Subgroups — C₂×#23777132 #35196613

Order 20224.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777132	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099277	C₂	1	2	yes	maximal, complemented
3	C₂×#19099265	C₂	1	2	yes	maximal, complemented
4	C₂×#19099260	C₂	1	2	yes	maximal, complemented
5	C₂×#19099244	C₂	1	4	yes	maximal, complemented
6	C₂×#19099213	C₂	1	2	yes	maximal, complemented
7	C₂×#19099200	C₂	1	4	yes	maximal, complemented
8	C₂×#19099191	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19099182	C₂	1	2	yes	maximal, complemented
10	C₂×#19099167	C₂	1	2	yes	maximal, complemented
11	C₂×#19099111	C₂	1	2	yes	maximal, complemented
12	C₂×#19099092	C₂	1	2	yes	maximal, complemented
13	C₂×#19099070	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#14579132	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19099046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#19099038	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#535×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11929623	C₂²	1	4	yes	complemented
20	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	—
21	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
22	#19099277	C₂²	1	32	yes	complemented
23	#19099265	C₂²	1	32	yes	complemented
24	#19099260	C₂²	1	32	yes	complemented
25	#19099244	C₂²	1	64	yes	complemented
26	#19099213	C₂²	1	32	yes	complemented
27	#19099200	C₂²	1	64	yes	complemented
28	#19099191	C₂²	1	16	yes	complemented
29	#19099182	C₂²	1	32	yes	complemented
30	#19099167	C₂²	1	32	yes	complemented
31	#19099111	C₂²	1	32	yes	complemented
32	C₂×#14579161	C₂²	1	2	yes	complemented
33	C₂×#14579160	C₂²	1	2	yes	complemented
34	#19099092	C₂²	1	32	yes	complemented
35	C₂×#14579154	C₂²	1	4	yes	complemented
36	C₂×#14579154	C₂²	1	4	yes	complemented
37	C₂×#14579153	C₂²	1	2	yes	complemented
38	C₂×#14579152	C₂²	1	2	yes	complemented
39	C₂×#14579148	C₂²	1	4	yes	complemented
40	C₂×#14579147	C₂²	1	4	yes	complemented
41	#19099070	C₂²	1	16	yes	complemented
42	C₂×#14579145	C₂²	1	4	yes	complemented
43	C₂×#14579143	C₂²	1	4	yes	complemented
44	C₂×#14579142	C₂²	1	2	yes	—
45	C₂×#14579142	C₂²	1	4	yes	complemented
46	C₂×#14579142	C₂²	1	4	yes	complemented
47	C₂×#14579138	C₂²	1	4	yes	—
48	C₂×#14579138	C₂²	1	4	yes	complemented
49	C₂×#14579137	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14579137	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14579133	C₂²	1	4	yes	complemented
52	C₂×#14579133	C₂²	1	4	yes	complemented
53	C₂×#14579132	C₂²	1	2	yes	—
54	C₂×#14579132	C₂²	1	2	yes	—
55	C₂×#14579132	C₂²	1	2	yes	—
56	C₂×#14579132	C₂²	1	2	yes	—
57	C₂×#14579132	C₂²	1	16	yes	complemented
58	C₂×#14579132	C₂²	1	4	yes	complemented
59	C₂×#14579132	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14579132	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14579129	C₂²	1	2	yes	—
62	#19099046	C₂²	1	16	yes	complemented
63	#19099038	C₂²	1	16	yes	complemented
64	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	complemented
65	C₂×D₄×Dic₇₉	C₂²	1	4	yes	—
66	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
67	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
68	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
69	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
70	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
71	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
72	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
73	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
74	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
75	C₂×#14579120	C₂²	1	1	yes	characteristic
76	C₂×#14579120	C₂²	1	1	yes	characteristic
77	C₂×#14579120	C₂²	1	2	yes	complemented
78	C₂×#14579119	C₂²	1	1	yes	characteristic, complemented
79	C₂×#14579119	C₂²	1	1	yes	characteristic, complemented
80	C₂×#14579118	C₂²	1	2	yes	complemented
81	C₂×#14579117	C₂²	1	2	yes	—
82	C₂×#14579117	C₂²	1	4	yes	complemented
83	#117×D₇₉	C₂²	1	16	yes	complemented
84	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
85	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
86	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
88	C₂²×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
89	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
90	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
91	C₂×C₄²×D₇₉	C₂²	1	2	yes	complemented
92	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
93	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
94	#535×C₇₉	C₂²	1	16	yes	complemented
95	C₂×#127×C₇₉	C₂²	1	2	yes	complemented
96	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
