Subgroups — C₂×#23777427 #35196256

Order 20224.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777427	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099279	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099274	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099265	C₂	1	2	yes	maximal, complemented
5	C₂×#19099263	C₂	1	2	yes	maximal, complemented
6	C₂×#19099233	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19099208	C₂	1	2	yes	maximal, complemented
8	C₂×#19099201	C₂	1	4	yes	maximal, complemented
9	C₂×#19099198	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19099197	C₂	1	2	yes	maximal, complemented
11	C₂×#19099164	C₂	1	2	yes	maximal, complemented
12	C₂×#19099147	C₂	1	4	yes	maximal, complemented
13	C₂×#19099097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#19099073	C₂	1	2	yes	maximal, complemented
15	C₂×#121×D₇₉	C₂	1	2	yes	maximal, complemented
16	C₂×#19099035	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#532×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11929623	C₂²	1	2	yes	complemented
20	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
21	C₂²×D₄×D₇₉	C₂²	1	2	yes	—
22	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
23	C₂²×D₄×D₇₉	C₂²	1	2	yes	complemented
24	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
25	#19099279	C₂²	1	16	yes	complemented
26	#19099274	C₂²	1	16	yes	complemented
27	#19099265	C₂²	1	32	yes	complemented
28	#19099263	C₂²	1	32	yes	complemented
29	#19099233	C₂²	1	16	yes	complemented
30	#19099208	C₂²	1	32	yes	complemented
31	#19099201	C₂²	1	64	yes	complemented
32	#19099198	C₂²	1	16	yes	complemented
33	#19099197	C₂²	1	32	yes	complemented
34	#19099164	C₂²	1	32	yes	complemented
35	#19099147	C₂²	1	64	yes	complemented
36	C₂×#14579157	C₂²	1	2	yes	complemented
37	#19099097	C₂²	1	16	yes	complemented
38	C₂×#14579155	C₂²	1	2	yes	complemented
39	C₂×#14579154	C₂²	1	4	yes	complemented
40	C₂×#14579153	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14579152	C₂²	1	2	yes	complemented
42	C₂×#14579150	C₂²	1	4	yes	complemented
43	C₂×#14579149	C₂²	1	1	yes	characteristic, complemented
44	#19099073	C₂²	1	32	yes	complemented
45	C₂×#14579145	C₂²	1	4	yes	complemented
46	C₂×#14579144	C₂²	1	2	yes	complemented
47	C₂×#14579144	C₂²	1	4	yes	complemented
48	C₂×#14579143	C₂²	1	4	yes	complemented
49	C₂×#14579141	C₂²	1	2	yes	complemented
50	C₂×#14579140	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14579137	C₂²	1	4	yes	complemented
52	C₂×#14579136	C₂²	1	2	yes	complemented
53	C₂×#14579136	C₂²	1	2	yes	complemented
54	C₂×#14579135	C₂²	1	1	yes	characteristic
55	C₂×#14579135	C₂²	1	4	yes	complemented
56	C₂×#14579134	C₂²	1	4	yes	complemented
57	C₂×#14579134	C₂²	1	4	yes	complemented
58	C₂×#14579133	C₂²	1	4	yes	complemented
59	C₂×#14579133	C₂²	1	4	yes	complemented
60	C₂×#14579132	C₂²	1	2	yes	complemented
61	C₂×#14579132	C₂²	1	2	yes	complemented
62	C₂×#14579132	C₂²	1	2	yes	complemented
63	#121×D₇₉	C₂²	1	32	yes	complemented
64	C₂×#14579131	C₂²	1	4	yes	complemented
65	C₂×#14579129	C₂²	1	4	yes	complemented
66	C₂×#14579129	C₂²	1	4	yes	complemented
67	#19099035	C₂²	1	32	yes	complemented
68	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
