Subgroups — C₂×#23777965 #35195615

Order 20224.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777965	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099317	C₂	1	2	yes	maximal, complemented
3	C₂×#19099311	C₂	1	2	yes	maximal, complemented
4	C₂×#19099285	C₂	1	2	yes	maximal, complemented
5	C₂×#19099237	C₂	1	4	yes	maximal, complemented
6	C₂×#19099226	C₂	1	2	yes	maximal, complemented
7	C₂×#19099225	C₂	1	2	yes	maximal, complemented
8	C₂×#19099204	C₂	1	2	yes	maximal, complemented
9	C₂×#19099188	C₂	1	2	yes	maximal, complemented
10	C₂×#19099187	C₂	1	2	yes	maximal, complemented
11	C₂×#19099185	C₂	1	4	yes	maximal, complemented
12	C₂×#19099153	C₂	1	2	yes	maximal, complemented
13	C₂×#19099138	C₂	1	2	yes	maximal, complemented
14	C₂×#19099097	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#14579149	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11929625	C₂²	1	2	yes	—
18	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×D₇₉	C₂²	1	2	yes	complemented
20	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
21	#19099317	C₂²	1	32	yes	complemented
22	#19099311	C₂²	1	32	yes	complemented
23	#19099285	C₂²	1	32	yes	complemented
24	#19099237	C₂²	1	64	yes	complemented
25	#19099226	C₂²	1	32	yes	complemented
26	#19099225	C₂²	1	32	yes	complemented
27	#19099204	C₂²	1	32	yes	complemented
28	#19099188	C₂²	1	32	yes	complemented
29	#19099187	C₂²	1	32	yes	complemented
30	#19099185	C₂²	1	64	yes	complemented
31	#19099153	C₂²	1	32	yes	complemented
32	#19099138	C₂²	1	32	yes	complemented
33	C₂×#14579160	C₂²	1	4	yes	complemented
34	C₂×#14579159	C₂²	1	2	yes	complemented
35	#19099097	C₂²	1	16	yes	complemented
36	C₂×#14579156	C₂²	1	4	yes	complemented
37	C₂×#14579156	C₂²	1	4	yes	complemented
38	C₂×#14579155	C₂²	1	2	yes	complemented
39	C₂×#14579155	C₂²	1	4	yes	complemented
40	C₂×#14579153	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14579150	C₂²	1	2	yes	—
42	C₂×#14579150	C₂²	1	4	yes	complemented
43	C₂×#14579149	C₂²	1	2	yes	—
44	C₂×#14579149	C₂²	1	2	yes	—
45	C₂×#14579149	C₂²	1	2	yes	—
46	C₂×#14579149	C₂²	1	2	yes	—
47	C₂×#14579149	C₂²	1	16	yes	complemented
48	C₂×#14579149	C₂²	1	4	yes	complemented
49	C₂×#14579149	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14579146	C₂²	1	4	yes	—
51	C₂×#14579146	C₂²	1	4	yes	complemented
52	C₂×#14579146	C₂²	1	4	yes	complemented
53	C₂×#14579146	C₂²	1	4	yes	complemented
54	C₂×#14579144	C₂²	1	2	yes	—
55	C₂×#14579141	C₂²	1	2	yes	complemented
56	C₂×#14579141	C₂²	1	4	yes	complemented
57	C₂×#14579140	C₂²	1	1	yes	characteristic
58	C₂×#14579139	C₂²	1	4	yes	complemented
59	C₂×#14579139	C₂²	1	4	yes	complemented
60	C₂×#14579139	C₂²	1	4	yes	complemented
61	C₂×#14579139	C₂²	1	4	yes	complemented
62	C₂×#14579138	C₂²	1	4	yes	—
63	C₂×#14579137	C₂²	1	4	yes	complemented
64	C₂×#14579136	C₂²	1	4	yes	—
65	C₂×#14579136	C₂²	1	2	yes	—
66	C₂×#14579136	C₂²	1	4	yes	complemented
67	C₂×#14579135	C₂²	1	1	yes	characteristic
68	C₂×#14579131	C₂²	1	4	yes	—
69	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14579126	C₂²	1	2	yes	complemented
71	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
72	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
73	C₂×#14579123	C₂²	1	2	yes	—
74	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
75	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	—
76	C₂×#14579118	C₂²	1	4	yes	complemented
77	C₂×#14579118	C₂²	1	2	yes	complemented
78	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
79	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
80	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
81	#533×C₇₉	C₂²	1	16	yes	complemented
82	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
84	C₂×#125×C₇₉	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
86	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
87	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