97	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
98	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
99	C₂×#120×C₇₉	C₂²	1	4	yes	—
100	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
101	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
102	C₂×#11929623	—	4	16	no	—
103	C₂×#11929623	C₂³	1	32	yes	complemented
104	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₇₉	—	4	8	no	—
106	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
108	C₂²×C₂²⋊D₇₉	C₂³	1	16	yes	—
109	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
110	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
111	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
112	C₂³×Dic₇₉	C₂³	1	2	yes	—
113	C₂³×Dic₇₉	C₂³	1	4	yes	—
114	C₂³×Dic₇₉	C₂³	1	4	yes	—
115	C₂³×Dic₇₉	C₂³	1	4	yes	—
116	C₂²×C₄×D₇₉	—	2	8	no	—
117	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
119	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
121	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
124	#14579161	C₂³	1	16	yes	complemented
125	#14579160	C₂³	1	16	yes	complemented
126	#14579154	C₂³	1	32	yes	complemented
127	#14579154	C₂³	1	32	yes	complemented
128	#14579153	C₂³	1	16	yes	complemented
129	#14579152	C₂³	1	16	yes	complemented
130	#14579148	C₂³	1	32	yes	complemented
131	#14579147	C₂³	1	32	yes	complemented
132	#14579145	C₂³	1	32	yes	complemented
133	#14579143	C₂³	1	32	yes	complemented
134	#14579142	C₂³	1	16	yes	—
135	#14579142	C₂³	1	32	yes	complemented
136	#14579142	C₂³	1	32	yes	complemented
137	#14579138	C₂³	1	32	yes	—
138	#14579138	C₂³	1	32	yes	complemented
139	#14579137	C₂³	1	8	yes	complemented
140	#14579137	C₂³	1	8	yes	complemented
141	#14579133	C₂³	1	32	yes	complemented
142	#14579133	C₂³	1	32	yes	complemented
143	#14579132	C₂³	1	16	yes	—
144	#14579132	C₂³	1	16	yes	—
145	#14579132	C₂³	1	16	yes	—
146	#14579132	C₂³	1	16	yes	—
147	#14579132	C₂³	1	8	yes	complemented
148	#14579132	C₂³	1	32	yes	complemented
149	#14579132	C₂³	1	8	yes	complemented
150	#14579129	C₂³	1	16	yes	—
151	Q₈×Dic₇₉	C₂³	1	16	yes	complemented
152	D₄×Dic₇₉	C₂³	1	32	yes	—
153	D₄×Dic₇₉	C₂³	1	16	yes	complemented
154	D₄×Dic₇₉	C₂³	1	16	yes	complemented
155	D₄×Dic₇₉	C₂³	1	16	yes	complemented
156	D₄×Dic₇₉	C₂³	1	16	yes	complemented
157	D₄×Dic₇₉	C₂³	1	32	yes	complemented
158	D₄×Dic₇₉	C₂³	1	16	yes	complemented
159	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
161	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
162	#14579120	C₂³	1	8	yes	—
163	#14579120	C₂³	1	8	yes	—
164	#14579120	C₂³	1	16	yes	complemented
165	#14579119	C₂³	1	8	yes	complemented
166	#14579119	C₂³	1	8	yes	complemented
167	#14579118	C₂³	1	16	yes	complemented
168	#14579117	C₂³	1	16	yes	—
169	#14579117	C₂³	1	32	yes	complemented
170	C₂×C₄⋊Dic₇₉	C₂³	1	8	yes	—
171	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
174	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
175	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
176	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
179	C₂×C₄⋊Dic₇₉	C₂³	1	16	yes	complemented
180	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
181	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
182	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
183	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
185	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
186	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
187	C₄⋊C₄×D₇₉	C₂³	1	8	yes	complemented
188	C₂×C₂²⋊Dic₇₉	C₂³	1	32	yes	—
189	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	—
190	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
193	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
194	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
195	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
196	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
197	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
199	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
200	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
201	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
202	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
203	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
204	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
205	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
206	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
207	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
208	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
209	C₄²×D₇₉	C₂³	1	16	yes	complemented
210	C₂⁵×C₇₉	C₂³	1	2	yes	—
