Subgroups — #35197279

Order 20224.

11770 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579206	C₂	1	2	yes	maximal, complemented
2	#23777161	C₂	1	8	yes	maximal, complemented
3	#23777157	C₂	1	8	yes	maximal, complemented
4	#23777041	C₂	1	8	yes	maximal, complemented
5	#23777038	C₂	1	8	yes	maximal, complemented
6	#23777032	C₂	1	8	yes	maximal, complemented
7	#23777029	C₂	1	8	yes	maximal, complemented
8	#23776726	C₂	1	4	yes	maximal, complemented
9	C₂×#19099125	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19099122	C₂	1	2	yes	maximal, complemented
11	#534×D₇₉	C₂	1	4	yes	maximal, complemented
12	C₂×#19099036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#534×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14579206	—	2	32	no	—
15	C₂×#14579206	C₂²	1	8	yes	complemented
16	C₂×#14579206	C₂²	1	8	yes	complemented
17	C₂×#14579206	C₂²	1	8	yes	complemented
18	C₂×#14579206	C₂²	1	8	yes	complemented
19	C₂²×#11929624	C₂²	1	4	yes	complemented
20	C₂²×#11929623	C₂²	1	4	yes	complemented
21	C₂²×#11929623	C₂²	1	4	yes	complemented
22	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
24	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
25	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
26	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
27	#19099214	C₂²	1	16	yes	complemented
28	#19099213	C₂²	1	16	yes	complemented
29	#19099211	C₂²	1	32	yes	complemented
30	#19099205	C₂²	1	32	yes	complemented
31	#19099203	C₂²	1	32	yes	complemented
32	#19099202	C₂²	1	32	yes	complemented
33	#19099200	C₂²	1	32	yes	complemented
34	#19099197	C₂²	1	16	yes	complemented
35	D₄×C₂²⋊D₇₉	C₂²	1	16	yes	complemented
36	#19099195	C₂²	1	32	yes	complemented
37	#19099140	C₂²	1	16	yes	complemented
38	#19099135	C₂²	1	16	yes	complemented
39	#19099128	C₂²	1	16	yes	complemented
40	#19099125	C₂²	1	4	yes	complemented
41	#19099125	C₂²	1	8	yes	complemented
42	#19099125	C₂²	1	4	yes	complemented
43	#19099124	C₂²	1	16	yes	complemented
44	#19099123	C₂²	1	16	yes	complemented
45	#19099122	C₂²	1	8	yes	complemented
46	#19099122	C₂²	1	8	yes	complemented
47	#19099122	C₂²	1	8	yes	complemented
48	#19099122	C₂²	1	8	yes	complemented
49	#19099121	C₂²	1	16	yes	complemented
50	#19099108	C₂²	1	16	yes	complemented
51	#19099071	C₂²	1	16	yes	complemented
52	#19099069	C₂²	1	16	yes	complemented
53	C₂×#14579145	C₂²	1	4	yes	complemented
54	C₂×#14579144	C₂²	1	4	yes	complemented
55	C₂×#14579142	C₂²	1	4	yes	complemented
56	#123×D₇₉	C₂²	1	16	yes	complemented
57	C₂×#14579135	C₂²	1	4	yes	complemented
58	C₂×#14579133	C₂²	1	8	yes	complemented
59	#121×D₇₉	C₂²	1	16	yes	complemented
60	C₂×#14579131	C₂²	1	4	yes	complemented
61	C₂×#14579130	C₂²	1	4	yes	complemented
62	C₂×#14579129	C₂²	1	4	yes	complemented
63	#120×D₇₉	C₂²	1	16	yes	complemented
64	#19099036	C₂²	1	8	yes	complemented
65	#19099036	C₂²	1	8	yes	complemented
66	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
67	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
68	C₂×#14579117	C₂²	1	2	yes	complemented
69	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
71	C₂³×D₄×C₇₉	C₂²	1	2	yes	complemented
72	#534×C₇₉	C₂²	1	4	yes	complemented
73	#534×C₇₉	C₂²	1	8	yes	complemented
74	#534×C₇₉	C₂²	1	4	yes	complemented
75	C₂×#123×C₇₉	C₂²	1	4	yes	complemented
76	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
77	C₂×#120×C₇₉	C₂²	1	4	yes	complemented
78	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
79	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
80	C₂⁴×D₇₉	C₂³	1	4	yes	complemented
81	C₂⁴×D₇₉	C₂³	1	2	yes	complemented
82	#14579206	—	2	64	no	—
83	#14579206	—	2	64	no	—
84	#14579206	—	2	64	no	—
85	#14579206	—	2	64	no	—
86	C₂×#11929624	—	2	32	no	—
87	C₂×#11929624	C₂³	1	16	yes	complemented
88	C₂×#11929624	C₂³	1	16	yes	complemented
89	C₂×#11929623	—	2	32	no	—
90	C₂×#11929623	—	2	32	no	—
91	C₂×#11929623	C₂³	1	16	yes	—
92	C₂×#11929623	C₂³	1	16	yes	complemented
93	C₂×#11929623	C₂³	1	16	yes	complemented
94	C₂×#11929623	C₂³	1	16	yes	complemented
95	C₂²×Dic₁₅₈	C₂³	1	4	yes	complemented
96	C₂²×D₃₁₆	C₂³	1	4	yes	complemented
97	C₂²×D₃₁₆	C₂³	1	4	yes	complemented
98	C₂²×C₂²⋊D₇₉	—	2	16	no	—
99	C₂²×C₂²⋊D₇₉	—	2	32	no	—
100	C₂²×C₂²⋊D₇₉	D₄	1	16	yes	complemented
101	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
109	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
110	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
111	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
112	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
113	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
