Subgroups — C₂×#23777451 #35196284

Order 20224.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777451	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099286	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099270	C₂	1	2	yes	maximal, complemented
4	C₂×#19099251	C₂	1	2	yes	maximal, complemented
5	C₂×#19099236	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19099221	C₂	1	2	yes	maximal, complemented
8	C₂×#19099218	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19099217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19099209	C₂	1	2	yes	maximal, complemented
11	C₂×#19099184	C₂	1	2	yes	maximal, complemented
12	C₂×#19099154	C₂	1	4	yes	maximal, complemented
13	C₂×#19099120	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19099073	C₂	1	2	yes	maximal, complemented
15	C₂×C₂²⋊Q₈×D₇₉	C₂	1	2	yes	maximal, complemented
16	C₂×#19099043	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11929624	C₂²	1	2	yes	—
20	C₂²×#11929623	C₂²	1	2	yes	complemented
21	C₂²×Q₈×D₇₉	C₂²	1	2	yes	complemented
22	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₇₉	C₂²	1	2	yes	—
24	#19099286	C₂²	1	16	yes	complemented
25	#19099270	C₂²	1	32	yes	complemented
26	#19099251	C₂²	1	32	yes	complemented
27	#19099236	C₂²	1	64	yes	complemented
28	Q₈×D₃₁₆	C₂²	1	16	yes	complemented
29	#19099221	C₂²	1	32	yes	complemented
30	#19099218	C₂²	1	16	yes	complemented
31	#19099217	C₂²	1	16	yes	complemented
32	#19099209	C₂²	1	32	yes	complemented
33	#19099184	C₂²	1	32	yes	complemented
34	#19099154	C₂²	1	64	yes	complemented
35	#19099120	C₂²	1	16	yes	complemented
36	C₂×#14579161	C₂²	1	2	yes	complemented
37	C₂×#14579161	C₂²	1	1	yes	characteristic, complemented
38	C₂×#14579161	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14579156	C₂²	1	4	yes	complemented
40	C₂×#14579156	C₂²	1	4	yes	complemented
41	C₂×#14579153	C₂²	1	2	yes	complemented
42	C₂×#14579152	C₂²	1	4	yes	complemented
43	C₂×#14579149	C₂²	1	2	yes	—
44	C₂×#14579147	C₂²	1	4	yes	complemented
45	#19099073	C₂²	1	32	yes	complemented
46	C₂×#14579146	C₂²	1	4	yes	—
47	C₂×#14579145	C₂²	1	4	yes	complemented
48	C₂×#14579143	C₂²	1	4	yes	complemented
49	C₂×#14579143	C₂²	1	4	yes	complemented
50	C₂×#14579141	C₂²	1	2	yes	complemented
51	C₂×#14579141	C₂²	1	4	yes	complemented
52	C₂×#14579141	C₂²	1	2	yes	complemented
53	C₂×#14579140	C₂²	1	2	yes	—
54	C₂×#14579140	C₂²	1	2	yes	—
55	C₂×#14579140	C₂²	1	2	yes	complemented
56	C₂×#14579139	C₂²	1	4	yes	complemented
57	C₂×#14579138	C₂²	1	4	yes	—
58	C₂×#14579138	C₂²	1	4	yes	complemented
59	C₂×#14579137	C₂²	1	2	yes	complemented
60	C₂²⋊Q₈×D₇₉	C₂²	1	32	yes	complemented
61	C₂×#14579135	C₂²	1	2	yes	—
62	C₂×#14579134	C₂²	1	4	yes	—
63	C₂×#14579132	C₂²	1	2	yes	complemented
64	C₂×#14579129	C₂²	1	4	yes	—
65	#19099043	C₂²	1	32	yes	complemented
66	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
67	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
69	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
73	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
74	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
75	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
76	C₂×C₄×D₃₁₆	C₂²	1	16	yes	complemented
77	C₂×D₄×Dic₇₉	C₂²	1	4	yes	—
78	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
79	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
80	C₂×#14579120	C₂²	1	2	yes	—
81	C₂×#14579119	C₂²	1	4	yes	complemented
82	C₂×#14579119	C₂²	1	2	yes	complemented
83	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
84	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
85	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	complemented
86	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
87	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
88	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
89	#529×C₇₉	C₂²	1	16	yes	complemented
90	C₂×#126×C₇₉	C₂²	1	2	yes	complemented
91	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
93	C₂×#123×C₇₉	C₂²	1	2	yes	—
94	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
95	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
98	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
