Subgroups — C₂×#23777085 #35196179

Order 20224.

9502 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777085	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099242	C₂	1	4	yes	maximal, complemented
3	C₂×#19099237	C₂	1	4	yes	maximal, complemented
4	C₂×#19099209	C₂	1	4	yes	maximal, complemented
5	C₂×#19099203	C₂	1	4	yes	maximal, complemented
6	C₂×#19099189	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19099146	C₂	1	4	yes	maximal, complemented
8	C₂×#19099122	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19099072	C₂	1	4	yes	maximal, complemented
10	C₂²×#14579131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#14579129	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#19099036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₂²⋊C₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#518×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁵×D₇₉	C₂²	1	1	yes	characteristic
16	C₂²×#11929624	C₂²	1	4	yes	complemented
17	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
18	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
19	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
20	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
21	#19099242	C₂²	1	64	yes	complemented
22	#19099237	C₂²	1	64	yes	complemented
23	#19099209	C₂²	1	64	yes	complemented
24	#19099203	C₂²	1	64	yes	complemented
25	#19099189	C₂²	1	16	yes	complemented
26	#19099146	C₂²	1	64	yes	complemented
27	#19099122	C₂²	1	16	yes	complemented
28	C₂×#14579156	C₂²	1	4	yes	complemented
29	C₂×#14579155	C₂²	1	4	yes	complemented
30	C₂×#14579149	C₂²	1	4	yes	complemented
31	C₂×#14579147	C₂²	1	4	yes	complemented
32	#19099072	C₂²	1	64	yes	complemented
33	C₂×#14579146	C₂²	1	4	yes	complemented
34	C₂×#14579146	C₂²	1	4	yes	complemented
35	C₂×#14579144	C₂²	1	2	yes	complemented
36	C₂×#14579144	C₂²	1	4	yes	complemented
37	C₂×#14579143	C₂²	1	4	yes	complemented
38	C₂×#14579142	C₂²	1	2	yes	complemented
39	C₂×#14579140	C₂²	1	4	yes	complemented
40	C₂×#14579139	C₂²	1	4	yes	complemented
41	C₂×#14579138	C₂²	1	4	yes	complemented
42	C₂×#14579138	C₂²	1	4	yes	complemented
43	C₂×#14579135	C₂²	1	4	yes	complemented
44	C₂×#14579134	C₂²	1	4	yes	complemented
45	C₂×#14579134	C₂²	1	4	yes	complemented
46	C₂×#14579133	C₂²	1	4	yes	complemented
47	C₂×#14579131	C₂²	1	4	yes	—
48	C₂×#14579131	C₂²	1	2	yes	complemented
49	C₂×#14579131	C₂²	1	2	yes	complemented
50	C₂×#14579131	C₂²	1	16	yes	complemented
51	C₂×#14579130	C₂²	1	2	yes	complemented
52	C₂×#14579129	C₂²	1	4	yes	—
53	C₂×#14579129	C₂²	1	2	yes	complemented
54	C₂×#14579129	C₂²	1	2	yes	complemented
55	C₂×#14579129	C₂²	1	16	yes	complemented
56	C₂×#14579129	C₂²	1	2	yes	complemented
57	#19099036	C₂²	1	16	yes	complemented
58	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
59	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
60	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
61	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
62	C₂×#14579118	C₂²	1	4	yes	complemented
63	C₂×#14579117	C₂²	1	2	yes	complemented
64	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
66	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
67	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
68	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
70	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊C₄×D₇₉	C₂²	1	16	yes	complemented
72	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
73	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
74	#518×C₇₉	C₂²	1	16	yes	complemented
75	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	complemented
77	C₂×#117×C₇₉	C₂²	1	2	yes	complemented
78	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
79	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
80	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
81	C₂⁴×D₇₉	—	2	8	no	—
82	C₂⁴×D₇₉	—	4	8	no	—
83	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
84	C₂⁴×D₇₉	C₂³	1	2	yes	—
85	C₂⁴×D₇₉	C₂³	1	2	yes	—
86	C₂⁴×D₇₉	C₂³	1	8	yes	—
87	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
88	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
89	C₂×#11929624	—	4	16	no	—
90	C₂×#11929624	C₂³	1	32	yes	complemented
91	C₂²×Dic₁₅₈	C₂³	1	4	yes	complemented
92	C₂²×D₃₁₆	—	4	8	no	—
93	C₂²×D₃₁₆	C₂³	1	4	yes	—
94	C₂²×D₃₁₆	C₂³	1	4	yes	—
95	C₂²×D₃₁₆	C₂³	1	16	yes	complemented