114	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
115	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	complemented
116	C₂×D₄×D₇₉	—	2	32	no	—
117	C₂×D₄×D₇₉	—	2	32	no	—
118	C₂×D₄×D₇₉	C₂³	1	16	yes	—
119	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
120	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
121	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
122	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
123	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
124	C₂³×Dic₇₉	C₂³	1	2	yes	complemented
125	C₂³×Dic₇₉	C₂³	1	4	yes	complemented
126	C₂³×Dic₇₉	C₂³	1	2	yes	complemented
127	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
128	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
129	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
130	#14579160	C₂³	1	16	yes	complemented
131	#14579157	C₂³	1	16	yes	complemented
132	#14579147	C₂³	1	32	yes	complemented
133	#14579146	C₂³	1	32	yes	complemented
134	#14579145	C₂³	1	16	yes	complemented
135	#14579145	C₂³	1	16	yes	complemented
136	#14579144	C₂³	1	16	yes	complemented
137	#14579144	C₂³	1	16	yes	complemented
138	#14579143	C₂³	1	32	yes	complemented
139	#14579142	C₂³	1	16	yes	complemented
140	#14579142	C₂³	1	16	yes	complemented
141	#14579139	C₂³	1	32	yes	complemented
142	#14579138	C₂³	1	32	yes	complemented
143	#14579136	C₂³	1	16	yes	complemented
144	#14579135	C₂³	1	16	yes	complemented
145	#14579135	C₂³	1	16	yes	complemented
146	#14579134	C₂³	1	32	yes	complemented
147	#14579134	C₂³	1	32	yes	complemented
148	#14579133	C₂³	1	32	yes	complemented
149	#14579133	C₂³	1	32	yes	complemented
150	#14579133	C₂³	1	32	yes	complemented
151	#14579132	C₂³	1	16	yes	complemented
152	#14579131	C₂³	1	16	yes	complemented
153	#14579131	C₂³	1	32	yes	complemented
154	#14579131	C₂³	1	16	yes	complemented
155	#14579130	C₂³	1	16	yes	complemented
156	#14579130	C₂³	1	16	yes	complemented
157	#14579129	C₂³	1	32	yes	complemented
158	#14579129	C₂³	1	16	yes	complemented
159	#14579129	C₂³	1	16	yes	complemented
160	D₄×Dic₇₉	C₂³	1	16	yes	complemented
161	#14579123	C₂³	1	16	yes	complemented
162	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
163	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
164	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
165	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
166	#14579117	C₂³	1	16	yes	complemented
167	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
168	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	complemented
169	C₂×Dic₇₉⋊C₄	C₂³	1	8	yes	complemented
170	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
171	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	complemented
173	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	complemented
174	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	complemented
175	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	complemented
176	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
177	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	complemented
178	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	complemented
179	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
180	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
181	C₂×C₄×Dic₇₉	C₂³	1	4	yes	complemented
182	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
183	C₂⁵×C₇₉	C₂³	1	2	yes	complemented
184	C₂²×D₄×C₇₉	—	2	16	no	—
185	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
186	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
187	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
188	C₂²×D₄×C₇₉	C₂³	1	4	yes	complemented
189	C₂²×D₄×C₇₉	C₂³	1	4	yes	complemented
190	C₂²×D₄×C₇₉	C₂³	1	4	yes	complemented
191	C₂²×D₄×C₇₉	C₂³	1	4	yes	complemented
192	C₂³×C₄×C₇₉	C₂³	1	2	yes	complemented
193	C₂³×C₄×C₇₉	C₂³	1	2	yes	complemented
194	#123×C₇₉	C₂³	1	16	yes	complemented
195	#123×C₇₉	C₂³	1	16	yes	complemented
196	#121×C₇₉	C₂³	1	16	yes	complemented
197	#121×C₇₉	C₂³	1	16	yes	complemented
198	#120×C₇₉	C₂³	1	16	yes	complemented
199	#120×C₇₉	C₂³	1	16	yes	complemented
200	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	complemented
201	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	complemented
203	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	complemented
204	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	complemented
205	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	complemented
206	C₂³×D₇₉	—	2	8	no	—
207	C₂³×D₇₉	—	2	16	no	—
208	C₂³×D₇₉	—	8	2	no	—
209	C₂³×D₇₉	—	8	8	no	—
210	C₂³×D₇₉	—	8	4	no	—
211	C₂³×D₇₉	C₂×D₄	1	8	yes	complemented