211	C₂×#41×C₇₉	—	2	8	no	—
212	C₂×#41×C₇₉	C₂³	1	8	yes	—
213	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₇₉	—	2	8	no	—
215	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
216	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
217	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
218	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
219	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
220	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
221	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
222	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
223	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
224	#127×C₇₉	C₂³	1	16	yes	complemented
225	#124×C₇₉	C₂³	1	16	yes	complemented
226	#121×C₇₉	C₂³	1	16	yes	complemented
227	#121×C₇₉	C₂³	1	16	yes	complemented
228	#120×C₇₉	C₂³	1	32	yes	—
229	#117×C₇₉	C₂³	1	8	yes	—
230	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
234	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
235	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
236	C₂³×D₇₉	—	2	4	no	—
237	C₂³×D₇₉	—	2	4	no	—
238	C₂³×D₇₉	—	4	2	no	—
239	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
240	C₂³×D₇₉	C₂⁴	1	4	yes	—
241	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
242	#11929623	—	4	64	no	—
243	C₂×Dic₁₅₈	—	4	8	no	—
244	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
245	C₂×C₂²⋊D₇₉	—	2	8	no	—
246	C₂×C₂²⋊D₇₉	—	2	16	no	—
247	C₂×C₂²⋊D₇₉	—	4	32	no	—
248	C₂×C₂²⋊D₇₉	—	4	8	no	—
249	C₂×C₂²⋊D₇₉	—	4	4	no	—
250	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
251	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
252	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
253	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
254	C₂²×Dic₇₉	—	2	4	no	—
255	C₂²×Dic₇₉	—	4	8	no	—
256	C₂²×Dic₇₉	—	4	8	no	—
257	C₂²×Dic₇₉	—	4	8	no	—
258	C₂²×Dic₇₉	—	4	4	no	—
259	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
260	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
261	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
262	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
263	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
264	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
266	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
267	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
268	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
269	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
270	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
271	C₂×C₄×D₇₉	—	2	8	no	—
272	C₂×C₄×D₇₉	—	2	4	no	—
273	C₂×C₄×D₇₉	—	2	4	no	—
274	C₂×C₄×D₇₉	—	2	4	no	—
275	C₂×C₄×D₇₉	—	2	4	no	—
276	C₂×C₄×D₇₉	—	2	32	no	—
277	C₂×C₄×D₇₉	—	4	4	no	—
278	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
279	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
280	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
281	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
282	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
283	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
284	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
285	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
286	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
287	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
288	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
289	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
290	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
291	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
292	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
293	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
294	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
295	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
296	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
297	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
298	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
299	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
300	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
301	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
302	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
303	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
304	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
305	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
306	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
307	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
308	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
309	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
