Subgroups — C₂×#23777675 #35195560

Order 20224.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777675	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099306	C₂	1	2	yes	maximal, complemented
3	C₂×#19099302	C₂	1	2	yes	maximal, complemented
4	C₂×#19099297	C₂	1	2	yes	maximal, complemented
5	C₂×#19099283	C₂	1	2	yes	maximal, complemented
6	C₂×#19099278	C₂	1	2	yes	maximal, complemented
7	C₂×#19099241	C₂	1	2	yes	maximal, complemented
8	C₂×#19099222	C₂	1	2	yes	maximal, complemented
9	C₂×#19099209	C₂	1	2	yes	maximal, complemented
10	C₂×#19099184	C₂	1	2	yes	maximal, complemented
11	C₂×#19099183	C₂	1	4	yes	maximal, complemented
12	C₂×#19099145	C₂	1	4	yes	maximal, complemented
13	C₂×#19099134	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19099127	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19099074	C₂	1	2	yes	maximal, complemented
16	C₂×#525×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11929624	C₂²	1	2	yes	—
18	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
20	#19099306	C₂²	1	32	yes	complemented
21	#19099302	C₂²	1	32	yes	complemented
22	#19099297	C₂²	1	32	yes	complemented
23	#19099283	C₂²	1	32	yes	complemented
24	#19099278	C₂²	1	32	yes	complemented
25	#19099241	C₂²	1	32	yes	complemented
26	#19099222	C₂²	1	32	yes	complemented
27	#19099209	C₂²	1	32	yes	complemented
28	#19099184	C₂²	1	32	yes	complemented
29	#19099183	C₂²	1	64	yes	complemented
30	#19099145	C₂²	1	64	yes	complemented
31	#19099134	C₂²	1	16	yes	complemented
32	#19099127	C₂²	1	16	yes	complemented
33	C₂×#14579161	C₂²	1	2	yes	complemented
34	C₂×#14579159	C₂²	1	2	yes	complemented
35	C₂×#14579157	C₂²	1	2	yes	—
36	C₂×#14579156	C₂²	1	4	yes	complemented
37	C₂×#14579154	C₂²	1	4	yes	complemented
38	C₂×#14579154	C₂²	1	4	yes	complemented
39	C₂×#14579150	C₂²	1	2	yes	complemented
40	C₂×#14579149	C₂²	1	2	yes	complemented
41	C₂×#14579148	C₂²	1	2	yes	—
42	C₂×#14579148	C₂²	1	4	yes	—
43	C₂×#14579147	C₂²	1	4	yes	complemented
44	C₂×#14579147	C₂²	1	4	yes	complemented
45	C₂×#14579147	C₂²	1	4	yes	complemented
46	C₂×#14579147	C₂²	1	4	yes	complemented
47	#19099074	C₂²	1	32	yes	complemented
48	C₂×#14579146	C₂²	1	4	yes	complemented
49	C₂×#14579144	C₂²	1	4	yes	complemented
50	C₂×#14579143	C₂²	1	4	yes	complemented
51	C₂×#14579142	C₂²	1	2	yes	complemented
52	C₂×#14579142	C₂²	1	2	yes	complemented
53	C₂×#14579140	C₂²	1	2	yes	complemented
54	C₂×#14579140	C₂²	1	2	yes	complemented
55	C₂×#14579140	C₂²	1	2	yes	complemented
56	C₂×#14579139	C₂²	1	4	yes	complemented
57	C₂×#14579139	C₂²	1	4	yes	complemented
58	C₂×#14579135	C₂²	1	2	yes	—
59	C₂×#14579135	C₂²	1	2	yes	—
60	C₂×#14579135	C₂²	1	2	yes	complemented
61	C₂×#14579134	C₂²	1	4	yes	—
62	C₂×#14579133	C₂²	1	4	yes	complemented
63	C₂×#14579132	C₂²	1	4	yes	complemented
64	C₂×#14579130	C₂²	1	4	yes	complemented
65	C₂×#14579129	C₂²	1	4	yes	—
66	C₂×#14579129	C₂²	1	2	yes	—
67	C₂×#14579129	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
69	C₂×#14579126	C₂²	1	4	yes	complemented
70	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
71	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
72	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
73	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
74	C₂×#14579120	C₂²	1	2	yes	complemented
75	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
76	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
77	C₂×#14579119	C₂²	1	4	yes	complemented
78	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
79	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
80	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
81	#525×C₇₉	C₂²	1	16	yes	complemented
82	C₂×#123×C₇₉	C₂²	1	1	yes	characteristic
83	C₂×#123×C₇₉	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
85	C₂×#121×C₇₉	C₂²	1	2	yes	—
86	C₂×#120×C₇₉	C₂²	1	1	yes	characteristic
87	C₂×#120×C₇₉	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
90	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₇₉	C₂³	1	2	yes	—
92	C₂×#11929624	—	4	8	no	—
93	C₂×#11929624	C₂³	1	16	yes	—