96	C₂²×C₂²⋊D₇₉	—	2	8	no	—
97	C₂²×C₂²⋊D₇₉	—	4	8	no	—
98	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
99	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
100	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
101	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
102	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
104	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	complemented
105	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
106	C₂³×Dic₇₉	C₂³	1	2	yes	—
107	C₂³×Dic₇₉	C₂³	1	2	yes	—
108	C₂²×C₄×D₇₉	—	4	8	no	—
109	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
110	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
111	C₂²×C₄×D₇₉	C₂³	1	16	yes	complemented
112	C₂²×C₄×D₇₉	C₂³	1	4	yes	complemented
113	#14579156	C₂³	1	32	yes	complemented
114	#14579155	C₂³	1	32	yes	complemented
115	#14579149	C₂³	1	32	yes	complemented
116	#14579147	C₂³	1	32	yes	complemented
117	#14579146	C₂³	1	32	yes	complemented
118	#14579146	C₂³	1	32	yes	complemented
119	#14579144	C₂³	1	32	yes	complemented
120	#14579144	C₂³	1	16	yes	complemented
121	#14579143	C₂³	1	32	yes	complemented
122	#14579142	C₂³	1	16	yes	complemented
123	#14579140	C₂³	1	32	yes	complemented
124	#14579139	C₂³	1	32	yes	complemented
125	#14579138	C₂³	1	32	yes	complemented
126	#14579138	C₂³	1	32	yes	complemented
127	#14579135	C₂³	1	32	yes	complemented
128	#14579134	C₂³	1	32	yes	complemented
129	#14579134	C₂³	1	32	yes	complemented
130	#14579133	C₂³	1	32	yes	complemented
131	#14579131	C₂³	1	32	yes	—
132	#14579131	C₂³	1	16	yes	complemented
133	#14579131	C₂³	1	16	yes	complemented
134	#14579130	C₂³	1	16	yes	complemented
135	#14579129	C₂³	1	32	yes	—
136	#14579129	C₂³	1	16	yes	complemented
137	#14579129	C₂³	1	16	yes	complemented
138	#14579129	C₂³	1	16	yes	complemented
139	C₄×D₃₁₆	C₂³	1	32	yes	complemented
140	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
141	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
142	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
143	#14579118	C₂³	1	32	yes	complemented
144	#14579117	C₂³	1	16	yes	complemented
145	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	complemented
146	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	complemented
147	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	complemented
148	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	complemented
149	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	complemented
150	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
151	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
152	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	complemented
157	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
159	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
160	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
161	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
162	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
163	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
164	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
165	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
166	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	complemented
167	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	complemented
168	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
169	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
170	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
171	C₂×C₄×Dic₇₉	C₂³	1	4	yes	complemented
172	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
173	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
174	C₂²×D₄×C₇₉	—	2	8	no	—
175	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
176	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
177	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
178	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
179	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
180	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
181	C₂³×C₄×C₇₉	C₂³	1	4	yes	complemented
182	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
183	C₄×D₄×C₇₉	C₂³	1	32	yes	complemented
184	#117×C₇₉	C₂³	1	16	yes	complemented
185	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	complemented
186	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
187	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