212	C₂³×D₇₉	C₂⁴	1	4	yes	—
213	C₂³×D₇₉	C₂⁴	1	16	yes	—
214	C₂³×D₇₉	C₂⁴	1	4	yes	—
215	C₂³×D₇₉	C₂⁴	1	4	yes	—
216	C₂³×D₇₉	C₂⁴	1	4	yes	—
217	C₂³×D₇₉	C₂⁴	1	2	yes	—
218	#11929624	—	2	64	no	—
219	#11929624	—	2	64	no	—
220	#11929623	—	2	64	no	—
221	#11929623	—	2	64	no	—
222	#11929623	—	2	64	no	—
223	#11929623	—	2	64	no	—
224	C₂×Dic₁₅₈	—	2	16	no	—
225	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
226	C₂×D₃₁₆	—	2	16	no	—
227	C₂×D₃₁₆	—	8	4	no	—
228	C₂×D₃₁₆	C₂⁴	1	16	yes	—
229	C₂×D₃₁₆	C₂⁴	1	16	yes	—
230	C₂×C₂²⋊D₇₉	—	2	16	no	—
231	C₂×C₂²⋊D₇₉	—	2	16	no	—
232	C₂×C₂²⋊D₇₉	—	2	16	no	—
233	C₂×C₂²⋊D₇₉	—	2	16	no	—
234	C₂×C₂²⋊D₇₉	—	2	16	no	—
235	C₂×C₂²⋊D₇₉	—	2	16	no	—
236	C₂×C₂²⋊D₇₉	—	2	16	no	—
237	C₂×C₂²⋊D₇₉	—	2	16	no	—
238	C₂×C₂²⋊D₇₉	—	2	64	no	—
239	C₂×C₂²⋊D₇₉	—	2	64	no	—
240	C₂×C₂²⋊D₇₉	—	8	8	no	—
241	C₂×C₂²⋊D₇₉	C₂×D₄	1	32	yes	complemented
242	C₂×C₂²⋊D₇₉	C₂×D₄	1	32	yes	complemented
243	C₂×C₂²⋊D₇₉	C₂×D₄	1	16	yes	complemented
244	C₂×C₂²⋊D₇₉	C₂×D₄	1	16	yes	complemented
245	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
246	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
247	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
248	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
249	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
250	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
251	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
252	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
253	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
254	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
255	D₄×D₇₉	—	2	64	no	—
256	D₄×D₇₉	—	2	64	no	—
257	D₄×D₇₉	—	2	64	no	—
258	D₄×D₇₉	—	2	64	no	—
259	D₄×D₇₉	—	8	16	no	—
260	C₂²×Dic₇₉	—	2	16	no	—
261	C₂²×Dic₇₉	—	2	8	no	—
262	C₂²×Dic₇₉	—	8	2	no	—
263	C₂²×Dic₇₉	C₂×D₄	1	8	yes	complemented
264	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
266	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
267	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
268	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
269	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
270	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
271	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
272	C₂×C₄×D₇₉	—	2	16	no	—
273	C₂×C₄×D₇₉	—	2	16	no	—
274	C₂×C₄×D₇₉	—	8	4	no	—
275	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
276	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
277	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
278	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
279	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
280	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
281	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
282	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
283	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
284	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
285	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
286	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
287	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
288	C₄×Dic₇₉	C₂⁴	1	16	yes	—
289	C₂⁴×C₇₉	—	2	8	no	—
290	C₂⁴×C₇₉	—	8	2	no	—
291	C₂⁴×C₇₉	—	8	4	no	—
292	C₂⁴×C₇₉	C₂×D₄	1	8	yes	complemented
293	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
294	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
295	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
296	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
297	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
298	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
299	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
301	C₂×D₄×C₇₉	—	2	16	no	—
302	C₂×D₄×C₇₉	—	2	16	no	—
303	C₂×D₄×C₇₉	—	2	16	no	—
304	C₂×D₄×C₇₉	—	2	16	no	—
305	C₂×D₄×C₇₉	—	2	16	no	—
306	C₂×D₄×C₇₉	—	2	16	no	—
307	C₂×D₄×C₇₉	—	8	4	no	—
308	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
309	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
310	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
311	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
312	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
313	C₂²×C₄×C₇₉	—	2	8	no	—
314	C₂²×C₄×C₇₉	—	8	2	no	—
315	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
319	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
320	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
322	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
325	C₂³×C₇₉	—	2	8	no	—
326	C₂³×C₇₉	—	2	8	no	—
327	C₂³×C₇₉	—	2	8	no	—
328	C₂³×C₇₉	—	4	2	no	—
329	C₂³×C₇₉	—	4	4	no	—
330	C₂³×C₇₉	—	4	2	no	—
331	C₂³×C₇₉	—	4	8	no	—
332	C₂³×C₇₉	—	4	2	no	—