99	C₂×#117×C₇₉	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
101	C₂⁴×D₇₉	C₂³	1	2	yes	—
102	C₂×#11929624	—	2	16	no	—
103	C₂×#11929624	C₂³	1	16	yes	—
104	C₂×#11929623	—	4	8	no	—
105	C₂×#11929623	C₂³	1	16	yes	complemented
106	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
107	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
108	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
109	C₂×Q₈×D₇₉	—	4	8	no	—
110	C₂×Q₈×D₇₉	C₂³	1	16	yes	complemented
111	C₂²×D₃₁₆	—	2	8	no	—
112	C₂²×D₃₁₆	C₂³	1	8	yes	—
113	C₂²×D₃₁₆	C₂³	1	2	yes	—
114	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
115	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
116	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
118	C₂³×Dic₇₉	C₂³	1	2	yes	—
119	C₂³×Dic₇₉	C₂³	1	4	yes	—
120	C₂²×C₄×D₇₉	—	4	8	no	—
121	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
122	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
123	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
124	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
125	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
126	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
127	C₂²×C₄×D₇₉	C₂³	1	16	yes	—
128	#14579161	C₂³	1	16	yes	complemented
129	#14579161	C₂³	1	8	yes	complemented
130	#14579161	C₂³	1	8	yes	complemented
131	#14579156	C₂³	1	32	yes	complemented
132	#14579156	C₂³	1	32	yes	complemented
133	#14579153	C₂³	1	16	yes	complemented
134	#14579152	C₂³	1	32	yes	complemented
135	#14579149	C₂³	1	16	yes	—
136	#14579147	C₂³	1	32	yes	complemented
137	#14579146	C₂³	1	32	yes	—
138	#14579145	C₂³	1	32	yes	complemented
139	#14579143	C₂³	1	32	yes	complemented
140	#14579143	C₂³	1	32	yes	complemented
141	#14579141	C₂³	1	32	yes	complemented
142	#14579141	C₂³	1	16	yes	complemented
143	#14579141	C₂³	1	16	yes	complemented
144	#14579140	C₂³	1	16	yes	—
145	#14579140	C₂³	1	16	yes	—
146	#14579140	C₂³	1	16	yes	complemented
147	#14579139	C₂³	1	32	yes	complemented
148	#14579138	C₂³	1	32	yes	—
149	#14579138	C₂³	1	32	yes	complemented
150	#14579137	C₂³	1	16	yes	complemented
151	#14579135	C₂³	1	16	yes	—
152	#14579134	C₂³	1	32	yes	—
153	#14579132	C₂³	1	16	yes	complemented
154	#14579129	C₂³	1	32	yes	—
155	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
156	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
157	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
158	C₄×D₃₁₆	C₂³	1	16	yes	—
159	C₄×D₃₁₆	C₂³	1	8	yes	—
160	C₄×D₃₁₆	C₂³	1	16	yes	—
161	C₄×D₃₁₆	C₂³	1	8	yes	—
162	C₄×D₃₁₆	C₂³	1	8	yes	—
163	C₄×D₃₁₆	C₂³	1	16	yes	—
164	C₄×D₃₁₆	C₂³	1	8	yes	—
165	D₄×Dic₇₉	C₂³	1	32	yes	—
166	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
167	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
168	#14579120	C₂³	1	16	yes	—
169	#14579119	C₂³	1	32	yes	complemented
170	#14579119	C₂³	1	16	yes	complemented
171	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
172	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊Dic₇₉	C₂³	1	8	yes	—
175	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
179	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
181	C₂×C₄⋊Dic₇₉	C₂³	1	16	yes	complemented
182	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
185	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
186	C₄⋊C₄×D₇₉	C₂³	1	32	yes	complemented
187	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
188	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
189	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
190	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
191	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
192	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
199	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
200	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
201	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
202	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
204	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
209	#126×C₇₉	C₂³	1	16	yes	complemented
210	#125×C₇₉	C₂³	1	8	yes	complemented
211	#124×C₇₉	C₂³	1	8	yes	complemented
212	#123×C₇₉	C₂³	1	16	yes	—
213	C₂²⋊Q₈×C₇₉	C₂³	1	8	yes	—
214	#121×C₇₉	C₂³	1	8	yes	—