192	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	complemented
193	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	complemented
194	C₂×C₄²×C₇₉	C₂³	1	4	yes	complemented
195	C₂³×D₇₉	—	2	4	no	—
196	C₂³×D₇₉	—	2	8	no	—
197	C₂³×D₇₉	—	2	8	no	—
198	C₂³×D₇₉	—	2	8	no	—
199	C₂³×D₇₉	—	2	4	no	—
200	C₂³×D₇₉	—	2	32	no	—
201	C₂³×D₇₉	—	2	4	no	—
202	C₂³×D₇₉	—	2	8	no	—
203	C₂³×D₇₉	—	2	8	no	—
204	C₂³×D₇₉	—	4	32	no	—
205	C₂³×D₇₉	—	4	4	no	—
206	C₂³×D₇₉	—	4	4	no	—
207	C₂³×D₇₉	—	4	4	no	—
208	C₂³×D₇₉	—	4	4	no	—
209	C₂³×D₇₉	—	4	64	no	—
210	C₂³×D₇₉	C₂⁴	1	2	yes	—
211	C₂³×D₇₉	C₂⁴	1	4	yes	—
212	C₂³×D₇₉	C₂⁴	1	2	yes	—
213	C₂³×D₇₉	C₂⁴	1	8	yes	—
214	C₂³×D₇₉	C₂⁴	1	8	yes	—
215	C₂³×D₇₉	C₂⁴	1	2	yes	—
216	C₂³×D₇₉	C₂⁴	1	4	yes	—
217	C₂³×D₇₉	C₂⁴	1	4	yes	—
218	#11929624	—	4	64	no	—
219	C₂×Dic₁₅₈	—	4	8	no	—
220	C₂×Dic₁₅₈	C₂⁴	1	16	yes	complemented
221	C₂×D₃₁₆	—	2	16	no	—
222	C₂×D₃₁₆	—	4	8	no	—
223	C₂×D₃₁₆	—	4	32	no	—
224	C₂×D₃₁₆	C₂⁴	1	16	yes	—
225	C₂×D₃₁₆	C₂⁴	1	16	yes	—
226	C₂×C₂²⋊D₇₉	—	2	8	no	—
227	C₂×C₂²⋊D₇₉	—	2	8	no	—
228	C₂×C₂²⋊D₇₉	—	2	32	no	—
229	C₂×C₂²⋊D₇₉	—	2	16	no	—
230	C₂×C₂²⋊D₇₉	—	4	32	no	—
231	C₂×C₂²⋊D₇₉	—	4	8	no	—
232	C₂×C₂²⋊D₇₉	—	4	8	no	—
233	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
234	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
235	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
236	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
237	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	complemented
238	C₂²×Dic₇₉	—	2	4	no	—
239	C₂²×Dic₇₉	—	4	4	no	—
240	C₂²×Dic₇₉	—	4	4	no	—
241	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
242	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
243	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
244	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
245	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
246	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
247	C₂×C₄×D₇₉	—	2	16	no	—
248	C₂×C₄×D₇₉	—	4	8	no	—
249	C₂×C₄×D₇₉	—	4	8	no	—
250	C₂×C₄×D₇₉	—	4	32	no	—
251	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
252	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
253	C₂×C₄×D₇₉	C₂⁴	1	16	yes	complemented
254	C₄⋊Dic₇₉	C₂⁴	1	16	yes	complemented
255	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
256	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
257	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
258	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
259	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
260	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
261	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
262	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
263	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	complemented
264	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
265	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
266	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
267	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
268	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
269	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
270	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
271	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
272	C₄×Dic₇₉	C₂⁴	1	16	yes	complemented
273	C₂⁴×C₇₉	—	2	4	no	—
274	C₂⁴×C₇₉	—	4	4	no	—
275	C₂⁴×C₇₉	—	4	4	no	—
276	C₂⁴×C₇₉	#41	1	8	yes	complemented
277	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
278	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
279	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
282	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
283	C₂×D₄×C₇₉	—	2	8	no	—
284	C₂×D₄×C₇₉	—	2	8	no	—
285	C₂×D₄×C₇₉	—	2	32	no	—
286	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
287	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₇₉	—	2	4	no	—
289	C₂²×C₄×C₇₉	—	4	8	no	—
290	C₂²×C₄×C₇₉	—	4	4	no	—
291	C₂²×C₄×C₇₉	—	4	4	no	—
292	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	complemented
299	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
300	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
301	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
303	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
304	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
305	C₄²×C₇₉	C₂⁴	1	16	yes	complemented