88	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
89	C₂×#117×C₇₉	C₂²	1	2	yes	—
90	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
91	C₂⁴×D₇₉	C₂³	1	2	yes	—
92	C₂×#11929625	—	4	8	no	—
93	C₂×#11929625	C₂³	1	16	yes	—
94	C₂²×Dic₁₅₈	—	4	4	no	—
95	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
96	C₂²×Dic₁₅₈	C₂³	1	8	yes	—
97	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
98	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
99	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
100	C₂×Q₈×D₇₉	—	4	8	no	—
101	C₂×Q₈×D₇₉	C₂³	1	16	yes	complemented
102	C₂²×D₃₁₆	—	4	4	no	—
103	C₂²×D₃₁₆	C₂³	1	2	yes	—
104	C₂²×D₃₁₆	C₂³	1	8	yes	—
105	C₂²×D₃₁₆	C₂³	1	4	yes	—
106	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
107	C₂²×D₃₁₆	C₂³	1	4	yes	—
108	C₂²×D₃₁₆	C₂³	1	2	yes	—
109	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
110	C₂³×Dic₇₉	C₂³	1	2	yes	—
111	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
112	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
113	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
114	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
115	#14579160	C₂³	1	32	yes	complemented
116	#14579159	C₂³	1	16	yes	complemented
117	#14579156	C₂³	1	32	yes	complemented
118	#14579156	C₂³	1	32	yes	complemented
119	#14579155	C₂³	1	16	yes	complemented
120	#14579155	C₂³	1	32	yes	complemented
121	#14579153	C₂³	1	8	yes	complemented
122	#14579150	C₂³	1	16	yes	—
123	#14579150	C₂³	1	32	yes	complemented
124	#14579149	C₂³	1	16	yes	—
125	#14579149	C₂³	1	16	yes	—
126	#14579149	C₂³	1	16	yes	—
127	#14579149	C₂³	1	16	yes	—
128	#14579149	C₂³	1	32	yes	complemented
129	#14579149	C₂³	1	8	yes	complemented
130	#14579146	C₂³	1	32	yes	—
131	#14579146	C₂³	1	32	yes	complemented
132	#14579146	C₂³	1	32	yes	complemented
133	#14579146	C₂³	1	32	yes	complemented
134	#14579144	C₂³	1	16	yes	—
135	#14579141	C₂³	1	16	yes	complemented
136	#14579141	C₂³	1	32	yes	complemented
137	#14579140	C₂³	1	8	yes	—
138	#14579139	C₂³	1	32	yes	complemented
139	#14579139	C₂³	1	32	yes	complemented
140	#14579139	C₂³	1	32	yes	complemented
141	#14579139	C₂³	1	32	yes	complemented
142	#14579138	C₂³	1	32	yes	—
143	#14579137	C₂³	1	32	yes	complemented
144	#14579136	C₂³	1	32	yes	—
145	#14579136	C₂³	1	16	yes	—
146	#14579136	C₂³	1	32	yes	complemented
147	#14579135	C₂³	1	8	yes	—
148	#14579131	C₂³	1	32	yes	—
149	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
150	#14579126	C₂³	1	16	yes	complemented
151	C₄×D₃₁₆	C₂³	1	32	yes	complemented
152	C₄×D₃₁₆	C₂³	1	8	yes	complemented
153	#14579123	C₂³	1	16	yes	—
154	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
155	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	—
156	#14579118	C₂³	1	16	yes	complemented
157	#14579118	C₂³	1	32	yes	complemented
158	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
159	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
161	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
162	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
164	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
165	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
166	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
167	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
168	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
169	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
170	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
171	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
174	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
176	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
179	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
180	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
181	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
182	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