94	C₂²×Dic₁₅₈	—	4	4	no	—
95	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
96	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
97	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
98	C₂²×Dic₁₅₈	C₂³	1	8	yes	complemented
99	C₂²×D₃₁₆	—	4	4	no	—
100	C₂²×D₃₁₆	C₂³	1	2	yes	—
101	C₂²×D₃₁₆	C₂³	1	2	yes	—
102	C₂²×D₃₁₆	C₂³	1	8	yes	complemented
103	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
107	C₂³×Dic₇₉	C₂³	1	2	yes	—
108	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
109	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
110	#14579161	C₂³	1	16	yes	complemented
111	#14579159	C₂³	1	16	yes	complemented
112	#14579157	C₂³	1	16	yes	—
113	#14579156	C₂³	1	32	yes	complemented
114	#14579154	C₂³	1	32	yes	complemented
115	#14579154	C₂³	1	32	yes	complemented
116	#14579150	C₂³	1	16	yes	complemented
117	#14579149	C₂³	1	16	yes	complemented
118	#14579148	C₂³	1	32	yes	—
119	#14579148	C₂³	1	16	yes	—
120	#14579147	C₂³	1	32	yes	complemented
121	#14579147	C₂³	1	32	yes	complemented
122	#14579147	C₂³	1	32	yes	complemented
123	#14579147	C₂³	1	32	yes	complemented
124	#14579146	C₂³	1	32	yes	complemented
125	#14579144	C₂³	1	32	yes	complemented
126	#14579143	C₂³	1	32	yes	complemented
127	#14579142	C₂³	1	16	yes	complemented
128	#14579142	C₂³	1	16	yes	complemented
129	#14579140	C₂³	1	16	yes	complemented
130	#14579140	C₂³	1	16	yes	complemented
131	#14579140	C₂³	1	16	yes	complemented
132	#14579139	C₂³	1	32	yes	complemented
133	#14579139	C₂³	1	32	yes	complemented
134	#14579135	C₂³	1	16	yes	—
135	#14579135	C₂³	1	16	yes	—
136	#14579135	C₂³	1	16	yes	complemented
137	#14579134	C₂³	1	32	yes	—
138	#14579133	C₂³	1	32	yes	complemented
139	#14579132	C₂³	1	32	yes	complemented
140	#14579130	C₂³	1	32	yes	complemented
141	#14579129	C₂³	1	32	yes	—
142	#14579129	C₂³	1	16	yes	—
143	#14579129	C₂³	1	16	yes	complemented
144	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
145	#14579126	C₂³	1	32	yes	complemented
146	C₄×D₃₁₆	C₂³	1	16	yes	complemented
147	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
148	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
149	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
150	#14579120	C₂³	1	8	yes	complemented
151	#14579120	C₂³	1	16	yes	complemented
152	#14579120	C₂³	1	8	yes	complemented
153	#14579119	C₂³	1	32	yes	complemented
154	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
155	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
157	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
158	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
159	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
160	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
161	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
166	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
167	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
168	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
169	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
170	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
171	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
173	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
174	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
175	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
176	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
177	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
178	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
179	C₂×#41×C₇₉	—	4	4	no	—
180	C₂×#41×C₇₉	C₂³	1	8	yes	—
181	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
182	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
183	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
184	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
185	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
186	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₇₉	—	4	4	no	—
188	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
189	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