72	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
74	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₃₁₆	C₂²	1	16	yes	complemented
77	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
78	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
79	C₂×#14579123	C₂²	1	2	yes	—
80	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
81	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
82	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
83	C₂×#14579119	C₂²	1	2	yes	complemented
84	C₂×#14579119	C₂²	1	2	yes	complemented
85	C₂×#14579118	C₂²	1	2	yes	complemented
86	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
88	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
89	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
90	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
91	C₂²×#41×C₇₉	C₂²	1	2	yes	complemented
92	#532×C₇₉	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
95	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
96	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
97	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
98	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
99	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₇₉	C₂³	1	2	yes	—
102	C₂⁴×D₇₉	C₂³	1	4	yes	—
103	C₂×#11929623	—	4	8	no	—
104	C₂×#11929623	C₂³	1	16	yes	complemented
105	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
106	C₂²×D₃₁₆	—	2	8	no	—
107	C₂²×D₃₁₆	C₂³	1	8	yes	—
108	C₂²×D₃₁₆	C₂³	1	2	yes	—
109	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
110	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
111	C₂²×D₃₁₆	C₂³	1	4	yes	—
112	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
113	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
115	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
118	C₂×D₄×D₇₉	—	2	16	no	—
119	C₂×D₄×D₇₉	—	4	8	no	—
120	C₂×D₄×D₇₉	—	4	16	no	—
121	C₂×D₄×D₇₉	C₂³	1	16	yes	—
122	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
123	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
124	C₂³×Dic₇₉	C₂³	1	2	yes	—
125	C₂³×Dic₇₉	C₂³	1	4	yes	—
126	C₂²×C₄×D₇₉	—	4	8	no	—
127	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
128	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
129	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
130	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
131	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
132	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
133	C₂²×C₄×D₇₉	C₂³	1	16	yes	complemented
134	#14579157	C₂³	1	16	yes	complemented
135	#14579155	C₂³	1	16	yes	complemented
136	#14579154	C₂³	1	32	yes	complemented
137	#14579153	C₂³	1	8	yes	complemented
138	#14579152	C₂³	1	16	yes	complemented
139	#14579150	C₂³	1	32	yes	complemented
140	#14579149	C₂³	1	8	yes	complemented
141	#14579145	C₂³	1	32	yes	complemented
142	#14579144	C₂³	1	32	yes	complemented
143	#14579144	C₂³	1	16	yes	complemented
144	#14579143	C₂³	1	32	yes	complemented
145	#14579141	C₂³	1	16	yes	complemented
146	#14579140	C₂³	1	8	yes	complemented
147	#14579137	C₂³	1	32	yes	complemented
148	#14579136	C₂³	1	16	yes	complemented
149	#14579136	C₂³	1	16	yes	complemented
150	#14579135	C₂³	1	8	yes	—
151	#14579135	C₂³	1	32	yes	complemented
152	#14579134	C₂³	1	32	yes	complemented