184	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
185	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
186	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
187	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
188	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
189	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
192	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
193	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
194	#125×C₇₉	C₂³	1	16	yes	complemented
195	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	—
196	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	—
197	C₄×Q₈×C₇₉	C₂³	1	16	yes	complemented
198	C₄×Q₈×C₇₉	C₂³	1	16	yes	complemented
199	#117×C₇₉	C₂³	1	16	yes	—
200	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
207	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇₉	C₂³	1	8	yes	—
212	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
213	C₂³×D₇₉	—	2	8	no	—
214	C₂³×D₇₉	—	4	4	no	—
215	C₂³×D₇₉	—	4	4	no	—
216	C₂³×D₇₉	C₂⁴	1	4	yes	—
217	C₂³×D₇₉	C₂⁴	1	2	yes	—
218	C₂³×D₇₉	C₂⁴	1	8	yes	—
219	#11929625	—	4	32	no	—
220	C₂×Dic₁₅₈	—	2	8	no	—
221	C₂×Dic₁₅₈	—	4	16	no	—
222	C₂×Dic₁₅₈	—	4	8	no	—
223	C₂×Dic₁₅₈	—	4	4	no	—
224	C₂×Dic₁₅₈	—	4	2	no	—
225	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
226	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
227	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
228	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
229	Q₈×D₇₉	—	4	32	no	—
230	C₂×D₃₁₆	—	2	8	no	—
231	C₂×D₃₁₆	—	4	8	no	—
232	C₂×D₃₁₆	—	4	4	no	—
233	C₂×D₃₁₆	—	4	8	no	—
234	C₂×D₃₁₆	—	4	2	no	—
235	C₂×D₃₁₆	—	4	16	no	—
236	C₂×D₃₁₆	C₂⁴	1	8	yes	—
237	C₂×D₃₁₆	C₂⁴	1	16	yes	—
238	C₂×D₃₁₆	C₂⁴	1	16	yes	—
239	C₂×D₃₁₆	C₂⁴	1	4	yes	—
240	C₂×D₃₁₆	C₂⁴	1	8	yes	—
241	C₂×C₂²⋊D₇₉	—	2	8	no	—
242	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
243	C₂²×Dic₇₉	—	4	4	no	—
244	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
245	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
246	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
247	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
248	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
249	C₂×C₄×D₇₉	—	2	8	no	—
250	C₂×C₄×D₇₉	—	4	8	no	—
251	C₂×C₄×D₇₉	—	4	8	no	—
252	C₂×C₄×D₇₉	—	4	8	no	—
253	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
254	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
255	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
256	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
257	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
258	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
259	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
260	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
261	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
262	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
263	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
264	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
265	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
266	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
267	C₂²⋊Dic₇₉	C₂⁴	1	8	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	—
271	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
272	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
273	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
274	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
275	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
276	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
277	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
278	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
279	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
280	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
281	C₄×Dic₇₉	C₂⁴	1	16	yes	—
282	C₄×Dic₇₉	C₂⁴	1	8	yes	—