191	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
193	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₇₉	C₂³	1	8	yes	complemented
195	#123×C₇₉	C₂³	1	8	yes	—
196	#123×C₇₉	C₂³	1	8	yes	complemented
197	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	complemented
198	#121×C₇₉	C₂³	1	16	yes	—
199	#120×C₇₉	C₂³	1	8	yes	—
200	#120×C₇₉	C₂³	1	8	yes	complemented
201	C₄×D₄×C₇₉	C₂³	1	16	yes	—
202	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
203	#117×C₇₉	C₂³	1	8	yes	complemented
204	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
214	C₂³×D₇₉	—	4	8	no	—
215	C₂³×D₇₉	—	4	4	no	—
216	C₂³×D₇₉	C₂⁴	1	4	yes	—
217	C₂³×D₇₉	C₂⁴	1	8	yes	—
218	#11929624	—	4	32	no	—
219	C₂×Dic₁₅₈	—	2	8	no	—
220	C₂×Dic₁₅₈	—	4	16	no	—
221	C₂×Dic₁₅₈	—	4	4	no	—
222	C₂×Dic₁₅₈	—	4	8	no	—
223	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
224	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
225	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
226	C₂×D₃₁₆	—	2	8	no	—
227	C₂×D₃₁₆	—	4	4	no	—
228	C₂×D₃₁₆	—	4	16	no	—
229	C₂×D₃₁₆	C₂⁴	1	8	yes	—
230	C₂×D₃₁₆	C₂⁴	1	8	yes	—
231	C₂×C₂²⋊D₇₉	—	4	8	no	—
232	C₂×C₂²⋊D₇₉	—	4	8	no	—
233	C₂×C₂²⋊D₇₉	—	4	8	no	—
234	C₂×C₂²⋊D₇₉	—	4	8	no	—
235	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
236	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
237	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
238	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
239	C₂²×Dic₇₉	—	4	4	no	—
240	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
241	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
242	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
243	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
244	C₂×C₄×D₇₉	—	4	8	no	—
245	C₂×C₄×D₇₉	—	4	8	no	—
246	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
247	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
248	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
249	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
250	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
251	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
252	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
253	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
254	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
255	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
256	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
257	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
258	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
259	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
260	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
261	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
262	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
263	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
264	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
265	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
266	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
267	C₄×Dic₇₉	C₂⁴	1	8	yes	—
268	C₄×Dic₇₉	C₂⁴	1	16	yes	—
269	C₄×Dic₇₉	C₂⁴	1	8	yes	—
270	C₄×Dic₇₉	C₂⁴	1	16	yes	—
271	C₂⁴×C₇₉	—	4	2	no	—
272	C₂⁴×C₇₉	—	4	4	no	—
273	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
275	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
276	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
277	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
278	#41×C₇₉	—	4	16	no	—
279	C₂×Q₈×C₇₉	—	4	2	no	—
280	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
281	C₂×D₄×C₇₉	—	4	4	no	—
282	C₂×D₄×C₇₉	—	4	4	no	—
283	C₂×D₄×C₇₉	—	4	2	no	—
284	C₂×D₄×C₇₉	—	4	2	no	—
285	C₂×D₄×C₇₉	—	4	2	no	—
286	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
287	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
288	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
289	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
290	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₇₉	—	2	4	no	—
292	C₂²×C₄×C₇₉	—	2	8	no	—
293	C₂²×C₄×C₇₉	—	2	4	no	—