153	#14579134	C₂³	1	32	yes	complemented
154	#14579133	C₂³	1	32	yes	complemented
155	#14579133	C₂³	1	32	yes	complemented
156	#14579132	C₂³	1	16	yes	complemented
157	#14579132	C₂³	1	16	yes	complemented
158	#14579132	C₂³	1	16	yes	complemented
159	#14579131	C₂³	1	32	yes	complemented
160	#14579129	C₂³	1	32	yes	complemented
161	#14579129	C₂³	1	32	yes	complemented
162	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
163	C₄×D₃₁₆	C₂³	1	8	yes	—
164	C₄×D₃₁₆	C₂³	1	8	yes	—
165	C₄×D₃₁₆	C₂³	1	16	yes	complemented
166	C₄×D₃₁₆	C₂³	1	8	yes	complemented
167	C₄×D₃₁₆	C₂³	1	8	yes	complemented
168	C₄×D₃₁₆	C₂³	1	16	yes	complemented
169	C₄×D₃₁₆	C₂³	1	8	yes	complemented
170	D₄×Dic₇₉	C₂³	1	32	yes	complemented
171	D₄×Dic₇₉	C₂³	1	16	yes	complemented
172	#14579123	C₂³	1	16	yes	—
173	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
174	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
175	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
176	#14579119	C₂³	1	16	yes	complemented
177	#14579119	C₂³	1	16	yes	complemented
178	#14579118	C₂³	1	16	yes	complemented
179	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
183	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
185	C₂×C₄⋊Dic₇₉	C₂³	1	8	yes	complemented
186	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
187	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
188	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
189	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
190	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
191	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
192	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
193	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
195	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
197	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
198	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	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	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
204	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
205	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
206	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	complemented
207	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	32	yes	complemented
208	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	complemented
209	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
210	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
211	C₂×#41×C₇₉	—	4	8	no	—
212	C₂×#41×C₇₉	C₂³	1	16	yes	complemented
213	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
214	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
215	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
216	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
217	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
218	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
219	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
221	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
222	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
223	#127×C₇₉	C₂³	1	8	yes	complemented
224	#124×C₇₉	C₂³	1	16	yes	complemented
225	#121×C₇₉	C₂³	1	16	yes	complemented
226	#121×C₇₉	C₂³	1	16	yes	complemented