215	C₄×Q₈×C₇₉	C₂³	1	8	yes	complemented
216	C₄×D₄×C₇₉	C₂³	1	16	yes	—
217	C₄×D₄×C₇₉	C₂³	1	8	yes	complemented
218	#117×C₇₉	C₂³	1	16	yes	complemented
219	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
221	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇₉	C₂³	1	8	yes	—
235	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
236	C₂³×D₇₉	—	2	8	no	—
237	C₂³×D₇₉	—	2	8	no	—
238	C₂³×D₇₉	—	4	4	no	—
239	C₂³×D₇₉	C₂⁴	1	2	yes	—
240	C₂³×D₇₉	C₂⁴	1	8	yes	—
241	C₂³×D₇₉	C₂⁴	1	2	yes	—
242	#11929624	—	2	64	no	—
243	#11929623	—	4	32	no	—
244	C₂×Dic₁₅₈	—	2	8	no	—
245	C₂×Dic₁₅₈	—	2	8	no	—
246	C₂×Dic₁₅₈	—	4	8	no	—
247	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
248	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
249	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
250	Q₈×D₇₉	—	4	32	no	—
251	C₂×D₃₁₆	—	2	32	no	—
252	C₂×D₃₁₆	—	2	8	no	—
253	C₂×D₃₁₆	—	2	4	no	—
254	C₂×D₃₁₆	#41	1	8	yes	complemented
255	C₂×D₃₁₆	C₂⁴	1	8	yes	—
256	C₂×D₃₁₆	C₂⁴	1	4	yes	—
257	C₂×D₃₁₆	C₂⁴	1	4	yes	—
258	C₂×C₂²⋊D₇₉	—	2	16	no	—
259	C₂×C₂²⋊D₇₉	—	4	8	no	—
260	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
261	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
262	C₂²×Dic₇₉	—	4	8	no	—
263	C₂²×Dic₇₉	—	4	4	no	—
264	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
266	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
267	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
268	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
269	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
270	C₂×C₄×D₇₉	—	2	16	no	—
271	C₂×C₄×D₇₉	—	2	8	no	—
272	C₂×C₄×D₇₉	—	2	8	no	—
273	C₂×C₄×D₇₉	—	4	8	no	—
274	C₂×C₄×D₇₉	—	4	4	no	—
275	C₂×C₄×D₇₉	—	4	4	no	—
276	C₂×C₄×D₇₉	—	4	32	no	—
277	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
278	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
279	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
280	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
281	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
282	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
283	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
284	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
285	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
286	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
287	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
288	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
289	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
290	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
291	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
292	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
293	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
294	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
295	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
296	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
297	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
298	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
299	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
300	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
301	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
302	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
303	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
304	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
305	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
306	C₄×Dic₇₉	C₂⁴	1	16	yes	—
307	C₄×Dic₇₉	C₂⁴	1	16	yes	—
308	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
309	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
310	C₂×Q₈×C₇₉	—	2	4	no	—
311	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
312	C₂×D₄×C₇₉	—	2	8	no	—
313	C₂×D₄×C₇₉	—	2	4	no	—
314	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
315	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
316	C₂²×C₄×C₇₉	—	2	4	no	—
317	C₂²×C₄×C₇₉	—	2	8	no	—
318	C₂²×C₄×C₇₉	—	2	4	no	—
319	C₂²×C₄×C₇₉	—	2	4	no	—
320	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
322	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
327	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