310	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
311	C₄×Dic₇₉	C₂⁴	1	8	yes	—
312	C₄×Dic₇₉	C₂⁴	1	8	yes	—
313	C₄×Dic₇₉	C₂⁴	1	8	yes	—
314	C₄×Dic₇₉	C₂⁴	1	16	yes	—
315	C₄×Dic₇₉	C₂⁴	1	8	yes	—
316	C₂⁴×C₇₉	—	2	8	no	—
317	C₂⁴×C₇₉	—	4	4	no	—
318	C₂⁴×C₇₉	—	4	4	no	—
319	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
320	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
321	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
322	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
323	#41×C₇₉	—	2	32	no	—
324	C₂×Q₈×C₇₉	—	2	4	no	—
325	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
326	C₂×D₄×C₇₉	—	2	8	no	—
327	C₂×D₄×C₇₉	—	2	8	no	—
328	C₂×D₄×C₇₉	—	2	8	no	—
329	C₂×D₄×C₇₉	—	2	4	no	—
330	C₂×D₄×C₇₉	—	2	32	no	—
331	C₂×D₄×C₇₉	—	4	8	no	—
332	C₂×D₄×C₇₉	—	4	8	no	—
333	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
334	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
335	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
336	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
337	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
338	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
339	C₂²×C₄×C₇₉	—	2	8	no	—
340	C₂²×C₄×C₇₉	#41	1	8	yes	complemented
341	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
348	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
349	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
350	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
352	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
353	C₄²×C₇₉	C₂⁴	1	8	yes	—
354	C₂³×C₇₉	—	2	2	no	—
355	C₂³×C₇₉	—	2	2	no	—
356	C₂³×C₇₉	—	2	4	no	—
357	C₂³×C₇₉	—	2	8	no	—
358	C₂³×C₇₉	—	2	4	no	—
359	C₂³×C₇₉	—	2	8	no	—
360	C₂³×C₇₉	—	2	8	no	—
361	C₂³×C₇₉	—	2	4	no	—
362	C₂³×C₇₉	—	2	16	no	—
363	C₂³×C₇₉	—	4	8	no	—
364	C₂³×C₇₉	—	4	8	no	—
365	C₂³×C₇₉	—	8	16	no	—
366	C₂³×C₇₉	C₂×#41	1	4	yes	—
367	C₂³×C₇₉	C₂⁵	1	8	yes	—
368	C₂³×C₇₉	C₂⁵	1	4	yes	—
369	C₂³×C₇₉	C₂⁵	1	2	yes	—
370	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
371	C₂²×D₇₉	—	2	2	no	—
372	C₂²×D₇₉	—	2	2	no	—
373	C₂²×D₇₉	—	2	8	no	—
374	C₂²×D₇₉	—	2	2	no	—
375	C₂²×D₇₉	—	2	2	no	—
376	C₂²×D₇₉	—	2	2	no	—
377	C₂²×D₇₉	—	2	8	no	—
378	C₂²×D₇₉	—	4	4	no	—
379	C₂²×D₇₉	—	4	16	no	—
380	C₂²×D₇₉	H(5,𝔽₂)	1	4	yes	—
381	C₂²×D₇₉	C₂⁵	1	2	yes	—
382	C₂²×D₇₉	C₂⁵	1	2	yes	—
383	Q₈×C₇₉	—	2	8	no	—
384	D₄×C₇₉	—	2	16	no	—
385	D₄×C₇₉	—	2	16	no	—
386	D₄×C₇₉	—	2	16	no	—
387	D₄×C₇₉	—	2	8	no	—
388	D₄×C₇₉	—	4	16	no	—
389	D₄×C₇₉	—	4	16	no	—
390	C₂×C₄×C₇₉	—	2	4	no	—
391	C₂×C₄×C₇₉	—	2	4	no	—
392	C₂×C₄×C₇₉	—	2	4	no	—
393	C₂×C₄×C₇₉	—	2	16	no	—
394	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
396	C₂×C₄×C₇₉	C₂×#41	1	16	yes	complemented
397	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
398	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
399	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
400	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
401	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
402	C₂²⋊D₇₉	—	2	32	no	—
403	C₂²⋊D₇₉	—	2	16	no	—
404	C₂²⋊D₇₉	—	4	16	no	—
405	C₂²⋊D₇₉	—	4	8	no	—
406	C₂×Dic₇₉	—	2	8	no	—
407	C₂×Dic₇₉	—	2	2	no	—
408	C₂×Dic₇₉	—	2	2	no	—
409	C₂×Dic₇₉	—	2	4	no	—
410	C₂×Dic₇₉	—	2	8	no	—
411	C₂×Dic₇₉	—	2	4	no	—
412	C₂×Dic₇₉	—	2	4	no	—
413	C₂×Dic₇₉	—	2	4	no	—
414	C₂×Dic₇₉	—	4	16	no	—
415	C₂×Dic₇₉	—	4	8	no	—
416	C₂×Dic₇₉	—	4	16	no	—
417	C₂×Dic₇₉	—	4	16	no	—
418	C₂×Dic₇₉	C₂⁵	1	4	yes	—
419	C₂×Dic₇₉	C₂⁵	1	2	yes	—
420	C₂×Dic₇₉	C₂⁵	1	4	yes	—
421	C₂×Dic₇₉	C₂⁵	1	4	yes	—
422	C₂×Dic₇₉	C₂⁵	1	4	yes	—
423	C₂×Dic₇₉	C₂⁵	1	8	yes	—
424	C₂×Dic₇₉	C₂⁵	1	2	yes	—
425	C₄×D₇₉	—	2	16	no	—
426	C₄×D₇₉	—	2	8	no	—
427	C₄×D₇₉	—	2	8	no	—
428	C₄×D₇₉	—	2	8	no	—
429	C₄×D₇₉	—	2	8	no	—
430	C₄×D₇₉	—	4	8	no	—
431	Dic₁₅₈	—	4	16	no	—
432	C₂²×C₇₉	—	2	2	no	—
433	C₂²×C₇₉	—	2	2	no	—
434	C₂²×C₇₉	—	2	8	no	—
435	C₂²×C₇₉	—	2	4	no	—
436	C₂²×C₇₉	—	2	8	no	—
437	C₂²×C₇₉	—	2	8	no	—
438	C₂²×C₇₉	—	2	4	no	—
439	C₂²×C₇₉	—	2	4	no	—
440	C₂²×C₇₉	—	2	8	no	—
441	C₂²×C₇₉	—	4	8	no	—
442	C₂²×C₇₉	—	4	16	no	—
443	C₂²×C₇₉	—	8	16	no	—
444	C₂²×C₇₉	C₂²×#41	1	4	yes	—
445	C₂²×C₇₉	C₂²×#41	1	2	yes	—
446	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₇₉	#585	1	2	yes	—
448	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
449	C₂×D₇₉	—	2	2	no	—
450	C₂×D₇₉	—	2	2	no	—
451	C₂×D₇₉	—	2	8	no	—
452	C₂×D₇₉	—	2	2	no	—
453	C₂×D₇₉	—	2	2	no	—
454	C₂×D₇₉	—	2	2	no	—
455	C₂×D₇₉	—	4	16	no	—
456	C₂×D₇₉	—	4	4	no	—
457	C₂×D₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
458	C₄×C₇₉	—	2	4	no	—
459	C₄×C₇₉	—	2	4	no	—
460	C₄×C₇₉	—	2	4	no	—
461	C₄×C₇₉	C₂²×#41	1	4	yes	—
462	C₄×C₇₉	C₂²×#41	1	4	yes	—