294	C₂²×C₄×C₇₉	—	2	4	no	—
295	C₂²×C₄×C₇₉	—	4	16	no	—
296	C₂²×C₄×C₇₉	—	4	2	no	—
297	C₂²×C₄×C₇₉	—	4	4	no	—
298	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
301	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
307	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
308	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
310	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
315	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
316	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
317	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
320	C₄²×C₇₉	C₂⁴	1	8	yes	—
321	C₂³×C₇₉	—	2	2	no	—
322	C₂³×C₇₉	—	2	4	no	—
323	C₂³×C₇₉	—	2	2	no	—
324	C₂³×C₇₉	—	2	2	no	—
325	C₂³×C₇₉	—	2	4	no	—
326	C₂³×C₇₉	—	2	4	no	—
327	C₂³×C₇₉	—	2	4	no	—
328	C₂³×C₇₉	—	2	4	no	—
329	C₂³×C₇₉	—	2	4	no	—
330	C₂³×C₇₉	—	4	4	no	—
331	C₂³×C₇₉	—	4	8	no	—
332	C₂³×C₇₉	—	4	16	no	—
333	C₂³×C₇₉	C₂⁵	1	2	yes	—
334	C₂³×C₇₉	C₂⁵	1	4	yes	—
335	C₂³×C₇₉	C₂⁵	1	2	yes	—
336	C₂³×C₇₉	C₂⁵	1	2	yes	—
337	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
338	C₂²×D₇₉	—	2	8	no	—
339	C₂²×D₇₉	—	2	8	no	—
340	C₂²×D₇₉	—	2	8	no	—
341	C₂²×D₇₉	—	4	8	no	—
342	C₂²×D₇₉	—	4	16	no	—
343	C₂²×D₇₉	—	8	16	no	—
344	C₂²×D₇₉	C₂⁵	1	8	yes	—
345	Q₈×C₇₉	—	4	4	no	—
346	D₄×C₇₉	—	4	8	no	—
347	D₄×C₇₉	—	4	8	no	—
348	D₄×C₇₉	—	4	4	no	—
349	D₄×C₇₉	—	4	4	no	—
350	D₄×C₇₉	—	4	4	no	—
351	C₂×C₄×C₇₉	—	2	4	no	—
352	C₂×C₄×C₇₉	—	2	2	no	—
353	C₂×C₄×C₇₉	—	2	2	no	—
354	C₂×C₄×C₇₉	—	2	2	no	—
355	C₂×C₄×C₇₉	—	2	4	no	—
356	C₂×C₄×C₇₉	—	2	4	no	—
357	C₂×C₄×C₇₉	—	2	8	no	—
358	C₂×C₄×C₇₉	—	2	8	no	—
359	C₂×C₄×C₇₉	—	2	16	no	—
360	C₂×C₄×C₇₉	—	2	8	no	—
361	C₂×C₄×C₇₉	—	4	8	no	—
362	C₂×C₄×C₇₉	—	4	4	no	—
363	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
364	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
365	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
366	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
367	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
368	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
369	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
370	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
371	C₂²⋊D₇₉	—	4	16	no	—
372	C₂²⋊D₇₉	—	4	16	no	—
373	C₂²⋊D₇₉	—	4	16	no	—
374	C₂²⋊D₇₉	—	4	16	no	—
375	C₂×Dic₇₉	—	2	8	no	—
376	C₂×Dic₇₉	—	2	8	no	—
377	C₂×Dic₇₉	—	2	8	no	—
378	C₂×Dic₇₉	—	4	8	no	—
379	C₂×Dic₇₉	C₂⁵	1	8	yes	—
380	C₂×Dic₇₉	C₂⁵	1	8	yes	—
381	C₂×Dic₇₉	C₂⁵	1	8	yes	—
382	D₃₁₆	—	2	16	no	—
383	D₃₁₆	—	4	8	no	—
384	C₄×D₇₉	—	4	16	no	—
385	C₄×D₇₉	—	4	16	no	—
386	Dic₁₅₈	—	2	16	no	—
387	Dic₁₅₈	—	4	8	no	—
388	Dic₁₅₈	—	4	16	no	—
389	C₂²×C₇₉	—	2	4	no	—
390	C₂²×C₇₉	—	2	2	no	—
391	C₂²×C₇₉	—	2	2	no	—
392	C₂²×C₇₉	—	2	2	no	—
393	C₂²×C₇₉	—	2	4	no	—
394	C₂²×C₇₉	—	2	4	no	—
395	C₂²×C₇₉	—	2	4	no	—
396	C₂²×C₇₉	—	2	4	no	—
397	C₂²×C₇₉	—	2	4	no	—
398	C₂²×C₇₉	—	4	16	no	—
399	C₂²×C₇₉	—	4	4	no	—
400	C₂²×C₇₉	—	4	4	no	—
401	C₂²×C₇₉	—	4	8	no	—
402	C₂²×C₇₉	—	4	4	no	—
403	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₇₉	#585	1	4	yes	—
405	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
406	C₂×D₇₉	—	2	8	no	—
407	C₂×D₇₉	—	2	8	no	—
408	C₂×D₇₉	—	2	8	no	—
409	C₂×D₇₉	—	4	16	no	—
410	C₂×D₇₉	—	8	16	no	—
411	C₄×C₇₉	—	2	2	no	—
412	C₄×C₇₉	—	2	4	no	—
413	C₄×C₇₉	—	2	2	no	—
414	C₄×C₇₉	—	2	2	no	—
415	C₄×C₇₉	—	2	4	no	—
416	C₄×C₇₉	—	2	4	no	—
417	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
418	Dic₇₉	—	2	8	no	—
419	Dic₇₉	—	2	8	no	—
420	Dic₇₉	—	2	8	no	—
421	C₂×#3540	—	79	1	no	maximal, Sylow
422	C₂×C₇₉	—	4	2	no	—
423	C₂×C₇₉	—	4	2	no	—
424	C₂×C₇₉	—	4	4	no	—
425	C₂×C₇₉	—	4	2	no	—
426	C₂×C₇₉	#3540	1	4	yes	complemented
427	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂×C₇₉	C₂×#585	1	2	yes	—
429	D₇₉	—	4	8	no	—
430	#3540	—	79	32	no	—
431	C₂×H(3,𝔽₄)	—	79	2	no	—
432	C₂×#560	—	79	2	no	—
433	C₂×#559	—	79	2	no	—
434	C₂×#556	—	79	2	no	—
435	C₂×#555	—	79	2	no	—
436	C₂×#551	—	79	2	no	—
437	C₂×#548	—	79	2	no	—
438	C₂×#546	—	79	2	no	—
439	C₂×#542	—	79	4	no	—
440	C₂×#542	—	79	2	no	—
441	C₂×#538	—	79	4	no	—
442	C₂×#536	—	79	1	no	—