227	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
228	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
229	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
233	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇₉	C₂³	1	8	yes	complemented
238	C₂³×D₇₉	—	2	8	no	—
239	C₂³×D₇₉	—	2	8	no	—
240	C₂³×D₇₉	—	2	16	no	—
241	C₂³×D₇₉	—	4	4	no	—
242	C₂³×D₇₉	—	4	8	no	—
243	C₂³×D₇₉	—	4	8	no	—
244	C₂³×D₇₉	C₂⁴	1	2	yes	—
245	C₂³×D₇₉	C₂⁴	1	2	yes	—
246	C₂³×D₇₉	C₂⁴	1	8	yes	—
247	C₂³×D₇₉	C₂⁴	1	2	yes	—
248	C₂³×D₇₉	C₂⁴	1	16	yes	—
249	#11929623	—	4	32	no	—
250	C₂×Dic₁₅₈	—	2	4	no	—
251	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
252	C₂×D₃₁₆	—	2	32	no	—
253	C₂×D₃₁₆	—	2	8	no	—
254	C₂×D₃₁₆	—	2	4	no	—
255	C₂×D₃₁₆	—	2	4	no	—
256	C₂×D₃₁₆	—	4	8	no	—
257	C₂×D₃₁₆	#41	1	8	yes	complemented
258	C₂×D₃₁₆	C₂⁴	1	8	yes	—
259	C₂×D₃₁₆	C₂⁴	1	4	yes	—
260	C₂×D₃₁₆	C₂⁴	1	4	yes	—
261	C₂×D₃₁₆	C₂⁴	1	16	yes	—
262	C₂×D₃₁₆	C₂⁴	1	4	yes	—
263	C₂×C₂²⋊D₇₉	—	2	8	no	—
264	C₂×C₂²⋊D₇₉	—	2	16	no	—
265	C₂×C₂²⋊D₇₉	—	4	8	no	—
266	C₂×C₂²⋊D₇₉	—	4	8	no	—
267	C₂×C₂²⋊D₇₉	—	4	8	no	—
268	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
269	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
270	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
271	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
272	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
273	D₄×D₇₉	—	2	64	no	—
274	D₄×D₇₉	—	4	64	no	—
275	D₄×D₇₉	—	4	32	no	—
276	C₂²×Dic₇₉	—	4	8	no	—
277	C₂²×Dic₇₉	—	4	4	no	—
278	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
279	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
280	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
281	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
282	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
283	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
284	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
285	C₂×C₄×D₇₉	—	2	8	no	—
286	C₂×C₄×D₇₉	—	2	8	no	—
287	C₂×C₄×D₇₉	—	2	8	no	—
288	C₂×C₄×D₇₉	—	4	4	no	—
289	C₂×C₄×D₇₉	—	4	4	no	—
290	C₂×C₄×D₇₉	—	4	8	no	—
291	C₂×C₄×D₇₉	—	4	32	no	—
292	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
293	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
294	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
295	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
296	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
297	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
298	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
299	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
300	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
301	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
302	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
303	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
304	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
305	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
306	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
307	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
308	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
309	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
310	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