306	C₂³×C₇₉	—	2	4	no	—
307	C₂³×C₇₉	—	2	4	no	—
308	C₂³×C₇₉	—	2	4	no	—
309	C₂³×C₇₉	—	2	4	no	—
310	C₂³×C₇₉	—	2	8	no	—
311	C₂³×C₇₉	—	2	8	no	—
312	C₂³×C₇₉	—	4	16	no	—
313	C₂³×C₇₉	—	4	8	no	—
314	C₂³×C₇₉	—	4	8	no	—
315	C₂³×C₇₉	—	8	8	no	—
316	C₂³×C₇₉	C₂×#41	1	4	yes	—
317	C₂³×C₇₉	C₂×#41	1	4	yes	—
318	C₂³×C₇₉	C₂×#41	1	4	yes	—
319	C₂³×C₇₉	C₂×#41	1	16	yes	complemented
320	C₂³×C₇₉	C₂⁵	1	4	yes	—
321	C₂³×C₇₉	C₂⁵	1	2	yes	—
322	C₂³×C₇₉	C₂⁵	1	2	yes	—
323	C₂³×C₇₉	C₂⁵	1	2	yes	—
324	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
325	C₂²×D₇₉	—	2	32	no	—
326	C₂²×D₇₉	—	2	8	no	—
327	C₂²×D₇₉	—	2	4	no	—
328	C₂²×D₇₉	—	2	4	no	—
329	C₂²×D₇₉	—	2	16	no	—
330	C₂²×D₇₉	—	2	4	no	—
331	C₂²×D₇₉	—	2	16	no	—
332	C₂²×D₇₉	—	2	16	no	—
333	C₂²×D₇₉	—	2	8	no	—
334	C₂²×D₇₉	—	2	4	no	—
335	C₂²×D₇₉	—	2	8	no	—
336	C₂²×D₇₉	—	2	4	no	—
337	C₂²×D₇₉	—	2	4	no	—
338	C₂²×D₇₉	—	2	8	no	—
339	C₂²×D₇₉	—	2	16	no	—
340	C₂²×D₇₉	—	2	16	no	—
341	C₂²×D₇₉	—	4	8	no	—
342	C₂²×D₇₉	—	4	8	no	—
343	C₂²×D₇₉	—	4	8	no	—
344	C₂²×D₇₉	—	4	8	no	—
345	C₂²×D₇₉	—	4	32	no	—
346	C₂²×D₇₉	—	4	32	no	—
347	C₂²×D₇₉	—	4	128	no	—
348	C₂²×D₇₉	—	4	16	no	—
349	C₂²×D₇₉	—	8	8	no	—
350	C₂²×D₇₉	H(5,𝔽₂)	1	8	yes	—
351	C₂²×D₇₉	C₂⁵	1	4	yes	—
352	C₂²×D₇₉	C₂⁵	1	4	yes	—
353	C₂²×D₇₉	C₂⁵	1	4	yes	—
354	D₄×C₇₉	—	2	16	no	—
355	D₄×C₇₉	—	2	16	no	—
356	C₂×C₄×C₇₉	—	2	8	no	—
357	C₂×C₄×C₇₉	—	2	4	no	—
358	C₂×C₄×C₇₉	—	2	8	no	—
359	C₂×C₄×C₇₉	—	2	8	no	—
360	C₂×C₄×C₇₉	—	4	8	no	—
361	C₂×C₄×C₇₉	—	4	8	no	—
362	C₂×C₄×C₇₉	—	4	16	no	—
363	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
364	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
365	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
366	C₂²⋊D₇₉	—	2	16	no	—
367	C₂²⋊D₇₉	—	2	16	no	—
368	C₂²⋊D₇₉	—	2	32	no	—
369	C₂²⋊D₇₉	—	4	16	no	—
370	C₂²⋊D₇₉	—	4	16	no	—
371	C₂×Dic₇₉	—	2	8	no	—
372	C₂×Dic₇₉	—	2	4	no	—
373	C₂×Dic₇₉	—	2	8	no	—
374	C₂×Dic₇₉	—	2	8	no	—
375	C₂×Dic₇₉	—	4	8	no	—
376	C₂×Dic₇₉	—	4	8	no	—
377	C₂×Dic₇₉	C₂⁵	1	4	yes	—
378	C₂×Dic₇₉	C₂⁵	1	8	yes	—
379	C₂×Dic₇₉	C₂⁵	1	8	yes	—
380	D₃₁₆	—	2	32	no	—
381	D₃₁₆	—	4	16	no	—
382	C₄×D₇₉	—	2	32	no	—
383	C₄×D₇₉	—	4	16	no	—
384	C₄×D₇₉	—	4	16	no	—
385	Dic₁₅₈	—	4	16	no	—
386	C₂²×C₇₉	—	2	4	no	—
387	C₂²×C₇₉	—	2	4	no	—
388	C₂²×C₇₉	—	2	4	no	—
389	C₂²×C₇₉	—	2	8	no	—
390	C₂²×C₇₉	—	2	8	no	—
391	C₂²×C₇₉	—	2	8	no	—
392	C₂²×C₇₉	—	2	4	no	—
393	C₂²×C₇₉	—	2	8	no	—
394	C₂²×C₇₉	—	4	16	no	—
395	C₂²×C₇₉	—	4	8	no	—
396	C₂²×C₇₉	—	8	8	no	—
397	C₂²×C₇₉	C₂²×#41	1	4	yes	—
398	C₂²×C₇₉	C₂²×#41	1	4	yes	—
399	C₂²×C₇₉	C₂²×#41	1	4	yes	—
400	C₂²×C₇₉	C₂²×#41	1	2	yes	—
401	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
402	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
403	C₂×D₇₉	—	2	32	no	—
404	C₂×D₇₉	—	2	4	no	—
405	C₂×D₇₉	—	2	4	no	—
406	C₂×D₇₉	—	2	16	no	—
407	C₂×D₇₉	—	2	4	no	—
408	C₂×D₇₉	—	2	4	no	—
409	C₂×D₇₉	—	2	4	no	—
410	C₂×D₇₉	—	2	8	no	—
411	C₂×D₇₉	—	2	4	no	—
412	C₂×D₇₉	—	4	32	no	—
413	C₂×D₇₉	—	4	32	no	—
414	C₂×D₇₉	—	4	16	no	—
415	C₂×D₇₉	—	4	8	no	—
416	C₂×D₇₉	—	4	8	no	—
417	C₂×D₇₉	—	8	8	no	—
418	C₂×D₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
419	C₄×C₇₉	—	2	4	no	—
420	C₄×C₇₉	—	2	8	no	—
421	C₄×C₇₉	—	2	8	no	—
422	Dic₇₉	—	2	4	no	—
423	Dic₇₉	—	2	8	no	—
424	Dic₇₉	—	2	8	no	—
425	C₂×#3490	—	79	1	no	maximal, Sylow
426	C₂×C₇₉	—	2	4	no	—
427	C₂×C₇₉	—	2	4	no	—
428	C₂×C₇₉	—	2	4	no	—
429	C₂×C₇₉	—	4	4	no	—
430	C₂×C₇₉	#3490	1	4	yes	complemented
431	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
432	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
433	D₇₉	—	2	8	no	—
434	D₇₉	—	4	4	no	—
435	D₇₉	—	4	4	no	—
436	#3490	—	79	32	no	—
437	C₂×#551	—	79	4	no	—
438	C₂×#551	—	79	4	no	—
439	C₂×#546	—	79	4	no	—
440	C₂×#546	—	79	4	no	—
441	C₂×#543	—	79	1	no	—
442	C₂×#538	—	79	4	no	—
443	C₂×#534	—	79	1	no	—
444	C₂×#525	—	79	4	no	—
445	C₂²×#120	—	79	1	no	—
446	C₂²×#120	—	79	1	no	—
447	C₂×#518	—	79	1	no	—
448	C₂×#518	D₇₉	1	1	yes	characteristic, complemented
449	C₂³×C₂²⋊C₄	—	79	1	no	—
450	C₇₉	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
451	C₂⁶	—	79	1	no	—
452	C₂²×#41	—	79	4	no	—
453	C₂³×D₄	—	79	2	no	—
454	C₂³×D₄	—	79	1	no	—
455	C₂³×D₄	—	79	2	no	—
456	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
457	C₂⁴×C₄	—	79	2	no	—
458	#551	—	79	64	no	—
459	#551	—	79	64	no	—
460	#546	—	79	64	no	—
461	#546	—	79	64	no	—
462	#543	—	79	16	no	—
463	#538	—	79	64	no	—
464	#534	—	79	16	no	—
465	C₂×#126	—	79	4	no	—