443	C₂×#535	—	79	1	no	—
444	C₂×#525	—	79	2	no	—
445	C₂×#525	D₇₉	1	1	yes	characteristic, complemented
446	C₇₉	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
447	C₂²×#41	—	79	2	no	—
448	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
449	C₂³×Q₈	—	79	1	no	—
450	C₂³×D₄	—	79	1	no	—
451	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
452	H(3,𝔽₄)	—	79	32	no	—
453	#560	—	79	32	no	—
454	#559	—	79	32	no	—
455	#556	—	79	32	no	—
456	#555	—	79	32	no	—
457	#551	—	79	32	no	—
458	#548	—	79	32	no	—
459	#546	—	79	32	no	—
460	#542	—	79	64	no	—
461	#542	—	79	32	no	—
462	#538	—	79	64	no	—
463	#536	—	79	16	no	—
464	#535	—	79	16	no	—
465	C₂×C₄⋊Q₈	—	79	2	no	—
466	C₂×C₄⋊Q₈	—	79	2	no	—
467	C₂×#127	—	79	2	no	—
468	C₂×#126	—	79	4	no	—
469	C₂×#126	—	79	4	no	—
470	C₂×#126	—	79	4	no	—
471	C₂×#124	—	79	2	no	—
472	C₂×#124	—	79	2	no	—
473	C₂×#124	—	79	4	no	—
474	C₂×#124	—	79	4	no	—
475	C₂×#124	—	79	4	no	—
476	C₂×#124	—	79	4	no	—
477	C₂×#124	—	79	4	no	—
478	C₂×#124	—	79	2	no	—
479	#525	—	79	32	no	—
480	#525	C₂×D₇₉	1	16	yes	complemented
481	C₂×#123	—	79	2	no	—
482	C₂×#123	—	79	2	no	—
483	C₂×#123	—	79	4	no	—
484	C₂×#123	—	79	4	no	—
485	C₂×#123	—	79	4	no	—
486	C₂×#123	C₂×D₇₉	1	1	yes	characteristic
487	C₂×#123	C₂×D₇₉	1	1	yes	characteristic, complemented
488	C₂×C₂²⋊Q₈	—	79	2	no	—
489	C₂×C₂²⋊Q₈	—	79	2	no	—
490	C₂×C₂²⋊Q₈	—	79	2	no	—
491	C₂×C₂²⋊Q₈	—	79	4	no	—
492	C₂×C₂²⋊Q₈	—	79	4	no	—
493	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
494	C₂×#121	—	79	4	no	—
495	C₂×#121	—	79	4	no	—
496	C₂×#121	—	79	2	no	—
497	C₂×#121	—	79	2	no	—
498	C₂×#121	—	79	2	no	—
499	C₂×#121	—	79	4	no	—
500	C₂×#121	C₂×D₇₉	1	2	yes	—
501	C₂×#120	—	79	4	no	—
502	C₂×#120	—	79	2	no	—
503	C₂×#120	—	79	2	no	—
504	C₂×#120	—	79	4	no	—
505	C₂×#120	C₂×D₇₉	1	1	yes	characteristic
506	C₂×#120	C₂×D₇₉	1	1	yes	characteristic, complemented
507	C₂×C₄×Q₈	—	79	4	no	—
508	C₂×C₄×Q₈	—	79	2	no	—
509	C₂×C₄×D₄	—	79	4	no	—
510	C₂×C₄×D₄	—	79	4	no	—
511	C₂×C₄×D₄	—	79	4	no	—
512	C₂×C₄×D₄	—	79	2	no	—
513	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
514	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
515	C₂×#117	—	79	2	no	—
516	C₂×#117	—	79	1	no	—
517	C₂×#117	—	79	1	no	—
518	C₂×#117	—	79	4	no	—
519	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
520	C₂²×C₂²⋊C₄	—	79	4	no	—
521	C₂⁵	—	79	2	no	—
522	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
523	C₂×#41	—	4	4	no	—
524	C₂×#41	—	316	8	no	—
525	C₂×#41	—	79	16	no	—
526	C₂×#41	C₂²×D₇₉	1	8	yes	—
527	C₂²×Q₈	—	316	4	no	—
528	C₂²×Q₈	—	79	4	no	—
529	C₂²×Q₈	—	79	2	no	—
530	C₂²×Q₈	—	79	8	no	—
531	C₂²×Q₈	—	79	2	no	—
532	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
533	C₂²×D₄	—	316	4	no	—
534	C₂²×D₄	—	79	4	no	—
535	C₂²×D₄	—	79	4	no	—
536	C₂²×D₄	—	79	4	no	—
537	C₂²×D₄	—	79	4	no	—
538	C₂²×D₄	—	79	2	no	—
539	C₂²×D₄	—	79	8	no	—
540	C₂²×D₄	—	79	2	no	—
541	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
542	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
543	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
544	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
545	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
546	C₂³×C₄	—	4	4	no	—
547	C₂³×C₄	—	79	2	no	—
548	C₂³×C₄	—	79	4	no	—
549	C₂³×C₄	—	79	4	no	—
550	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
551	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
552	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
553	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
554	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
555	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
556	C₂³×C₄	C₂²×D₇₉	1	8	yes	complemented
557	C₄⋊Q₈	—	79	16	no	—
558	C₄⋊Q₈	—	79	16	no	—
559	#127	—	79	16	no	—
560	#126	—	79	32	no	—
561	#126	—	79	32	no	—
562	#126	—	79	32	no	—
563	#124	—	79	16	no	—
564	#124	—	79	16	no	—
565	#124	—	79	32	no	—
566	#124	—	79	32	no	—
567	#124	—	79	32	no	—
568	#124	—	79	32	no	—
569	#124	—	79	32	no	—
570	#124	—	79	16	no	—
571	#123	—	79	16	no	—
572	#123	—	79	16	no	—
573	#123	—	79	32	no	—