337	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
338	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
341	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
342	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
344	C₄²×C₇₉	C₂⁴	1	4	yes	—
345	C₄²×C₇₉	C₂⁴	1	4	yes	—
346	C₄²×C₇₉	C₂⁴	1	4	yes	—
347	C₄²×C₇₉	C₂⁴	1	4	yes	—
348	C₄²×C₇₉	C₂⁴	1	8	yes	—
349	C₂³×C₇₉	—	2	2	no	—
350	C₂³×C₇₉	—	2	2	no	—
351	C₂³×C₇₉	—	2	4	no	—
352	C₂³×C₇₉	—	2	4	no	—
353	C₂³×C₇₉	—	2	4	no	—
354	C₂³×C₇₉	2₋¹⁺⁴	1	4	yes	—
355	C₂³×C₇₉	C₂⁵	1	4	yes	—
356	C₂³×C₇₉	C₂⁵	1	2	yes	—
357	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
358	C₂²×D₇₉	—	2	4	no	—
359	C₂²×D₇₉	—	2	4	no	—
360	C₂²×D₇₉	—	2	4	no	—
361	C₂²×D₇₉	—	2	4	no	—
362	C₂²×D₇₉	—	2	16	no	—
363	C₂²×D₇₉	—	2	4	no	—
364	C₂²×D₇₉	—	2	16	no	—
365	C₂²×D₇₉	—	4	8	no	—
366	C₂²×D₇₉	—	4	32	no	—
367	C₂²×D₇₉	C₂×#41	1	8	yes	—
368	C₂²×D₇₉	C₂⁵	1	4	yes	—
369	C₂²×D₇₉	C₂⁵	1	4	yes	—
370	Q₈×C₇₉	—	2	8	no	—
371	D₄×C₇₉	—	2	16	no	—
372	D₄×C₇₉	—	2	8	no	—
373	C₂×C₄×C₇₉	—	2	4	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	2	no	—
376	C₂×C₄×C₇₉	—	2	4	no	—
377	C₂×C₄×C₇₉	—	2	8	no	—
378	C₂×C₄×C₇₉	—	2	2	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	4	no	—
381	C₂×C₄×C₇₉	—	2	8	no	—
382	C₂×C₄×C₇₉	—	2	16	no	—
383	C₂×C₄×C₇₉	—	2	8	no	—
384	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
385	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
386	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
387	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
388	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
389	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
390	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
391	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
392	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
393	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
394	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
395	C₂²⋊D₇₉	—	2	32	no	—
396	C₂²⋊D₇₉	—	4	16	no	—
397	C₂×Dic₇₉	—	2	8	no	—
398	C₂×Dic₇₉	—	2	4	no	—
399	C₂×Dic₇₉	—	2	4	no	—
400	C₂×Dic₇₉	—	2	8	no	—
401	C₂×Dic₇₉	—	4	8	no	—
402	C₂×Dic₇₉	—	4	16	no	—
403	C₂×Dic₇₉	C₂⁵	1	8	yes	—
404	C₂×Dic₇₉	C₂⁵	1	4	yes	—
405	C₂×Dic₇₉	C₂⁵	1	8	yes	—
406	C₂×Dic₇₉	C₂⁵	1	4	yes	—
407	D₃₁₆	—	2	16	no	—
408	D₃₁₆	—	2	8	no	—
409	D₃₁₆	C₂×#41	1	16	yes	complemented
410	C₄×D₇₉	—	2	32	no	—
411	C₄×D₇₉	—	2	16	no	—
412	C₄×D₇₉	—	2	16	no	—
413	C₄×D₇₉	—	4	8	no	—
414	C₄×D₇₉	—	4	8	no	—
415	C₄×D₇₉	—	4	16	no	—
416	Dic₁₅₈	—	2	16	no	—
417	Dic₁₅₈	—	2	16	no	—
418	Dic₁₅₈	—	4	16	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	2	2	no	—
421	C₂²×C₇₉	—	2	8	no	—
422	C₂²×C₇₉	—	2	4	no	—
423	C₂²×C₇₉	—	2	4	no	—
424	C₂²×C₇₉	—	2	4	no	—
425	C₂²×C₇₉	—	4	8	no	—
426	C₂²×C₇₉	C₂²×#41	1	2	yes	—
427	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	4	yes	—
429	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	2	yes	—
430	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
431	C₂×D₇₉	—	2	4	no	—
432	C₂×D₇₉	—	2	4	no	—
433	C₂×D₇₉	—	2	16	no	—
434	C₂×D₇₉	—	2	4	no	—
435	C₂×D₇₉	—	2	4	no	—
436	C₂×D₇₉	—	2	4	no	—
437	C₂×D₇₉	—	4	32	no	—
438	C₂×D₇₉	—	4	8	no	—
439	C₂×D₇₉	C₂²×#41	1	8	yes	—
440	C₄×C₇₉	—	2	4	no	—
441	C₄×C₇₉	—	2	2	no	—
442	C₄×C₇₉	—	2	2	no	—
443	C₄×C₇₉	—	2	4	no	—
444	C₄×C₇₉	—	2	2	no	—
445	C₄×C₇₉	—	2	2	no	—
446	C₄×C₇₉	—	2	4	no	—
447	C₄×C₇₉	C₂²×#41	1	4	yes	—
448	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
449	Dic₇₉	—	2	8	no	—
450	Dic₇₉	—	2	8	no	—
451	Dic₇₉	—	2	4	no	—
452	Dic₇₉	—	2	4	no	—
453	C₂×#3520	—	79	1	no	maximal, Sylow
454	C₂×C₇₉	—	2	4	no	—
455	C₂×C₇₉	—	4	4	no	—
456	C₂×C₇₉	#3520	1	4	yes	complemented
457	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
458	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
460	D₇₉	—	2	8	no	—
461	D₇₉	—	4	4	no	—
462	#3520	—	79	32	no	—
463	C₂×#556	—	79	1	no	—
464	C₂×#554	—	79	2	no	—
465	C₂×#552	—	79	2	no	—
466	C₂×#551	—	79	4	no	—
467	C₂×D₄×Q₈	—	79	1	no	—
468	C₂×#548	—	79	2	no	—
469	C₂×#547	—	79	1	no	—
470	C₂×#547	—	79	1	no	—
471	C₂×#546	—	79	2	no	—
472	C₂×#542	—	79	2	no	—
473	C₂×#539	—	79	4	no	—
474	C₂×#533	—	79	1	no	—
475	C₂×#529	D₇₉	1	1	yes	characteristic, complemented
476	C₂×#525	—	79	2	no	—
