Subgroups — #35196987

Order 20224.

7330 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777970	C₂	1	4	yes	maximal, complemented
2	#23777965	C₂	1	4	yes	maximal, complemented
3	#23777923	C₂	1	4	yes	maximal, complemented
4	#23777916	C₂	1	4	yes	maximal, complemented
5	#23777752	C₂	1	8	yes	maximal, complemented
6	#23777361	C₂	1	8	yes	maximal, complemented
7	#23777349	C₂	1	8	yes	maximal, complemented
8	#23777298	C₂	1	2	yes	maximal, complemented
9	#23777296	C₂	1	2	yes	maximal, complemented
10	#23777193	C₂	1	2	yes	maximal, complemented
11	#23777187	C₂	1	2	yes	maximal, complemented
12	#23777083	C₂	1	8	yes	maximal, complemented
13	#23777047	C₂	1	2	yes	maximal, complemented
14	#23777033	C₂	1	2	yes	maximal, complemented
15	#23776696	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#14579149	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14579208	C₂²	1	2	yes	complemented
19	C₂×#14579207	C₂²	1	2	yes	complemented
20	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
22	#19099317	C₂²	1	8	yes	complemented
23	#19099311	C₂²	1	8	yes	complemented
24	#19099307	C₂²	1	8	yes	complemented
25	#19099305	C₂²	1	8	yes	complemented
26	#19099298	C₂²	1	8	yes	complemented
27	#19099296	C₂²	1	8	yes	complemented
28	#19099286	C₂²	1	8	yes	complemented
29	#19099285	C₂²	1	8	yes	complemented
30	#19099276	C₂²	1	16	yes	complemented
31	#19099242	C₂²	1	16	yes	complemented
32	#19099240	C₂²	1	16	yes	complemented
33	#19099237	C₂²	1	16	yes	complemented
34	#19099237	C₂²	1	16	yes	complemented
35	#19099236	C₂²	1	16	yes	complemented
36	D₄×Dic₁₅₈	C₂²	1	8	yes	complemented
37	#19099226	C₂²	1	8	yes	complemented
38	#19099225	C₂²	1	8	yes	complemented
39	#19099222	C₂²	1	8	yes	complemented
40	#19099222	C₂²	1	8	yes	complemented
41	#19099219	C₂²	1	8	yes	complemented
42	#19099209	C₂²	1	8	yes	complemented
43	#19099209	C₂²	1	8	yes	complemented
44	#19099208	C₂²	1	16	yes	complemented
45	#19099208	C₂²	1	8	yes	complemented
46	#19099205	C₂²	1	16	yes	complemented
47	#19099204	C₂²	1	8	yes	complemented
48	#19099202	C₂²	1	16	yes	complemented
49	#19099201	C₂²	1	16	yes	complemented
50	D₄×D₃₁₆	C₂²	1	8	yes	complemented
51	#19099197	C₂²	1	8	yes	complemented
52	#19099188	C₂²	1	8	yes	complemented
53	#19099187	C₂²	1	8	yes	complemented
54	#19099185	C₂²	1	16	yes	complemented
55	#19099184	C₂²	1	8	yes	complemented
56	#19099179	C₂²	1	16	yes	complemented
57	#19099153	C₂²	1	8	yes	complemented
58	#19099152	C₂²	1	16	yes	complemented
59	#19099150	C₂²	1	8	yes	complemented
60	#19099146	C₂²	1	16	yes	complemented
61	#19099146	C₂²	1	16	yes	complemented
62	#19099139	C₂²	1	2	yes	complemented
63	#19099139	C₂²	1	4	yes	complemented
64	#19099138	C₂²	1	4	yes	complemented
65	#19099135	C₂²	1	8	yes	complemented
66	#19099134	C₂²	1	2	yes	complemented
67	#19099132	C₂²	1	2	yes	—
68	#19099132	C₂²	1	4	yes	complemented
69	#19099127	C₂²	1	2	yes	—
70	#19099126	C₂²	1	4	yes	complemented
71	#19099124	C₂²	1	8	yes	complemented
72	#19099121	C₂²	1	8	yes	complemented
73	#19099120	C₂²	1	1	yes	characteristic, complemented
74	#19099120	C₂²	1	2	yes	complemented
75	#19099113	C₂²	1	2	yes	complemented
76	#19099113	C₂²	1	1	yes	characteristic, complemented
77	#19099113	C₂²	1	4	yes	complemented
78	#19099112	C₂²	1	4	yes	complemented
79	#19099098	C₂²	1	8	yes	complemented
80	#19099097	C₂²	1	4	yes	complemented
81	#19099097	C₂²	1	4	yes	complemented
82	#19099097	C₂²	1	4	yes	complemented
83	#19099097	C₂²	1	8	yes	complemented
84	C₂×#14579149	C₂²	1	2	yes	complemented
85	C₂×#14579149	C₂²	1	2	yes	complemented
86	C₂×#14579149	C₂²	1	4	yes	complemented
87	C₂×#14579149	C₂²	1	4	yes	complemented
88	C₂×#14579149	C₂²	1	4	yes	complemented
89	C₂×#14579149	C₂²	1	4	yes	complemented
90	C₂×#14579149	C₂²	1	4	yes	complemented
91	C₂×#14579149	C₂²	1	4	yes	complemented
92	#124×D₇₉	C₂²	1	4	yes	complemented
93	#19099074	C₂²	1	2	yes	complemented
94	#19099074	C₂²	1	4	yes	complemented
95	#19099069	C₂²	1	8	yes	complemented
96	#120×D₇₉	C₂²	1	8	yes	complemented
97	#19099040	C₂²	1	2	yes	complemented
98	#19099037	C₂²	1	2	yes	complemented
99	#19099035	C₂²	1	16	yes	complemented
100	C₄×#11929624	C₂²	1	2	yes	complemented
101	C₄×#11929624	C₂²	1	4	yes	complemented
102	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
103	#533×C₇₉	C₂²	1	1	yes	characteristic, complemented
104	#533×C₇₉	C₂²	1	2	yes	complemented
105	#532×C₇₉	C₂²	1	2	yes	complemented
106	#532×C₇₉	C₂²	1	1	yes	characteristic, complemented
107	#529×C₇₉	C₂²	1	4	yes	complemented
108	#529×C₇₉	C₂²	1	4	yes	complemented
109	#529×C₇₉	C₂²	1	4	yes	complemented
110	#525×C₇₉	C₂²	1	2	yes	complemented
111	#525×C₇₉	C₂²	1	4	yes	complemented
112	C₄×#41×C₇₉	C₂²	1	2	yes	complemented
113	C₄×#41×C₇₉	C₂²	1	4	yes	complemented
114	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	C₂⁴×D₇₉	C₂³	1	2	yes	—
116	#14579208	—	4	8	no	—
117	#14579207	—	4	8	no	—
118	C₂×#11929625	C₂³	1	4	yes	—
119	C₂×#11929624	C₂³	1	2	yes	—
120	C₂×#11929624	C₂³	1	4	yes	—
121	C₂×#11929624	C₂³	1	4	yes	—
122	C₂×#11929624	C₂³	1	4	yes	complemented
123	C₂×#11929623	C₂³	1	8	yes	—
124	C₂×#11929623	C₂³	1	4	yes	complemented
125	C₂²×Dic₁₅₈	—	4	4	no	—
126	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
127	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