574	#123	—	79	32	no	—
575	#123	—	79	32	no	—
576	#123	C₂²×D₇₉	1	8	yes	—
577	#123	C₂²×D₇₉	1	8	yes	complemented
578	C₂²⋊Q₈	—	79	16	no	—
579	C₂²⋊Q₈	—	79	16	no	—
580	C₂²⋊Q₈	—	79	16	no	—
581	C₂²⋊Q₈	—	79	32	no	—
582	C₂²⋊Q₈	—	79	32	no	—
583	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	complemented
584	#121	—	79	32	no	—
585	#121	—	79	32	no	—
586	#121	—	79	16	no	—
587	#121	—	79	16	no	—
588	#121	—	79	16	no	—
589	#121	—	79	32	no	—
590	#121	C₂²×D₇₉	1	16	yes	—
591	#120	—	79	32	no	—
592	#120	—	79	16	no	—
593	#120	—	79	16	no	—
594	#120	—	79	32	no	—
595	#120	C₂²×D₇₉	1	8	yes	—
596	#120	C₂²×D₇₉	1	8	yes	complemented
597	C₄×Q₈	—	79	32	no	—
598	C₄×Q₈	—	79	16	no	—
599	C₄×D₄	—	79	32	no	—
600	C₄×D₄	—	79	32	no	—
601	C₄×D₄	—	79	32	no	—
602	C₄×D₄	—	79	16	no	—
603	C₄×D₄	C₂²×D₇₉	1	16	yes	—
604	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
605	#117	—	79	16	no	—
606	#117	—	79	8	no	—
607	#117	—	79	8	no	—
608	#117	—	79	32	no	—
609	#117	C₂²×D₇₉	1	8	yes	complemented
610	C₂×C₄⋊C₄	—	79	2	no	—
611	C₂×C₄⋊C₄	—	79	2	no	—
612	C₂×C₄⋊C₄	—	79	4	no	—
613	C₂×C₄⋊C₄	—	79	4	no	—
614	C₂×C₄⋊C₄	—	79	4	no	—
615	C₂×C₄⋊C₄	—	79	4	no	—
616	C₂×C₄⋊C₄	—	79	4	no	—
617	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
620	C₂×C₂²⋊C₄	—	79	4	no	—
621	C₂×C₂²⋊C₄	—	79	2	no	—
622	C₂×C₂²⋊C₄	—	79	4	no	—
623	C₂×C₂²⋊C₄	—	79	2	no	—
624	C₂×C₂²⋊C₄	—	79	4	no	—
625	C₂×C₂²⋊C₄	—	79	4	no	—
626	C₂×C₂²⋊C₄	—	79	4	no	—
627	C₂×C₂²⋊C₄	—	79	4	no	—
628	C₂×C₂²⋊C₄	—	79	4	no	—
629	C₂×C₂²⋊C₄	—	79	4	no	—
630	C₂×C₂²⋊C₄	—	79	4	no	—
631	C₂×C₂²⋊C₄	—	79	4	no	—
632	C₂×C₂²⋊C₄	—	79	32	no	—
633	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
639	C₂×C₄²	—	79	2	no	—
640	C₂×C₄²	—	79	4	no	—
641	C₂×C₄²	—	79	2	no	—
642	C₂×C₄²	—	79	4	no	—
643	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
644	C₂⁴	—	4	2	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	316	4	no	—
647	C₂⁴	—	316	8	no	—
648	C₂⁴	—	79	8	no	—
649	C₂⁴	—	79	4	no	—
650	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
651	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
652	C₂⁴	C₂³×D₇₉	1	2	yes	—
653	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
654	C₂⁴	C₂³×D₇₉	1	4	yes	—
655	#41	—	4	16	no	—
656	#41	—	316	32	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	316	16	no	—
659	C₂×Q₈	—	316	4	no	—
660	C₂×Q₈	—	316	8	no	—
661	C₂×Q₈	—	79	16	no	—
662	C₂×Q₈	—	79	8	no	—
663	C₂×Q₈	—	79	8	no	—
664	C₂×Q₈	—	158	8	no	—
665	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	316	4	no	—
672	C₂×D₄	—	316	16	no	—
673	C₂×D₄	—	316	8	no	—
674	C₂×D₄	—	316	8	no	—
675	C₂×D₄	—	316	8	no	—
676	C₂×D₄	—	316	8	no	—
677	C₂×D₄	—	79	16	no	—
678	C₂×D₄	—	79	16	no	—
679	C₂×D₄	—	79	16	no	—
680	C₂×D₄	—	79	16	no	—
681	C₂×D₄	—	79	8	no	—
682	C₂×D₄	—	79	8	no	—
683	C₂×D₄	—	158	8	no	—
684	C₂×D₄	C₂³×D₇₉	1	8	yes	—
685	C₂×D₄	C₂³×D₇₉	1	8	yes	—
686	C₂×D₄	C₂³×D₇₉	1	4	yes	—
687	C₂×D₄	C₂³×D₇₉	1	4	yes	—
688	C₂×D₄	C₂³×D₇₉	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	8	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	16	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	316	8	no	—
697	C₂²×C₄	—	316	8	no	—
698	C₂²×C₄	—	316	4	no	—
699	C₂²×C₄	—	79	8	no	—
700	C₂²×C₄	—	79	16	no	—
701	C₂²×C₄	—	79	16	no	—
702	C₂²×C₄	—	79	4	no	—
703	C₂²×C₄	—	79	4	no	—
704	C₂²×C₄	—	79	4	no	—
705	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
706	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
707	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
708	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
709	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
710	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
711	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
712	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
713	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
714	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
715	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
716	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
717	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