477	C₂²×C₂²⋊Q₈	—	79	2	no	—
478	C₂×#520	—	79	2	no	—
479	C₂²×C₄×D₄	—	79	1	no	—
480	C₇₉	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
481	C₂²×#41	—	79	2	no	—
482	C₂²×#41	—	79	2	no	—
483	C₂³×Q₈	—	79	2	no	—
484	C₂³×D₄	—	79	1	no	—
485	C₂⁴×C₄	—	79	2	no	—
486	#556	—	79	16	no	—
487	#554	—	79	32	no	—
488	#552	—	79	32	no	—
489	#551	—	79	64	no	—
490	D₄×Q₈	—	79	16	no	—
491	#548	—	79	32	no	—
492	#547	—	79	16	no	—
493	#547	—	79	16	no	—
494	#546	—	79	32	no	—
495	#542	—	79	32	no	—
496	#539	—	79	64	no	—
497	#533	—	79	16	no	—
498	C₂×C₄⋊Q₈	—	79	1	no	—
499	C₂×C₄⋊Q₈	—	79	1	no	—
500	C₂×C₄⋊Q₈	—	79	2	no	—
501	#529	C₂×D₇₉	1	16	yes	complemented
502	C₂×#126	—	79	4	no	—
503	C₂×#126	—	79	4	no	—
504	C₂×#126	C₂×D₇₉	1	2	yes	complemented
505	C₂×#125	—	79	4	no	—
506	C₂×#125	—	79	2	no	—
507	C₂×#125	C₂×D₇₉	1	1	yes	characteristic, complemented
508	C₂×#124	—	79	4	no	—
509	C₂×#124	—	79	2	no	—
510	C₂×#124	C₂×D₇₉	1	1	yes	characteristic, complemented
511	#525	—	79	32	no	—
512	C₂×#123	—	79	4	no	—
513	C₂×#123	—	79	4	no	—
514	C₂×#123	—	79	4	no	—
515	C₂×#123	—	79	4	no	—
516	C₂×#123	C₂×D₇₉	1	2	yes	—
517	C₂×C₂²⋊Q₈	—	79	2	no	—
518	C₂×C₂²⋊Q₈	—	79	2	no	—
519	C₂×C₂²⋊Q₈	—	79	2	no	—
520	C₂×C₂²⋊Q₈	—	79	2	no	—
521	C₂×C₂²⋊Q₈	—	79	32	no	—
522	C₂×C₂²⋊Q₈	—	79	4	no	—
523	C₂×C₂²⋊Q₈	—	79	2	no	—
524	C₂×C₂²⋊Q₈	—	79	2	no	—
525	C₂×C₂²⋊Q₈	—	79	4	no	—
526	C₂×C₂²⋊Q₈	—	79	4	no	—
527	C₂×C₂²⋊Q₈	—	79	4	no	—
528	C₂×C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
529	C₂×#121	—	79	2	no	—
530	C₂×#121	—	79	2	no	—
531	C₂×#121	—	79	4	no	—
532	C₂×#121	C₂×D₇₉	1	1	yes	characteristic
533	C₂×#120	—	79	4	no	—
534	#520	—	79	32	no	—
535	C₂×C₄×Q₈	—	79	2	no	—
536	C₂×C₄×Q₈	—	79	2	no	—
537	C₂×C₄×Q₈	—	79	2	no	—
538	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
539	C₂×C₄×D₄	—	79	4	no	—
540	C₂×C₄×D₄	—	79	4	no	—
541	C₂×C₄×D₄	—	79	4	no	—
542	C₂×C₄×D₄	—	79	1	no	—
543	C₂×C₄×D₄	—	79	2	no	—
544	C₂×C₄×D₄	—	79	1	no	—
545	C₂×C₄×D₄	—	79	1	no	—
546	C₂×C₄×D₄	—	79	1	no	—
547	C₂×C₄×D₄	—	79	2	no	—
548	C₂×C₄×D₄	—	79	16	no	—
549	C₂×C₄×D₄	—	79	2	no	—
550	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
551	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
552	C₂×#117	—	79	2	no	—
553	C₂×#117	—	79	4	no	—
554	C₂×#117	—	79	2	no	—
555	C₂×#117	C₂×D₇₉	1	2	yes	complemented
556	C₂²×C₄⋊C₄	—	79	1	no	—
557	C₂²×C₄⋊C₄	—	79	2	no	—
558	C₂²×C₄⋊C₄	—	79	4	no	—
559	C₂²×C₄⋊C₄	—	79	2	no	—
560	C₂²×C₂²⋊C₄	—	79	2	no	—
561	C₂²×C₂²⋊C₄	—	79	4	no	—
562	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
563	C₂⁵	—	79	2	no	—
564	C₂×#41	—	316	8	no	—
565	C₂×#41	—	79	16	no	—
566	C₂×#41	—	79	16	no	—
567	C₂×#41	—	158	16	no	—
568	C₂²×Q₈	—	316	8	no	—
569	C₂²×Q₈	—	79	16	no	—
570	C₂²×Q₈	—	79	4	no	—
571	C₂²×Q₈	—	79	2	no	—
572	C₂²×Q₈	—	79	2	no	—
573	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
574	C₂²×D₄	—	79	4	no	—
575	C₂²×D₄	—	79	4	no	—
576	C₂²×D₄	—	79	1	no	—
577	C₂²×D₄	—	79	2	no	—
578	C₂²×D₄	—	79	1	no	—
579	C₂²×D₄	—	79	8	no	—
580	C₂²×D₄	—	158	8	no	—
581	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
582	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
583	C₂³×C₄	—	316	8	no	—
584	C₂³×C₄	—	79	2	no	—
585	C₂³×C₄	—	79	4	no	—
586	C₂³×C₄	—	79	4	no	—
587	C₂³×C₄	—	79	2	no	—
588	C₂³×C₄	—	79	2	no	—
589	C₂³×C₄	—	79	16	no	—
590	C₂³×C₄	—	79	4	no	—
591	C₂³×C₄	—	79	2	no	—
592	C₂³×C₄	—	79	2	no	—
593	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
594	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
595	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
596	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
597	C₄⋊Q₈	—	79	8	no	—
598	C₄⋊Q₈	—	79	8	no	—
599	C₄⋊Q₈	—	79	16	no	—
600	#126	—	79	32	no	—
601	#126	—	79	32	no	—
602	#126	C₂²×D₇₉	1	16	yes	complemented
603	#125	—	79	32	no	—
604	#125	—	79	16	no	—
605	#125	C₂²×D₇₉	1	8	yes	complemented
606	#124	—	79	32	no	—
607	#124	—	79	16	no	—
608	#124	C₂²×D₇₉	1	8	yes	complemented
609	#123	—	79	32	no	—
610	#123	—	79	32	no	—
611	#123	—	79	32	no	—
612	#123	—	79	32	no	—
613	#123	C₂²×D₇₉	1	16	yes	—
614	C₂²⋊Q₈	—	79	16	no	—
615	C₂²⋊Q₈	—	79	16	no	—
616	C₂²⋊Q₈	—	79	16	no	—
617	C₂²⋊Q₈	—	79	16	no	—
618	C₂²⋊Q₈	—	79	32	no	—
619	C₂²⋊Q₈	—	79	16	no	—
620	C₂²⋊Q₈	—	79	16	no	—