283	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
284	C₂×Q₈×C₇₉	—	2	8	no	—
285	C₂×Q₈×C₇₉	—	4	4	no	—
286	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
287	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₇₉	—	2	4	no	—
289	C₂²×C₄×C₇₉	—	2	4	no	—
290	C₂²×C₄×C₇₉	—	4	2	no	—
291	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
304	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
305	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
309	C₄²×C₇₉	C₂⁴	1	4	yes	—
310	C₄²×C₇₉	C₂⁴	1	4	yes	—
311	C₄²×C₇₉	C₂⁴	1	4	yes	—
312	C₄²×C₇₉	C₂⁴	1	4	yes	—
313	C₄²×C₇₉	C₂⁴	1	16	yes	—
314	C₂³×C₇₉	—	2	2	no	—
315	C₂³×C₇₉	—	2	2	no	—
316	C₂³×C₇₉	2₋¹⁺⁴	1	4	yes	—
317	C₂³×C₇₉	C₂⁵	1	2	yes	—
318	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
319	C₂²×D₇₉	—	2	4	no	—
320	C₂²×D₇₉	—	2	8	no	—
321	C₂²×D₇₉	—	2	4	no	—
322	C₂²×D₇₉	—	2	8	no	—
323	C₂²×D₇₉	—	2	8	no	—
324	C₂²×D₇₉	—	2	4	no	—
325	C₂²×D₇₉	—	2	16	no	—
326	C₂²×D₇₉	—	4	8	no	—
327	C₂²×D₇₉	—	4	8	no	—
328	C₂²×D₇₉	—	8	16	no	—
329	C₂²×D₇₉	C₂⁵	1	8	yes	—
330	C₂²×D₇₉	C₂⁵	1	4	yes	—
331	Q₈×C₇₉	—	2	16	no	—
332	Q₈×C₇₉	—	4	8	no	—
333	C₂×C₄×C₇₉	—	2	8	no	—
334	C₂×C₄×C₇₉	—	2	2	no	—
335	C₂×C₄×C₇₉	—	2	8	no	—
336	C₂×C₄×C₇₉	—	2	2	no	—
337	C₂×C₄×C₇₉	—	2	2	no	—
338	C₂×C₄×C₇₉	—	2	8	no	—
339	C₂×C₄×C₇₉	—	2	2	no	—
340	C₂×C₄×C₇₉	—	2	2	no	—
341	C₂×C₄×C₇₉	—	2	8	no	—
342	C₂×C₄×C₇₉	—	4	4	no	—
343	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
344	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
345	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
346	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
347	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
348	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
349	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
350	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
351	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
352	C₂²⋊D₇₉	—	2	16	no	—
353	C₂×Dic₇₉	—	2	4	no	—
354	C₂×Dic₇₉	—	2	8	no	—
355	C₂×Dic₇₉	—	2	4	no	—
356	C₂×Dic₇₉	—	2	4	no	—
357	C₂×Dic₇₉	—	4	8	no	—
358	C₂×Dic₇₉	C₂⁵	1	4	yes	—
359	C₂×Dic₇₉	C₂⁵	1	8	yes	—
360	C₂×Dic₇₉	C₂⁵	1	4	yes	—
361	C₂×Dic₇₉	C₂⁵	1	4	yes	—
362	D₃₁₆	—	2	16	no	—
363	D₃₁₆	—	4	8	no	—
364	D₃₁₆	—	4	4	no	—
365	D₃₁₆	—	4	16	no	—
366	D₃₁₆	—	4	16	no	—
367	C₄×D₇₉	—	2	16	no	—
368	C₄×D₇₉	—	4	16	no	—
369	C₄×D₇₉	—	4	16	no	—
370	C₄×D₇₉	—	4	16	no	—
371	Dic₁₅₈	—	2	16	no	—
372	Dic₁₅₈	—	4	16	no	—
373	Dic₁₅₈	—	4	8	no	—
374	Dic₁₅₈	—	4	4	no	—
375	C₂²×C₇₉	—	2	2	no	—
376	C₂²×C₇₉	—	2	2	no	—
377	C₂²×C₇₉	—	2	8	no	—
378	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
379	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	4	yes	—
380	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	2	yes	—
381	C₂²×C₇₉	#585	1	2	yes	—
382	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
383	C₂×D₇₉	—	2	8	no	—
384	C₂×D₇₉	—	2	4	no	—
385	C₂×D₇₉	—	2	4	no	—
386	C₂×D₇₉	—	2	8	no	—
387	C₂×D₇₉	—	2	8	no	—
388	C₂×D₇₉	—	2	4	no	—
389	C₂×D₇₉	—	4	8	no	—
390	C₂×D₇₉	—	4	16	no	—
391	C₂×D₇₉	—	8	16	no	—
392	C₄×C₇₉	—	2	2	no	—
393	C₄×C₇₉	—	2	8	no	—
394	C₄×C₇₉	—	2	2	no	—
395	C₄×C₇₉	—	2	2	no	—
396	C₄×C₇₉	—	2	2	no	—
397	C₄×C₇₉	—	2	2	no	—
398	C₄×C₇₉	—	2	8	no	—
399	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
400	Dic₇₉	—	2	8	no	—
401	Dic₇₉	—	2	4	no	—
402	Dic₇₉	—	2	4	no	—
403	Dic₇₉	—	2	4	no	—
404	C₂×#3561	—	79	1	no	maximal, Sylow
405	C₂×C₇₉	—	2	4	no	—
406	C₂×C₇₉	#3561	1	4	yes	complemented
407	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂×C₇₉	C₂×#585	1	1	yes	characteristic
410	D₇₉	—	4	4	no	—
411	D₇₉	—	4	8	no	—
412	#3561	—	79	32	no	—
413	C₂×#563	—	79	2	no	—
414	C₂×#562	—	79	2	no	—
415	C₂×#556	—	79	2	no	—
416	C₂×#551	—	79	4	no	—
417	C₂×D₄×Q₈	—	79	2	no	—
418	C₂×#548	—	79	2	no	—
419	C₂×#546	—	79	2	no	—
420	C₂×#543	—	79	2	no	—
421	C₂×#542	—	79	2	no	—
422	C₂×#542	—	79	4	no	—
423	C₂×#538	—	79	2	no	—
424	C₂×#536	—	79	2	no	—