128	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
129	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
130	C₂²×Dic₁₅₈	C₂³	1	4	yes	complemented
131	C₂×Q₈×D₇₉	C₂³	1	4	yes	complemented
132	C₂²×D₃₁₆	—	4	4	no	—
133	C₂²×D₃₁₆	C₂³	1	2	yes	—
134	C₂²×D₃₁₆	C₂³	1	4	yes	—
135	C₂²×D₃₁₆	C₂³	1	4	yes	—
136	C₂²×D₃₁₆	C₂³	1	4	yes	—
137	C₂²×D₃₁₆	C₂³	1	2	yes	—
138	C₂×D₄×D₇₉	C₂³	1	4	yes	—
139	C₂×D₄×D₇₉	C₂³	1	8	yes	—
140	C₂×D₄×D₇₉	C₂³	1	16	yes	—
141	C₂³×Dic₇₉	C₂³	1	2	yes	—
142	#14579161	C₂³	1	1	yes	characteristic, complemented
143	#14579161	C₂³	1	4	yes	complemented
144	#14579161	C₂³	1	2	yes	complemented
145	#14579160	C₂³	1	16	yes	complemented
146	#14579159	C₂³	1	4	yes	complemented
147	#14579158	C₂³	1	4	yes	—
148	#14579158	C₂³	1	1	yes	characteristic, complemented
149	#14579157	C₂³	1	4	yes	—
150	#14579156	C₂³	1	16	yes	complemented
151	#14579156	C₂³	1	16	yes	complemented
152	#14579156	C₂³	1	16	yes	complemented
153	#14579155	C₂³	1	8	yes	complemented
154	#14579155	C₂³	1	16	yes	complemented
155	#14579153	C₂³	1	4	yes	complemented
156	#14579153	C₂³	1	2	yes	complemented
157	#14579150	C₂³	1	4	yes	—
158	#14579150	C₂³	1	16	yes	complemented
159	#14579149	C₂³	1	4	yes	—
160	#14579149	C₂³	1	4	yes	—
161	#14579149	C₂³	1	4	yes	—
162	#14579149	C₂³	1	8	yes	—
163	#14579149	C₂³	1	8	yes	—
164	#14579149	C₂³	1	8	yes	—
165	#14579149	C₂³	1	8	yes	—
166	#14579149	C₂³	1	8	yes	—
167	#14579149	C₂³	1	8	yes	—
168	#14579149	C₂³	1	4	yes	—
169	#14579149	C₂³	1	4	yes	—
170	#14579149	C₂³	1	4	yes	complemented
171	#14579149	C₂³	1	16	yes	complemented
172	#14579149	C₂³	1	4	yes	complemented
173	#14579149	C₂³	1	2	yes	complemented
174	#14579148	C₂³	1	4	yes	complemented
175	#14579147	C₂³	1	16	yes	complemented
176	#14579147	C₂³	1	16	yes	complemented
177	#14579147	C₂³	1	16	yes	complemented
178	#14579146	C₂³	1	16	yes	—
179	#14579146	C₂³	1	16	yes	complemented
180	#14579146	C₂³	1	16	yes	complemented
181	#14579146	C₂³	1	16	yes	complemented
182	#14579145	C₂³	1	8	yes	—
183	#14579145	C₂³	1	16	yes	complemented
184	#14579144	C₂³	1	8	yes	—
185	#14579144	C₂³	1	4	yes	—
186	#14579144	C₂³	1	16	yes	complemented
187	#14579143	C₂³	1	16	yes	complemented
188	#14579142	C₂³	1	8	yes	—
189	#14579141	C₂³	1	16	yes	complemented
190	#14579141	C₂³	1	8	yes	complemented
191	#14579140	C₂³	1	4	yes	—
192	#14579140	C₂³	1	4	yes	—
193	#14579140	C₂³	1	4	yes	—
194	#14579140	C₂³	1	8	yes	complemented
195	#14579139	C₂³	1	16	yes	complemented
196	#14579139	C₂³	1	16	yes	complemented
197	#14579139	C₂³	1	16	yes	complemented
198	#14579138	C₂³	1	16	yes	—
199	#14579138	C₂³	1	16	yes	complemented
200	#14579137	C₂³	1	16	yes	complemented
201	#14579136	C₂³	1	16	yes	—
202	#14579136	C₂³	1	8	yes	—
203	#14579136	C₂³	1	16	yes	complemented
204	#14579135	C₂³	1	4	yes	—
205	#14579135	C₂³	1	8	yes	—
206	#14579135	C₂³	1	4	yes	—
207	#14579135	C₂³	1	4	yes	—
208	#14579135	C₂³	1	16	yes	complemented
209	#14579134	C₂³	1	16	yes	—
210	#14579134	C₂³	1	16	yes	complemented
211	#14579133	C₂³	1	16	yes	—
212	#14579133	C₂³	1	16	yes	complemented
213	#14579131	C₂³	1	16	yes	—
214	#14579131	C₂³	1	16	yes	—
215	#14579131	C₂³	1	8	yes	—
216	#14579131	C₂³	1	16	yes	complemented
217	#14579130	C₂³	1	4	yes	—
218	#14579129	C₂³	1	16	yes	—
219	#14579129	C₂³	1	8	yes	—
220	#14579129	C₂³	1	16	yes	complemented
221	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
222	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
223	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
224	C₄×Dic₁₅₈	C₂³	1	4	yes	complemented
225	#14579126	C₂³	1	8	yes	complemented
226	C₄×D₃₁₆	C₂³	1	8	yes	—
227	C₄×D₃₁₆	C₂³	1	4	yes	complemented
228	C₄×D₃₁₆	C₂³	1	16	yes	complemented
229	C₄×D₃₁₆	C₂³	1	4	yes	complemented
230	C₄×D₃₁₆	C₂³	1	4	yes	complemented
231	D₄×Dic₇₉	C₂³	1	16	yes	—
232	#14579123	C₂³	1	8	yes	—
233	#14579123	C₂³	1	16	yes	complemented
234	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
235	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
236	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
237	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
238	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	—
239	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	complemented
240	#14579120	C₂³	1	4	yes	—
241	#14579120	C₂³	1	2	yes	—
242	#14579119	C₂³	1	16	yes	complemented
243	#14579118	C₂³	1	4	yes	complemented
244	#14579118	C₂³	1	16	yes	complemented
245	#14579118	C₂³	1	8	yes	complemented
246	#14579117	C₂³	1	8	yes	—
247	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
248	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
249	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
250	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
251	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
252	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
253	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
254	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
255	C₂²⋊C₄×D₇₉	C₂³	1	8	yes	—
256	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
257	C₄²×D₇₉	C₂³	1	4	yes	complemented
258	C₂×#41×C₇₉	C₂³	1	2	yes	—
259	C₂×#41×C₇₉	C₂³	1	4	yes	—
260	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
261	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