621	C₂²⋊Q₈	—	79	32	no	—
622	C₂²⋊Q₈	—	79	32	no	—
623	C₂²⋊Q₈	—	79	32	no	—
624	C₂²⋊Q₈	C₂²×D₇₉	1	8	yes	—
625	#121	—	79	16	no	—
626	#121	—	79	16	no	—
627	#121	—	79	32	no	—
628	#121	C₂²×D₇₉	1	8	yes	—
629	#120	—	79	32	no	—
630	C₄×Q₈	—	79	16	no	—
631	C₄×Q₈	—	79	16	no	—
632	C₄×Q₈	—	79	16	no	—
633	C₄×Q₈	C₂²×D₇₉	1	8	yes	complemented
634	C₄×D₄	—	79	32	no	—
635	C₄×D₄	—	79	32	no	—
636	C₄×D₄	—	79	32	no	—
637	C₄×D₄	—	79	8	no	—
638	C₄×D₄	—	79	16	no	—
639	C₄×D₄	—	79	8	no	—
640	C₄×D₄	—	79	8	no	—
641	C₄×D₄	—	79	8	no	—
642	C₄×D₄	—	79	16	no	—
643	C₄×D₄	—	79	16	no	—
644	C₄×D₄	C₂²×D₇₉	1	16	yes	—
645	C₄×D₄	C₂²×D₇₉	1	8	yes	complemented
646	#117	—	79	16	no	—
647	#117	—	79	32	no	—
648	#117	—	79	16	no	—
649	#117	C₂²×D₇₉	1	16	yes	complemented
650	C₂×C₄⋊C₄	—	79	1	no	—
651	C₂×C₄⋊C₄	—	79	4	no	—
652	C₂×C₄⋊C₄	—	79	2	no	—
653	C₂×C₄⋊C₄	—	79	2	no	—
654	C₂×C₄⋊C₄	—	79	1	no	—
655	C₂×C₄⋊C₄	—	79	8	no	—
656	C₂×C₄⋊C₄	—	79	2	no	—
657	C₂×C₄⋊C₄	—	79	4	no	—
658	C₂×C₄⋊C₄	—	79	4	no	—
659	C₂×C₄⋊C₄	—	79	16	no	—
660	C₂×C₄⋊C₄	—	79	4	no	—
661	C₂×C₄⋊C₄	—	79	2	no	—
662	C₂×C₄⋊C₄	—	79	2	no	—
663	C₂×C₄⋊C₄	—	79	4	no	—
664	C₂×C₄⋊C₄	—	79	4	no	—
665	C₂×C₄⋊C₄	—	79	32	no	—
666	C₂×C₄⋊C₄	—	79	16	no	—
667	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
668	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
673	C₂×C₂²⋊C₄	—	79	4	no	—
674	C₂×C₂²⋊C₄	—	79	4	no	—
675	C₂×C₂²⋊C₄	—	79	2	no	—
676	C₂×C₂²⋊C₄	—	79	2	no	—
677	C₂×C₂²⋊C₄	—	79	2	no	—
678	C₂×C₂²⋊C₄	—	79	2	no	—
679	C₂×C₂²⋊C₄	—	79	16	no	—
680	C₂×C₂²⋊C₄	—	79	4	no	—
681	C₂×C₂²⋊C₄	—	79	4	no	—
682	C₂×C₂²⋊C₄	—	79	4	no	—
683	C₂×C₂²⋊C₄	—	79	4	no	—
684	C₂×C₂²⋊C₄	—	79	32	no	—
685	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
690	C₂×C₄²	—	79	4	no	—
691	C₂×C₄²	—	79	4	no	—
692	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
693	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
694	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
695	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
696	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
697	C₂×C₄²	C₂²×D₇₉	1	8	yes	—
698	C₂⁴	—	316	4	no	—
699	C₂⁴	—	79	8	no	—
700	C₂⁴	—	79	2	no	—
701	C₂⁴	—	79	2	no	—
702	C₂⁴	—	158	8	no	—
703	C₂⁴	—	158	8	no	—
704	C₂⁴	C₂³×D₇₉	1	2	yes	—
705	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
706	#41	—	316	32	no	—
707	#41	—	158	64	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	316	8	no	—
710	C₂×Q₈	—	316	32	no	—
711	C₂×Q₈	—	79	16	no	—
712	C₂×Q₈	—	79	8	no	—
713	C₂×Q₈	—	79	8	no	—
714	C₂×Q₈	—	158	8	no	—
715	C₂×Q₈	—	158	8	no	—
716	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	316	8	no	—
720	C₂×D₄	—	79	16	no	—
721	C₂×D₄	—	79	16	no	—
722	C₂×D₄	—	79	8	no	—
723	C₂×D₄	—	79	4	no	—
724	C₂×D₄	—	79	8	no	—
725	C₂×D₄	—	79	4	no	—
726	C₂×D₄	—	158	32	no	—
727	C₂×D₄	—	158	8	no	—
728	C₂×D₄	—	158	16	no	—
729	C₂×D₄	—	158	4	no	—
730	C₂×D₄	C₂³×D₇₉	1	8	yes	—
731	C₂×D₄	C₂³×D₇₉	1	4	yes	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	316	4	no	—
737	C₂²×C₄	—	316	4	no	—
738	C₂²×C₄	—	316	8	no	—
739	C₂²×C₄	—	316	32	no	—
740	C₂²×C₄	—	316	4	no	—
741	C₂²×C₄	—	316	8	no	—
742	C₂²×C₄	—	79	8	no	—
743	C₂²×C₄	—	79	16	no	—
744	C₂²×C₄	—	79	16	no	—
745	C₂²×C₄	—	79	8	no	—
746	C₂²×C₄	—	79	8	no	—
747	C₂²×C₄	—	79	4	no	—
748	C₂²×C₄	—	79	2	no	—
749	C₂²×C₄	—	79	4	no	—
750	C₂²×C₄	—	79	2	no	—
751	C₂²×C₄	—	79	16	no	—
752	C₂²×C₄	—	79	8	no	—
753	C₂²×C₄	—	79	8	no	—
754	C₂²×C₄	—	158	16	no	—
755	C₂²×C₄	—	158	8	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	8	yes	—
761	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
763	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
765	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
766	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
767	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
768	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
770	C₄⋊C₄	—	79	16	no	—
771	C₄⋊C₄	—	79	16	no	—
772	C₄⋊C₄	—	79	16	no	—
773	C₄⋊C₄	—	79	16	no	—
774	C₄⋊C₄	—	79	4	no	—
775	C₄⋊C₄	—	79	16	no	—
776	C₄⋊C₄	—	79	8	no	—
777	C₄⋊C₄	—	79	8	no	—
778	C₄⋊C₄	—	79	4	no	—
779	C₄⋊C₄	—	79	8	no	—
780	C₄⋊C₄	—	79	8	no	—
781	C₄⋊C₄	—	79	8	no	—
782	C₄⋊C₄	—	79	16	no	—
783	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