466	C₂×#126	—	79	4	no	—
467	C₂×#124	—	79	4	no	—
468	C₂×#124	—	79	4	no	—
469	#525	—	79	64	no	—
470	C₂×#123	—	79	2	no	—
471	C₂×#123	—	79	2	no	—
472	C₂×#123	—	79	4	no	—
473	C₂×#123	—	79	4	no	—
474	C₂×#123	—	79	4	no	—
475	C₂×#123	—	79	4	no	—
476	C₂×C₂²⋊Q₈	—	79	4	no	—
477	C₂×C₂²⋊Q₈	—	79	4	no	—
478	C₂×C₂²⋊Q₈	—	79	4	no	—
479	C₂×C₂²⋊Q₈	—	79	4	no	—
480	C₂×#121	—	79	4	no	—
481	C₂×#121	—	79	4	no	—
482	C₂×#121	—	79	4	no	—
483	C₂×#121	—	79	4	no	—
484	C₂×#120	—	79	2	no	—
485	C₂×#120	—	79	2	no	—
486	C₂×#120	—	79	2	no	—
487	C₂×#120	—	79	4	no	—
488	C₂×#120	—	79	16	no	—
489	C₂×#120	—	79	2	no	—
490	C₂×#120	—	79	2	no	—
491	C₂×#120	—	79	2	no	—
492	C₂×#120	—	79	4	no	—
493	C₂×#120	—	79	16	no	—
494	#518	—	79	16	no	—
495	#518	C₂×D₇₉	1	16	yes	complemented
496	C₂×C₄×D₄	—	79	4	no	—
497	C₂×C₄×D₄	—	79	4	no	—
498	C₂×C₄×D₄	—	79	4	no	—
499	C₂×C₄×D₄	—	79	4	no	—
500	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
501	C₂×C₄×D₄	C₂×D₇₉	1	4	yes	complemented
502	C₂×#117	—	79	2	no	—
503	C₂×#117	—	79	4	no	—
504	C₂×#117	C₂×D₇₉	1	2	yes	complemented
505	C₂²×C₂²⋊C₄	—	79	1	no	—
506	C₂²×C₂²⋊C₄	—	79	1	no	—
507	C₂²×C₂²⋊C₄	—	79	2	no	—
508	C₂²×C₂²⋊C₄	—	79	2	no	—
509	C₂²×C₂²⋊C₄	—	79	2	no	—
510	C₂²×C₂²⋊C₄	—	79	4	no	—
511	C₂²×C₂²⋊C₄	—	79	4	no	—
512	C₂²×C₂²⋊C₄	—	79	16	no	—
513	C₂²×C₂²⋊C₄	—	79	2	no	—
514	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
515	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
516	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
517	C₂⁵	—	316	8	no	—
518	C₂⁵	—	79	1	no	—
519	C₂⁵	—	79	8	no	—
520	C₂⁵	—	79	1	no	—
521	C₂⁵	—	79	2	no	—
522	C₂⁵	—	79	2	no	—
523	C₂⁵	—	79	1	no	—
524	C₂⁵	—	158	8	no	—
525	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
526	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
527	C₂×#41	—	316	16	no	—
528	C₂×#41	—	79	32	no	—
529	C₂²×Q₈	—	79	4	no	—
530	C₂²×D₄	—	2	8	no	—
531	C₂²×D₄	—	316	8	no	—
532	C₂²×D₄	—	316	8	no	—
533	C₂²×D₄	—	79	4	no	—
534	C₂²×D₄	—	79	4	no	—
535	C₂²×D₄	—	79	16	no	—
536	C₂²×D₄	—	79	2	no	—
537	C₂²×D₄	—	79	2	no	—
538	C₂²×D₄	—	79	4	no	—
539	C₂²×D₄	—	79	8	no	—
540	C₂²×D₄	—	79	4	no	—
541	C₂²×D₄	—	79	16	no	—
542	C₂²×D₄	—	79	4	no	—
543	C₂²×D₄	—	158	8	no	—
544	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
545	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
546	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
547	C₂³×C₄	—	316	8	no	—
548	C₂³×C₄	—	79	2	no	—
549	C₂³×C₄	—	79	2	no	—
550	C₂³×C₄	—	79	4	no	—
551	C₂³×C₄	—	79	16	no	—
552	C₂³×C₄	—	79	4	no	—
553	C₂³×C₄	—	79	1	no	—
554	C₂³×C₄	—	79	4	no	—
555	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
556	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
557	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
558	C₂³×C₄	C₂²×D₇₉	1	4	yes	complemented
559	#126	—	79	32	no	—
560	#126	—	79	32	no	—
561	#124	—	79	32	no	—
562	#124	—	79	32	no	—
563	#123	—	79	16	no	—
564	#123	—	79	16	no	—
565	#123	—	79	32	no	—
566	#123	—	79	32	no	—
567	#123	—	79	32	no	—
568	#123	—	79	32	no	—
569	C₂²⋊Q₈	—	79	32	no	—
570	C₂²⋊Q₈	—	79	32	no	—
571	C₂²⋊Q₈	—	79	32	no	—
572	C₂²⋊Q₈	—	79	32	no	—
573	#121	—	79	32	no	—
574	#121	—	79	32	no	—
575	#121	—	79	32	no	—
576	#121	—	79	32	no	—
577	#120	—	79	16	no	—
578	#120	—	79	16	no	—
579	#120	—	79	16	no	—
580	#120	—	79	32	no	—
581	#120	—	79	16	no	—
582	#120	—	79	16	no	—
583	#120	—	79	16	no	—
584	#120	—	79	32	no	—
585	C₄×D₄	—	79	32	no	—
586	C₄×D₄	—	79	32	no	—
587	C₄×D₄	—	79	32	no	—
588	C₄×D₄	—	79	32	no	—
589	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
590	C₄×D₄	C₂²×D₇₉	1	32	yes	complemented
591	#117	—	79	16	no	—
592	#117	—	79	32	no	—
593	#117	C₂²×D₇₉	1	16	yes	complemented
594	C₂×C₄⋊C₄	—	79	4	no	—
595	C₂×C₄⋊C₄	—	79	4	no	—
596	C₂×C₄⋊C₄	—	79	4	no	—
597	C₂×C₄⋊C₄	—	79	4	no	—
598	C₂×C₄⋊C₄	—	79	4	no	—
599	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	complemented
600	C₂×C₂²⋊C₄	—	79	2	no	—
601	C₂×C₂²⋊C₄	—	79	2	no	—
602	C₂×C₂²⋊C₄	—	79	8	no	—
603	C₂×C₂²⋊C₄	—	79	2	no	—
604	C₂×C₂²⋊C₄	—	79	2	no	—
605	C₂×C₂²⋊C₄	—	79	8	no	—
606	C₂×C₂²⋊C₄	—	79	4	no	—
607	C₂×C₂²⋊C₄	—	79	4	no	—
608	C₂×C₂²⋊C₄	—	79	4	no	—
609	C₂×C₂²⋊C₄	—	79	16	no	—
610	C₂×C₂²⋊C₄	—	79	4	no	—
611	C₂×C₂²⋊C₄	—	79	4	no	—
612	C₂×C₂²⋊C₄	—	79	4	no	—
613	C₂×C₂²⋊C₄	—	79	4	no	—
614	C₂×C₂²⋊C₄	—	79	4	no	—
615	C₂×C₂²⋊C₄	—	79	16	no	—
616	C₂×C₂²⋊C₄	—	79	16	no	—
617	C₂×C₂²⋊C₄	—	79	4	no	—
618	C₂×C₂²⋊C₄	—	79	32	no	—