425	C₂×#533	D₇₉	1	1	yes	characteristic, complemented
426	C₂×#529	—	79	1	no	—
427	C₂²×#124	—	79	1	no	—
428	C₇₉	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
429	C₂²×#41	—	79	2	no	—
430	C₂³×Q₈	—	79	2	no	—
431	C₂³×Q₈	—	79	1	no	—
432	C₂³×D₄	—	79	1	no	—
433	#563	—	79	32	no	—
434	#562	—	79	32	no	—
435	#556	—	79	32	no	—
436	#551	—	79	64	no	—
437	D₄×Q₈	—	79	32	no	—
438	#548	—	79	32	no	—
439	#546	—	79	32	no	—
440	#543	—	79	32	no	—
441	#542	—	79	32	no	—
442	#542	—	79	64	no	—
443	#538	—	79	32	no	—
444	#536	—	79	32	no	—
445	#533	C₂×D₇₉	1	16	yes	complemented
446	C₂×C₄⋊Q₈	—	79	2	no	—
447	C₂×C₄⋊Q₈	—	79	4	no	—
448	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
449	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
450	#529	—	79	16	no	—
451	C₂×#126	—	79	4	no	—
452	C₂×#126	—	79	4	no	—
453	C₂×#126	—	79	2	no	—
454	C₂×#126	—	79	4	no	—
455	C₂×#125	—	79	1	no	—
456	C₂×#125	C₂×D₇₉	1	2	yes	complemented
457	C₂×#124	—	79	2	no	—
458	C₂×#124	—	79	4	no	—
459	C₂×#124	—	79	2	no	—
460	C₂×#124	—	79	2	no	—
461	C₂×#124	—	79	2	no	—
462	C₂×#124	—	79	2	no	—
463	C₂×#124	—	79	16	no	—
464	C₂×#124	—	79	1	no	—
465	C₂×#124	—	79	4	no	—
466	C₂×#123	—	79	2	no	—
467	C₂×#123	—	79	4	no	—
468	C₂×#123	—	79	4	no	—
469	C₂×#123	—	79	4	no	—
470	C₂×#123	—	79	4	no	—
471	C₂×C₂²⋊Q₈	—	79	4	no	—
472	C₂×C₂²⋊Q₈	—	79	1	no	—
473	C₂×C₂²⋊Q₈	—	79	4	no	—
474	C₂×C₂²⋊Q₈	—	79	4	no	—
475	C₂×C₂²⋊Q₈	—	79	2	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×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
482	C₂×#121	—	79	1	no	—
483	C₂×#121	—	79	4	no	—
484	C₂×#121	—	79	2	no	—
485	C₂×#121	—	79	4	no	—
486	C₂×#120	—	79	4	no	—
487	C₂×C₄×Q₈	—	79	2	no	—
488	C₂×C₄×Q₈	—	79	1	no	—
489	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	complemented
490	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	complemented
491	C₂×C₄×D₄	—	79	2	no	—
492	C₂×C₄×D₄	—	79	2	no	—
493	C₂×C₄×D₄	—	79	4	no	—
494	C₂×C₄×D₄	—	79	1	no	—
495	C₂×C₄×D₄	—	79	4	no	—
496	C₂×#117	—	79	2	no	—
497	C₂×#117	—	79	4	no	—
498	C₂×#117	C₂×D₇₉	1	2	yes	—
499	C₂²×C₂²⋊C₄	—	79	2	no	—
500	C₂²×C₂²⋊C₄	—	79	2	no	—
501	C₂²×C₂²⋊C₄	—	79	4	no	—
502	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
503	C₂⁵	—	79	2	no	—
504	C₂×#41	—	316	8	no	—
505	C₂×#41	—	79	16	no	—
506	C₂²×Q₈	—	316	4	no	—
507	C₂²×Q₈	—	316	8	no	—
508	C₂²×Q₈	—	79	16	no	—
509	C₂²×Q₈	—	79	1	no	—
510	C₂²×Q₈	—	79	4	no	—
511	C₂²×Q₈	—	79	2	no	—
512	C₂²×Q₈	—	79	8	no	—
513	C₂²×Q₈	—	79	2	no	—
514	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
515	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
516	C₂²×D₄	—	316	4	no	—
517	C₂²×D₄	—	79	2	no	—
518	C₂²×D₄	—	79	4	no	—
519	C₂²×D₄	—	79	1	no	—
520	C₂²×D₄	—	79	4	no	—
521	C₂²×D₄	—	79	2	no	—
522	C₂²×D₄	—	79	8	no	—
523	C₂²×D₄	—	79	2	no	—
524	C₂³×C₄	—	79	2	no	—
525	C₂³×C₄	—	79	4	no	—
526	C₂³×C₄	—	79	4	no	—
527	C₂³×C₄	—	79	4	no	—
528	C₂³×C₄	—	79	2	no	—
529	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
530	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
531	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
532	C₄⋊Q₈	—	79	16	no	—
533	C₄⋊Q₈	—	79	32	no	—
534	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
535	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
536	#126	—	79	32	no	—
537	#126	—	79	32	no	—
538	#126	—	79	16	no	—
539	#126	—	79	32	no	—
540	#125	—	79	8	no	—
541	#125	C₂²×D₇₉	1	16	yes	complemented
542	#124	—	79	16	no	—
543	#124	—	79	32	no	—
544	#124	—	79	16	no	—
545	#124	—	79	16	no	—
546	#124	—	79	16	no	—
547	#124	—	79	16	no	—
548	#124	—	79	8	no	—
549	#124	—	79	32	no	—
550	#123	—	79	16	no	—
551	#123	—	79	32	no	—
552	#123	—	79	32	no	—
553	#123	—	79	32	no	—
554	#123	—	79	32	no	—
555	C₂²⋊Q₈	—	79	32	no	—
556	C₂²⋊Q₈	—	79	8	no	—
557	C₂²⋊Q₈	—	79	32	no	—
558	C₂²⋊Q₈	—	79	32	no	—
559	C₂²⋊Q₈	—	79	16	no	—
560	C₂²⋊Q₈	—	79	32	no	—
561	C₂²⋊Q₈	—	79	32	no	—
562	C₂²⋊Q₈	—	79	32	no	—