311	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
312	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
313	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
315	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
316	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
317	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
318	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
319	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
320	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
321	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
322	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
323	C₄×Dic₇₉	C₂⁴	1	8	yes	—
324	C₄×Dic₇₉	C₂⁴	1	16	yes	—
325	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
326	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
327	#41×C₇₉	—	4	32	no	—
328	C₂×Q₈×C₇₉	—	4	4	no	—
329	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
330	C₂×D₄×C₇₉	—	2	16	no	—
331	C₂×D₄×C₇₉	—	2	8	no	—
332	C₂×D₄×C₇₉	—	2	8	no	—
333	C₂×D₄×C₇₉	—	4	4	no	—
334	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
335	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
336	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
337	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
338	C₂²×C₄×C₇₉	—	2	4	no	—
339	C₂²×C₄×C₇₉	—	2	4	no	—
340	C₂²×C₄×C₇₉	—	2	4	no	—
341	C₂²×C₄×C₇₉	—	4	8	no	—
342	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
351	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
353	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
354	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
355	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
356	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
357	C₄²×C₇₉	C₂⁴	1	4	yes	—
358	C₄²×C₇₉	C₂⁴	1	4	yes	—
359	C₄²×C₇₉	C₂⁴	1	4	yes	—
360	C₄²×C₇₉	C₂⁴	1	4	yes	—
361	C₂³×C₇₉	—	2	2	no	—
362	C₂³×C₇₉	—	2	2	no	—
363	C₂³×C₇₉	—	2	8	no	—
364	C₂³×C₇₉	—	2	8	no	—
365	C₂³×C₇₉	—	2	8	no	—
366	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₇₉	C₂⁵	1	8	yes	—
368	C₂³×C₇₉	C₂⁵	1	2	yes	—
369	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
370	C₂²×D₇₉	—	2	4	no	—
371	C₂²×D₇₉	—	2	4	no	—
372	C₂²×D₇₉	—	2	4	no	—
373	C₂²×D₇₉	—	2	4	no	—
374	C₂²×D₇₉	—	2	4	no	—
375	C₂²×D₇₉	—	2	16	no	—
376	C₂²×D₇₉	—	2	4	no	—
377	C₂²×D₇₉	—	2	4	no	—
378	C₂²×D₇₉	—	2	4	no	—
379	C₂²×D₇₉	—	2	16	no	—
380	C₂²×D₇₉	—	2	32	no	—
381	C₂²×D₇₉	—	4	8	no	—
382	C₂²×D₇₉	—	4	16	no	—
383	C₂²×D₇₉	—	4	16	no	—
384	C₂²×D₇₉	—	4	32	no	—
385	C₂²×D₇₉	—	8	32	no	—
386	C₂²×D₇₉	C₂×#41	1	8	yes	—
387	C₂²×D₇₉	C₂⁵	1	4	yes	—
388	C₂²×D₇₉	C₂⁵	1	4	yes	—
389	C₂²×D₇₉	C₂⁵	1	4	yes	—
390	Q₈×C₇₉	—	4	8	no	—
391	D₄×C₇₉	—	2	32	no	—
392	D₄×C₇₉	—	2	16	no	—
393	D₄×C₇₉	—	2	16	no	—
394	D₄×C₇₉	—	4	8	no	—
395	C₂×C₄×C₇₉	—	2	2	no	—
396	C₂×C₄×C₇₉	—	2	2	no	—
397	C₂×C₄×C₇₉	—	2	8	no	—
398	C₂×C₄×C₇₉	—	2	2	no	—
399	C₂×C₄×C₇₉	—	2	2	no	—
400	C₂×C₄×C₇₉	—	2	8	no	—
401	C₂×C₄×C₇₉	—	2	8	no	—
402	C₂×C₄×C₇₉	—	2	8	no	—
403	C₂×C₄×C₇₉	—	4	16	no	—
404	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
405	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
407	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
408	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
409	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