262	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic, complemented
263	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	complemented
264	#127×C₇₉	C₂³	1	1	yes	characteristic, complemented
265	#126×C₇₉	C₂³	1	8	yes	complemented
266	#125×C₇₉	C₂³	1	4	yes	complemented
267	#125×C₇₉	C₂³	1	2	yes	complemented
268	#124×C₇₉	C₂³	1	4	yes	complemented
269	#124×C₇₉	C₂³	1	2	yes	complemented
270	#123×C₇₉	C₂³	1	8	yes	—
271	#123×C₇₉	C₂³	1	4	yes	—
272	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
273	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
274	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
275	#121×C₇₉	C₂³	1	4	yes	—
276	#121×C₇₉	C₂³	1	4	yes	—
277	#121×C₇₉	C₂³	1	4	yes	—
278	#120×C₇₉	C₂³	1	4	yes	—
279	C₄×Q₈×C₇₉	C₂³	1	4	yes	complemented
280	C₄×Q₈×C₇₉	C₂³	1	4	yes	complemented
281	C₄×Q₈×C₇₉	C₂³	1	4	yes	complemented
282	C₄×D₄×C₇₉	C₂³	1	8	yes	—
283	C₄×D₄×C₇₉	C₂³	1	8	yes	—
284	C₄×D₄×C₇₉	C₂³	1	8	yes	—
285	C₄×D₄×C₇₉	C₂³	1	4	yes	complemented
286	C₄×D₄×C₇₉	C₂³	1	4	yes	complemented
287	C₄×D₄×C₇₉	C₂³	1	4	yes	complemented
288	#117×C₇₉	C₂³	1	2	yes	—
289	#117×C₇₉	C₂³	1	4	yes	—
290	#117×C₇₉	C₂³	1	4	yes	complemented
291	#117×C₇₉	C₂³	1	8	yes	complemented
292	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
293	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
295	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
296	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
297	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
299	C₂×C₄²×C₇₉	C₂³	1	4	yes	complemented
300	C₂³×D₇₉	—	4	8	no	—
301	C₂³×D₇₉	—	4	4	no	—
302	C₂³×D₇₉	C₂⁴	1	4	yes	—
303	C₂³×D₇₉	C₂⁴	1	8	yes	—
304	C₂³×D₇₉	C₂⁴	1	8	yes	—
305	#11929625	—	4	8	no	—
306	#11929624	—	2	8	no	—
307	#11929624	—	4	8	no	—
308	#11929624	—	4	8	no	—
309	#11929624	—	4	8	no	—
310	#11929623	—	4	16	no	—
311	#11929623	—	4	8	no	—
312	C₂×Dic₁₅₈	—	2	8	no	—
313	C₂×Dic₁₅₈	—	4	8	no	—
314	C₂×Dic₁₅₈	—	4	8	no	—
315	C₂×Dic₁₅₈	—	4	8	no	—
316	C₂×Dic₁₅₈	—	4	4	no	—
317	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
318	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
319	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
320	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
321	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
322	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
323	Q₈×D₇₉	—	4	8	no	—
324	C₂×D₃₁₆	—	2	8	no	—
325	C₂×D₃₁₆	—	4	4	no	—
326	C₂×D₃₁₆	—	4	8	no	—
327	C₂×D₃₁₆	—	4	8	no	—
328	C₂×D₃₁₆	—	4	8	no	—
329	C₂×D₃₁₆	C₂⁴	1	2	yes	—
330	C₂×D₃₁₆	C₂⁴	1	4	yes	—
331	C₂×D₃₁₆	C₂⁴	1	4	yes	—
332	C₂×D₃₁₆	C₂⁴	1	4	yes	—
333	C₂×D₃₁₆	C₂⁴	1	8	yes	—
334	C₂×D₃₁₆	C₂⁴	1	16	yes	—
335	C₂×D₃₁₆	C₂⁴	1	8	yes	—
336	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
337	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
338	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
339	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
340	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
341	D₄×D₇₉	—	4	16	no	—
342	D₄×D₇₉	—	4	32	no	—
343	D₄×D₇₉	—	4	8	no	—
344	C₂²×Dic₇₉	—	4	4	no	—
345	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
346	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
347	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
348	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
349	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
350	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
351	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
352	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
353	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
354	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
355	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
356	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
357	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
358	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
359	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
360	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
361	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
362	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
363	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
364	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
365	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
366	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
367	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
368	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
369	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
370	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
371	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
372	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
373	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
374	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
375	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
376	C₄×Dic₇₉	C₂⁴	1	8	yes	—
377	C₄×Dic₇₉	C₂⁴	1	4	yes	—
378	C₄×Dic₇₉	C₂⁴	1	16	yes	—
379	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
380	#41×C₇₉	—	2	8	no	—
381	#41×C₇₉	—	4	8	no	—
382	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
383	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