563	C₂²⋊Q₈	—	79	32	no	—
564	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	—
565	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	—
566	#121	—	79	8	no	—
567	#121	—	79	32	no	—
568	#121	—	79	16	no	—
569	#121	—	79	32	no	—
570	#120	—	79	32	no	—
571	C₄×Q₈	—	79	16	no	—
572	C₄×Q₈	—	79	8	no	—
573	C₄×Q₈	C₂²×D₇₉	1	16	yes	complemented
574	C₄×Q₈	C₂²×D₇₉	1	16	yes	complemented
575	C₄×D₄	—	79	16	no	—
576	C₄×D₄	—	79	16	no	—
577	C₄×D₄	—	79	32	no	—
578	C₄×D₄	—	79	8	no	—
579	C₄×D₄	—	79	32	no	—
580	#117	—	79	16	no	—
581	#117	—	79	32	no	—
582	#117	C₂²×D₇₉	1	16	yes	—
583	C₂×C₄⋊C₄	—	79	2	no	—
584	C₂×C₄⋊C₄	—	79	2	no	—
585	C₂×C₄⋊C₄	—	79	4	no	—
586	C₂×C₄⋊C₄	—	79	2	no	—
587	C₂×C₄⋊C₄	—	79	1	no	—
588	C₂×C₄⋊C₄	—	79	4	no	—
589	C₂×C₄⋊C₄	—	79	4	no	—
590	C₂×C₄⋊C₄	—	79	2	no	—
591	C₂×C₄⋊C₄	—	79	1	no	—
592	C₂×C₄⋊C₄	—	79	4	no	—
593	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
597	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
598	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
599	C₂×C₂²⋊C₄	—	79	2	no	—
600	C₂×C₂²⋊C₄	—	79	4	no	—
601	C₂×C₂²⋊C₄	—	79	4	no	—
602	C₂×C₂²⋊C₄	—	79	4	no	—
603	C₂×C₂²⋊C₄	—	79	4	no	—
604	C₂×C₂²⋊C₄	—	79	4	no	—
605	C₂×C₂²⋊C₄	—	79	4	no	—
606	C₂×C₂²⋊C₄	—	79	16	no	—
607	C₂×C₂²⋊C₄	—	79	16	no	—
608	C₂×C₂²⋊C₄	—	79	4	no	—
609	C₂×C₂²⋊C₄	—	79	2	no	—
610	C₂×C₂²⋊C₄	—	79	2	no	—
611	C₂×C₂²⋊C₄	—	79	2	no	—
612	C₂×C₂²⋊C₄	—	79	4	no	—
613	C₂×C₂²⋊C₄	—	79	2	no	—
614	C₂×C₂²⋊C₄	—	79	4	no	—
615	C₂×C₂²⋊C₄	—	79	32	no	—
616	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
617	C₂×C₄²	—	79	2	no	—
618	C₂×C₄²	—	79	4	no	—
619	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
620	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
621	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
622	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
623	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
624	C₂×C₄²	C₂²×D₇₉	1	8	yes	—
625	C₂⁴	—	316	4	no	—
626	C₂⁴	—	316	4	no	—
627	C₂⁴	—	79	8	no	—
628	C₂⁴	—	79	4	no	—
629	C₂⁴	—	79	2	no	—
630	C₂⁴	—	158	8	no	—
631	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
632	#41	—	316	32	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	4	4	no	—
635	C₂×Q₈	—	316	16	no	—
636	C₂×Q₈	—	316	4	no	—
637	C₂×Q₈	—	316	8	no	—
638	C₂×Q₈	—	316	2	no	—
639	C₂×Q₈	—	316	32	no	—
640	C₂×Q₈	—	79	4	no	—
641	C₂×Q₈	—	79	16	no	—
642	C₂×Q₈	—	79	8	no	—
643	C₂×Q₈	—	79	8	no	—
644	C₂×Q₈	—	158	8	no	—
645	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
646	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
647	C₂×D₄	—	316	4	no	—
648	C₂×D₄	—	316	2	no	—
649	C₂×D₄	—	316	8	no	—
650	C₂×D₄	—	316	8	no	—
651	C₂×D₄	—	316	16	no	—
652	C₂×D₄	—	79	8	no	—
653	C₂×D₄	—	79	16	no	—
654	C₂×D₄	—	79	4	no	—
655	C₂×D₄	—	79	16	no	—
656	C₂×D₄	—	79	8	no	—
657	C₂×D₄	—	79	8	no	—
658	C₂×D₄	—	158	8	no	—
659	C₂×D₄	—	158	8	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	316	8	no	—
664	C₂²×C₄	—	316	8	no	—
665	C₂²×C₄	—	316	8	no	—
666	C₂²×C₄	—	316	4	no	—
667	C₂²×C₄	—	79	8	no	—
668	C₂²×C₄	—	79	16	no	—
669	C₂²×C₄	—	79	16	no	—
670	C₂²×C₄	—	79	16	no	—
671	C₂²×C₄	—	79	2	no	—
672	C₂²×C₄	—	79	2	no	—
673	C₂²×C₄	—	79	4	no	—
674	C₂²×C₄	—	79	2	no	—
675	C₂²×C₄	—	79	8	no	—
676	C₂²×C₄	—	158	8	no	—
677	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
678	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
679	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
680	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
681	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
682	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
683	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
684	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
685	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
686	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
687	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
688	C₄⋊C₄	—	79	8	no	—
