—
809	C₂⁴	—	8	2	no	—
810	C₂⁴	—	79	8	no	—
811	C₂⁴	C₂³×D₇₉	1	8	yes	—
812	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
813	C₂⁴	C₂³×D₇₉	1	2	yes	—
814	C₂⁴	C₂³×D₇₉	1	2	yes	—
815	#41	—	632	8	no	—
816	#41	—	632	8	no	—
817	#41	—	158	32	no	—
818	#41	—	158	16	no	—
819	C₂×Q₈	—	79	4	no	—
820	C₂×Q₈	—	79	4	no	—
821	C₂×Q₈	—	79	8	no	—
822	C₂×Q₈	—	79	4	no	—
823	C₂×Q₈	—	632	4	no	—
824	C₂×D₄	—	2	8	no	—
825	C₂×D₄	—	2	32	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	79	8	no	—
828	C₂×D₄	—	79	16	no	—
829	C₂×D₄	—	79	8	no	—
830	C₂×D₄	—	79	16	no	—
831	C₂×D₄	—	79	8	no	—
832	C₂×D₄	—	79	16	no	—
833	C₂×D₄	—	79	4	no	—
834	C₂×D₄	—	79	8	no	—
835	C₂×D₄	—	79	4	no	—
836	C₂×D₄	—	79	4	no	—
837	C₂×D₄	—	632	4	no	—
838	C₂×D₄	—	632	8	no	—
839	C₂×D₄	—	632	8	no	—
840	C₂×D₄	—	158	32	no	—
841	C₂×D₄	—	158	32	no	—
842	C₂×D₄	#11929624	1	8	yes	complemented
843	C₂×D₄	C₂³×D₇₉	1	8	yes	—
844	C₂×D₄	C₂³×D₇₉	1	4	yes	—
845	C₂×D₄	C₂³×D₇₉	1	4	yes	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	8	2	no	—
848	C₂²×C₄	—	8	2	no	—
849	C₂²×C₄	—	8	2	no	—
850	C₂²×C₄	—	8	2	no	—
851	C₂²×C₄	—	79	8	no	—
852	C₂²×C₄	—	79	8	no	—
853	C₂²×C₄	—	79	8	no	—
854	C₂²×C₄	—	79	8	no	—
855	C₂²×C₄	—	79	16	no	—
856	C₂²×C₄	—	79	8	no	—
857	C₂²×C₄	—	79	8	no	—
858	C₂²×C₄	—	632	8	no	—
859	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
860	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
861	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
862	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
863	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
864	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
865	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
866	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
867	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
868	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
869	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
870	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
871	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
872	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
873	C₄⋊C₄	—	79	16	no	—
874	C₄⋊C₄	—	79	8	no	—
875	C₄⋊C₄	—	79	8	no	—
876	C₄⋊C₄	—	79	16	no	—
877	C₄⋊C₄	—	79	8	no	—
878	C₄⋊C₄	—	79	8	no	—
879	C₄⋊C₄	—	79	8	no	—
880	C₄⋊C₄	—	79	8	no	—
881	C₄⋊C₄	—	79	4	no	—
882	C₄⋊C₄	—	79	4	no	—
883	C₄⋊C₄	—	79	4	no	—
884	C₄⋊C₄	—	79	8	no	—
885	C₄⋊C₄	—	79	8	no	—
886	C₄⋊C₄	—	79	4	no	—
887	C₄⋊C₄	—	79	4	no	—
888	C₄⋊C₄	—	79	4	no	—
889	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
890	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
891	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
892	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
893	C₄⋊C₄	C₂³×D₇₉	1	2	yes	—
894	C₂²⋊C₄	—	79	8	no	—
895	C₂²⋊C₄	—	79	16	no	—
896	C₂²⋊C₄	—	79	8	no	—
897	C₂²⋊C₄	—	79	8	no	—
898	C₂²⋊C₄	—	79	16	no	—
899	C₂²⋊C₄	—	79	16	no	—
900	C₂²⋊C₄	—	79	8	no	—
901	C₂²⋊C₄	—	79	16	no	—
902	C₂²⋊C₄	—	79	8	no	—
903	C₂²⋊C₄	—	79	8	no	—
904	C₂²⋊C₄	—	79	16	no	—
905	C₂²⋊C₄	—	79	8	no	—
906	C₂²⋊C₄	—	79	8	no	—
907	C₂²⋊C₄	—	79	8	no	—
908	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
909	C₂²⋊C₄	C₂³×D₇₉	1	2	yes	—
910	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
911	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
912	C₂²⋊C₄	C₂³×D₇₉	1	2	yes	—