333	C₂³×C₇₉	—	4	4	no	—
334	C₂³×C₇₉	—	4	8	no	—
335	C₂³×C₇₉	—	4	8	no	—
336	C₂³×C₇₉	—	8	8	no	—
337	C₂³×C₇₉	—	8	16	no	—
338	C₂³×C₇₉	C₂²×D₄	1	8	yes	—
339	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
340	C₂³×C₇₉	C₂²×D₄	1	8	yes	—
341	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
342	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
343	C₂³×C₇₉	C₂⁵	1	8	yes	—
344	C₂³×C₇₉	C₂⁵	1	2	yes	—
345	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
346	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
347	C₂³×C₇₉	C₂⁵	1	2	yes	—
348	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
349	C₂²×D₇₉	—	2	8	no	—
350	C₂²×D₇₉	—	2	8	no	—
351	C₂²×D₇₉	—	2	8	no	—
352	C₂²×D₇₉	—	2	32	no	—
353	C₂²×D₇₉	—	4	4	no	—
354	C₂²×D₇₉	—	4	8	no	—
355	C₂²×D₇₉	—	4	8	no	—
356	C₂²×D₇₉	—	4	32	no	—
357	C₂²×D₇₉	—	4	8	no	—
358	C₂²×D₇₉	—	4	8	no	—
359	C₂²×D₇₉	—	8	8	no	—
360	C₂²×D₇₉	—	8	32	no	—
361	C₂²×D₇₉	—	8	16	no	—
362	C₂²×D₇₉	C₂²×D₄	1	16	yes	—
363	C₂²×D₇₉	C₂²×D₄	1	8	yes	—
364	C₂²×D₇₉	C₂⁵	1	8	yes	—
365	C₂²×D₇₉	C₂⁵	1	4	yes	—
366	D₄×C₇₉	—	2	16	no	—
367	D₄×C₇₉	—	2	16	no	—
368	D₄×C₇₉	—	2	16	no	—
369	D₄×C₇₉	—	2	16	no	—
370	D₄×C₇₉	—	4	16	no	—
371	C₂×C₄×C₇₉	—	2	8	no	—
372	C₂×C₄×C₇₉	—	2	8	no	—
373	C₂×C₄×C₇₉	—	2	8	no	—
374	C₂×C₄×C₇₉	—	4	4	no	—
375	C₂×C₄×C₇₉	—	4	4	no	—
376	C₂×C₄×C₇₉	—	4	4	no	—
377	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
378	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
379	C₂²⋊D₇₉	—	2	16	no	—
380	C₂²⋊D₇₉	—	2	16	no	—
381	C₂²⋊D₇₉	—	2	16	no	—
382	C₂²⋊D₇₉	—	2	16	no	—
383	C₂²⋊D₇₉	—	2	32	no	—
384	C₂²⋊D₇₉	—	2	32	no	—
385	C₂²⋊D₇₉	—	4	32	no	—
386	C₂²⋊D₇₉	C₂²×D₄	1	16	yes	—
387	C₂²⋊D₇₉	C₂²×D₄	1	32	yes	—
388	C₂²⋊D₇₉	C₂²×D₄	1	16	yes	—
389	C₂×Dic₇₉	—	2	8	no	—
390	C₂×Dic₇₉	—	2	8	no	—
391	C₂×Dic₇₉	—	2	8	no	—
392	C₂×Dic₇₉	—	2	32	no	—
393	C₂×Dic₇₉	—	4	4	no	—
394	C₂×Dic₇₉	—	4	8	no	—
395	C₂×Dic₇₉	C₂²×D₄	1	16	yes	—
396	C₂×Dic₇₉	C₂²×D₄	1	8	yes	—
397	C₂×Dic₇₉	C₂⁵	1	8	yes	—
398	C₂×Dic₇₉	C₂⁵	1	8	yes	—
399	C₂×Dic₇₉	C₂⁵	1	4	yes	—
400	D₃₁₆	—	2	32	no	—
401	D₃₁₆	—	4	16	no	—
402	C₄×D₇₉	—	2	32	no	—
403	C₄×D₇₉	—	2	32	no	—
404	C₄×D₇₉	—	4	16	no	—
405	Dic₁₅₈	—	2	32	no	—
406	C₂²×C₇₉	—	2	2	no	—
407	C₂²×C₇₉	—	2	2	no	—
408	C₂²×C₇₉	—	2	2	no	—
409	C₂²×C₇₉	—	2	4	no	—
410	C₂²×C₇₉	—	2	4	no	—
411	C₂²×C₇₉	—	2	8	no	—
412	C₂²×C₇₉	—	2	16	no	—
413	C₂²×C₇₉	—	4	4	no	—
414	C₂²×C₇₉	—	4	8	no	—
415	C₂²×C₇₉	—	4	8	no	—
416	C₂²×C₇₉	—	4	4	no	—
417	C₂²×C₇₉	—	4	4	no	—
418	C₂²×C₇₉	—	4	16	no	—
419	C₂²×C₇₉	—	8	8	no	—
420	C₂²×C₇₉	—	8	8	no	—
421	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
422	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
423	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
424	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
425	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
426	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
427	C₂×D₇₉	—	2	8	no	—
428	C₂×D₇₉	—	2	8	no	—
429	C₂×D₇₉	—	2	16	no	—
430	C₂×D₇₉	—	4	16	no	—
431	C₂×D₇₉	—	4	8	no	—
432	C₂×D₇₉	—	4	16	no	—
433	C₂×D₇₉	—	8	32	no	—
434	C₂×D₇₉	—	8	8	no	—
435	C₂×D₇₉	—	8	8	no	—
436	C₂×D₇₉	C₂³×D₄	1	8	yes	—
437	C₄×C₇₉	—	2	8	no	—
438	C₄×C₇₉	—	2	8	no	—
439	Dic₇₉	—	2	8	no	—
440	Dic₇₉	—	2	8	no	—
441	Dic₇₉	C₂³×D₄	1	8	yes	—
442	#62842	—	79	1	no	maximal, Sylow
443	C₂×C₇₉	—	2	4	no	—
444	C₂×C₇₉	—	2	2	no	—
445	C₂×C₇₉	—	2	2	no	—
446	C₂×C₇₉	—	2	4	no	—
447	C₂×C₇₉	—	2	2	no	—
448	C₂×C₇₉	—	4	8	no	—
449	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
450	C₂×C₇₉	H(7,𝔽₂)	1	2	yes	—
451	D₇₉	—	2	8	no	—
452	D₇₉	—	4	8	no	—
453	C₂²×H(5,𝔽₂)	—	79	2	no	—
454	#3496	—	79	8	no	—
455	#3496	—	79	8	no	—
456	#3485	—	79	8	no	—
457	#3485	—	79	8	no	—
458	#3484	—	79	8	no	—
459	#3484	—	79	8	no	—
460	#3449	—	79	4	no	—
461	C₂×#534	—	79	2	no	—
462	C₂×#534	—	79	4	no	—
463	C₂×#534	—	79	1	no	—
464	C₂×#534	D₇₉	1	1	yes	characteristic, complemented
465	C₂×#518	—	79	1	no	—
466	C₇₉	#62842	1	1	yes	characteristic, complemented, Sylow
467	C₂×H(5,𝔽₂)	—	79	8	no	—
468	C₂×H(5,𝔽₂)	—	79	8	no	—
469	C₂×H(5,𝔽₂)	—	79	8	no	—
470	C₂×H(5,𝔽₂)	—	79	8	no	—
471	C₂×H(5,𝔽₂)	—	158	32	no	—
472	C₂²×#41	—	79	4	no	—
473	C₂²×#41	—	79	4	no	—
474	C₂²×#41	—	79	4	no	—
475	C₂³×D₄	—	79	1	no	—
476	C₂³×D₄	—	79	2	no	—
477	C₂³×D₄	—	79	4	no	—
478	C₂³×D₄	—	79	4	no	—
479	C₂³×D₄	—	79	4	no	—
480	C₂³×D₄	C₂×D₇₉	1	2	yes	complemented
481	#547	—	79	32	no	—
482	#547	—	79	16	no	—
483	#547	—	79	16	no	—
484	#546	—	79	32	no	—
485	#546	—	79	32	no	—
486	#546	—	79	32	no	—
487	#546	—	79	32	no	—
488	D₄²	—	79	16	no	—
489	D₄²	—	79	16	no	—
490	D₄²	—	79	32	no	—
491	#537	—	79	16	no	—
492	#536	—	79	16	no	—
493	#535	—	79	16	no	—
494	#534	—	79	8	no	—
495	#534	—	79	8	no	—