463	Dic₇₉	—	2	2	no	—
464	Dic₇₉	—	2	2	no	—
465	Dic₇₉	—	2	8	no	—
466	Dic₇₉	—	2	4	no	—
467	Dic₇₉	—	2	4	no	—
468	Dic₇₉	—	2	4	no	—
469	Dic₇₉	—	2	4	no	—
470	C₂×#3494	—	79	1	no	maximal, Sylow
471	C₂×C₇₉	—	2	4	no	—
472	C₂×C₇₉	—	4	4	no	—
473	C₂×C₇₉	—	4	8	no	—
474	C₂×C₇₉	#3494	1	4	yes	complemented
475	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
476	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₇₉	C₂×#585	1	1	yes	characteristic
478	D₇₉	—	2	4	no	—
479	D₇₉	—	4	2	no	—
480	#3494	—	79	32	no	—
481	C₂×#555	—	79	2	no	—
482	C₂×#553	—	79	2	no	—
483	C₂×#553	—	79	2	no	—
484	C₂×#551	—	79	4	no	—
485	C₂×#547	—	79	2	no	—
486	C₂×#546	—	79	4	no	—
487	C₂×#544	—	79	1	no	—
488	C₂×#542	—	79	2	no	—
489	C₂×#540	—	79	2	no	—
490	C₂×#535	D₇₉	1	1	yes	characteristic, complemented
491	C₂×#532	—	79	2	no	—
492	C₂×#529	—	79	2	no	—
493	C₂×#525	—	79	1	no	—
494	C₂²×#121	—	79	1	no	—
495	C₂×#520	—	79	1	no	—
496	C₂×#518	—	79	1	no	—
497	C₂²×#117	—	79	1	no	—
498	C₇₉	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
499	C₂²×#41	—	79	4	no	—
500	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
501	C₂³×D₄	—	79	2	no	—
502	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
503	C₂⁴×C₄	—	79	1	no	—
504	#555	—	79	32	no	—
505	#553	—	79	32	no	—
506	#553	—	79	32	no	—
507	#551	—	79	64	no	—
508	#547	—	79	32	no	—
509	#546	—	79	64	no	—
510	#544	—	79	16	no	—
511	#542	—	79	32	no	—
512	#540	—	79	32	no	—
513	#535	C₂×D₇₉	1	16	yes	complemented
514	#532	—	79	32	no	—
515	C₂×C₄⋊Q₈	—	79	2	no	—
516	C₂×C₄⋊Q₈	—	79	2	no	—
517	C₂×#127	C₂×D₇₉	1	2	yes	complemented
518	#529	—	79	32	no	—
519	C₂×#126	—	79	4	no	—
520	C₂×#126	—	79	4	no	—
521	C₂×#125	—	79	2	no	—
522	C₂×#125	—	79	2	no	—
523	C₂×#124	—	79	4	no	—
524	C₂×#124	—	79	4	no	—
525	C₂×#124	C₂×D₇₉	1	2	yes	complemented
526	#525	—	79	16	no	—
527	C₂×#123	—	79	2	no	—
528	C₂×#123	—	79	4	no	—
529	C₂×#123	—	79	4	no	—
530	C₂×#123	—	79	4	no	—
531	C₂×#123	—	79	4	no	—
532	C₂×C₂²⋊Q₈	—	79	1	no	—
533	C₂×C₂²⋊Q₈	—	79	1	no	—
534	C₂×C₂²⋊Q₈	—	79	4	no	—
535	C₂×C₂²⋊Q₈	—	79	4	no	—
536	C₂×#121	—	79	2	no	—
537	C₂×#121	—	79	2	no	—
538	C₂×#121	—	79	2	no	—
539	C₂×#121	—	79	2	no	—
540	C₂×#121	—	79	16	no	—
541	C₂×#121	—	79	1	no	—
542	C₂×#121	—	79	1	no	—
543	C₂×#121	—	79	4	no	—
544	C₂×#121	—	79	4	no	—
545	C₂×#121	—	79	4	no	—
546	C₂×#121	C₂×D₇₉	1	2	yes	complemented
547	C₂×#121	C₂×D₇₉	1	2	yes	complemented
548	C₂×#120	—	79	2	no	—
549	C₂×#120	C₂×D₇₉	1	4	yes	—
550	#520	—	79	16	no	—
551	#518	—	79	16	no	—
552	C₂×C₄×Q₈	—	79	2	no	—
553	C₂×C₄×D₄	—	79	2	no	—
554	C₂×C₄×D₄	—	79	2	no	—
555	C₂×C₄×D₄	—	79	2	no	—
556	C₂×C₄×D₄	—	79	2	no	—
557	C₂×C₄×D₄	—	79	2	no	—
558	C₂×C₄×D₄	—	79	4	no	—
559	C₂×C₄×D₄	—	79	4	no	—
560	C₂×C₄×D₄	—	79	2	no	—
561	C₂×C₄×D₄	—	79	2	no	—
562	C₂×C₄×D₄	—	79	4	no	—
563	C₂×#117	—	79	1	no	—
564	C₂×#117	—	79	1	no	—
565	C₂×#117	—	79	2	no	—
566	C₂×#117	—	79	16	no	—
567	C₂×#117	—	79	1	no	—
568	C₂×#117	—	79	1	no	—
569	C₂×#117	—	79	2	no	—
570	C₂×#117	—	79	4	no	—
571	C₂×#117	—	79	2	no	—
572	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
573	C₂²×C₄⋊C₄	—	79	1	no	—
574	C₂²×C₄⋊C₄	—	79	2	no	—
575	C₂²×C₄⋊C₄	—	79	1	no	—
576	C₂²×C₄⋊C₄	—	79	1	no	—
577	C₂²×C₂²⋊C₄	—	79	4	no	—
578	C₂²×C₂²⋊C₄	—	79	2	no	—
579	C₂²×C₂²⋊C₄	—	79	2	no	—
580	C₂²×C₄²	—	79	2	no	—
581	C₂⁵	—	79	1	no	—
582	C₂⁵	C₂²×D₇₉	1	2	yes	—
583	C₂×#41	—	2	8	no	—
584	C₂×#41	—	316	16	no	—
585	C₂×#41	—	79	32	no	—
586	C₂×#41	C₂²×D₇₉	1	8	yes	—
587	C₂²×Q₈	—	79	4	no	—
588	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	316	8	no	—
591	C₂²×D₄	—	79	2	no	—
592	C₂²×D₄	—	79	4	no	—
593	C₂²×D₄	—	79	16	no	—
594	C₂²×D₄	—	79	2	no	—
595	C₂²×D₄	—	79	4	no	—
596	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
597	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
598	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
599	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
600	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
601	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
602	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
603	C₂³×C₄	—	79	2	no	—
604	C₂³×C₄	—	79	4	no	—
605	C₂³×C₄	—	79	4	no	—
606	C₂³×C₄	—	79	4	no	—
607	C₂³×C₄	—	79	2	no	—
608	C₂³×C₄	—	79	1	no	—
609	C₂³×C₄	—	79	2	no	—
610	C₂³×C₄	—	79	1	no	—
611	C₂³×C₄	—	79	1	no	—
612	C₂³×C₄	—	79	1	no	—
613	C₂³×C₄	—	79	8	no	—
614	C₂³×C₄	—	79	1	no	—
615	C₂³×C₄	—	158	8	no	—
616	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
617	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
618	C₄⋊Q₈	—	79	16	no	—
619	C₄⋊Q₈	—	79	16	no	—
620	#127	C₂²×D₇₉	1	16	yes	complemented
621	#126	—	79	32	no	—
622	#126	—	79	32	no	—