913	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
914	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
915	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
916	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
917	C₄²	—	79	8	no	—
918	C₄²	—	79	8	no	—
919	C₄²	—	79	16	no	—
920	C₄²	—	79	8	no	—
921	C₄²	C₂³×D₇₉	1	4	yes	—
922	C₄²	C₂³×D₇₉	1	8	yes	—
923	C₄²	C₂³×D₇₉	1	2	yes	—
924	C₄²	C₂³×D₇₉	1	2	yes	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	16	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	2	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	1	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	8	no	—
935	C₂³	—	4	8	no	—
936	C₂³	—	8	16	no	—
937	C₂³	—	316	8	no	—
938	C₂³	—	316	8	no	—
939	C₂³	—	79	8	no	—
940	C₂³	—	158	16	no	—
941	C₂³	C₂×#11929624	1	8	yes	—
942	C₂³	C₂⁴×D₇₉	1	2	yes	—
943	C₂³	C₂⁴×D₇₉	1	4	yes	—
944	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
945	C₂³	C₂⁴×D₇₉	1	4	yes	—
946	Q₈	—	316	4	no	—
947	Q₈	—	316	8	no	—
948	Q₈	—	316	4	no	—
949	Q₈	—	158	8	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	8	no	—
952	D₄	—	316	4	no	—
953	D₄	—	316	8	no	—
954	D₄	—	316	4	no	—
955	D₄	—	316	8	no	—
956	D₄	—	316	8	no	—
957	D₄	—	316	16	no	—
958	D₄	—	316	16	no	—
959	D₄	—	158	16	no	—
960	D₄	—	158	32	no	—
961	D₄	—	158	8	no	—
962	D₄	C₂×#11929624	1	16	yes	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	2	no	—
970	C₂×C₄	—	4	1	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	4	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	8	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	316	8	no	—
977	C₂×C₄	—	316	16	no	—
978	C₂×C₄	—	316	8	no	—
979	C₂×C₄	—	316	8	no	—
980	C₂×C₄	—	316	8	no	—
981	C₂×C₄	—	79	8	no	—
982	C₂×C₄	—	79	8	no	—
983	C₂×C₄	—	79	8	no	—
984	C₂×C₄	—	158	16	no	—
985	C₂×C₄	—	158	16	no	—
986	C₂×C₄	C₂×#11929624	1	4	yes	—
987	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
988	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
989	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
990	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
991	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
992	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
993	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
994	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	8	no	—
1007	C₂²	—	4	4	no	—
1008	C₂²	—	4	8	no	—
1009	C₂²	—	8	16	no	—
1010	C₂²	—	632	16	no	—
1011	C₂²	—	158	8	no	—
1012	C₂²	—	158	8	no	—
1013	C₂²	—	158	8	no	—
1014	C₂²	C₂²×#11929624	1	2	yes	—
1015	C₂²	C₂²×#11929624	1	8	yes	—
1016	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	4	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	158	8	no	—
1026	C₄	—	158	8	no	—
1027	C₄	—	158	8	no	—
1028	C₄	C₂²×#11929624	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	4	no	—
1033	C₂	—	316	8	no	—
1034	C₂	C₂³×#11929624	1	1	yes	characteristic
1035	C₂	#23778210	1	1	yes	characteristic
1036	C₂	#23778210	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₂×#518×C₇₉	C₂
hypercenter	C₂×#518	D₇₉
hypocenter	C₇₉	#62846
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. #23777456	C₂	semidirect
2. #23777422	C₂	semidirect
3. #23777351	C₂	semidirect
4. #23777328	C₂	semidirect
5. #23777252	C₂	semidirect
6. #23777239	C₂	semidirect