496	#534	—	79	8	no	—
497	#534	—	79	8	no	—
498	#534	—	79	16	no	—
499	#534	—	79	16	no	—
500	#534	—	79	16	no	—
501	#534	—	79	4	no	—
502	#534	—	79	8	no	—
503	#534	—	79	4	no	—
504	#534	C₂×D₇₉	1	4	yes	complemented
505	#534	C₂×D₇₉	1	8	yes	complemented
506	#534	C₂×D₇₉	1	4	yes	complemented
507	#532	—	79	16	no	—
508	#525	—	79	16	no	—
509	#525	—	79	16	no	—
510	C₂×#123	—	79	4	no	—
511	C₂×#123	—	79	4	no	—
512	C₂×#123	—	79	16	no	—
513	C₂×#123	—	79	4	no	—
514	C₂×#123	C₂×D₇₉	1	4	yes	complemented
515	C₂×#121	—	79	8	no	—
516	C₂×#121	—	79	4	no	—
517	C₂×#121	—	79	16	no	—
518	C₂×#121	C₂×D₇₉	1	4	yes	complemented
519	C₂×#120	—	79	4	no	—
520	C₂×#120	—	79	4	no	—
521	C₂×#120	—	79	16	no	—
522	C₂×#120	—	79	4	no	—
523	C₂×#120	C₂×D₇₉	1	4	yes	complemented
524	#518	—	79	8	no	—
525	#518	—	79	8	no	—
526	C₂×C₄×D₄	—	79	4	no	—
527	C₂×C₄×D₄	—	79	4	no	—
528	C₂×#117	—	79	2	no	—
529	C₂²×C₂²⋊C₄	—	79	1	no	—
530	C₂²×C₂²⋊C₄	—	79	2	no	—
531	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
532	C₂⁵	—	79	1	no	—
533	C₂⁵	—	79	4	no	—
534	C₂⁵	—	79	2	no	—
535	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
536	C₂⁵	C₂²×D₇₉	1	2	yes	complemented
537	H(5,𝔽₂)	—	158	64	no	—
538	H(5,𝔽₂)	—	158	64	no	—
539	H(5,𝔽₂)	—	158	64	no	—
540	H(5,𝔽₂)	—	158	64	no	—
541	C₂×#41	—	79	16	no	—
542	C₂×#41	—	79	16	no	—
543	C₂×#41	—	79	16	no	—
544	C₂×#41	—	79	16	no	—
545	C₂×#41	—	79	16	no	—
546	C₂×#41	—	79	16	no	—
547	C₂×#41	—	158	32	no	—
548	C₂×#41	—	158	32	no	—
549	C₂×#41	—	158	32	no	—
550	C₂²×Q₈	—	79	4	no	—
551	C₂²×D₄	—	2	16	no	—
552	C₂²×D₄	—	79	16	no	—
553	C₂²×D₄	—	79	2	no	—
554	C₂²×D₄	—	79	2	no	—
555	C₂²×D₄	—	79	4	no	—
556	C₂²×D₄	—	79	4	no	—
557	C₂²×D₄	—	79	8	no	—
558	C₂²×D₄	—	79	4	no	—
559	C₂²×D₄	—	79	4	no	—
560	C₂²×D₄	—	79	4	no	—
561	C₂²×D₄	—	79	4	no	—
562	C₂²×D₄	—	79	4	no	—
563	C₂²×D₄	—	79	4	no	—
564	C₂²×D₄	—	79	4	no	—
565	C₂²×D₄	—	79	4	no	—
566	C₂²×D₄	—	79	16	no	—
567	C₂²×D₄	—	79	16	no	—
568	C₂²×D₄	—	79	16	no	—
569	C₂²×D₄	—	79	16	no	—
570	C₂²×D₄	—	79	16	no	—
571	C₂²×D₄	—	79	16	no	—
572	C₂²×D₄	—	79	16	no	—
573	C₂²×D₄	—	79	4	no	—
574	C₂²×D₄	—	79	4	no	—
575	C₂²×D₄	—	158	32	no	—
576	C₂²×D₄	—	158	32	no	—
577	C₂²×D₄	—	158	32	no	—
578	C₂²×D₄	—	158	16	no	—
579	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
580	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
581	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
582	C₂²×D₄	C₂²×D₇₉	1	4	yes	complemented
583	C₂²×D₄	C₂²×D₇₉	1	4	yes	complemented
584	C₂²×D₄	C₂²×D₇₉	1	4	yes	complemented
585	C₂²×D₄	C₂²×D₇₉	1	4	yes	complemented
586	C₂³×C₄	—	79	1	no	—
587	C₂³×C₄	—	79	2	no	—
588	C₂³×C₄	—	79	2	no	—
589	C₂³×C₄	—	79	4	no	—
590	C₂³×C₄	—	79	4	no	—
591	C₂³×C₄	—	79	4	no	—
592	C₂³×C₄	—	79	4	no	—
593	C₂³×C₄	C₂²×D₇₉	1	2	yes	complemented
594	C₂³×C₄	C₂²×D₇₉	1	2	yes	complemented
595	C₄⋊Q₈	—	79	16	no	—
596	#127	—	79	16	no	—
597	#124	—	79	32	no	—
598	#123	—	79	16	no	—
599	#123	—	79	16	no	—
600	#123	—	79	16	no	—
601	#123	—	79	16	no	—
602	#123	—	79	32	no	—
603	#123	—	79	16	no	—
604	#123	—	79	32	no	—
605	#123	—	79	16	no	—
606	#123	C₂²×D₇₉	1	16	yes	complemented
607	#123	C₂²×D₇₉	1	16	yes	complemented
608	C₂²⋊Q₈	—	79	32	no	—
609	C₂²⋊Q₈	—	79	32	no	—
610	#121	—	79	32	no	—
611	#121	—	79	16	no	—
612	#121	—	79	32	no	—
613	#121	—	79	32	no	—
614	#121	—	79	16	no	—
615	#121	—	79	16	no	—
616	#121	—	79	16	no	—
617	#121	—	79	32	no	—
618	#121	—	79	32	no	—
619	#121	C₂²×D₇₉	1	16	yes	complemented
620	#121	C₂²×D₇₉	1	16	yes	complemented
621	#120	—	79	16	no	—
622	#120	—	79	16	no	—
623	#120	—	79	16	no	—
624	#120	—	79	16	no	—
625	#120	—	79	32	no	—
626	#120	—	79	16	no	—
627	#120	—	79	32	no	—
628	#120	—	79	16	no	—
629	#120	C₂²×D₇₉	1	16	yes	complemented
630	#120	C₂²×D₇₉	1	16	yes	complemented
631	C₄×D₄	—	79	16	no	—
632	C₄×D₄	—	79	16	no	—
633	C₄×D₄	—	79	16	no	—
634	C₄×D₄	—	79	16	no	—
635	C₄×D₄	—	79	32	no	—
636	C₄×D₄	—	79	32	no	—
637	#117	—	79	16	no	—
638	C₂×C₄⋊C₄	—	79	4	no	—
639	C₂×C₄⋊C₄	—	79	8	no	—
640	C₂×C₄⋊C₄	—	79	4	no	—
641	C₂×C₄⋊C₄	—	79	16	no	—
642	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	complemented
643	C₂×C₂²⋊C₄	—	79	2	no	—
644	C₂×C₂²⋊C₄	—	79	2	no	—
645	C₂×C₂²⋊C₄	—	79	4	no	—
646	C₂×C₂²⋊C₄	—	79	4	no	—
647	C₂×C₂²⋊C₄	—	79	8	no	—
648	C₂×C₂²⋊C₄	—	79	4	no	—
649	C₂×C₂²⋊C₄	—	79	8	no	—
650	C₂×C₂²⋊C₄	—	79	8	no	—
651	C₂×C₂²⋊C₄	—	79	16	no	—
652	C₂×C₂²⋊C₄	—	79	32	no	—
653	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	complemented
655	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	complemented
656	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	complemented
657	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	complemented