623	#125	—	79	16	no	—
624	#125	—	79	16	no	—
625	#124	—	79	32	no	—
626	#124	—	79	32	no	—
627	#124	C₂²×D₇₉	1	16	yes	complemented
628	#123	—	79	16	no	—
629	#123	—	79	32	no	—
630	#123	—	79	32	no	—
631	#123	—	79	32	no	—
632	#123	—	79	32	no	—
633	C₂²⋊Q₈	—	79	8	no	—
634	C₂²⋊Q₈	—	79	8	no	—
635	C₂²⋊Q₈	—	79	32	no	—
636	C₂²⋊Q₈	—	79	32	no	—
637	#121	—	79	16	no	—
638	#121	—	79	16	no	—
639	#121	—	79	16	no	—
640	#121	—	79	16	no	—
641	#121	—	79	8	no	—
642	#121	—	79	8	no	—
643	#121	—	79	32	no	—
644	#121	—	79	32	no	—
645	#121	—	79	32	no	—
646	#121	C₂²×D₇₉	1	16	yes	complemented
647	#121	C₂²×D₇₉	1	16	yes	complemented
648	#120	—	79	16	no	—
649	#120	C₂²×D₇₉	1	32	yes	—
650	C₄×Q₈	—	79	16	no	—
651	C₄×D₄	—	79	16	no	—
652	C₄×D₄	—	79	16	no	—
653	C₄×D₄	—	79	16	no	—
654	C₄×D₄	—	79	16	no	—
655	C₄×D₄	—	79	16	no	—
656	C₄×D₄	—	79	32	no	—
657	C₄×D₄	—	79	32	no	—
658	C₄×D₄	—	79	16	no	—
659	C₄×D₄	—	79	16	no	—
660	C₄×D₄	—	79	32	no	—
661	#117	—	79	8	no	—
662	#117	—	79	8	no	—
663	#117	—	79	16	no	—
664	#117	—	79	8	no	—
665	#117	—	79	8	no	—
666	#117	—	79	16	no	—
667	#117	—	79	32	no	—
668	#117	—	79	16	no	—
669	#117	C₂²×D₇₉	1	8	yes	—
670	C₂×C₄⋊C₄	—	79	1	no	—
671	C₂×C₄⋊C₄	—	79	2	no	—
672	C₂×C₄⋊C₄	—	79	1	no	—
673	C₂×C₄⋊C₄	—	79	2	no	—
674	C₂×C₄⋊C₄	—	79	2	no	—
675	C₂×C₄⋊C₄	—	79	2	no	—
676	C₂×C₄⋊C₄	—	79	4	no	—
677	C₂×C₄⋊C₄	—	79	8	no	—
678	C₂×C₄⋊C₄	—	79	16	no	—
679	C₂×C₄⋊C₄	—	79	2	no	—
680	C₂×C₄⋊C₄	—	79	1	no	—
681	C₂×C₄⋊C₄	—	79	1	no	—
682	C₂×C₄⋊C₄	—	79	4	no	—
683	C₂×C₄⋊C₄	—	79	4	no	—
684	C₂×C₄⋊C₄	—	79	4	no	—
685	C₂×C₄⋊C₄	—	79	2	no	—
686	C₂×C₄⋊C₄	—	79	8	no	—
687	C₂×C₄⋊C₄	—	79	8	no	—
688	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
690	C₂×C₂²⋊C₄	—	79	2	no	—
691	C₂×C₂²⋊C₄	—	79	2	no	—
692	C₂×C₂²⋊C₄	—	79	4	no	—
693	C₂×C₂²⋊C₄	—	79	4	no	—
694	C₂×C₂²⋊C₄	—	79	4	no	—
695	C₂×C₂²⋊C₄	—	79	32	no	—
696	C₂×C₂²⋊C₄	—	79	4	no	—
697	C₂×C₂²⋊C₄	—	79	16	no	—
698	C₂×C₂²⋊C₄	—	79	4	no	—
699	C₂×C₂²⋊C₄	—	79	2	no	—
700	C₂×C₂²⋊C₄	—	79	2	no	—
701	C₂×C₂²⋊C₄	—	79	2	no	—
702	C₂×C₂²⋊C₄	—	79	2	no	—
703	C₂×C₂²⋊C₄	—	79	2	no	—
704	C₂×C₂²⋊C₄	—	79	2	no	—
705	C₂×C₂²⋊C₄	—	79	16	no	—
706	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
709	C₂×C₄²	—	79	2	no	—
710	C₂×C₄²	—	79	2	no	—
711	C₂×C₄²	—	79	4	no	—
712	C₂×C₄²	—	79	2	no	—
713	C₂×C₄²	—	79	2	no	—
714	C₂×C₄²	—	79	16	no	—
715	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
716	C₂⁴	—	2	8	no	—
717	C₂⁴	—	4	4	no	—
718	C₂⁴	—	4	4	no	—
719	C₂⁴	—	316	2	no	—
720	C₂⁴	—	79	4	no	—
721	C₂⁴	—	79	1	no	—
722	C₂⁴	—	79	1	no	—
723	C₂⁴	—	158	4	no	—
724	C₂⁴	—	158	4	no	—
725	C₂⁴	C₂³×D₇₉	1	4	yes	—
726	C₂⁴	C₂³×D₇₉	1	2	yes	—
727	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
728	C₂⁴	C₂³×D₇₉	1	8	yes	—
729	#41	—	2	32	no	—
730	#41	—	316	64	no	—
731	C₂×Q₈	—	2	4	no	—
732	C₂×Q₈	—	316	8	no	—
733	C₂×Q₈	—	79	16	no	—
734	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
735	C₂×D₄	—	2	8	no	—
736	C₂×D₄	—	2	8	no	—
737	C₂×D₄	—	2	8	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	32	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	316	32	no	—
743	C₂×D₄	—	316	8	no	—
744	C₂×D₄	—	316	4	no	—
745	C₂×D₄	—	79	8	no	—
746	C₂×D₄	—	79	16	no	—
747	C₂×D₄	—	79	8	no	—
748	C₂×D₄	—	79	16	no	—
749	C₂×D₄	—	158	16	no	—
750	C₂×D₄	—	158	8	no	—
751	C₂×D₄	C₂³×D₇₉	1	8	yes	—
752	C₂×D₄	C₂³×D₇₉	1	8	yes	—
753	C₂×D₄	C₂³×D₇₉	1	8	yes	—
754	C₂×D₄	C₂³×D₇₉	1	4	yes	—
755	C₂×D₄	C₂³×D₇₉	1	16	yes	—
756	C₂×D₄	C₂³×D₇₉	1	16	yes	—
757	C₂²×C₄	—	2	8	no	—
758	C₂²×C₄	—	316	4	no	—
759	C₂²×C₄	—	316	8	no	—
760	C₂²×C₄	—	316	4	no	—
761	C₂²×C₄	—	316	8	no	—
762	C₂²×C₄	—	316	8	no	—
763	C₂²×C₄	—	79	8	no	—
764	C₂²×C₄	—	79	16	no	—
765	C₂²×C₄	—	79	16	no	—
766	C₂²×C₄	—	79	16	no	—
767	C₂²×C₄	—	79	8	no	—
768	C₂²×C₄	—	79	4	no	—
769	C₂²×C₄	—	79	2	no	—
770	C₂²×C₄	—	79	1	no	—
771	C₂²×C₄	—	79	2	no	—
772	C₂²×C₄	—	79	2	no	—
773	C₂²×C₄	—	79	2	no	—
774	C₂²×C₄	—	79	4	no	—
775	C₂²×C₄	—	79	1	no	—
776	C₂²×C₄	—	79	4	no	—
777	C₂²×C₄	—	79	8	no	—
778	C₂²×C₄	—	79	4	no	—
779	C₂²×C₄	—	79	4	no	—
780	C₂²×C₄	—	79	4	no	—
781	C₂²×C₄	—	158	8	no	—
782	C₂²×C₄	—	158	4	no	—
783	C₂²×C₄	—	158	4	no	—
784	C₂²×C₄	—	158	4	no	—
785	C₂²×C₄	—	158	4	no	—
786	C₂²×C₄	—	158	4	no	—
787	C₂²×C₄	—	158	32	no	—
788	C₂²×C₄	#11929623	1	8	yes	complemented
789	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
790	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
791	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
792	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
793	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
794	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
796	C₄⋊C₄	—	79	8	no	—
797	C₄⋊C₄	—	79	8	no	—
798	C₄⋊C₄	—	79	8	no	—