7. #23777203	C₂	semidirect
8. #23777164	C₂	semidirect
9. #23777120	C₂	semidirect
10. #23777089	C₂	semidirect
11. #23777035	C₂	semidirect
12. #23776822	C₂	semidirect
13. #23776809	C₂	semidirect
14. #23776790	C₂	semidirect
15. C₂×#19099151	C₂	semidirect
16. C₄×#14579206	C₂	semidirect
17. C₂×#518×C₇₉	C₂	semidirect
19. #19099296	C₂²	semidirect
20. #19099283	C₂²	semidirect
21. #19099281	C₂²	semidirect
22. #19099278	C₂²	semidirect
23. #19099276	C₂²	semidirect
24. #19099272	C₂²	semidirect
25. #19099270	C₂²	semidirect
26. #19099263	C₂²	semidirect
27. #19099262	C₂²	semidirect
28. #19099259	C₂²	semidirect
29. #19099257	C₂²	semidirect
30. #19099253	C₂²	semidirect
31. #19099252	C₂²	semidirect
32. #19099242	C₂²	semidirect
33. #19099239	C₂²	semidirect
34. #19099239	C₂²	semidirect
35. #19099234	C₂²	semidirect
36. D₄×Dic₁₅₈	C₂²	semidirect
37. #19099222	C₂²	semidirect
38. #19099218	C₂²	semidirect
39. #19099217	C₂²	semidirect
40. #19099209	C₂²	semidirect
41. #19099208	C₂²	semidirect
42. #19099207	C₂²	semidirect
43. #19099207	C₂²	semidirect
44. #19099203	C₂²	semidirect
45. #19099203	C₂²	semidirect
46. D₄×D₃₁₆	C₂²	semidirect
47. D₄×C₂²⋊D₇₉	C₂²	semidirect
48. D₄×C₂²⋊D₇₉	C₂²	semidirect
49. #19099194	C₂²	semidirect
50. #19099189	C₂²	semidirect
51. #19099184	C₂²	semidirect
52. #19099184	C₂²	semidirect
53. #19099178	C₂²	semidirect
54. #19099175	C₂²	semidirect
55. #19099168	C₂²	semidirect
56. #19099164	C₂²	semidirect
57. #19099160	C₂²	semidirect
58. #19099160	C₂²	semidirect
59. #19099155	C₂²	semidirect
60. #19099151	C₂²	semidirect
61. #19099151	C₂²	semidirect
62. #19099151	C₂²	semidirect
63. #19099151	C₂²	semidirect
64. #19099151	C₂²	semidirect
65. #19099151	C₂²	semidirect
66. #19099151	C₂²	semidirect
67. #19099146	C₂²	semidirect
68. #19099144	C₂²	semidirect
69. #19099130	C₂²	semidirect
70. #19099125	C₂²	semidirect
71. #19099122	C₂²	semidirect
72. #19099120	C₂²	semidirect
73. #19099113	C₂²	semidirect
74. #19099110	C₂²	semidirect
75. #19099097	C₂²	semidirect
76. #19099095	C₂²	semidirect
77. #19099093	C₂²	semidirect
78. #19099091	C₂²	semidirect
79. #19099091	C₂²	semidirect
80. C₂×#14579154	C₂²	semidirect
81. C₂×#14579147	C₂²	semidirect
82. #19099074	C₂²	semidirect
83. #19099074	C₂²	semidirect
84. #19099074	C₂²	semidirect
85. #19099072	C₂²	semidirect
86. C₂×#14579143	C₂²	semidirect
87. C₂×#14579140	C₂²	semidirect
88. C₂×#14579135	C₂²	semidirect
89. C₂×#14579134	C₂²	semidirect
90. C₂×#14579130	C₂²	semidirect
91. #19099044	C₂²	semidirect
92. #19099042	C₂²	semidirect
94. #19099036	C₂²	semidirect
95. #19099035	C₂²	semidirect
96. C₄×#11929624	C₂²	semidirect
97. C₄×#11929623	C₂²	semidirect
98. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
99. C₄×D₄×D₇₉	C₂²	semidirect
101. #518×C₇₉	C₂²	semidirect
102. #518×C₇₉	C₂²	semidirect
105. C₂×C₄×D₄×C₇₉	C₂²	semidirect
106. C₂×C₄×D₄×C₇₉	C₂²	semidirect
107. C₂×C₄×D₄×C₇₉	C₂²	semidirect
108. C₂×C₄×D₄×C₇₉	C₂²	semidirect
109. C₂×#117×C₇₉	C₂²	semidirect
110. C₂×#117×C₇₉	C₂²	semidirect
111. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
112. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
115. C₂×#11929624	C₂³	semidirect
116. C₂×#11929624	C₂³	semidirect
118. C₂²×Dic₁₅₈	C₂³	semidirect
119. C₂²×D₃₁₆	C₂³	semidirect
124. C₂²×C₄×D₇₉	C₂³	semidirect