658	C₂×C₄²	—	79	4	no	—
659	C₂⁴	—	2	8	no	—
660	C₂⁴	—	8	2	no	—
661	C₂⁴	—	8	4	no	—
662	C₂⁴	—	79	4	no	—
663	C₂⁴	—	79	2	no	—
664	C₂⁴	—	79	16	no	—
665	C₂⁴	—	79	4	no	—
666	C₂⁴	—	79	4	no	—
667	C₂⁴	—	79	4	no	—
668	C₂⁴	—	79	8	no	—
669	C₂⁴	—	632	2	no	—
670	C₂⁴	—	632	4	no	—
671	C₂⁴	—	632	8	no	—
672	C₂⁴	—	158	16	no	—
673	C₂⁴	—	158	8	no	—
674	C₂⁴	D₄×D₇₉	1	8	yes	complemented
675	C₂⁴	C₂³×D₇₉	1	4	yes	—
676	C₂⁴	C₂³×D₇₉	1	4	yes	—
677	C₂⁴	C₂³×D₇₉	1	4	yes	—
678	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
679	C₂⁴	C₂³×D₇₉	1	2	yes	—
680	C₂⁴	C₂³×D₇₉	1	2	yes	—
681	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
682	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
683	#41	—	158	64	no	—
684	#41	—	158	64	no	—
685	#41	—	158	64	no	—
686	#41	—	158	64	no	—
687	#41	—	158	64	no	—
688	#41	—	158	64	no	—
689	C₂×Q₈	—	79	16	no	—
690	C₂×Q₈	—	158	16	no	—
691	C₂×D₄	—	2	16	no	—
692	C₂×D₄	—	2	16	no	—
693	C₂×D₄	—	2	16	no	—
694	C₂×D₄	—	2	16	no	—
695	C₂×D₄	—	2	16	no	—
696	C₂×D₄	—	2	16	no	—
697	C₂×D₄	—	8	4	no	—
698	C₂×D₄	—	79	32	no	—
699	C₂×D₄	—	79	4	no	—
700	C₂×D₄	—	79	4	no	—
701	C₂×D₄	—	79	8	no	—
702	C₂×D₄	—	79	32	no	—
703	C₂×D₄	—	79	32	no	—
704	C₂×D₄	—	79	16	no	—
705	C₂×D₄	—	79	16	no	—
706	C₂×D₄	—	79	8	no	—
707	C₂×D₄	—	79	16	no	—
708	C₂×D₄	—	79	8	no	—
709	C₂×D₄	—	79	8	no	—
710	C₂×D₄	—	79	8	no	—
711	C₂×D₄	—	79	16	no	—
712	C₂×D₄	—	79	16	no	—
713	C₂×D₄	—	79	16	no	—
714	C₂×D₄	—	632	4	no	—
715	C₂×D₄	—	632	16	no	—
716	C₂×D₄	—	632	8	no	—
717	C₂×D₄	—	158	16	no	—
718	C₂×D₄	—	158	16	no	—
719	C₂×D₄	—	158	64	no	—
720	C₂×D₄	—	158	64	no	—
721	C₂×D₄	—	158	64	no	—
722	C₂×D₄	—	158	64	no	—
723	C₂×D₄	—	158	64	no	—
724	C₂×D₄	—	158	64	no	—
725	C₂×D₄	—	158	16	no	—
726	C₂×D₄	—	158	16	no	—
727	C₂×D₄	—	158	16	no	—
728	C₂×D₄	—	158	16	no	—
729	C₂×D₄	—	158	16	no	—
730	C₂×D₄	—	158	16	no	—
731	C₂×D₄	—	158	16	no	—
732	C₂×D₄	C₂³×D₇₉	1	8	yes	—
733	C₂×D₄	C₂³×D₇₉	1	8	yes	—
734	C₂×D₄	C₂³×D₇₉	1	8	yes	—
735	C₂×D₄	C₂³×D₇₉	1	8	yes	—
736	C₂×D₄	C₂³×D₇₉	1	16	yes	—
737	C₂²×C₄	—	2	8	no	—
738	C₂²×C₄	—	8	2	no	—
739	C₂²×C₄	—	79	4	no	—
740	C₂²×C₄	—	79	8	no	—
741	C₂²×C₄	—	79	16	no	—
742	C₂²×C₄	—	79	2	no	—
743	C₂²×C₄	—	79	4	no	—
744	C₂²×C₄	—	79	8	no	—
745	C₂²×C₄	—	79	4	no	—
746	C₂²×C₄	—	79	4	no	—
747	C₂²×C₄	—	79	16	no	—
748	C₂²×C₄	—	79	4	no	—
749	C₂²×C₄	—	79	16	no	—
750	C₂²×C₄	—	79	16	no	—
751	C₂²×C₄	—	632	4	no	—
752	C₂²×C₄	—	632	2	no	—
753	C₂²×C₄	—	158	16	no	—
754	C₂²×C₄	—	158	16	no	—
755	C₂²×C₄	—	158	16	no	—
756	C₂²×C₄	—	158	8	no	—
757	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
758	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
759	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
760	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
761	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
762	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
763	C₄⋊C₄	—	79	32	no	—
764	C₄⋊C₄	—	79	16	no	—
765	C₄⋊C₄	—	79	16	no	—
766	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
767	C₂²⋊C₄	—	79	8	no	—
768	C₂²⋊C₄	—	79	4	no	—
769	C₂²⋊C₄	—	79	4	no	—
770	C₂²⋊C₄	—	79	32	no	—
771	C₂²⋊C₄	—	79	16	no	—
772	C₂²⋊C₄	—	79	32	no	—
773	C₂²⋊C₄	—	79	32	no	—
774	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
775	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
776	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
777	C₄²	—	79	16	no	—
778	C₂³	—	2	8	no	—
779	C₂³	—	2	8	no	—
780	C₂³	—	2	8	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	8	no	—
787	C₂³	—	4	8	no	—
788	C₂³	—	4	8	no	—
789	C₂³	—	8	8	no	—
790	C₂³	—	8	16	no	—
791	C₂³	—	316	4	no	—
792	C₂³	—	316	8	no	—
793	C₂³	—	316	8	no	—
794	C₂³	—	316	8	no	—
795	C₂³	—	316	8	no	—
796	C₂³	—	316	32	no	—
797	C₂³	—	79	16	no	—
798	C₂³	—	79	8	no	—
799	C₂³	—	79	4	no	—
800	C₂³	—	79	8	no	—
801	C₂³	—	632	8	no	—
802	C₂³	—	632	16	no	—
803	C₂³	—	632	32	no	—
804	C₂³	—	158	32	no	—
805	C₂³	—	158	8	no	—
806	C₂³	—	158	8	no	—
807	C₂³	—	158	8	no	—
808	C₂³	C₂×D₄×D₇₉	1	8	yes	—
809	C₂³	C₂×D₄×D₇₉	1	4	yes	—
810	C₂³	C₂×D₄×D₇₉	1	8	yes	—
811	C₂³	C₂×D₄×D₇₉	1	4	yes	—
812	C₂³	C₂×D₄×D₇₉	1	4	yes	—
813	C₂³	C₂⁴×D₇₉	1	8	yes	—
814	C₂³	C₂⁴×D₇₉	1	2	yes	—
815	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
816	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
817	C₂³	C₂⁴×D₇₉	1	2	yes	—
818	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
819	Q₈	—	158	32	no	—
820	D₄	—	2	16	no	—
821	D₄	—	2	16	no	—
822	D₄	—	2	16	no	—
823	D₄	—	2	16	no	—
824	D₄	—	4	16	no	—
825	D₄	—	316	16	no	—
826	D₄	—	316	32	no	—
827	D₄	—	79	16	no	—
828	D₄	—	79	32	no	—
829	D₄	—	79	16	no	—
830	D₄	—	158	32	no	—
831	D₄	—	158	32	no	—
832	D₄	—	158	32	no	—
833	D₄	—	158	16	no	—