784	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
785	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
786	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
787	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
788	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
789	C₂²⋊C₄	—	79	16	no	—
790	C₂²⋊C₄	—	79	16	no	—
791	C₂²⋊C₄	—	79	8	no	—
792	C₂²⋊C₄	—	79	8	no	—
793	C₂²⋊C₄	—	79	8	no	—
794	C₂²⋊C₄	—	79	8	no	—
795	C₂²⋊C₄	—	79	16	no	—
796	C₂²⋊C₄	—	79	16	no	—
797	C₂²⋊C₄	—	79	16	no	—
798	C₂²⋊C₄	—	79	16	no	—
799	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
800	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
801	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
802	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
803	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
804	C₄²	—	79	16	no	—
805	C₄²	—	79	16	no	—
806	C₄²	C₂³×D₇₉	1	4	yes	—
807	C₄²	C₂³×D₇₉	1	4	yes	—
808	C₄²	C₂³×D₇₉	1	4	yes	—
809	C₄²	C₂³×D₇₉	1	4	yes	—
810	C₄²	C₂³×D₇₉	1	8	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	316	32	no	—
817	C₂³	—	316	8	no	—
818	C₂³	—	79	4	no	—
819	C₂³	—	79	8	no	—
820	C₂³	—	79	4	no	—
821	C₂³	—	158	16	no	—
822	C₂³	—	158	4	no	—
823	C₂³	—	158	16	no	—
824	C₂³	—	158	4	no	—
825	C₂³	—	158	4	no	—
826	C₂³	—	158	4	no	—
827	C₂³	—	158	4	no	—
828	C₂³	#14579208	1	4	yes	—
829	C₂³	C₂⁴×D₇₉	1	4	yes	—
830	C₂³	C₂⁴×D₇₉	1	2	yes	—
831	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
832	Q₈	—	2	8	no	—
833	Q₈	—	316	16	no	—
834	Q₈	—	158	16	no	—
835	Q₈	—	158	16	no	—
836	D₄	—	2	16	no	—
837	D₄	—	2	8	no	—
838	D₄	—	316	16	no	—
839	D₄	—	79	16	no	—
840	D₄	—	158	16	no	—
841	D₄	—	158	32	no	—
842	D₄	—	158	8	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	16	no	—
854	C₂×C₄	—	316	8	no	—
855	C₂×C₄	—	316	8	no	—
856	C₂×C₄	—	316	16	no	—
857	C₂×C₄	—	316	8	no	—
858	C₂×C₄	—	316	16	no	—
859	C₂×C₄	—	79	8	no	—
860	C₂×C₄	—	79	4	no	—
861	C₂×C₄	—	79	8	no	—
862	C₂×C₄	—	79	4	no	—
863	C₂×C₄	—	158	32	no	—
864	C₂×C₄	—	158	4	no	—
865	C₂×C₄	—	158	4	no	—
866	C₂×C₄	—	158	8	no	—
867	C₂×C₄	—	158	8	no	—
868	C₂×C₄	—	158	16	no	—
869	C₂×C₄	—	158	16	no	—
870	C₂×C₄	#41×D₇₉	1	4	yes	—
871	C₂×C₄	#14579207	1	4	yes	—
872	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
873	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
874	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
875	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
876	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
877	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
878	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
879	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
880	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	4	8	no	—
888	C₂²	—	316	32	no	—
889	C₂²	—	316	8	no	—
890	C₂²	—	79	8	no	—
891	C₂²	—	158	4	no	—
892	C₂²	—	158	4	no	—
893	C₂²	—	158	4	no	—
894	C₂²	—	158	4	no	—
895	C₂²	—	158	4	no	—
896	C₂²	—	158	16	no	—
897	C₂²	C₂×#41×D₇₉	1	2	yes	—
898	C₂²	C₂×#14579207	1	2	yes	—
899	C₂²	C₂×#14579208	1	4	yes	—
900	C₂²	C₂×#14579208	1	2	yes	—
901	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	158	8	no	—
910	C₄	—	158	4	no	—
911	C₄	—	158	4	no	—
912	C₄	—	158	8	no	—
913	C₄	C₂×#41×D₇₉	1	4	yes	—
914	C₄	C₂×#14579207	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	4	4	no	—
917	C₂	—	316	4	no	—
918	C₂	—	158	8	no	—
919	C₂	#23777451	1	4	yes	direct product factor
920	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
921	C₂	C₂²×#14579207	1	1	yes	characteristic
922	C₂	C₂²×#14579208	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#529×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#529	D₇₉
hypocenter	C₇₉	C₂×#3520
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #23777451	C₂	direct (N × H)
2. C₂×#19099286	C₂	semidirect
3. C₂×#19099270	C₂	semidirect
4. C₂×#19099251	C₂	semidirect
5. C₂×#19099236	C₂	semidirect
6. C₂×Q₈×D₃₁₆	C₂	semidirect
7. C₂×#19099221	C₂	semidirect
8. C₂×#19099218	C₂	semidirect
9. C₂×#19099217	C₂	semidirect
10. C₂×#19099209	C₂	semidirect
11. C₂×#19099184	C₂	semidirect
12. C₂×#19099154	C₂	semidirect
13. C₂×#19099120	C₂	semidirect
14. C₂×#19099073	C₂	semidirect
15. C₂×C₂²⋊Q₈×D₇₉	C₂	semidirect