410	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
411	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
412	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
413	C₂²⋊D₇₉	—	2	16	no	—
414	C₂²⋊D₇₉	—	2	32	no	—
415	C₂²⋊D₇₉	—	4	16	no	—
416	C₂²⋊D₇₉	—	4	16	no	—
417	C₂²⋊D₇₉	—	4	16	no	—
418	C₂×Dic₇₉	—	2	4	no	—
419	C₂×Dic₇₉	—	2	4	no	—
420	C₂×Dic₇₉	—	2	4	no	—
421	C₂×Dic₇₉	—	2	4	no	—
422	C₂×Dic₇₉	—	2	4	no	—
423	C₂×Dic₇₉	—	4	8	no	—
424	C₂×Dic₇₉	—	4	16	no	—
425	C₂×Dic₇₉	C₂⁵	1	4	yes	—
426	C₂×Dic₇₉	C₂⁵	1	4	yes	—
427	C₂×Dic₇₉	C₂⁵	1	4	yes	—
428	C₂×Dic₇₉	C₂⁵	1	4	yes	—
429	C₂×Dic₇₉	C₂⁵	1	4	yes	—
430	D₃₁₆	—	2	16	no	—
431	D₃₁₆	—	2	8	no	—
432	D₃₁₆	—	2	8	no	—
433	D₃₁₆	—	4	16	no	—
434	D₃₁₆	C₂×#41	1	16	yes	complemented
435	C₄×D₇₉	—	2	16	no	—
436	C₄×D₇₉	—	2	16	no	—
437	C₄×D₇₉	—	2	16	no	—
438	C₄×D₇₉	—	4	8	no	—
439	C₄×D₇₉	—	4	8	no	—
440	C₄×D₇₉	—	4	16	no	—
441	Dic₁₅₈	—	2	8	no	—
442	C₂²×C₇₉	—	2	2	no	—
443	C₂²×C₇₉	—	2	2	no	—
444	C₂²×C₇₉	—	2	8	no	—
445	C₂²×C₇₉	—	2	8	no	—
446	C₂²×C₇₉	—	2	8	no	—
447	C₂²×C₇₉	—	2	8	no	—
448	C₂²×C₇₉	—	4	16	no	—
449	C₂²×C₇₉	C₂²×#41	1	2	yes	—
450	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
451	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
452	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
454	C₂×D₇₉	—	2	4	no	—
455	C₂×D₇₉	—	2	4	no	—
456	C₂×D₇₉	—	2	16	no	—
457	C₂×D₇₉	—	2	4	no	—
458	C₂×D₇₉	—	2	4	no	—
459	C₂×D₇₉	—	2	4	no	—
460	C₂×D₇₉	—	2	4	no	—
461	C₂×D₇₉	—	2	4	no	—
462	C₂×D₇₉	—	2	4	no	—
463	C₂×D₇₉	—	4	32	no	—
464	C₂×D₇₉	—	4	8	no	—
465	C₂×D₇₉	—	4	8	no	—
466	C₂×D₇₉	—	8	32	no	—
467	C₂×D₇₉	C₂²×#41	1	8	yes	—
468	C₄×C₇₉	—	2	2	no	—
469	C₄×C₇₉	—	2	2	no	—
470	C₄×C₇₉	—	2	2	no	—
471	C₄×C₇₉	—	2	2	no	—
472	C₄×C₇₉	—	2	8	no	—
473	C₄×C₇₉	C₂²×#41	1	4	yes	—
474	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
475	Dic₇₉	—	2	4	no	—
476	Dic₇₉	—	2	4	no	—
477	Dic₇₉	—	2	4	no	—
478	Dic₇₉	—	2	4	no	—
479	Dic₇₉	—	2	4	no	—
480	C₂×#3519	—	79	1	no	maximal, Sylow
481	C₂×C₇₉	—	2	4	no	—
482	C₂×C₇₉	—	4	8	no	—
483	C₂×C₇₉	#3519	1	4	yes	complemented
484	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
485	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
487	D₇₉	—	2	8	no	—
488	D₇₉	—	4	4	no	—
489	D₇₉	—	4	4	no	—
490	#3519	—	79	32	no	—
491	C₂×#555	—	79	1	no	—
492	C₂×#554	—	79	1	no	—
493	C₂×#553	—	79	2	no	—
494	C₂×#553	—	79	2	no	—
495	C₂×#550	—	79	1	no	—
496	C₂×#546	—	79	4	no	—
497	C₂×#546	—	79	2	no	—
498	C₂×D₄²	—	79	1	no	—
499	C₂×D₄²	—	79	2	no	—
500	C₂×#540	—	79	2	no	—
501	C₂×#538	—	79	4	no	—
502	C₂×#532	D₇₉	1	1	yes	characteristic, complemented
503	C₂×#529	—	79	1	no	—
504	C₂×#525	—	79	2	no	—
505	C₂²×#121	—	79	2	no	—
506	C₂×#518	—	79	2	no	—
507	C₂²×C₄×D₄	—	79	1	no	—
508	C₇₉	C₂×#3519	1	1	yes	characteristic, complemented, Sylow
509	C₂²×#41	—	79	2	no	—
510	C₂²×#41	C₂×D₇₉	1	2	yes	complemented
511	C₂³×D₄	—	79	4	no	—
512	C₂³×D₄	—	79	2	no	—
513	C₂³×D₄	—	79	2	no	—
514	C₂³×D₄	—	79	1	no	—
515	C₂⁴×C₄	—	79	2	no	—
516	#555	—	79	16	no	—
517	#554	—	79	16	no	—
518	#553	—	79	32	no	—
519	#553	—	79	32	no	—
520	#550	—	79	16	no	—
521	#546	—	79	64	no	—
522	#546	—	79	32	no	—
523	D₄²	—	79	16	no	—
524	D₄²	—	79	32	no	—
525	#540	—	79	32	no	—
526	#538	—	79	64	no	—
527	#532	C₂×D₇₉	1	16	yes	complemented