834	D₄	—	158	16	no	—
835	D₄	—	158	16	no	—
836	D₄	—	158	16	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	316	16	no	—
844	C₂×C₄	—	316	4	no	—
845	C₂×C₄	—	316	8	no	—
846	C₂×C₄	—	79	4	no	—
847	C₂×C₄	—	79	16	no	—
848	C₂×C₄	—	79	8	no	—
849	C₂×C₄	—	79	8	no	—
850	C₂×C₄	—	79	8	no	—
851	C₂×C₄	—	158	32	no	—
852	C₂×C₄	—	158	32	no	—
853	C₂×C₄	—	158	32	no	—
854	C₂×C₄	—	158	8	no	—
855	C₂×C₄	—	158	8	no	—
856	C₂×C₄	—	158	8	no	—
857	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
858	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	8	no	—
865	C₂²	—	2	16	no	—
866	C₂²	—	4	8	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	4	8	no	—
869	C₂²	—	4	4	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	16	no	—
872	C₂²	—	8	8	no	—
873	C₂²	—	8	8	no	—
874	C₂²	—	316	16	no	—
875	C₂²	—	316	16	no	—
876	C₂²	—	316	8	no	—
877	C₂²	—	79	8	no	—
878	C₂²	—	632	8	no	—
879	C₂²	—	632	8	no	—
880	C₂²	—	632	32	no	—
881	C₂²	—	158	8	no	—
882	C₂²	—	158	16	no	—
883	C₂²	—	158	8	no	—
884	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
885	C₂²	C₂²×D₄×D₇₉	1	4	yes	—
886	C₂²	C₂²×D₄×D₇₉	1	4	yes	—
887	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
888	C₂²	C₂²×D₄×D₇₉	1	2	yes	—
889	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
890	C₄	—	2	8	no	—
891	C₄	—	2	8	no	—
892	C₄	—	79	8	no	—
893	C₄	—	158	8	no	—
894	C₄	—	158	8	no	—
895	C₂	—	2	4	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	4	no	—
898	C₂	—	2	2	no	—
899	C₂	—	2	2	no	—
900	C₂	—	4	8	no	—
901	C₂	—	316	8	no	—
902	C₂	—	158	8	no	—
903	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
904	C₂	#23778210	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₂×#534×C₇₉	C₂
hypercenter	C₂×#534	D₇₉
hypocenter	C₇₉	#62842
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×#14579206	C₂	semidirect
2. #23777161	C₂	semidirect
3. #23777157	C₂	semidirect
4. #23777041	C₂	semidirect
5. #23777038	C₂	semidirect
6. #23777032	C₂	semidirect
7. #23777029	C₂	semidirect
8. #23776726	C₂	semidirect
9. C₂×#19099125	C₂	semidirect
10. C₂×#19099122	C₂	semidirect
11. #534×D₇₉	C₂	semidirect
12. C₂×#19099036	C₂	semidirect
13. C₂×#534×C₇₉	C₂	semidirect
15. C₂×#14579206	C₂²	semidirect
16. C₂×#14579206	C₂²	semidirect
17. C₂×#14579206	C₂²	semidirect
18. C₂×#14579206	C₂²	semidirect
19. C₂²×#11929624	C₂²	semidirect
20. C₂²×#11929623	C₂²	semidirect
21. C₂²×#11929623	C₂²	semidirect
23. C₂³×C₂²⋊D₇₉	C₂²	semidirect
24. C₂³×C₂²⋊D₇₉	C₂²	semidirect
25. C₂²×D₄×D₇₉	C₂²	semidirect
26. C₂²×D₄×D₇₉	C₂²	semidirect
27. #19099214	C₂²	semidirect
28. #19099213	C₂²	semidirect
29. #19099211	C₂²	semidirect
30. #19099205	C₂²	semidirect
31. #19099203	C₂²	semidirect
32. #19099202	C₂²	semidirect
33. #19099200	C₂²	semidirect
34. #19099197	C₂²	semidirect
35. D₄×C₂²⋊D₇₉	C₂²	semidirect
36. #19099195	C₂²	semidirect
37. #19099140	C₂²	semidirect
38. #19099135	C₂²	semidirect
39. #19099128	C₂²	semidirect
40. #19099125	C₂²	semidirect
41. #19099125	C₂²	semidirect
42. #19099125	C₂²	semidirect
43. #19099124	C₂²	semidirect
44. #19099123	C₂²	semidirect
45. #19099122	C₂²	semidirect
46. #19099122	C₂²	semidirect
47. #19099122	C₂²	semidirect
48. #19099122	C₂²	semidirect
49. #19099121	C₂²	semidirect
50. #19099108	C₂²	semidirect
51. #19099071	C₂²	semidirect
52. #19099069	C₂²	semidirect
53. C₂×#14579145	C₂²	semidirect
54. C₂×#14579144	C₂²	semidirect
55. C₂×#14579142	C₂²	semidirect
56. #123×D₇₉	C₂²	semidirect
57. C₂×#14579135	C₂²	semidirect
58. C₂×#14579133	C₂²	semidirect
59. #121×D₇₉	C₂²	semidirect
60. C₂×#14579131	C₂²	semidirect
61. C₂×#14579130	C₂²	semidirect
62. C₂×#14579129	C₂²	semidirect
63. #120×D₇₉	C₂²	semidirect
64. #19099036	C₂²	semidirect
65. #19099036	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
67. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
68. C₂×#14579117	C₂²	semidirect
69. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
71. C₂³×D₄×C₇₉	C₂²	semidirect
72. #534×C₇₉	C₂²	semidirect
73. #534×C₇₉	C₂²	semidirect
74. #534×C₇₉	C₂²	semidirect
75. C₂×#123×C₇₉	C₂²	semidirect
76. C₂×#121×C₇₉	C₂²	semidirect
77. C₂×#120×C₇₉	C₂²	semidirect
78. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
80. C₂⁴×D₇₉	C₂³	semidirect
81. C₂⁴×D₇₉	C₂³	semidirect
87. C₂×#11929624	C₂³	semidirect
88. C₂×#11929624	C₂³	semidirect
92. C₂×#11929623	C₂³	semidirect
93. C₂×#11929623	C₂³	semidirect
94. C₂×#11929623	C₂³	semidirect
95. C₂²×Dic₁₅₈	C₂³	semidirect
96. C₂²×D₃₁₆	C₂³	semidirect
97. C₂²×D₃₁₆	C₂³	semidirect
100. C₂²×C₂²⋊D₇₉	D₄	semidirect
108. C₂²×C₂²⋊D₇₉	C₂³	semidirect
109. C₂²×C₂²⋊D₇₉	C₂³	semidirect
110. C₂²×C₂²⋊D₇₉	C₂³	semidirect