16. C₂×#19099043	C₂	semidirect
17. C₂²×C₄×D₃₁₆	C₂	semidirect
18. C₂×#529×C₇₉	C₂	semidirect
20. C₂²×#11929623	C₂²	semidirect
21. C₂²×Q₈×D₇₉	C₂²	semidirect
24. #19099286	C₂²	semidirect
25. #19099270	C₂²	semidirect
26. #19099251	C₂²	semidirect
27. #19099236	C₂²	semidirect
28. Q₈×D₃₁₆	C₂²	semidirect
29. #19099221	C₂²	semidirect
30. #19099218	C₂²	semidirect
31. #19099217	C₂²	semidirect
32. #19099209	C₂²	semidirect
33. #19099184	C₂²	semidirect
34. #19099154	C₂²	semidirect
35. #19099120	C₂²	semidirect
36. C₂×#14579161	C₂²	semidirect
37. C₂×#14579161	C₂²	semidirect
38. C₂×#14579161	C₂²	semidirect
39. C₂×#14579156	C₂²	semidirect
40. C₂×#14579156	C₂²	semidirect
41. C₂×#14579153	C₂²	semidirect
42. C₂×#14579152	C₂²	semidirect
44. C₂×#14579147	C₂²	semidirect
45. #19099073	C₂²	semidirect
47. C₂×#14579145	C₂²	semidirect
48. C₂×#14579143	C₂²	semidirect
49. C₂×#14579143	C₂²	semidirect
50. C₂×#14579141	C₂²	semidirect
51. C₂×#14579141	C₂²	semidirect
52. C₂×#14579141	C₂²	semidirect
55. C₂×#14579140	C₂²	semidirect
56. C₂×#14579139	C₂²	semidirect
58. C₂×#14579138	C₂²	semidirect
59. C₂×#14579137	C₂²	semidirect
60. C₂²⋊Q₈×D₇₉	C₂²	semidirect
63. C₂×#14579132	C₂²	semidirect
65. #19099043	C₂²	semidirect
66. C₂×C₄×Dic₁₅₈	C₂²	semidirect
67. C₂×C₄×Dic₁₅₈	C₂²	semidirect
68. C₂×C₄×Dic₁₅₈	C₂²	semidirect
76. C₂×C₄×D₃₁₆	C₂²	semidirect
78. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
79. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
81. C₂×#14579119	C₂²	semidirect
82. C₂×#14579119	C₂²	semidirect
84. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
85. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
86. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
89. #529×C₇₉	C₂²	semidirect
90. C₂×#126×C₇₉	C₂²	semidirect
91. C₂×#125×C₇₉	C₂²	semidirect
92. C₂×#124×C₇₉	C₂²	semidirect
96. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
98. C₂×C₄×D₄×C₇₉	C₂²	semidirect
99. C₂×#117×C₇₉	C₂²	semidirect
105. C₂×#11929623	C₂³	semidirect
110. C₂×Q₈×D₇₉	C₂³	semidirect
128. #14579161	C₂³	semidirect
129. #14579161	C₂³	semidirect
130. #14579161	C₂³	semidirect
131. #14579156	C₂³	semidirect
132. #14579156	C₂³	semidirect
133. #14579153	C₂³	semidirect
134. #14579152	C₂³	semidirect
136. #14579147	C₂³	semidirect
138. #14579145	C₂³	semidirect
139. #14579143	C₂³	semidirect
140. #14579143	C₂³	semidirect
141. #14579141	C₂³	semidirect
142. #14579141	C₂³	semidirect
143. #14579141	C₂³	semidirect
146. #14579140	C₂³	semidirect
147. #14579139	C₂³	semidirect
149. #14579138	C₂³	semidirect
150. #14579137	C₂³	semidirect
153. #14579132	C₂³	semidirect
155. C₄×Dic₁₅₈	C₂³	semidirect
156. C₄×Dic₁₅₈	C₂³	semidirect
157. C₄×Dic₁₅₈	C₂³	semidirect
166. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
167. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
169. #14579119	C₂³	semidirect
170. #14579119	C₂³	semidirect
181. C₂×C₄⋊Dic₇₉	C₂³	semidirect
186. C₄⋊C₄×D₇₉	C₂³	semidirect
187. C₄⋊C₄×D₇₉	C₂³	semidirect
209. #126×C₇₉	C₂³	semidirect
210. #125×C₇₉	C₂³	semidirect
211. #124×C₇₉	C₂³	semidirect
215. C₄×Q₈×C₇₉	C₂³	semidirect
217. C₄×D₄×C₇₉	C₂³	semidirect
218. #117×C₇₉	C₂³	semidirect
254. C₂×D₃₁₆	#41	semidirect
409. D₃₁₆	C₂×#41	semidirect
456. C₂×C₇₉	#3520	semidirect
475. C₂×#529	D₇₉	semidirect
480. C₇₉	C₂×#3520	semidirect
501. #529	C₂×D₇₉	semidirect
504. C₂×#126	C₂×D₇₉	semidirect
507. C₂×#125	C₂×D₇₉	semidirect
510. C₂×#124	C₂×D₇₉	semidirect
538. C₂×C₄×Q₈	C₂×D₇₉	semidirect
551. C₂×C₄×D₄	C₂×D₇₉	semidirect
555. C₂×#117	C₂×D₇₉	semidirect
602. #126	C₂²×D₇₉	semidirect
605. #125	C₂²×D₇₉	semidirect
608. #124	C₂²×D₇₉	semidirect
633. C₄×Q₈	C₂²×D₇₉	semidirect
645. C₄×D₄	C₂²×D₇₉	semidirect
649. #117	C₂²×D₇₉	semidirect
919. C₂	#23777451	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777451	2
C₂×#19099286	2
C₂×#19099270	2
C₂×#19099251	2
C₂×#19099236	2
C₂×Q₈×D₃₁₆	2
C₂×#19099221	2
C₂×#19099218	2
C₂×#19099217	2
C₂×#19099209	2
C₂×#19099184	2
C₂×#19099154	2
C₂×#19099120	2
C₂×#19099073	2
C₂×C₂²⋊Q₈×D₇₉	2
C₂×#19099043	2
C₂²×C₄×D₃₁₆	2
C₂×#529×C₇₉	2
C₂×#3520	79

Subgroups — C2×#23777451 #35196284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777451 #35196284