619	C₂×C₂²⋊C₄	—	79	32	no	—
620	C₂×C₂²⋊C₄	—	79	16	no	—
621	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
624	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
627	C₂×C₂²⋊C₄	C₂²×D₇₉	1	16	yes	complemented
628	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	complemented
629	C₂×C₄²	—	79	4	no	—
630	C₂×C₄²	C₂²×D₇₉	1	4	yes	complemented
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	316	4	no	—
635	C₂⁴	—	316	4	no	—
636	C₂⁴	—	316	4	no	—
637	C₂⁴	—	316	4	no	—
638	C₂⁴	—	316	64	no	—
639	C₂⁴	—	316	32	no	—
640	C₂⁴	—	79	4	no	—
641	C₂⁴	—	79	4	no	—
642	C₂⁴	—	79	8	no	—
643	C₂⁴	—	79	8	no	—
644	C₂⁴	—	79	2	no	—
645	C₂⁴	—	79	4	no	—
646	C₂⁴	—	79	2	no	—
647	C₂⁴	—	79	2	no	—
648	C₂⁴	—	158	8	no	—
649	C₂⁴	—	158	8	no	—
650	C₂⁴	—	158	8	no	—
651	C₂⁴	—	158	4	no	—
652	C₂⁴	—	158	8	no	—
653	C₂⁴	—	158	8	no	—
654	C₂⁴	—	158	32	no	—
655	C₂⁴	—	158	4	no	—
656	C₂⁴	—	158	4	no	—
657	C₂⁴	#11929624	1	8	yes	complemented
658	C₂⁴	C₂³×D₇₉	1	2	yes	—
659	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
660	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
661	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
662	C₂⁴	C₂³×D₇₉	1	4	yes	—
663	C₂⁴	C₂³×D₇₉	1	4	yes	—
664	#41	—	316	64	no	—
665	C₂×Q₈	—	316	8	no	—
666	C₂×Q₈	—	79	16	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	32	no	—
670	C₂×D₄	—	316	8	no	—
671	C₂×D₄	—	316	32	no	—
672	C₂×D₄	—	316	32	no	—
673	C₂×D₄	—	316	8	no	—
674	C₂×D₄	—	316	8	no	—
675	C₂×D₄	—	79	16	no	—
676	C₂×D₄	—	79	16	no	—
677	C₂×D₄	—	79	8	no	—
678	C₂×D₄	—	79	8	no	—
679	C₂×D₄	—	79	16	no	—
680	C₂×D₄	—	79	16	no	—
681	C₂×D₄	—	79	16	no	—
682	C₂×D₄	—	158	16	no	—
683	C₂×D₄	—	158	16	no	—
684	C₂×D₄	—	158	8	no	—
685	C₂×D₄	—	158	8	no	—
686	C₂×D₄	—	158	32	no	—
687	C₂×D₄	C₂³×D₇₉	1	8	yes	—
688	C₂×D₄	C₂³×D₇₉	1	8	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	4	4	no	—
692	C₂²×C₄	—	4	8	no	—
693	C₂²×C₄	—	316	8	no	—
694	C₂²×C₄	—	316	8	no	—
695	C₂²×C₄	—	316	32	no	—
696	C₂²×C₄	—	316	4	no	—
697	C₂²×C₄	—	316	4	no	—
698	C₂²×C₄	—	79	8	no	—
699	C₂²×C₄	—	79	8	no	—
700	C₂²×C₄	—	79	16	no	—
701	C₂²×C₄	—	79	16	no	—
702	C₂²×C₄	—	79	4	no	—
703	C₂²×C₄	—	79	2	no	—
704	C₂²×C₄	—	79	4	no	—
705	C₂²×C₄	—	79	4	no	—
706	C₂²×C₄	—	79	16	no	—
707	C₂²×C₄	—	158	16	no	—
708	C₂²×C₄	—	158	4	no	—
709	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
710	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
711	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
712	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
713	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
714	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
715	C₂²×C₄	C₂³×D₇₉	1	16	yes	complemented
716	C₄⋊C₄	—	79	16	no	—
717	C₄⋊C₄	—	79	16	no	—
718	C₄⋊C₄	—	79	16	no	—
719	C₄⋊C₄	—	79	16	no	—
720	C₄⋊C₄	—	79	16	no	—
721	C₄⋊C₄	C₂³×D₇₉	1	16	yes	complemented
722	C₂²⋊C₄	—	79	8	no	—
723	C₂²⋊C₄	—	79	8	no	—
724	C₂²⋊C₄	—	79	8	no	—
725	C₂²⋊C₄	—	79	8	no	—
726	C₂²⋊C₄	—	79	16	no	—
727	C₂²⋊C₄	—	79	16	no	—
728	C₂²⋊C₄	—	79	16	no	—
729	C₂²⋊C₄	—	79	16	no	—
730	C₂²⋊C₄	—	79	16	no	—
731	C₂²⋊C₄	—	79	16	no	—
732	C₂²⋊C₄	—	79	16	no	—
733	C₂²⋊C₄	—	79	16	no	—
734	C₂²⋊C₄	—	79	16	no	—
735	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
736	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
737	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
738	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
739	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	complemented
740	C₄²	—	79	16	no	—
741	C₄²	C₂³×D₇₉	1	16	yes	complemented
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	8	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	8	no	—
748	C₂³	—	4	16	no	—
749	C₂³	—	4	8	no	—
750	C₂³	—	4	8	no	—
751	C₂³	—	8	8	no	—
752	C₂³	—	316	16	no	—
753	C₂³	—	316	32	no	—
754	C₂³	—	316	32	no	—
755	C₂³	—	316	8	no	—
756	C₂³	—	316	8	no	—
757	C₂³	—	316	8	no	—
758	C₂³	—	316	8	no	—
759	C₂³	—	316	128	no	—
760	C₂³	—	79	8	no	—
761	C₂³	—	79	4	no	—
762	C₂³	—	79	4	no	—
763	C₂³	—	79	4	no	—
764	C₂³	—	632	8	no	—
765	C₂³	—	158	16	no	—
766	C₂³	—	158	16	no	—
767	C₂³	—	158	16	no	—
768	C₂³	—	158	32	no	—
769	C₂³	—	158	8	no	—
770	C₂³	—	158	4	no	—
771	C₂³	—	158	4	no	—
772	C₂³	—	158	4	no	—
773	C₂³	—	158	8	no	—
774	C₂³	—	158	16	no	—
775	C₂³	—	158	16	no	—
776	C₂³	—	158	4	no	—
777	C₂³	—	158	8	no	—
778	C₂³	—	158	4	no	—
779	C₂³	—	158	8	no	—
780	C₂³	—	158	4	no	—
781	C₂³	C₂×#11929624	1	4	yes	—