689	C₄⋊C₄	—	79	8	no	—
690	C₄⋊C₄	—	79	16	no	—
691	C₄⋊C₄	—	79	8	no	—
692	C₄⋊C₄	—	79	16	no	—
693	C₄⋊C₄	—	79	8	no	—
694	C₄⋊C₄	—	79	16	no	—
695	C₄⋊C₄	—	79	4	no	—
696	C₄⋊C₄	—	79	16	no	—
697	C₄⋊C₄	—	79	4	no	—
698	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
699	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
700	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
701	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
702	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
703	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
704	C₂²⋊C₄	—	79	8	no	—
705	C₂²⋊C₄	—	79	16	no	—
706	C₂²⋊C₄	—	79	16	no	—
707	C₂²⋊C₄	—	79	16	no	—
708	C₂²⋊C₄	—	79	16	no	—
709	C₂²⋊C₄	—	79	16	no	—
710	C₂²⋊C₄	—	79	16	no	—
711	C₂²⋊C₄	—	79	16	no	—
712	C₂²⋊C₄	—	79	8	no	—
713	C₂²⋊C₄	—	79	8	no	—
714	C₂²⋊C₄	—	79	8	no	—
715	C₂²⋊C₄	—	79	16	no	—
716	C₂²⋊C₄	—	79	8	no	—
717	C₂²⋊C₄	—	79	16	no	—
718	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
719	C₄²	—	79	8	no	—
720	C₄²	—	79	16	no	—
721	C₄²	C₂³×D₇₉	1	4	yes	—
722	C₄²	C₂³×D₇₉	1	4	yes	—
723	C₄²	C₂³×D₇₉	1	4	yes	—
724	C₄²	C₂³×D₇₉	1	4	yes	—
725	C₄²	C₂³×D₇₉	1	16	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	316	8	no	—
729	C₂³	—	316	8	no	—
730	C₂³	—	79	8	no	—
731	C₂³	—	79	4	no	—
732	C₂³	—	632	16	no	—
733	C₂³	—	158	4	no	—
734	C₂³	—	158	8	no	—
735	C₂³	—	158	4	no	—
736	C₂³	—	158	8	no	—
737	C₂³	—	158	8	no	—
738	C₂³	—	158	4	no	—
739	C₂³	—	158	16	no	—
740	C₂³	#14579209	1	4	yes	—
741	C₂³	C₂⁴×D₇₉	1	2	yes	—
742	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
743	Q₈	—	2	16	no	—
744	Q₈	—	4	8	no	—
745	Q₈	—	316	8	no	—
746	Q₈	—	316	16	no	—
747	Q₈	—	316	4	no	—
748	Q₈	—	158	16	no	—
749	D₄	—	316	8	no	—
750	D₄	—	316	16	no	—
751	D₄	—	316	4	no	—
752	D₄	—	316	16	no	—
753	D₄	—	158	16	no	—
754	D₄	—	158	16	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	2	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	316	16	no	—
766	C₂×C₄	—	316	16	no	—
767	C₂×C₄	—	316	16	no	—
768	C₂×C₄	—	316	8	no	—
769	C₂×C₄	—	79	4	no	—
770	C₂×C₄	—	79	4	no	—
771	C₂×C₄	—	79	8	no	—
772	C₂×C₄	—	79	4	no	—
773	C₂×C₄	—	158	4	no	—
774	C₂×C₄	—	158	8	no	—
775	C₂×C₄	—	158	4	no	—
776	C₂×C₄	—	158	4	no	—
777	C₂×C₄	—	158	16	no	—
778	C₂×C₄	#14579207	1	4	yes	—
779	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
780	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
781	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
782	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
783	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
784	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
785	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
786	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	316	16	no	—
791	C₂²	—	316	8	no	—
792	C₂²	—	632	16	no	—
793	C₂²	—	158	4	no	—
794	C₂²	—	158	8	no	—
795	C₂²	—	158	4	no	—
796	C₂²	—	158	8	no	—
797	C₂²	—	158	8	no	—
798	C₂²	—	158	4	no	—
799	C₂²	C₂×#14579207	1	2	yes	—
800	C₂²	C₂×#14579209	1	4	yes	—
801	C₂²	C₂×#14579209	1	2	yes	—
802	C₂²	#19099399	1	2	yes	—
803	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	8	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	8	no	—
811	C₄	—	158	4	no	—
812	C₄	—	158	8	no	—
813	C₄	—	158	4	no	—
814	C₄	—	158	4	no	—
815	C₄	C₂×#14579207	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	316	8	no	—
818	C₂	—	316	4	no	—
819	C₂	#23777965	1	4	yes	direct product factor
820	C₂	C₂²×#14579207	1	1	yes	characteristic
821	C₂	C₂²×#14579209	1	1	yes	characteristic
822	C₂	C₂×#19099399	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#533×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	C₂×#3561
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #23777965	C₂	direct (N × H)
2. C₂×#19099317	C₂	semidirect
3. C₂×#19099311	C₂	semidirect
4. C₂×#19099285	C₂	semidirect
5. C₂×#19099237	C₂	semidirect
6. C₂×#19099226	C₂	semidirect