384	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
385	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
386	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
387	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₇₉	—	2	4	no	—
389	C₂²×C₄×C₇₉	—	4	4	no	—
390	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
394	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
401	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
403	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
404	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
406	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
407	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
409	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
411	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
413	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
414	C₄²×C₇₉	C₂⁴	1	2	yes	—
415	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
416	C₄²×C₇₉	C₂⁴	1	2	yes	—
417	C₄²×C₇₉	C₂⁴	1	2	yes	—
418	C₄²×C₇₉	C₂⁴	1	2	yes	—
419	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
420	C₄²×C₇₉	C₂⁴	1	2	yes	—
421	C₄²×C₇₉	C₂⁴	1	2	yes	—
422	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
423	C₄²×C₇₉	C₂⁴	1	8	yes	—
424	C₄²×C₇₉	C₂⁴	1	4	yes	—
425	C₂³×C₇₉	—	2	2	no	—
426	C₂³×C₇₉	—	2	4	no	—
427	C₂³×C₇₉	C₂⁵	1	4	yes	—
428	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
429	C₂³×C₇₉	C₂⁵	1	2	yes	—
430	C₂²×D₇₉	—	2	8	no	—
431	C₂²×D₇₉	—	2	16	no	—
432	C₂²×D₇₉	—	4	8	no	—
433	C₂²×D₇₉	—	4	8	no	—
434	C₂²×D₇₉	—	4	8	no	—
435	C₂²×D₇₉	—	4	8	no	—
436	C₂²×D₇₉	—	4	16	no	—
437	C₂²×D₇₉	—	8	16	no	—
438	C₂²×D₇₉	C₂⁵	1	8	yes	—
439	C₂²×D₇₉	C₂⁵	1	4	yes	—
440	Q₈×C₇₉	—	2	4	no	—
441	Q₈×C₇₉	—	4	4	no	—
442	D₄×C₇₉	—	2	8	no	—
443	D₄×C₇₉	—	2	16	no	—
444	D₄×C₇₉	—	2	4	no	—
445	D₄×C₇₉	—	4	4	no	—
446	C₂×C₄×C₇₉	—	2	2	no	—
447	C₂×C₄×C₇₉	—	2	4	no	—
448	C₂×C₄×C₇₉	—	2	4	no	—
449	C₂×C₄×C₇₉	—	2	4	no	—
450	C₂×C₄×C₇₉	—	2	4	no	—
451	C₂×C₄×C₇₉	—	2	8	no	—
452	C₂×C₄×C₇₉	—	4	2	no	—
453	C₂×C₄×C₇₉	—	4	2	no	—
454	C₂×C₄×C₇₉	—	4	2	no	—
455	C₂×C₄×C₇₉	—	4	2	no	—
456	C₂×C₄×C₇₉	—	4	8	no	—
457	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
458	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
459	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
460	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
461	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
462	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
463	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
464	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
465	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
466	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
467	C₂²⋊D₇₉	—	2	8	no	—
468	C₂²⋊D₇₉	—	2	16	no	—
469	C₂²⋊D₇₉	—	4	8	no	—
470	C₂²⋊D₇₉	—	4	16	no	—
471	C₂²⋊D₇₉	—	4	8	no	—
472	C₂×Dic₇₉	—	2	8	no	—
473	C₂×Dic₇₉	—	4	8	no	—
474	C₂×Dic₇₉	—	4	8	no	—
475	C₂×Dic₇₉	C₂⁵	1	8	yes	—
476	C₂×Dic₇₉	C₂⁵	1	8	yes	—
477	C₂×Dic₇₉	C₂⁵	1	4	yes	—
478	D₃₁₆	—	2	8	no	—
479	D₃₁₆	—	2	8	no	—
480	D₃₁₆	—	2	4	no	—
481	D₃₁₆	—	4	8	no	—
482	D₃₁₆	—	4	16	no	—
483	D₃₁₆	—	4	8	no	—
484	D₃₁₆	—	4	4	no	—
485	C₄×D₇₉	—	2	8	no	—
486	C₄×D₇₉	—	4	16	no	—
487	C₄×D₇₉	—	4	8	no	—
488	C₄×D₇₉	—	4	8	no	—
489	C₄×D₇₉	—	4	8	no	—
490	Dic₁₅₈	—	2	8	no	—
491	Dic₁₅₈	—	2	8	no	—
492	Dic₁₅₈	—	2	4	no	—
493	Dic₁₅₈	—	4	8	no	—
494	Dic₁₅₈	—	4	8	no	—
495	Dic₁₅₈	—	4	4	no	—
496	C₂²×C₇₉	—	2	8	no	—
497	C₂²×C₇₉	—	2	2	no	—
498	C₂²×C₇₉	—	2	2	no	—
499	C₂²×C₇₉	—	2	2	no	—
500	C₂²×C₇₉	—	2	4	no	—
501	C₂²×C₇₉	—	2	8	no	—
502	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
503	C₂²×C₇₉	#585	1	4	yes	—
504	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
505	C₂×D₇₉	—	2	4	no	—
506	C₂×D₇₉	—	2	8	no	—
507	C₂×D₇₉	—	2	8	no	—
508	C₂×D₇₉	—	2	16	no	—
509	C₂×D₇₉	—	8	8	no	—
510	C₂×D₇₉	—	8	16	no	—
511	C₂×D₇₉	—	16	8	no	—
512	C₄×C₇₉	—	2	2	no	—
513	C₄×C₇₉	—	2	4	no	—
514	C₄×C₇₉	—	2	2	no	—
515	C₄×C₇₉	—	2	2	no	—
516	C₄×C₇₉	—	2	2	no	—
517	C₄×C₇₉	—	2	2	no	—
518	C₄×C₇₉	—	2	8	no	—
519	C₄×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
520	C₄×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
521	Dic₇₉	—	2	4	no	—
522	Dic₇₉	—	2	8	no	—
523	Dic₇₉	—	2	8	no	—
524	#62824	—	79	1	no	maximal, Sylow
525	C₂×C₇₉	—	2	2	no	—
526	C₂×C₇₉	—	2	4	no	—
527	C₂×C₇₉	—	4	4	no	—
528	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂×C₇₉	C₂×#585	1	2	yes	—
530	D₇₉	—	4	8	no	—
531	D₇₉	—	4	4	no	—
532	#3561	—	79	4	no	—
533	#3561	—	79	4	no	—
534	#3558	—	79	4	no	—
535	#3558	—	79	4	no	—
536	#3545	—	79	8	no	—
537	#3514	—	79	8	no	—
538	#3514	—	79	8	no	—
539	#3510	—	79	2	no	—
540	#3510	—	79	2	no	—
541	#3500	—	79	2	no	—
542	#3500	—	79	2	no	—
543	#3490	—	79	8	no	—
544	#3486	—	79	2	no	—
545	#3484	—	79	2	no	—
546	#3444	—	79	1	no	—
547	#3444	D₇₉	1	1	yes	characteristic, complemented
548	C₂²×#124	—	79	1	no	—
549	C₇₉	#62824	1	1	yes	characteristic, complemented, Sylow
550	C₂×2₋¹⁺⁴	—	79	2	no	—
551	C₂×H(5,𝔽₂)	—	79	2	no	—
552	C₂³×Q₈	—	79	1	no	—
553	C₂³×D₄	—	79	1	no	—
554	#563	—	79	8	no	—
555	#562	—	79	8	no	—
556	#562	—	79	8	no	—
557	H(3,𝔽₄)	—	79	8	no	—
558	#559	—	79	8	no	—
559	#559	—	79	8	no	—
560	#556	—	79	8	no	—
561	#556	—	79	8	no	—
562	#555	—	79	16	no	—
563	#551	—	79	16	no	—
564	#551	—	79	16	no	—
565	#551	—	79	16	no	—
566	#551	—	79	16	no	—