782	C₂³	C₂×#11929624	1	4	yes	—
783	C₂³	C₂×#11929624	1	4	yes	—
784	C₂³	C₂×#11929624	1	16	yes	complemented
785	C₂³	C₂⁴×D₇₉	1	4	yes	—
786	C₂³	C₂⁴×D₇₉	1	2	yes	—
787	C₂³	C₂⁴×D₇₉	1	2	yes	—
788	C₂³	C₂⁴×D₇₉	1	2	yes	—
789	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
790	Q₈	—	316	16	no	—
791	D₄	—	2	16	no	—
792	D₄	—	2	16	no	—
793	D₄	—	316	16	no	—
794	D₄	—	316	16	no	—
795	D₄	—	316	16	no	—
796	D₄	—	158	32	no	—
797	D₄	—	158	32	no	—
798	D₄	—	158	16	no	—
799	D₄	—	158	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	16	no	—
807	C₂×C₄	—	316	16	no	—
808	C₂×C₄	—	316	16	no	—
809	C₂×C₄	—	316	8	no	—
810	C₂×C₄	—	316	8	no	—
811	C₂×C₄	—	79	4	no	—
812	C₂×C₄	—	79	8	no	—
813	C₂×C₄	—	79	8	no	—
814	C₂×C₄	—	158	32	no	—
815	C₂×C₄	—	158	8	no	—
816	C₂×C₄	—	158	8	no	—
817	C₂×C₄	—	158	8	no	—
818	C₂×C₄	—	158	4	no	—
819	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
820	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
821	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
822	C₂²	—	2	8	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	8	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	8	8	no	—
833	C₂²	—	316	16	no	—
834	C₂²	—	316	32	no	—
835	C₂²	—	316	32	no	—
836	C₂²	—	316	8	no	—
837	C₂²	—	316	8	no	—
838	C₂²	—	79	8	no	—
839	C₂²	—	632	8	no	—
840	C₂²	—	158	32	no	—
841	C₂²	—	158	4	no	—
842	C₂²	—	158	4	no	—
843	C₂²	—	158	8	no	—
844	C₂²	—	158	4	no	—
845	C₂²	—	158	4	no	—
846	C₂²	—	158	16	no	—
847	C₂²	—	158	4	no	—
848	C₂²	—	158	4	no	—
849	C₂²	C₂²×#11929624	1	4	yes	—
850	C₂²	C₂²×#11929624	1	4	yes	—
851	C₂²	C₂²×#11929624	1	4	yes	—
852	C₂²	C₂²×#11929624	1	2	yes	—
853	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
854	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	8	no	—
858	C₄	—	158	4	no	—
859	C₄	—	158	8	no	—
860	C₄	—	158	8	no	—
861	C₂	—	2	4	no	—
862	C₂	—	2	4	no	—
863	C₂	—	2	4	no	—
864	C₂	—	4	4	no	—
865	C₂	—	316	4	no	—
866	C₂	—	316	4	no	—
867	C₂	—	158	8	no	—
868	C₂	#23777085	1	4	yes	direct product factor
869	C₂	C₂³×#11929624	1	1	yes	characteristic
870	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#518×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#518	D₇₉
hypocenter	C₇₉	C₂×#3490
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. #23777085	C₂	direct (N × H)
2. C₂×#19099242	C₂	semidirect
3. C₂×#19099237	C₂	semidirect
4. C₂×#19099209	C₂	semidirect
5. C₂×#19099203	C₂	semidirect
6. C₂×#19099189	C₂	semidirect
7. C₂×#19099146	C₂	semidirect
8. C₂×#19099122	C₂	semidirect
9. C₂×#19099072	C₂	semidirect
10. C₂²×#14579131	C₂	semidirect
11. C₂²×#14579129	C₂	semidirect
12. C₂×#19099036	C₂	semidirect
13. C₂²×C₂²⋊C₄×D₇₉	C₂	semidirect
14. C₂×#518×C₇₉	C₂	semidirect
16. C₂²×#11929624	C₂²	semidirect
17. C₂³×D₃₁₆	C₂²	semidirect
19. C₂³×C₂²⋊D₇₉	C₂²	semidirect
20. C₂³×C₄×D₇₉	C₂²	semidirect
21. #19099242	C₂²	semidirect
22. #19099237	C₂²	semidirect
23. #19099209	C₂²	semidirect
24. #19099203	C₂²	semidirect
25. #19099189	C₂²	semidirect
26. #19099146	C₂²	semidirect
27. #19099122	C₂²	semidirect
28. C₂×#14579156	C₂²	semidirect
29. C₂×#14579155	C₂²	semidirect
30. C₂×#14579149	C₂²	semidirect
31. C₂×#14579147	C₂²	semidirect
32. #19099072	C₂²	semidirect
33. C₂×#14579146	C₂²	semidirect
34. C₂×#14579146	C₂²	semidirect
35. C₂×#14579144	C₂²	semidirect
36. C₂×#14579144	C₂²	semidirect
37. C₂×#14579143	C₂²	semidirect
38. C₂×#14579142	C₂²	semidirect
39. C₂×#14579140	C₂²	semidirect
40. C₂×#14579139	C₂²	semidirect
41. C₂×#14579138	C₂²	semidirect
42. C₂×#14579138	C₂²	semidirect
43. C₂×#14579135	C₂²	semidirect
44. C₂×#14579134	C₂²	semidirect
45. C₂×#14579134	C₂²	semidirect
46. C₂×#14579133	C₂²	semidirect
48. C₂×#14579131	C₂²	semidirect
49. C₂×#14579131	C₂²	semidirect
50. C₂×#14579131	C₂²	semidirect
51. C₂×#14579130	C₂²	semidirect
53. C₂×#14579129	C₂²	semidirect
54. C₂×#14579129	C₂²	semidirect
55. C₂×#14579129	C₂²	semidirect
56. C₂×#14579129	C₂²	semidirect
57. #19099036	C₂²	semidirect
58. C₂×C₄×D₃₁₆	C₂²	semidirect
59. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
60. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
61. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
62. C₂×#14579118	C₂²	semidirect
63. C₂×#14579117	C₂²	semidirect
66. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
67. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
68. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
69. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
72. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
74. #518×C₇₉	C₂²	semidirect
75. C₂×C₄×D₄×C₇₉	C₂²	semidirect
76. C₂×C₄×D₄×C₇₉	C₂²	semidirect
77. C₂×#117×C₇₉	C₂²	semidirect
80. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
90. C₂×#11929624	C₂³	semidirect
91. C₂²×Dic₁₅₈	C₂³	semidirect
95. C₂²×D₃₁₆	C₂³	semidirect
103. C₂²×C₂²⋊D₇₉	C₂³	semidirect
104. C₂²×C₂²⋊D₇₉	C₂³	semidirect
111. C₂²×C₄×D₇₉	C₂³	semidirect
112. C₂²×C₄×D₇₉	C₂³	semidirect
113. #14579156	C₂³	semidirect
114. #14579155	C₂³	semidirect
115. #14579149	C₂³	semidirect
116. #14579147	C₂³	semidirect
117. #14579146	C₂³	semidirect
118. #14579146	C₂³	semidirect
119. #14579144	C₂³	semidirect
120. #14579144	C₂³	semidirect
121. #14579143	C₂³	semidirect
122. #14579142	C₂³	semidirect
123. #14579140	C₂³	semidirect
124. #14579139	C₂³	semidirect
125. #14579138	C₂³	semidirect
126. #14579138	C₂³	semidirect
127. #14579135	C₂³	semidirect
128. #14579134	C₂³	semidirect
129. #14579134	C₂³	semidirect
130. #14579133	C₂³	semidirect
132. #14579131	C₂³	semidirect
133. #14579131	C₂³	semidirect
134. #14579130	C₂³	semidirect
136. #14579129	C₂³	semidirect
137. #14579129	C₂³	semidirect
138. #14579129	C₂³	semidirect
139. C₄×D₃₁₆	C₂³	semidirect
140. C₄×C₂²⋊D₇₉	C₂³	semidirect
141. C₄×C₂²⋊D₇₉	C₂³	semidirect
142. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
143. #14579118	C₂³	semidirect
144. #14579117	C₂³	semidirect
145. C₂×C₄⋊Dic₇₉	C₂³	semidirect
146. C₂×Dic₇₉⋊C₄	C₂³	semidirect
147. C₂×Dic₇₉⋊C₄	C₂³	semidirect
148. C₂×Dic₇₉⋊C₄	C₂³	semidirect
149. C₂×Dic₇₉⋊C₄	C₂³	semidirect
156. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
163. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
164. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
165. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
166. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
167. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
168. C₂²⋊C₄×D₇₉	C₂³	semidirect
169. C₂²⋊C₄×D₇₉	C₂³	semidirect
170. C₂²⋊C₄×D₇₉	C₂³	semidirect
171. C₂×C₄×Dic₇₉	C₂³	semidirect
181. C₂³×C₄×C₇₉	C₂³	semidirect
182. C₄×D₄×C₇₉	C₂³	semidirect
183. C₄×D₄×C₇₉	C₂³	semidirect
184. #117×C₇₉	C₂³	semidirect
185. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
192. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
193. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
194. C₂×C₄²×C₇₉	C₂³	semidirect
220. C₂×Dic₁₅₈	C₂⁴	semidirect
237. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
253. C₂×C₄×D₇₉	C₂⁴	semidirect
254. C₄⋊Dic₇₉	C₂⁴	semidirect
255. Dic₇₉⋊C₄	C₂⁴	semidirect
256. Dic₇₉⋊C₄	C₂⁴	semidirect
257. Dic₇₉⋊C₄	C₂⁴	semidirect
258. Dic₇₉⋊C₄	C₂⁴	semidirect
263. C₂²⋊Dic₇₉	C₂⁴	semidirect
270. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
271. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
272. C₄×Dic₇₉	C₂⁴	semidirect
276. C₂⁴×C₇₉	#41	semidirect
298. C₂²×C₄×C₇₉	C₂⁴	semidirect
299. C₄⋊C₄×C₇₉	C₂⁴	semidirect
304. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
305. C₄²×C₇₉	C₂⁴	semidirect
319. C₂³×C₇₉	C₂×#41	semidirect
430. C₂×C₇₉	#3490	semidirect
448. C₂×#518	D₇₉	semidirect
450. C₇₉	C₂×#3490	semidirect
495. #518	C₂×D₇₉	semidirect
500. C₂×C₄×D₄	C₂×D₇₉	semidirect
501. C₂×C₄×D₄	C₂×D₇₉	semidirect
504. C₂×#117	C₂×D₇₉	semidirect
516. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
558. C₂³×C₄	C₂²×D₇₉	semidirect
589. C₄×D₄	C₂²×D₇₉	semidirect
590. C₄×D₄	C₂²×D₇₉	semidirect
593. #117	C₂²×D₇₉	semidirect
599. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
627. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
628. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
630. C₂×C₄²	C₂²×D₇₉	semidirect
657. C₂⁴	#11929624	semidirect
715. C₂²×C₄	C₂³×D₇₉	semidirect
721. C₄⋊C₄	C₂³×D₇₉	semidirect
739. C₂²⋊C₄	C₂³×D₇₉	semidirect
741. C₄²	C₂³×D₇₉	semidirect
784. C₂³	C₂×#11929624	semidirect
868. C₂	#23777085	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777085	2
C₂×#19099242	2
C₂×#19099237	2
C₂×#19099209	2
C₂×#19099203	2
C₂×#19099189	2
C₂×#19099146	2
C₂×#19099122	2
C₂×#19099072	2
C₂²×#14579131	2
C₂²×#14579129	2
C₂×#19099036	2
C₂²×C₂²⋊C₄×D₇₉	2
C₂×#518×C₇₉	2
C₂×#3490	79

Subgroups — C2×#23777085 #35196179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777085 #35196179