799	C₄⋊C₄	—	79	16	no	—
800	C₄⋊C₄	—	79	16	no	—
801	C₄⋊C₄	—	79	8	no	—
802	C₄⋊C₄	—	79	4	no	—
803	C₄⋊C₄	—	79	8	no	—
804	C₄⋊C₄	—	79	4	no	—
805	C₄⋊C₄	—	79	8	no	—
806	C₄⋊C₄	—	79	16	no	—
807	C₄⋊C₄	—	79	4	no	—
808	C₄⋊C₄	—	79	4	no	—
809	C₄⋊C₄	—	79	16	no	—
810	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
811	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
812	C₂²⋊C₄	—	79	8	no	—
813	C₂²⋊C₄	—	79	8	no	—
814	C₂²⋊C₄	—	79	16	no	—
815	C₂²⋊C₄	—	79	16	no	—
816	C₂²⋊C₄	—	79	16	no	—
817	C₂²⋊C₄	—	79	16	no	—
818	C₂²⋊C₄	—	79	16	no	—
819	C₂²⋊C₄	—	79	8	no	—
820	C₂²⋊C₄	—	79	8	no	—
821	C₂²⋊C₄	—	79	8	no	—
822	C₂²⋊C₄	—	79	8	no	—
823	C₂²⋊C₄	—	79	8	no	—
824	C₂²⋊C₄	—	79	8	no	—
825	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
826	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
827	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
828	C₄²	—	79	8	no	—
829	C₄²	—	79	8	no	—
830	C₄²	—	79	8	no	—
831	C₄²	—	79	16	no	—
832	C₄²	—	79	8	no	—
833	C₄²	C₂³×D₇₉	1	8	yes	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	4	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	4	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	8	no	—
842	C₂³	—	2	16	no	—
843	C₂³	—	4	8	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	8	16	no	—
846	C₂³	—	316	16	no	—
847	C₂³	—	316	4	no	—
848	C₂³	—	79	4	no	—
849	C₂³	—	79	2	no	—
850	C₂³	—	79	2	no	—
851	C₂³	—	158	8	no	—
852	C₂³	—	158	2	no	—
853	C₂³	—	158	2	no	—
854	C₂³	—	158	8	no	—
855	C₂³	—	158	2	no	—
856	C₂³	—	158	2	no	—
857	C₂³	—	158	2	no	—
858	C₂³	C₂×#11929623	1	4	yes	—
859	C₂³	C₂⁴×D₇₉	1	8	yes	—
860	C₂³	C₂⁴×D₇₉	1	4	yes	—
861	C₂³	C₂⁴×D₇₉	1	2	yes	—
862	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	316	16	no	—
865	D₄	—	2	16	no	—
866	D₄	—	2	16	no	—
867	D₄	—	2	16	no	—
868	D₄	—	2	8	no	—
869	D₄	—	4	16	no	—
870	D₄	—	4	16	no	—
871	D₄	—	316	16	no	—
872	D₄	—	316	8	no	—
873	D₄	—	158	32	no	—
874	D₄	—	158	16	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	4	no	—
878	C₂×C₄	—	2	16	no	—
879	C₂×C₄	—	316	8	no	—
880	C₂×C₄	—	316	8	no	—
881	C₂×C₄	—	316	16	no	—
882	C₂×C₄	—	316	16	no	—
883	C₂×C₄	—	316	16	no	—
884	C₂×C₄	—	79	2	no	—
885	C₂×C₄	—	79	4	no	—
886	C₂×C₄	—	79	4	no	—
887	C₂×C₄	—	79	4	no	—
888	C₂×C₄	—	79	4	no	—
889	C₂×C₄	—	79	8	no	—
890	C₂×C₄	—	79	2	no	—
891	C₂×C₄	—	158	16	no	—
892	C₂×C₄	—	158	4	no	—
893	C₂×C₄	—	158	8	no	—
894	C₂×C₄	—	158	4	no	—
895	C₂×C₄	—	158	4	no	—
896	C₂×C₄	—	158	4	no	—
897	C₂×C₄	—	158	8	no	—
898	C₂×C₄	—	158	2	no	—
899	C₂×C₄	—	158	2	no	—
900	C₂×C₄	—	158	8	no	—
901	C₂×C₄	—	158	8	no	—
902	C₂×C₄	—	158	8	no	—
903	C₂×C₄	—	158	8	no	—
904	C₂×C₄	C₂×#11929623	1	4	yes	—
905	C₂×C₄	C₂×#11929623	1	4	yes	—
906	C₂×C₄	C₂×#11929623	1	16	yes	complemented
907	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
908	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
909	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
910	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
911	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	2	8	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	8	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	8	no	—
923	C₂²	—	8	16	no	—
924	C₂²	—	316	16	no	—
925	C₂²	—	316	4	no	—
926	C₂²	—	79	4	no	—
927	C₂²	—	158	2	no	—
928	C₂²	—	158	2	no	—
929	C₂²	—	158	2	no	—
930	C₂²	—	158	8	no	—
931	C₂²	—	158	2	no	—
932	C₂²	—	158	2	no	—
933	C₂²	C₂²×#11929623	1	4	yes	—
934	C₂²	C₂²×#11929623	1	2	yes	—
935	C₂²	H(5,𝔽₂)×D₇₉	1	2	yes	—
936	C₂²	#19099398	1	2	yes	—
937	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
938	C₄	—	2	4	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	158	2	no	—
942	C₄	—	158	2	no	—
943	C₄	—	158	4	no	—
944	C₄	—	158	8	no	—
945	C₄	—	158	4	no	—
946	C₄	—	158	4	no	—
947	C₄	—	158	4	no	—
948	C₄	C₂²×#11929623	1	4	yes	—
949	C₄	C₂²×#11929623	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	4	8	no	—
952	C₂	—	4	4	no	—
953	C₂	—	316	2	no	—
954	C₂	—	158	4	no	—
955	C₂	#23777132	1	4	yes	direct product factor
956	C₂	C₂³×#11929623	1	1	yes	characteristic
957	C₂	C₂×H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
958	C₂	C₂×#19099398	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#535×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#535	D₇₉
hypocenter	C₇₉	C₂×#3494
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. #23777132	C₂	direct (N × H)
2. C₂×#19099277	C₂	semidirect
3. C₂×#19099265	C₂	semidirect
4. C₂×#19099260	C₂	semidirect
5. C₂×#19099244	C₂	semidirect
6. C₂×#19099213	C₂	semidirect
7. C₂×#19099200	C₂	semidirect
8. C₂×#19099191	C₂	semidirect
9. C₂×#19099182	C₂	semidirect
10. C₂×#19099167	C₂	semidirect