528	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
529	C₂×#127	—	79	2	no	—
530	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
531	#529	—	79	16	no	—
532	C₂×#126	—	79	4	no	—
533	C₂×#126	—	79	2	no	—
534	C₂×#125	—	79	2	no	—
535	C₂×#125	—	79	1	no	—
536	C₂×#124	—	79	4	no	—
537	C₂×#124	—	79	1	no	—
538	C₂×#124	C₂×D₇₉	1	2	yes	complemented
539	#525	—	79	32	no	—
540	C₂×#123	—	79	2	no	—
541	C₂×#123	—	79	4	no	—
542	C₂×#123	—	79	4	no	—
543	C₂×#123	—	79	4	no	—
544	C₂×C₂²⋊Q₈	—	79	4	no	—
545	C₂×C₂²⋊Q₈	—	79	1	no	—
546	C₂×C₂²⋊Q₈	—	79	2	no	—
547	C₂×#121	—	79	4	no	—
548	C₂×#121	—	79	2	no	—
549	C₂×#121	—	79	2	no	—
550	C₂×#121	—	79	4	no	—
551	C₂×#121	—	79	2	no	—
552	C₂×#121	—	79	1	no	—
553	C₂×#121	—	79	4	no	—
554	C₂×#121	—	79	32	no	—
555	C₂×#121	—	79	2	no	—
556	C₂×#121	—	79	2	no	—
557	C₂×#121	—	79	4	no	—
558	C₂×#121	—	79	4	no	—
559	C₂×#121	C₂×D₇₉	1	2	yes	complemented
560	C₂×#121	C₂×D₇₉	1	2	yes	complemented
561	C₂×#120	—	79	4	no	—
562	C₂×#120	—	79	4	no	—
563	C₂×#120	—	79	4	no	—
564	#518	—	79	32	no	—
565	C₂×C₄×Q₈	—	79	1	no	—
566	C₂×C₄×D₄	—	79	2	no	—
567	C₂×C₄×D₄	—	79	4	no	—
568	C₂×C₄×D₄	—	79	4	no	—
569	C₂×C₄×D₄	—	79	2	no	—
570	C₂×C₄×D₄	—	79	2	no	—
571	C₂×C₄×D₄	—	79	4	no	—
572	C₂×C₄×D₄	—	79	1	no	—
573	C₂×C₄×D₄	—	79	2	no	—
574	C₂×C₄×D₄	—	79	1	no	—
575	C₂×C₄×D₄	—	79	1	no	—
576	C₂×C₄×D₄	—	79	2	no	—
577	C₂×C₄×D₄	—	79	1	no	—
578	C₂×C₄×D₄	—	79	1	no	—
579	C₂×C₄×D₄	—	79	16	no	—
580	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
581	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
582	C₂×#117	—	79	2	no	—
583	C₂×#117	—	79	2	no	—
584	C₂×#117	—	79	2	no	—
585	C₂²×C₄⋊C₄	—	79	1	no	—
586	C₂²×C₄⋊C₄	—	79	2	no	—
587	C₂²×C₂²⋊C₄	—	79	2	no	—
588	C₂²×C₂²⋊C₄	—	79	4	no	—
589	C₂²×C₂²⋊C₄	—	79	4	no	—
590	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
591	C₂⁵	—	79	4	no	—
592	C₂⁵	—	79	2	no	—
593	C₂×#41	—	4	8	no	—
594	C₂×#41	—	316	8	no	—
595	C₂×#41	—	79	16	no	—
596	C₂×#41	C₂²×D₇₉	1	16	yes	complemented
597	C₂²×Q₈	—	79	1	no	—
598	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
599	C₂²×D₄	—	316	16	no	—
600	C₂²×D₄	—	316	8	no	—
601	C₂²×D₄	—	79	4	no	—
602	C₂²×D₄	—	79	4	no	—
603	C₂²×D₄	—	79	4	no	—
604	C₂²×D₄	—	79	32	no	—
605	C₂²×D₄	—	79	16	no	—
606	C₂²×D₄	—	79	4	no	—
607	C₂²×D₄	—	79	2	no	—
608	C₂²×D₄	—	79	16	no	—
609	C₂²×D₄	—	79	4	no	—
610	C₂²×D₄	—	79	1	no	—
611	C₂²×D₄	—	79	2	no	—
612	C₂²×D₄	—	79	1	no	—
613	C₂²×D₄	—	79	8	no	—
614	C₂²×D₄	—	79	1	no	—
615	C₂²×D₄	—	158	8	no	—
616	C₂²×D₄	—	158	16	no	—
617	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
618	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
619	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
620	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
621	C₂³×C₄	—	316	8	no	—
622	C₂³×C₄	—	79	2	no	—
623	C₂³×C₄	—	79	4	no	—
624	C₂³×C₄	—	79	2	no	—
625	C₂³×C₄	—	79	4	no	—
626	C₂³×C₄	—	79	2	no	—
627	C₂³×C₄	—	79	16	no	—
628	C₂³×C₄	—	79	2	no	—
629	C₂³×C₄	—	79	2	no	—
630	C₂³×C₄	—	79	2	no	—
631	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
632	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
633	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
634	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
635	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
636	#127	—	79	16	no	—