125. #14579161	C₂³	semidirect
126. #14579161	C₂³	semidirect
127. #14579161	C₂³	semidirect
128. #14579160	C₂³	semidirect
129. #14579158	C₂³	semidirect
131. #14579156	C₂³	semidirect
132. #14579156	C₂³	semidirect
133. #14579155	C₂³	semidirect
137. #14579154	C₂³	semidirect
138. #14579154	C₂³	semidirect
139. #14579153	C₂³	semidirect
140. #14579153	C₂³	semidirect
141. #14579152	C₂³	semidirect
142. #14579151	C₂³	semidirect
143. #14579151	C₂³	semidirect
144. #14579149	C₂³	semidirect
145. #14579149	C₂³	semidirect
150. #14579147	C₂³	semidirect
151. #14579147	C₂³	semidirect
152. #14579146	C₂³	semidirect
153. #14579146	C₂³	semidirect
154. #14579145	C₂³	semidirect
156. #14579144	C₂³	semidirect
157. #14579144	C₂³	semidirect
161. #14579143	C₂³	semidirect
162. #14579143	C₂³	semidirect
164. #14579141	C₂³	semidirect
170. #14579140	C₂³	semidirect
171. #14579140	C₂³	semidirect
172. #14579140	C₂³	semidirect
173. #14579140	C₂³	semidirect
174. #14579139	C₂³	semidirect
175. #14579139	C₂³	semidirect
176. #14579138	C₂³	semidirect
177. #14579138	C₂³	semidirect
178. #14579136	C₂³	semidirect
184. #14579135	C₂³	semidirect
185. #14579135	C₂³	semidirect
186. #14579135	C₂³	semidirect
187. #14579135	C₂³	semidirect
191. #14579134	C₂³	semidirect
192. #14579134	C₂³	semidirect
197. #14579131	C₂³	semidirect
203. C₄×Dic₁₅₈	C₂³	semidirect
204. C₄×Dic₁₅₈	C₂³	semidirect
205. C₄×Dic₁₅₈	C₂³	semidirect
206. C₄×Dic₁₅₈	C₂³	semidirect
207. C₄×Dic₁₅₈	C₂³	semidirect
208. #14579126	C₂³	semidirect
209. C₄×D₃₁₆	C₂³	semidirect
210. C₄×D₃₁₆	C₂³	semidirect
211. C₄×D₃₁₆	C₂³	semidirect
212. C₄×D₃₁₆	C₂³	semidirect
213. C₄×D₃₁₆	C₂³	semidirect
216. #14579123	C₂³	semidirect
222. C₄×C₂²⋊D₇₉	C₂³	semidirect
223. C₄×C₂²⋊D₇₉	C₂³	semidirect
224. C₄×C₂²⋊D₇₉	C₂³	semidirect
225. C₄×C₂²⋊D₇₉	C₂³	semidirect
226. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
227. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
229. #14579120	C₂³	semidirect
230. #14579120	C₂³	semidirect
231. #14579119	C₂³	semidirect
232. #14579118	C₂³	semidirect
233. #14579118	C₂³	semidirect
234. #14579117	C₂³	semidirect
235. C₂×C₄⋊Dic₇₉	C₂³	semidirect
236. C₂×C₄⋊Dic₇₉	C₂³	semidirect
237. C₂×Dic₇₉⋊C₄	C₂³	semidirect
238. C₂×Dic₇₉⋊C₄	C₂³	semidirect
239. C₄⋊C₄×D₇₉	C₂³	semidirect
243. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
244. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
245. C₂²⋊C₄×D₇₉	C₂³	semidirect
246. C₂×C₄×Dic₇₉	C₂³	semidirect
247. C₄²×D₇₉	C₂³	semidirect
365. C₂×D₄×C₇₉	#41	semidirect
535. C₂×#518	D₇₉	semidirect
536. C₇₉	#62846	semidirect
616. #518	C₂×D₇₉	semidirect
617. #518	C₂×D₇₉	semidirect
624. C₂×C₄×D₄	C₂×D₇₉	semidirect
625. C₂×C₄×D₄	C₂×D₇₉	semidirect
626. C₂×C₄×D₄	C₂×D₇₉	semidirect
627. C₂×C₄×D₄	C₂×D₇₉	semidirect
628. C₂×#117	C₂×D₇₉	semidirect
629. C₂×#117	C₂×D₇₉	semidirect
630. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
631. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
842. C₂×D₄	#11929624	semidirect

Maximal subgroups

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

subgroup	index
#23777456	2
#23777422	2
#23777351	2
#23777328	2
#23777252	2
#23777239	2
#23777203	2
#23777164	2
#23777120	2
#23777089	2
#23777035	2
#23776822	2
#23776809	2
#23776790	2
C₂×#19099151	2
C₄×#14579206	2
C₂×#518×C₇₉	2
#62846	79