567	#551	—	79	16	no	—
568	D₄×Q₈	—	79	8	no	—
569	D₄×Q₈	—	79	8	no	—
570	#548	—	79	8	no	—
571	#548	—	79	8	no	—
572	#548	—	79	8	no	—
573	#548	—	79	8	no	—
574	#546	—	79	16	no	—
575	#546	—	79	16	no	—
576	#546	—	79	8	no	—
577	#546	—	79	16	no	—
578	#546	—	79	16	no	—
579	#546	—	79	8	no	—
580	#546	—	79	8	no	—
581	#546	—	79	8	no	—
582	D₄²	—	79	8	no	—
583	D₄²	—	79	8	no	—
584	#543	—	79	8	no	—
585	#542	—	79	8	no	—
586	#542	—	79	16	no	—
587	#542	—	79	16	no	—
588	#542	—	79	8	no	—
589	#538	—	79	16	no	—
590	#538	—	79	8	no	—
591	#538	—	79	8	no	—
592	#538	—	79	16	no	—
593	#538	—	79	16	no	—
594	#536	—	79	2	no	—
595	#536	—	79	4	no	—
596	#536	—	79	8	no	—
597	#536	—	79	2	no	—
598	#536	—	79	4	no	—
599	#535	—	79	2	no	—
600	#535	—	79	4	no	—
601	#535	—	79	2	no	—
602	#535	—	79	4	no	—
603	#534	—	79	8	no	—
604	#534	—	79	8	no	—
605	#533	—	79	1	no	—
606	#533	—	79	2	no	—
607	#533	C₂×D₇₉	1	1	yes	characteristic, complemented
608	#533	C₂×D₇₉	1	2	yes	complemented
609	#532	—	79	4	no	—
610	#532	—	79	1	no	—
611	#532	—	79	2	no	—
612	#532	—	79	4	no	—
613	#532	C₂×D₇₉	1	1	yes	characteristic, complemented
614	#532	C₂×D₇₉	1	2	yes	complemented
615	#529	—	79	8	no	—
616	#529	—	79	4	no	—
617	#529	—	79	4	no	—
618	#529	—	79	4	no	—
619	#529	—	79	8	no	—
620	#529	C₂×D₇₉	1	4	yes	complemented
621	#529	C₂×D₇₉	1	4	yes	complemented
622	#529	C₂×D₇₉	1	4	yes	complemented
623	C₂×#124	—	79	4	no	—
624	C₂×#124	—	79	2	no	—
625	C₂×#124	—	79	2	no	—
626	C₂×#124	—	79	4	no	—
627	C₂×#124	—	79	4	no	—
628	C₂×#124	—	79	4	no	—
629	C₂×#124	—	79	4	no	—
630	C₂×#124	—	79	4	no	—
631	C₂×#124	—	79	4	no	—
632	#525	—	79	2	no	—
633	#525	—	79	4	no	—
634	#525	—	79	8	no	—
635	#525	C₂×D₇₉	1	2	yes	complemented
636	#525	C₂×D₇₉	1	4	yes	complemented
637	C₂×#120	—	79	8	no	—
638	#519	—	79	2	no	—
639	#518	—	79	16	no	—
640	#518	—	79	2	no	—
641	C₄×#41	—	79	2	no	—
642	C₄×#41	—	79	4	no	—
643	C₄×#41	C₂×D₇₉	1	2	yes	complemented
644	C₄×#41	C₂×D₇₉	1	4	yes	complemented
645	C₂²×C₂²⋊C₄	—	79	4	no	—
646	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
647	C₂⁵	—	79	2	no	—
648	2₋¹⁺⁴	—	316	8	no	—
649	H(5,𝔽₂)	—	316	8	no	—
650	C₂×#41	—	79	4	no	—
651	C₂×#41	—	79	8	no	—
652	C₂×#41	—	79	4	no	—
653	C₂×#41	—	79	4	no	—
654	C₂×#41	—	79	4	no	—
655	C₂×#41	—	79	4	no	—
656	C₂×#41	—	79	2	no	—
657	C₂×#41	C₂²×D₇₉	1	2	yes	—
658	C₂×#41	C₂²×D₇₉	1	4	yes	—
659	C₂²×Q₈	—	316	4	no	—
660	C₂²×Q₈	—	79	4	no	—
661	C₂²×Q₈	—	79	2	no	—
662	C₂²×Q₈	—	79	4	no	—
663	C₂²×Q₈	—	79	4	no	—
664	C₂²×Q₈	—	79	4	no	—
665	C₂²×Q₈	—	79	2	no	—
666	C₂²×D₄	—	316	4	no	—
667	C₂²×D₄	—	79	16	no	—
668	C₂²×D₄	—	79	8	no	—
669	C₂²×D₄	—	79	4	no	—
670	C₂²×D₄	—	79	2	no	—
671	C₂²×D₄	—	79	4	no	—
672	C₂²×D₄	—	79	4	no	—
673	C₂²×D₄	—	79	4	no	—
674	C₂²×D₄	—	79	2	no	—
675	C₂³×C₄	—	79	2	no	—
676	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
677	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
678	C₄⋊Q₈	—	79	4	no	—
679	C₄⋊Q₈	—	79	16	no	—
680	C₄⋊Q₈	—	79	1	no	—
681	C₄⋊Q₈	—	79	2	no	—
682	C₄⋊Q₈	—	79	4	no	—
683	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic, complemented
684	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	complemented
685	#127	—	79	4	no	—
686	#127	—	79	1	no	—
687	#127	—	79	4	no	—
688	#127	C₂²×D₇₉	1	1	yes	characteristic, complemented
689	#126	—	79	16	no	—
690	#126	—	79	16	no	—
691	#126	—	79	16	no	—
692	#126	—	79	8	no	—
693	#126	—	79	16	no	—
694	#126	C₂²×D₇₉	1	8	yes	complemented
695	#125	—	79	2	no	—
696	#125	—	79	4	no	—
697	#125	C₂²×D₇₉	1	2	yes	complemented
698	#125	C₂²×D₇₉	1	4	yes	complemented
699	#124	—	79	4	no	—
700	#124	—	79	16	no	—
701	#124	—	79	4	no	—
702	#124	—	79	16	no	—
703	#124	—	79	16	no	—
704	#124	—	79	16	no	—
705	#124	—	79	4	no	—
706	#124	—	79	4	no	—
707	#124	—	79	4	no	—
708	#124	—	79	4	no	—
709	#124	—	79	8	no	—
710	#124	—	79	8	no	—
711	#124	—	79	8	no	—
712	#124	—	79	8	no	—
713	#124	—	79	8	no	—
714	#124	—	79	8	no	—
715	#124	—	79	2	no	—
716	#124	—	79	4	no	—
717	#124	—	79	4	no	—
718	#124	—	79	16	no	—
719	#124	—	79	4	no	—
720	#124	C₂²×D₇₉	1	2	yes	complemented
721	#124	C₂²×D₇₉	1	4	yes	complemented
722	#123	—	79	8	no	—
723	#123	—	79	4	no	—
724	#123	—	79	8	no	—
725	#123	—	79	16	no	—
726	#123	—	79	16	no	—
727	#123	—	79	16	no	—
728	#123	—	79	16	no	—
729	#123	—	79	16	no	—
730	#123	—	79	8	no	—
731	#123	—	79	16	no	—
732	#123	—	79	16	no	—
733	#123	C₂²×D₇₉	1	4	yes	—
734	#123	C₂²×D₇₉	1	8	yes	—
735	C₂²⋊Q₈	—	79	16	no	—
736	C₂²⋊Q₈	—	79	4	no	—
737	C₂²⋊Q₈	—	79	4	no	—
738	C₂²⋊Q₈	—	79	4	no	—
739	C₂²⋊Q₈	—	79	8	no	—
740	C₂²⋊Q₈	—	79	8	no	—
741	C₂²⋊Q₈	—	79	16	no	—
742	C₂²⋊Q₈	—	79	16	no	—
743	C₂²⋊Q₈	—	79	16	no	—
744	C₂²⋊Q₈	—	79	16	no	—
745	C₂²⋊Q₈	—	79	16	no	—
746	C₂²⋊Q₈	—	79	16	no	—
747	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
748	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
749	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
750	#121	—	79	16	no	—
751	#121	—	79	16	no	—
752	#121	—	79	4	no	—
753	#121	—	79	4	no	—
754	#121	—	79	4	no	—
755	#121	—	79	8	no	—
756	#121	—	79	16	no	—
757	#121	—	79	8	no	—
758	#121	—	79	16	no	—
759	#121	—	79	16	no	—
760	#121	—	79	16	no	—
761	#121	—	79	16	no	—
762	#121	C₂²×D₇₉	1	4	yes	—
763	#121	C₂²×D₇₉	1	4	yes	—
764	#121	C₂²×D₇₉	1	4	yes	—
765	#120	—	79	4	no	—
766	#120	—	79	8	no	—
767	#120	—	79	16	no	—