718	C₄⋊C₄	—	79	16	no	—
719	C₄⋊C₄	—	79	16	no	—
720	C₄⋊C₄	—	79	16	no	—
721	C₄⋊C₄	—	79	16	no	—
722	C₄⋊C₄	—	79	8	no	—
723	C₄⋊C₄	—	79	8	no	—
724	C₄⋊C₄	—	79	16	no	—
725	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
726	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
727	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
728	C₂²⋊C₄	—	79	16	no	—
729	C₂²⋊C₄	—	79	8	no	—
730	C₂²⋊C₄	—	79	16	no	—
731	C₂²⋊C₄	—	79	8	no	—
732	C₂²⋊C₄	—	79	16	no	—
733	C₂²⋊C₄	—	79	16	no	—
734	C₂²⋊C₄	—	79	16	no	—
735	C₂²⋊C₄	—	79	16	no	—
736	C₂²⋊C₄	—	79	16	no	—
737	C₂²⋊C₄	—	79	16	no	—
738	C₂²⋊C₄	—	79	16	no	—
739	C₂²⋊C₄	—	79	16	no	—
740	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
741	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
742	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
743	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
744	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
745	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
746	C₄²	—	79	8	no	—
747	C₄²	—	79	16	no	—
748	C₄²	—	79	8	no	—
749	C₄²	—	79	16	no	—
750	C₄²	C₂³×D₇₉	1	8	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	316	8	no	—
764	C₂³	—	316	16	no	—
765	C₂³	—	79	8	no	—
766	C₂³	—	632	16	no	—
767	C₂³	—	158	8	no	—
768	C₂³	—	158	8	no	—
769	C₂³	—	158	8	no	—
770	C₂³	C₂⁴×D₇₉	1	2	yes	—
771	C₂³	C₂⁴×D₇₉	1	2	yes	—
772	C₂³	C₂⁴×D₇₉	1	4	yes	—
773	C₂³	C₂⁴×D₇₉	1	2	yes	—
774	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	316	8	no	—
777	Q₈	—	316	16	no	—
778	Q₈	—	158	16	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	316	8	no	—
785	D₄	—	316	16	no	—
786	D₄	—	316	16	no	—
787	D₄	—	316	16	no	—
788	D₄	—	316	16	no	—
789	D₄	—	158	16	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	16	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	316	16	no	—
803	C₂×C₄	—	316	16	no	—
804	C₂×C₄	—	316	8	no	—
805	C₂×C₄	—	79	8	no	—
806	C₂×C₄	—	79	8	no	—
807	C₂×C₄	—	79	8	no	—
808	C₂×C₄	—	158	8	no	—
809	C₂×C₄	—	158	8	no	—
810	C₂×C₄	—	158	8	no	—
811	C₂×C₄	#14579206	1	4	yes	—
812	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
813	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
814	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
815	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
816	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
817	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
818	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	16	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	8	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	316	16	no	—
834	C₂²	—	632	16	no	—
835	C₂²	—	158	8	no	—
836	C₂²	—	158	8	no	—
837	C₂²	—	158	8	no	—
838	C₂²	C₂×#14579206	1	2	yes	—
839	C₂²	#19099399	1	4	yes	—
840	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	158	8	no	—
848	C₄	—	158	8	no	—
849	C₄	—	158	8	no	—
850	C₄	C₂×#14579206	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	316	8	no	—
856	C₂	#23777675	1	4	yes	direct product factor
857	C₂	C₂²×#14579206	1	1	yes	characteristic
858	C₂	C₂×#19099399	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#525×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#525	D₇₉
hypocenter	C₇₉	C₂×#3540
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #23777675	C₂	direct (N × H)
2. C₂×#19099306	C₂	semidirect
3. C₂×#19099302	C₂	semidirect
4. C₂×#19099297	C₂	semidirect
5. C₂×#19099283	C₂	semidirect
6. C₂×#19099278	C₂	semidirect
7. C₂×#19099241	C₂	semidirect
8. C₂×#19099222	C₂	semidirect
9. C₂×#19099209	C₂	semidirect
10. C₂×#19099184	C₂	semidirect
11. C₂×#19099183	C₂	semidirect
12. C₂×#19099145	C₂	semidirect
13. C₂×#19099134	C₂	semidirect
14. C₂×#19099127	C₂	semidirect
15. C₂×#19099074	C₂	semidirect
16. C₂×#525×C₇₉	C₂	semidirect
18. C₂³×Dic₁₅₈	C₂²	semidirect
19. C₂³×D₃₁₆	C₂²	semidirect
20. #19099306	C₂²	semidirect
21. #19099302	C₂²	semidirect
22. #19099297	C₂²	semidirect
23. #19099283	C₂²	semidirect
24. #19099278	C₂²	semidirect
25. #19099241	C₂²	semidirect
26. #19099222	C₂²	semidirect
27. #19099209	C₂²	semidirect