11. C₂×#19099111	C₂	semidirect
12. C₂×#19099092	C₂	semidirect
13. C₂×#19099070	C₂	semidirect
14. C₂²×#14579132	C₂	semidirect
15. C₂×#19099046	C₂	semidirect
16. C₂×#19099038	C₂	semidirect
17. C₂×#117×D₇₉	C₂	semidirect
18. C₂×#535×C₇₉	C₂	semidirect
19. C₂²×#11929623	C₂²	semidirect
22. #19099277	C₂²	semidirect
23. #19099265	C₂²	semidirect
24. #19099260	C₂²	semidirect
25. #19099244	C₂²	semidirect
26. #19099213	C₂²	semidirect
27. #19099200	C₂²	semidirect
28. #19099191	C₂²	semidirect
29. #19099182	C₂²	semidirect
30. #19099167	C₂²	semidirect
31. #19099111	C₂²	semidirect
32. C₂×#14579161	C₂²	semidirect
33. C₂×#14579160	C₂²	semidirect
34. #19099092	C₂²	semidirect
35. C₂×#14579154	C₂²	semidirect
36. C₂×#14579154	C₂²	semidirect
37. C₂×#14579153	C₂²	semidirect
38. C₂×#14579152	C₂²	semidirect
39. C₂×#14579148	C₂²	semidirect
40. C₂×#14579147	C₂²	semidirect
41. #19099070	C₂²	semidirect
42. C₂×#14579145	C₂²	semidirect
43. C₂×#14579143	C₂²	semidirect
45. C₂×#14579142	C₂²	semidirect
46. C₂×#14579142	C₂²	semidirect
48. C₂×#14579138	C₂²	semidirect
49. C₂×#14579137	C₂²	semidirect
50. C₂×#14579137	C₂²	semidirect
51. C₂×#14579133	C₂²	semidirect
52. C₂×#14579133	C₂²	semidirect
57. C₂×#14579132	C₂²	semidirect
58. C₂×#14579132	C₂²	semidirect
59. C₂×#14579132	C₂²	semidirect
60. C₂×#14579132	C₂²	semidirect
62. #19099046	C₂²	semidirect
63. #19099038	C₂²	semidirect
64. C₂×Q₈×Dic₇₉	C₂²	semidirect
66. C₂×D₄×Dic₇₉	C₂²	semidirect
67. C₂×D₄×Dic₇₉	C₂²	semidirect
68. C₂×D₄×Dic₇₉	C₂²	semidirect
69. C₂×D₄×Dic₇₉	C₂²	semidirect
70. C₂×D₄×Dic₇₉	C₂²	semidirect
71. C₂×D₄×Dic₇₉	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
74. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
77. C₂×#14579120	C₂²	semidirect
78. C₂×#14579119	C₂²	semidirect
79. C₂×#14579119	C₂²	semidirect
80. C₂×#14579118	C₂²	semidirect
82. C₂×#14579117	C₂²	semidirect
83. #117×D₇₉	C₂²	semidirect
85. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
86. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
87. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
91. C₂×C₄²×D₇₉	C₂²	semidirect
94. #535×C₇₉	C₂²	semidirect
95. C₂×#127×C₇₉	C₂²	semidirect
96. C₂×#124×C₇₉	C₂²	semidirect
97. C₂×#121×C₇₉	C₂²	semidirect
98. C₂×#121×C₇₉	C₂²	semidirect
103. C₂×#11929623	C₂³	semidirect
124. #14579161	C₂³	semidirect
125. #14579160	C₂³	semidirect
126. #14579154	C₂³	semidirect
127. #14579154	C₂³	semidirect
128. #14579153	C₂³	semidirect
129. #14579152	C₂³	semidirect
130. #14579148	C₂³	semidirect
131. #14579147	C₂³	semidirect
132. #14579145	C₂³	semidirect
133. #14579143	C₂³	semidirect
135. #14579142	C₂³	semidirect
136. #14579142	C₂³	semidirect
138. #14579138	C₂³	semidirect
139. #14579137	C₂³	semidirect
140. #14579137	C₂³	semidirect
141. #14579133	C₂³	semidirect
142. #14579133	C₂³	semidirect
147. #14579132	C₂³	semidirect
148. #14579132	C₂³	semidirect
149. #14579132	C₂³	semidirect
151. Q₈×Dic₇₉	C₂³	semidirect
153. D₄×Dic₇₉	C₂³	semidirect
154. D₄×Dic₇₉	C₂³	semidirect
155. D₄×Dic₇₉	C₂³	semidirect
156. D₄×Dic₇₉	C₂³	semidirect
157. D₄×Dic₇₉	C₂³	semidirect
158. D₄×Dic₇₉	C₂³	semidirect
159. C₄×C₂²⋊D₇₉	C₂³	semidirect
160. C₄×C₂²⋊D₇₉	C₂³	semidirect
161. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
164. #14579120	C₂³	semidirect
165. #14579119	C₂³	semidirect
166. #14579119	C₂³	semidirect
167. #14579118	C₂³	semidirect
169. #14579117	C₂³	semidirect
179. C₂×C₄⋊Dic₇₉	C₂³	semidirect
186. C₄⋊C₄×D₇₉	C₂³	semidirect
187. C₄⋊C₄×D₇₉	C₂³	semidirect
209. C₄²×D₇₉	C₂³	semidirect
224. #127×C₇₉	C₂³	semidirect
225. #124×C₇₉	C₂³	semidirect
226. #121×C₇₉	C₂³	semidirect
227. #121×C₇₉	C₂³	semidirect
340. C₂²×C₄×C₇₉	#41	semidirect
396. C₂×C₄×C₇₉	C₂×#41	semidirect
474. C₂×C₇₉	#3494	semidirect
490. C₂×#535	D₇₉	semidirect
498. C₇₉	C₂×#3494	semidirect
513. #535	C₂×D₇₉	semidirect
517. C₂×#127	C₂×D₇₉	semidirect
525. C₂×#124	C₂×D₇₉	semidirect
546. C₂×#121	C₂×D₇₉	semidirect
547. C₂×#121	C₂×D₇₉	semidirect
620. #127	C₂²×D₇₉	semidirect
627. #124	C₂²×D₇₉	semidirect
646. #121	C₂²×D₇₉	semidirect
647. #121	C₂²×D₇₉	semidirect
788. C₂²×C₄	#11929623	semidirect
906. C₂×C₄	C₂×#11929623	semidirect
955. C₂	#23777132	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777132	2
C₂×#19099277	2
C₂×#19099265	2
C₂×#19099260	2
C₂×#19099244	2
C₂×#19099213	2
C₂×#19099200	2
C₂×#19099191	2
C₂×#19099182	2
C₂×#19099167	2
C₂×#19099111	2
C₂×#19099092	2
C₂×#19099070	2
C₂²×#14579132	2
C₂×#19099046	2
C₂×#19099038	2
C₂×#117×D₇₉	2
C₂×#535×C₇₉	2
C₂×#3494	79

Subgroups — C2×#23777132 #35196613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777132 #35196613