768	#120	—	79	16	no	—
769	#120	—	79	8	no	—
770	#120	—	79	16	no	—
771	#120	—	79	16	no	—
772	#120	—	79	16	no	—
773	#120	C₂²×D₇₉	1	4	yes	—
774	C₄×Q₈	—	79	8	no	—
775	C₄×Q₈	—	79	4	no	—
776	C₄×Q₈	—	79	4	no	—
777	C₄×Q₈	—	79	4	no	—
778	C₄×Q₈	—	79	8	no	—
779	C₄×Q₈	C₂²×D₇₉	1	4	yes	complemented
780	C₄×Q₈	C₂²×D₇₉	1	4	yes	complemented
781	C₄×Q₈	C₂²×D₇₉	1	4	yes	complemented
782	C₄×D₄	—	79	16	no	—
783	C₄×D₄	—	79	8	no	—
784	C₄×D₄	—	79	8	no	—
785	C₄×D₄	—	79	8	no	—
786	C₄×D₄	—	79	16	no	—
787	C₄×D₄	—	79	16	no	—
788	C₄×D₄	—	79	8	no	—
789	C₄×D₄	—	79	16	no	—
790	C₄×D₄	—	79	16	no	—
791	C₄×D₄	—	79	4	no	—
792	C₄×D₄	—	79	4	no	—
793	C₄×D₄	—	79	4	no	—
794	C₄×D₄	—	79	8	no	—
795	C₄×D₄	—	79	16	no	—
796	C₄×D₄	C₂²×D₇₉	1	8	yes	—
797	C₄×D₄	C₂²×D₇₉	1	8	yes	—
798	C₄×D₄	C₂²×D₇₉	1	8	yes	—
799	C₄×D₄	C₂²×D₇₉	1	4	yes	complemented
800	C₄×D₄	C₂²×D₇₉	1	4	yes	complemented
801	C₄×D₄	C₂²×D₇₉	1	4	yes	complemented
802	#117	—	79	2	no	—
803	#117	—	79	4	no	—
804	#117	—	79	16	no	—
805	#117	—	79	8	no	—
806	#117	—	79	4	no	—
807	#117	—	79	8	no	—
808	#117	—	79	16	no	—
809	#117	C₂²×D₇₉	1	2	yes	—
810	#117	C₂²×D₇₉	1	4	yes	—
811	#117	C₂²×D₇₉	1	4	yes	complemented
812	#117	C₂²×D₇₉	1	8	yes	complemented
813	C₂×C₂²⋊C₄	—	79	8	no	—
814	C₂×C₂²⋊C₄	—	79	8	no	—
815	C₂×C₂²⋊C₄	—	79	8	no	—
816	C₂×C₂²⋊C₄	—	79	8	no	—
817	C₂×C₂²⋊C₄	—	79	8	no	—
818	C₂×C₂²⋊C₄	—	79	8	no	—
819	C₂×C₂²⋊C₄	—	79	16	no	—
820	C₂×C₂²⋊C₄	—	79	8	no	—
821	C₂×C₂²⋊C₄	—	79	16	no	—
822	C₂×C₂²⋊C₄	—	79	16	no	—
823	C₂×C₄²	—	79	4	no	—
824	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
825	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
826	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
827	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
828	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
829	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
830	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
831	C₂×C₄²	C₂²×D₇₉	1	4	yes	complemented
832	C₂⁴	—	316	4	no	—
833	C₂⁴	—	316	8	no	—
834	C₂⁴	—	79	8	no	—
835	C₂⁴	—	79	8	no	—
836	C₂⁴	—	79	4	no	—
837	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
838	#41	—	2	8	no	—
839	#41	—	4	8	no	—
840	#41	—	316	8	no	—
841	#41	—	316	8	no	—
842	#41	—	316	8	no	—
843	#41	—	316	8	no	—
844	#41	—	316	16	no	—
845	#41	—	316	8	no	—
846	#41	—	158	8	no	—
847	C₂×Q₈	—	316	8	no	—
848	C₂×Q₈	—	316	8	no	—
849	C₂×Q₈	—	316	8	no	—
850	C₂×Q₈	—	316	4	no	—
851	C₂×Q₈	—	316	8	no	—
852	C₂×Q₈	—	79	4	no	—
853	C₂×Q₈	—	79	8	no	—
854	C₂×Q₈	—	79	8	no	—
855	C₂×Q₈	—	79	4	no	—
856	C₂×Q₈	—	79	4	no	—
857	C₂×Q₈	—	79	2	no	—
858	C₂×Q₈	—	158	8	no	—
859	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
860	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
861	C₂×D₄	—	316	4	no	—
862	C₂×D₄	—	316	8	no	—
863	C₂×D₄	—	316	8	no	—
864	C₂×D₄	—	316	8	no	—
865	C₂×D₄	—	316	32	no	—
866	C₂×D₄	—	316	16	no	—
867	C₂×D₄	—	316	8	no	—
868	C₂×D₄	—	79	16	no	—
869	C₂×D₄	—	79	8	no	—
870	C₂×D₄	—	79	8	no	—
871	C₂×D₄	—	79	8	no	—
872	C₂×D₄	—	79	4	no	—
873	C₂×D₄	—	79	4	no	—
874	C₂×D₄	—	79	16	no	—
875	C₂×D₄	—	79	8	no	—
876	C₂×D₄	—	79	8	no	—
877	C₂×D₄	—	79	4	no	—
878	C₂×D₄	—	79	4	no	—
879	C₂×D₄	—	79	2	no	—
880	C₂×D₄	—	158	8	no	—
881	C₂×D₄	C₂³×D₇₉	1	8	yes	—
882	C₂×D₄	C₂³×D₇₉	1	4	yes	—
883	C₂×D₄	C₂³×D₇₉	1	2	yes	—
884	C₂×D₄	C₂³×D₇₉	1	4	yes	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	4	4	no	—
887	C₂²×C₄	—	316	4	no	—
888	C₂²×C₄	—	79	8	no	—
889	C₂²×C₄	—	79	8	no	—
890	C₂²×C₄	—	79	8	no	—
891	C₂²×C₄	—	79	16	no	—
892	C₂²×C₄	—	79	8	no	—
893	C₂²×C₄	—	79	8	no	—
894	C₂²×C₄	—	79	4	no	—
895	C₂²×C₄	—	79	4	no	—
896	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
897	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
898	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
899	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
900	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
901	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
902	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
903	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
904	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
905	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
906	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
907	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
908	C₄⋊C₄	—	79	8	no	—
909	C₄⋊C₄	—	79	16	no	—
910	C₄⋊C₄	—	79	8	no	—
911	C₄⋊C₄	—	79	8	no	—
912	C₄⋊C₄	—	79	16	no	—
913	C₄⋊C₄	—	79	4	no	—
914	C₄⋊C₄	—	79	16	no	—
915	C₄⋊C₄	—	79	4	no	—
916	C₄⋊C₄	—	79	4	no	—
917	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
918	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
919	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
920	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
921	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
922	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
923	C₂²⋊C₄	—	79	4	no	—
924	C₂²⋊C₄	—	79	8	no	—
925	C₂²⋊C₄	—	79	16	no	—
926	C₂²⋊C₄	—	79	16	no	—
927	C₂²⋊C₄	—	79	16	no	—
928	C₂²⋊C₄	—	79	16	no	—
929	C₂²⋊C₄	—	79	16	no	—
930	C₂²⋊C₄	—	79	8	no	—
931	C₂²⋊C₄	—	79	16	no	—
932	C₂²⋊C₄	—	79	16	no	—
933	C₂²⋊C₄	—	79	16	no	—
934	C₂²⋊C₄	—	79	16	no	—
935	C₂²⋊C₄	—	79	8	no	—
936	C₂²⋊C₄	—	79	8	no	—
937	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