7. C₂×#19099225	C₂	semidirect
8. C₂×#19099204	C₂	semidirect
9. C₂×#19099188	C₂	semidirect
10. C₂×#19099187	C₂	semidirect
11. C₂×#19099185	C₂	semidirect
12. C₂×#19099153	C₂	semidirect
13. C₂×#19099138	C₂	semidirect
14. C₂×#19099097	C₂	semidirect
15. C₂²×#14579149	C₂	semidirect
16. C₂×#533×C₇₉	C₂	semidirect
19. C₂²×Q₈×D₇₉	C₂²	semidirect
21. #19099317	C₂²	semidirect
22. #19099311	C₂²	semidirect
23. #19099285	C₂²	semidirect
24. #19099237	C₂²	semidirect
25. #19099226	C₂²	semidirect
26. #19099225	C₂²	semidirect
27. #19099204	C₂²	semidirect
28. #19099188	C₂²	semidirect
29. #19099187	C₂²	semidirect
30. #19099185	C₂²	semidirect
31. #19099153	C₂²	semidirect
32. #19099138	C₂²	semidirect
33. C₂×#14579160	C₂²	semidirect
34. C₂×#14579159	C₂²	semidirect
35. #19099097	C₂²	semidirect
36. C₂×#14579156	C₂²	semidirect
37. C₂×#14579156	C₂²	semidirect
38. C₂×#14579155	C₂²	semidirect
39. C₂×#14579155	C₂²	semidirect
40. C₂×#14579153	C₂²	semidirect
42. C₂×#14579150	C₂²	semidirect
47. C₂×#14579149	C₂²	semidirect
48. C₂×#14579149	C₂²	semidirect
49. C₂×#14579149	C₂²	semidirect
51. C₂×#14579146	C₂²	semidirect
52. C₂×#14579146	C₂²	semidirect
53. C₂×#14579146	C₂²	semidirect
55. C₂×#14579141	C₂²	semidirect
56. C₂×#14579141	C₂²	semidirect
58. C₂×#14579139	C₂²	semidirect
59. C₂×#14579139	C₂²	semidirect
60. C₂×#14579139	C₂²	semidirect
61. C₂×#14579139	C₂²	semidirect
63. C₂×#14579137	C₂²	semidirect
66. C₂×#14579136	C₂²	semidirect
69. C₂×C₄×Dic₁₅₈	C₂²	semidirect
70. C₂×#14579126	C₂²	semidirect
71. C₂×C₄×D₃₁₆	C₂²	semidirect
72. C₂×C₄×D₃₁₆	C₂²	semidirect
76. C₂×#14579118	C₂²	semidirect
77. C₂×#14579118	C₂²	semidirect
81. #533×C₇₉	C₂²	semidirect
82. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
83. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
84. C₂×#125×C₇₉	C₂²	semidirect
87. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
88. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
101. C₂×Q₈×D₇₉	C₂³	semidirect
115. #14579160	C₂³	semidirect
116. #14579159	C₂³	semidirect
117. #14579156	C₂³	semidirect
118. #14579156	C₂³	semidirect
119. #14579155	C₂³	semidirect
120. #14579155	C₂³	semidirect
121. #14579153	C₂³	semidirect
123. #14579150	C₂³	semidirect
128. #14579149	C₂³	semidirect
129. #14579149	C₂³	semidirect
131. #14579146	C₂³	semidirect
132. #14579146	C₂³	semidirect
133. #14579146	C₂³	semidirect
135. #14579141	C₂³	semidirect
136. #14579141	C₂³	semidirect
138. #14579139	C₂³	semidirect
139. #14579139	C₂³	semidirect
140. #14579139	C₂³	semidirect
141. #14579139	C₂³	semidirect
143. #14579137	C₂³	semidirect
146. #14579136	C₂³	semidirect
149. C₄×Dic₁₅₈	C₂³	semidirect
150. #14579126	C₂³	semidirect
151. C₄×D₃₁₆	C₂³	semidirect
152. C₄×D₃₁₆	C₂³	semidirect
156. #14579118	C₂³	semidirect
157. #14579118	C₂³	semidirect
192. C₄⋊Q₈×C₇₉	C₂³	semidirect
193. C₄⋊Q₈×C₇₉	C₂³	semidirect
194. #125×C₇₉	C₂³	semidirect
197. C₄×Q₈×C₇₉	C₂³	semidirect
198. C₄×Q₈×C₇₉	C₂³	semidirect
406. C₂×C₇₉	#3561	semidirect
425. C₂×#533	D₇₉	semidirect
428. C₇₉	C₂×#3561	semidirect
445. #533	C₂×D₇₉	semidirect
448. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
449. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
456. C₂×#125	C₂×D₇₉	semidirect
489. C₂×C₄×Q₈	C₂×D₇₉	semidirect
490. C₂×C₄×Q₈	C₂×D₇₉	semidirect
534. C₄⋊Q₈	C₂²×D₇₉	semidirect
535. C₄⋊Q₈	C₂²×D₇₉	semidirect
541. #125	C₂²×D₇₉	semidirect
573. C₄×Q₈	C₂²×D₇₉	semidirect
574. C₄×Q₈	C₂²×D₇₉	semidirect
819. C₂	#23777965	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777965	2
C₂×#19099317	2
C₂×#19099311	2
C₂×#19099285	2
C₂×#19099237	2
C₂×#19099226	2
C₂×#19099225	2
C₂×#19099204	2
C₂×#19099188	2
C₂×#19099187	2
C₂×#19099185	2
C₂×#19099153	2
C₂×#19099138	2
C₂×#19099097	2
C₂²×#14579149	2
C₂×#533×C₇₉	2
C₂×#3561	79

Subgroups — C2×#23777965 #35195615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777965 #35195615