28. #19099184	C₂²	semidirect
29. #19099183	C₂²	semidirect
30. #19099145	C₂²	semidirect
31. #19099134	C₂²	semidirect
32. #19099127	C₂²	semidirect
33. C₂×#14579161	C₂²	semidirect
34. C₂×#14579159	C₂²	semidirect
36. C₂×#14579156	C₂²	semidirect
37. C₂×#14579154	C₂²	semidirect
38. C₂×#14579154	C₂²	semidirect
39. C₂×#14579150	C₂²	semidirect
40. C₂×#14579149	C₂²	semidirect
43. C₂×#14579147	C₂²	semidirect
44. C₂×#14579147	C₂²	semidirect
45. C₂×#14579147	C₂²	semidirect
46. C₂×#14579147	C₂²	semidirect
47. #19099074	C₂²	semidirect
48. C₂×#14579146	C₂²	semidirect
49. C₂×#14579144	C₂²	semidirect
50. C₂×#14579143	C₂²	semidirect
51. C₂×#14579142	C₂²	semidirect
52. C₂×#14579142	C₂²	semidirect
53. C₂×#14579140	C₂²	semidirect
54. C₂×#14579140	C₂²	semidirect
55. C₂×#14579140	C₂²	semidirect
56. C₂×#14579139	C₂²	semidirect
57. C₂×#14579139	C₂²	semidirect
60. C₂×#14579135	C₂²	semidirect
62. C₂×#14579133	C₂²	semidirect
63. C₂×#14579132	C₂²	semidirect
64. C₂×#14579130	C₂²	semidirect
67. C₂×#14579129	C₂²	semidirect
68. C₂×C₄×Dic₁₅₈	C₂²	semidirect
69. C₂×#14579126	C₂²	semidirect
70. C₂×C₄×D₃₁₆	C₂²	semidirect
71. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
73. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
74. C₂×#14579120	C₂²	semidirect
75. C₂×#14579120	C₂²	semidirect
76. C₂×#14579120	C₂²	semidirect
77. C₂×#14579119	C₂²	semidirect
78. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
80. C₂⁴×C₄×C₇₉	C₂²	semidirect
81. #525×C₇₉	C₂²	semidirect
83. C₂×#123×C₇₉	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
87. C₂×#120×C₇₉	C₂²	semidirect
89. C₂×C₄×D₄×C₇₉	C₂²	semidirect
90. C₂×#117×C₇₉	C₂²	semidirect
98. C₂²×Dic₁₅₈	C₂³	semidirect
102. C₂²×D₃₁₆	C₂³	semidirect
110. #14579161	C₂³	semidirect
111. #14579159	C₂³	semidirect
113. #14579156	C₂³	semidirect
114. #14579154	C₂³	semidirect
115. #14579154	C₂³	semidirect
116. #14579150	C₂³	semidirect
117. #14579149	C₂³	semidirect
120. #14579147	C₂³	semidirect
121. #14579147	C₂³	semidirect
122. #14579147	C₂³	semidirect
123. #14579147	C₂³	semidirect
124. #14579146	C₂³	semidirect
125. #14579144	C₂³	semidirect
126. #14579143	C₂³	semidirect
127. #14579142	C₂³	semidirect
128. #14579142	C₂³	semidirect
129. #14579140	C₂³	semidirect
130. #14579140	C₂³	semidirect
131. #14579140	C₂³	semidirect
132. #14579139	C₂³	semidirect
133. #14579139	C₂³	semidirect
136. #14579135	C₂³	semidirect
138. #14579133	C₂³	semidirect
139. #14579132	C₂³	semidirect
140. #14579130	C₂³	semidirect
143. #14579129	C₂³	semidirect
144. C₄×Dic₁₅₈	C₂³	semidirect
145. #14579126	C₂³	semidirect
146. C₄×D₃₁₆	C₂³	semidirect
147. C₄×C₂²⋊D₇₉	C₂³	semidirect
148. C₄×C₂²⋊D₇₉	C₂³	semidirect
149. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
150. #14579120	C₂³	semidirect
151. #14579120	C₂³	semidirect
152. #14579120	C₂³	semidirect
153. #14579119	C₂³	semidirect
173. C₂²⋊C₄×D₇₉	C₂³	semidirect
194. C₂³×C₄×C₇₉	C₂³	semidirect
196. #123×C₇₉	C₂³	semidirect
197. C₂²⋊Q₈×C₇₉	C₂³	semidirect
200. #120×C₇₉	C₂³	semidirect
202. C₄×D₄×C₇₉	C₂³	semidirect
203. #117×C₇₉	C₂³	semidirect
426. C₂×C₇₉	#3540	semidirect
445. C₂×#525	D₇₉	semidirect
446. C₇₉	C₂×#3540	semidirect
451. C₂⁴×C₄	C₂×D₇₉	semidirect
480. #525	C₂×D₇₉	semidirect
487. C₂×#123	C₂×D₇₉	semidirect
493. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
506. C₂×#120	C₂×D₇₉	semidirect
514. C₂×C₄×D₄	C₂×D₇₉	semidirect
519. C₂×#117	C₂×D₇₉	semidirect
556. C₂³×C₄	C₂²×D₇₉	semidirect
577. #123	C₂²×D₇₉	semidirect
583. C₂²⋊Q₈	C₂²×D₇₉	semidirect
596. #120	C₂²×D₇₉	semidirect
604. C₄×D₄	C₂²×D₇₉	semidirect
609. #117	C₂²×D₇₉	semidirect
856. C₂	#23777675	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777675	2
C₂×#19099306	2
C₂×#19099302	2
C₂×#19099297	2
C₂×#19099283	2
C₂×#19099278	2
C₂×#19099241	2
C₂×#19099222	2
C₂×#19099209	2
C₂×#19099184	2
C₂×#19099183	2
C₂×#19099145	2
C₂×#19099134	2
C₂×#19099127	2
C₂×#19099074	2
C₂×#525×C₇₉	2
C₂×#3540	79

Subgroups — C2×#23777675 #35195560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777675 #35195560