938	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
939	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
940	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
941	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
942	C₄²	—	79	8	no	—
943	C₄²	—	79	4	no	—
944	C₄²	—	79	16	no	—
945	C₄²	C₂³×D₇₉	1	1	yes	characteristic
946	C₄²	C₂³×D₇₉	1	1	yes	characteristic
947	C₄²	C₂³×D₇₉	1	2	yes	—
948	C₄²	C₂³×D₇₉	1	1	yes	characteristic
949	C₄²	C₂³×D₇₉	1	1	yes	characteristic
950	C₄²	C₂³×D₇₉	1	2	yes	—
951	C₄²	C₂³×D₇₉	1	2	yes	—
952	C₄²	C₂³×D₇₉	1	2	yes	—
953	C₄²	C₂³×D₇₉	1	2	yes	—
954	C₄²	C₂³×D₇₉	1	2	yes	—
955	C₄²	C₂³×D₇₉	1	8	yes	—
956	C₄²	C₂³×D₇₉	1	4	yes	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	4	no	—
959	C₂³	—	316	8	no	—
960	C₂³	—	316	8	no	—
961	C₂³	—	316	8	no	—
962	C₂³	—	316	8	no	—
963	C₂³	—	316	16	no	—
964	C₂³	—	79	8	no	—
965	C₂³	—	79	4	no	—
966	C₂³	—	632	16	no	—
967	C₂³	—	158	8	no	—
968	C₂³	—	158	16	no	—
969	C₂³	C₂⁴×D₇₉	1	4	yes	—
970	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
971	C₂³	C₂⁴×D₇₉	1	2	yes	—
972	Q₈	—	2	4	no	—
973	Q₈	—	4	4	no	—
974	Q₈	—	316	8	no	—
975	Q₈	—	316	8	no	—
976	Q₈	—	316	4	no	—
977	Q₈	—	158	8	no	—
978	Q₈	—	158	8	no	—
979	Q₈	—	158	4	no	—
980	D₄	—	2	8	no	—
981	D₄	—	2	16	no	—
982	D₄	—	2	4	no	—
983	D₄	—	4	4	no	—
984	D₄	—	316	8	no	—
985	D₄	—	316	8	no	—
986	D₄	—	316	16	no	—
987	D₄	—	316	4	no	—
988	D₄	—	316	8	no	—
989	D₄	—	316	16	no	—
990	D₄	—	316	8	no	—
991	D₄	—	158	8	no	—
992	D₄	—	158	16	no	—
993	D₄	—	158	8	no	—
994	D₄	—	158	8	no	—
995	D₄	—	158	4	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	4	no	—
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	4	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	8	no	—
1007	C₂×C₄	—	316	8	no	—
1008	C₂×C₄	—	316	16	no	—
1009	C₂×C₄	—	316	8	no	—
1010	C₂×C₄	—	316	8	no	—
1011	C₂×C₄	—	316	8	no	—
1012	C₂×C₄	—	316	8	no	—
1013	C₂×C₄	—	79	8	no	—
1014	C₂×C₄	—	79	8	no	—
1015	C₂×C₄	—	79	4	no	—
1016	C₂×C₄	—	158	8	no	—
1017	C₂×C₄	—	158	8	no	—
1018	C₂×C₄	#14579207	1	4	yes	—
1019	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1020	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
1021	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1022	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1023	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1024	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
1025	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
1026	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1027	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
1028	C₂²	—	2	8	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	8	no	—
1034	C₂²	—	632	8	no	—
1035	C₂²	—	632	16	no	—
1036	C₂²	—	158	4	no	—
1037	C₂²	—	158	8	no	—
1038	C₂²	—	158	8	no	—
1039	C₂²	—	158	16	no	—
1040	C₂²	—	1264	8	no	—
1041	C₂²	C₂×#14579207	1	2	yes	—
1042	C₂²	#19099399	1	4	yes	—
1043	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	8	no	—
1051	C₄	—	158	4	no	—
1052	C₄	—	158	8	no	—
1053	C₄	—	158	8	no	—
1054	C₄	C₂×#14579207	1	2	yes	—
1055	C₄	C₂×#14579207	1	2	yes	—
1056	C₂	—	2	2	no	—
1057	C₂	—	2	4	no	—
1058	C₂	—	4	4	no	—
1059	C₂	—	316	8	no	—
1060	C₂	—	316	4	no	—
1061	C₂	C₂²×#14579207	1	1	yes	characteristic
1062	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3444	C₂
hypercenter	#3444	D₇₉
hypocenter	C₇₉	#62824
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #23777970	C₂	semidirect
2. #23777965	C₂	semidirect
3. #23777923	C₂	semidirect
4. #23777916	C₂	semidirect
5. #23777752	C₂	semidirect
6. #23777361	C₂	semidirect
7. #23777349	C₂	semidirect
8. #23777298	C₂	semidirect
9. #23777296	C₂	semidirect
10. #23777193	C₂	semidirect
11. #23777187	C₂	semidirect
12. #23777083	C₂	semidirect
13. #23777047	C₂	semidirect
14. #23777033	C₂	semidirect
15. #23776696	C₂	semidirect
16. C₂²×#14579149	C₂	semidirect
17. C₇₉×#3444	C₂	semidirect
18. C₂×#14579208	C₂²	semidirect
19. C₂×#14579207	C₂²	semidirect
20. C₂³×Dic₁₅₈	C₂²	semidirect
22. #19099317	C₂²	semidirect
23. #19099311	C₂²	semidirect
24. #19099307	C₂²	semidirect
25. #19099305	C₂²	semidirect
26. #19099298	C₂²	semidirect
27. #19099296	C₂²	semidirect
28. #19099286	C₂²	semidirect
29. #19099285	C₂²	semidirect
30. #19099276	C₂²	semidirect
31. #19099242	C₂²	semidirect
32. #19099240	C₂²	semidirect
33. #19099237	C₂²	semidirect
34. #19099237	C₂²	semidirect
35. #19099236	C₂²	semidirect
36. D₄×Dic₁₅₈	C₂²	semidirect
37. #19099226	C₂²	semidirect
38. #19099225	C₂²	semidirect
39. #19099222	C₂²	semidirect
40. #19099222	C₂²	semidirect
41. #19099219	C₂²	semidirect
42. #19099209	C₂²	semidirect
43. #19099209	C₂²	semidirect
44. #19099208	C₂²	semidirect
45. #19099208	C₂²	semidirect
46. #19099205	C₂²	semidirect
47. #19099204	C₂²	semidirect
48. #19099202	C₂²	semidirect
49. #19099201	C₂²	semidirect
50. D₄×D₃₁₆	C₂²	semidirect
51. #19099197	C₂²	semidirect
52. #19099188	C₂²	semidirect
53. #19099187	C₂²	semidirect
54. #19099185	C₂²	semidirect
55. #19099184	C₂²	semidirect
56. #19099179	C₂²	semidirect
57. #19099153	C₂²	semidirect
58. #19099152	C₂²	semidirect
59. #19099150	C₂²	semidirect
60. #19099146	C₂²	semidirect
61. #19099146	C₂²	semidirect
62. #19099139	C₂²	semidirect
63. #19099139	C₂²	semidirect
64. #19099138	C₂²	semidirect
65. #19099135	C₂²	semidirect