111. C₂²×C₂²⋊D₇₉	C₂³	semidirect
112. C₂²×C₂²⋊D₇₉	C₂³	semidirect
113. C₂²×C₂²⋊D₇₉	C₂³	semidirect
114. C₂²×C₂²⋊D₇₉	C₂³	semidirect
115. C₂²×C₂²⋊D₇₉	C₂³	semidirect
119. C₂×D₄×D₇₉	C₂³	semidirect
120. C₂×D₄×D₇₉	C₂³	semidirect
121. C₂×D₄×D₇₉	C₂³	semidirect
122. C₂×D₄×D₇₉	C₂³	semidirect
124. C₂³×Dic₇₉	C₂³	semidirect
125. C₂³×Dic₇₉	C₂³	semidirect
126. C₂³×Dic₇₉	C₂³	semidirect
127. C₂²×C₄×D₇₉	C₂³	semidirect
128. C₂²×C₄×D₇₉	C₂³	semidirect
129. C₂²×C₄×D₇₉	C₂³	semidirect
130. #14579160	C₂³	semidirect
131. #14579157	C₂³	semidirect
132. #14579147	C₂³	semidirect
133. #14579146	C₂³	semidirect
134. #14579145	C₂³	semidirect
135. #14579145	C₂³	semidirect
136. #14579144	C₂³	semidirect
137. #14579144	C₂³	semidirect
138. #14579143	C₂³	semidirect
139. #14579142	C₂³	semidirect
140. #14579142	C₂³	semidirect
141. #14579139	C₂³	semidirect
142. #14579138	C₂³	semidirect
143. #14579136	C₂³	semidirect
144. #14579135	C₂³	semidirect
145. #14579135	C₂³	semidirect
146. #14579134	C₂³	semidirect
147. #14579134	C₂³	semidirect
148. #14579133	C₂³	semidirect
149. #14579133	C₂³	semidirect
150. #14579133	C₂³	semidirect
151. #14579132	C₂³	semidirect
152. #14579131	C₂³	semidirect
153. #14579131	C₂³	semidirect
154. #14579131	C₂³	semidirect
155. #14579130	C₂³	semidirect
156. #14579130	C₂³	semidirect
157. #14579129	C₂³	semidirect
158. #14579129	C₂³	semidirect
159. #14579129	C₂³	semidirect
160. D₄×Dic₇₉	C₂³	semidirect
161. #14579123	C₂³	semidirect
162. C₄×C₂²⋊D₇₉	C₂³	semidirect
163. C₄×C₂²⋊D₇₉	C₂³	semidirect
164. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
165. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
166. #14579117	C₂³	semidirect
167. C₂×C₄⋊Dic₇₉	C₂³	semidirect
168. C₂×Dic₇₉⋊C₄	C₂³	semidirect
169. C₂×Dic₇₉⋊C₄	C₂³	semidirect
170. C₄⋊C₄×D₇₉	C₂³	semidirect
172. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
173. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
174. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
175. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
176. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
177. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
178. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
179. C₂²⋊C₄×D₇₉	C₂³	semidirect
180. C₂²⋊C₄×D₇₉	C₂³	semidirect
181. C₂×C₄×Dic₇₉	C₂³	semidirect
183. C₂⁵×C₇₉	C₂³	semidirect
188. C₂²×D₄×C₇₉	C₂³	semidirect
189. C₂²×D₄×C₇₉	C₂³	semidirect
190. C₂²×D₄×C₇₉	C₂³	semidirect
191. C₂²×D₄×C₇₉	C₂³	semidirect
192. C₂³×C₄×C₇₉	C₂³	semidirect
193. C₂³×C₄×C₇₉	C₂³	semidirect
194. #123×C₇₉	C₂³	semidirect
195. #123×C₇₉	C₂³	semidirect
196. #121×C₇₉	C₂³	semidirect
197. #121×C₇₉	C₂³	semidirect
198. #120×C₇₉	C₂³	semidirect
199. #120×C₇₉	C₂³	semidirect
200. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
202. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
203. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
204. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
205. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
211. C₂³×D₇₉	C₂×D₄	semidirect
241. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
242. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
243. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
244. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
263. C₂²×Dic₇₉	C₂×D₄	semidirect
292. C₂⁴×C₇₉	C₂×D₄	semidirect
464. C₂×#534	D₇₉	semidirect
466. C₇₉	#62842	semidirect
480. C₂³×D₄	C₂×D₇₉	semidirect
504. #534	C₂×D₇₉	semidirect
505. #534	C₂×D₇₉	semidirect
506. #534	C₂×D₇₉	semidirect
514. C₂×#123	C₂×D₇₉	semidirect
518. C₂×#121	C₂×D₇₉	semidirect
523. C₂×#120	C₂×D₇₉	semidirect
531. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
536. C₂⁵	C₂²×D₇₉	semidirect
582. C₂²×D₄	C₂²×D₇₉	semidirect
583. C₂²×D₄	C₂²×D₇₉	semidirect
584. C₂²×D₄	C₂²×D₇₉	semidirect
585. C₂²×D₄	C₂²×D₇₉	semidirect
593. C₂³×C₄	C₂²×D₇₉	semidirect
594. C₂³×C₄	C₂²×D₇₉	semidirect
606. #123	C₂²×D₇₉	semidirect
607. #123	C₂²×D₇₉	semidirect
619. #121	C₂²×D₇₉	semidirect
620. #121	C₂²×D₇₉	semidirect
629. #120	C₂²×D₇₉	semidirect
630. #120	C₂²×D₇₉	semidirect
642. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
654. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
655. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
656. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
657. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
674. C₂⁴	D₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579206	2
#23777161	2
#23777157	2
#23777041	2
#23777038	2
#23777032	2
#23777029	2
#23776726	2
C₂×#19099125	2
C₂×#19099122	2
#534×D₇₉	2
C₂×#19099036	2
C₂×#534×C₇₉	2
#62842	79