66. #19099134	C₂²	semidirect
68. #19099132	C₂²	semidirect
70. #19099126	C₂²	semidirect
71. #19099124	C₂²	semidirect
72. #19099121	C₂²	semidirect
73. #19099120	C₂²	semidirect
74. #19099120	C₂²	semidirect
75. #19099113	C₂²	semidirect
76. #19099113	C₂²	semidirect
77. #19099113	C₂²	semidirect
78. #19099112	C₂²	semidirect
79. #19099098	C₂²	semidirect
80. #19099097	C₂²	semidirect
81. #19099097	C₂²	semidirect
82. #19099097	C₂²	semidirect
83. #19099097	C₂²	semidirect
84. C₂×#14579149	C₂²	semidirect
85. C₂×#14579149	C₂²	semidirect
86. C₂×#14579149	C₂²	semidirect
87. C₂×#14579149	C₂²	semidirect
88. C₂×#14579149	C₂²	semidirect
89. C₂×#14579149	C₂²	semidirect
90. C₂×#14579149	C₂²	semidirect
91. C₂×#14579149	C₂²	semidirect
92. #124×D₇₉	C₂²	semidirect
93. #19099074	C₂²	semidirect
94. #19099074	C₂²	semidirect
95. #19099069	C₂²	semidirect
96. #120×D₇₉	C₂²	semidirect
97. #19099040	C₂²	semidirect
98. #19099037	C₂²	semidirect
99. #19099035	C₂²	semidirect
100. C₄×#11929624	C₂²	semidirect
101. C₄×#11929624	C₂²	semidirect
102. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
103. #533×C₇₉	C₂²	semidirect
104. #533×C₇₉	C₂²	semidirect
105. #532×C₇₉	C₂²	semidirect
106. #532×C₇₉	C₂²	semidirect
107. #529×C₇₉	C₂²	semidirect
108. #529×C₇₉	C₂²	semidirect
109. #529×C₇₉	C₂²	semidirect
110. #525×C₇₉	C₂²	semidirect
111. #525×C₇₉	C₂²	semidirect
112. C₄×#41×C₇₉	C₂²	semidirect
113. C₄×#41×C₇₉	C₂²	semidirect
114. C₂²×C₄²×C₇₉	C₂²	semidirect
122. C₂×#11929624	C₂³	semidirect
124. C₂×#11929623	C₂³	semidirect
130. C₂²×Dic₁₅₈	C₂³	semidirect
131. C₂×Q₈×D₇₉	C₂³	semidirect
142. #14579161	C₂³	semidirect
143. #14579161	C₂³	semidirect
144. #14579161	C₂³	semidirect
145. #14579160	C₂³	semidirect
146. #14579159	C₂³	semidirect
148. #14579158	C₂³	semidirect
150. #14579156	C₂³	semidirect
151. #14579156	C₂³	semidirect
152. #14579156	C₂³	semidirect
153. #14579155	C₂³	semidirect
154. #14579155	C₂³	semidirect
155. #14579153	C₂³	semidirect
156. #14579153	C₂³	semidirect
158. #14579150	C₂³	semidirect
170. #14579149	C₂³	semidirect
171. #14579149	C₂³	semidirect
172. #14579149	C₂³	semidirect
173. #14579149	C₂³	semidirect
174. #14579148	C₂³	semidirect
175. #14579147	C₂³	semidirect
176. #14579147	C₂³	semidirect
177. #14579147	C₂³	semidirect
179. #14579146	C₂³	semidirect
180. #14579146	C₂³	semidirect
181. #14579146	C₂³	semidirect
183. #14579145	C₂³	semidirect
186. #14579144	C₂³	semidirect
187. #14579143	C₂³	semidirect
189. #14579141	C₂³	semidirect
190. #14579141	C₂³	semidirect
194. #14579140	C₂³	semidirect
195. #14579139	C₂³	semidirect
196. #14579139	C₂³	semidirect
197. #14579139	C₂³	semidirect
199. #14579138	C₂³	semidirect
200. #14579137	C₂³	semidirect
203. #14579136	C₂³	semidirect
208. #14579135	C₂³	semidirect
210. #14579134	C₂³	semidirect
212. #14579133	C₂³	semidirect
216. #14579131	C₂³	semidirect
220. #14579129	C₂³	semidirect
221. C₄×Dic₁₅₈	C₂³	semidirect
222. C₄×Dic₁₅₈	C₂³	semidirect
223. C₄×Dic₁₅₈	C₂³	semidirect
224. C₄×Dic₁₅₈	C₂³	semidirect
225. #14579126	C₂³	semidirect
227. C₄×D₃₁₆	C₂³	semidirect
228. C₄×D₃₁₆	C₂³	semidirect
229. C₄×D₃₁₆	C₂³	semidirect
230. C₄×D₃₁₆	C₂³	semidirect
233. #14579123	C₂³	semidirect
237. C₄×C₂²⋊D₇₉	C₂³	semidirect
239. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
242. #14579119	C₂³	semidirect
243. #14579118	C₂³	semidirect
244. #14579118	C₂³	semidirect
245. #14579118	C₂³	semidirect
253. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
256. C₂²⋊C₄×D₇₉	C₂³	semidirect
257. C₄²×D₇₉	C₂³	semidirect
262. C₄⋊Q₈×C₇₉	C₂³	semidirect
263. C₄⋊Q₈×C₇₉	C₂³	semidirect
264. #127×C₇₉	C₂³	semidirect
265. #126×C₇₉	C₂³	semidirect
266. #125×C₇₉	C₂³	semidirect
267. #125×C₇₉	C₂³	semidirect
268. #124×C₇₉	C₂³	semidirect
269. #124×C₇₉	C₂³	semidirect
279. C₄×Q₈×C₇₉	C₂³	semidirect
280. C₄×Q₈×C₇₉	C₂³	semidirect
281. C₄×Q₈×C₇₉	C₂³	semidirect
285. C₄×D₄×C₇₉	C₂³	semidirect
286. C₄×D₄×C₇₉	C₂³	semidirect
287. C₄×D₄×C₇₉	C₂³	semidirect
290. #117×C₇₉	C₂³	semidirect
291. #117×C₇₉	C₂³	semidirect
299. C₂×C₄²×C₇₉	C₂³	semidirect
547. #3444	D₇₉	semidirect
549. C₇₉	#62824	semidirect
607. #533	C₂×D₇₉	semidirect
608. #533	C₂×D₇₉	semidirect
613. #532	C₂×D₇₉	semidirect
614. #532	C₂×D₇₉	semidirect
620. #529	C₂×D₇₉	semidirect
621. #529	C₂×D₇₉	semidirect
622. #529	C₂×D₇₉	semidirect
635. #525	C₂×D₇₉	semidirect
636. #525	C₂×D₇₉	semidirect
643. C₄×#41	C₂×D₇₉	semidirect
644. C₄×#41	C₂×D₇₉	semidirect
646. C₂²×C₄²	C₂×D₇₉	semidirect
683. C₄⋊Q₈	C₂²×D₇₉	semidirect
684. C₄⋊Q₈	C₂²×D₇₉	semidirect
688. #127	C₂²×D₇₉	semidirect
694. #126	C₂²×D₇₉	semidirect
697. #125	C₂²×D₇₉	semidirect
698. #125	C₂²×D₇₉	semidirect
720. #124	C₂²×D₇₉	semidirect
721. #124	C₂²×D₇₉	semidirect
779. C₄×Q₈	C₂²×D₇₉	semidirect
780. C₄×Q₈	C₂²×D₇₉	semidirect
781. C₄×Q₈	C₂²×D₇₉	semidirect
799. C₄×D₄	C₂²×D₇₉	semidirect
800. C₄×D₄	C₂²×D₇₉	semidirect
801. C₄×D₄	C₂²×D₇₉	semidirect
811. #117	C₂²×D₇₉	semidirect
812. #117	C₂²×D₇₉	semidirect
831. C₂×C₄²	C₂²×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777970	2
#23777965	2
#23777923	2
#23777916	2
#23777752	2
#23777361	2
#23777349	2
#23777298	2
#23777296	2
#23777193	2
#23777187	2
#23777083	2
#23777047	2
#23777033	2
#23776696	2
C₂²×#14579149	2
C₇₉×#3444	2
#62824	79