637	#127	C₂²×D₇₉	1	8	yes	complemented
638	#126	—	79	32	no	—
639	#126	—	79	16	no	—
640	#125	—	79	16	no	—
641	#125	—	79	8	no	—
642	#124	—	79	32	no	—
643	#124	—	79	8	no	—
644	#124	C₂²×D₇₉	1	16	yes	complemented
645	#123	—	79	16	no	—
646	#123	—	79	32	no	—
647	#123	—	79	32	no	—
648	#123	—	79	32	no	—
649	C₂²⋊Q₈	—	79	32	no	—
650	C₂²⋊Q₈	—	79	8	no	—
651	C₂²⋊Q₈	—	79	16	no	—
652	#121	—	79	32	no	—
653	#121	—	79	16	no	—
654	#121	—	79	16	no	—
655	#121	—	79	32	no	—
656	#121	—	79	16	no	—
657	#121	—	79	8	no	—
658	#121	—	79	32	no	—
659	#121	—	79	16	no	—
660	#121	—	79	16	no	—
661	#121	—	79	32	no	—
662	#121	—	79	32	no	—
663	#121	C₂²×D₇₉	1	16	yes	complemented
664	#121	C₂²×D₇₉	1	16	yes	complemented
665	#120	—	79	32	no	—
666	#120	—	79	32	no	—
667	#120	—	79	32	no	—
668	C₄×Q₈	—	79	8	no	—
669	C₄×D₄	—	79	16	no	—
670	C₄×D₄	—	79	32	no	—
671	C₄×D₄	—	79	32	no	—
672	C₄×D₄	—	79	16	no	—
673	C₄×D₄	—	79	16	no	—
674	C₄×D₄	—	79	32	no	—
675	C₄×D₄	—	79	8	no	—
676	C₄×D₄	—	79	16	no	—
677	C₄×D₄	—	79	8	no	—
678	C₄×D₄	—	79	8	no	—
679	C₄×D₄	—	79	16	no	—
680	C₄×D₄	—	79	8	no	—
681	C₄×D₄	—	79	8	no	—
682	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
683	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
684	#117	—	79	16	no	—
685	#117	—	79	16	no	—
686	#117	—	79	16	no	—
687	C₂×C₄⋊C₄	—	79	1	no	—
688	C₂×C₄⋊C₄	—	79	1	no	—
689	C₂×C₄⋊C₄	—	79	1	no	—
690	C₂×C₄⋊C₄	—	79	2	no	—
691	C₂×C₄⋊C₄	—	79	8	no	—
692	C₂×C₄⋊C₄	—	79	4	no	—
693	C₂×C₄⋊C₄	—	79	1	no	—
694	C₂×C₄⋊C₄	—	79	2	no	—
695	C₂×C₄⋊C₄	—	79	2	no	—
696	C₂×C₄⋊C₄	—	79	2	no	—
697	C₂×C₄⋊C₄	—	79	4	no	—
698	C₂×C₄⋊C₄	—	79	2	no	—
699	C₂×C₄⋊C₄	—	79	16	no	—
700	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
702	C₂×C₂²⋊C₄	—	79	4	no	—
703	C₂×C₂²⋊C₄	—	79	2	no	—
704	C₂×C₂²⋊C₄	—	79	4	no	—
705	C₂×C₂²⋊C₄	—	79	2	no	—
706	C₂×C₂²⋊C₄	—	79	2	no	—
707	C₂×C₂²⋊C₄	—	79	4	no	—
708	C₂×C₂²⋊C₄	—	79	2	no	—
709	C₂×C₂²⋊C₄	—	79	4	no	—
710	C₂×C₂²⋊C₄	—	79	2	no	—
711	C₂×C₂²⋊C₄	—	79	2	no	—
712	C₂×C₂²⋊C₄	—	79	2	no	—
713	C₂×C₂²⋊C₄	—	79	16	no	—
714	C₂×C₂²⋊C₄	—	79	32	no	—
715	C₂×C₂²⋊C₄	—	79	4	no	—
716	C₂×C₂²⋊C₄	—	79	2	no	—
717	C₂×C₂²⋊C₄	—	79	2	no	—
718	C₂×C₂²⋊C₄	—	79	32	no	—
719	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
720	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
721	C₂×C₄²	—	79	4	no	—
722	C₂×C₄²	—	79	2	no	—
723	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
724	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
725	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
726	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
727	C₂×C₄²	C₂²×D₇₉	1	8	yes	complemented
728	C₂⁴	—	316	4	no	—
729	C₂⁴	—	316	8	no	—
730	C₂⁴	—	316	8	no	—
731	C₂⁴	—	79	16	no	—
732	C₂⁴	—	79	8	no	—
733	C₂⁴	—	79	2	no	—
734	C₂⁴	—	79	2	no	—
735	C₂⁴	—	79	2	no	—
736	C₂⁴	—	158	8	no	—
737	C₂⁴	—	158	16	no	—
738	C₂⁴	—	158	8	no	—
739	C₂⁴	C₂³×D₇₉	1	4	yes	—
740	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
741	#41	—	4	32	no	—
742	#41	—	316	32	no	—
743	C₂×Q₈	—	4	4	no	—
744	C₂×Q₈	—	79	4	no	—
745	C₂×Q₈	—	158	4	no	—
746	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
747	C₂×D₄	—	2	16	no	—
748	C₂×D₄	—	2	8	no	—
749	C₂×D₄	—	2	8	no	—
750	C₂×D₄	—	4	4	no	—
751	C₂×D₄	—	316	8	no	—
752	C₂×D₄	—	316	64	no	—
753	C₂×D₄	—	316	32	no	—
754	C₂×D₄	—	316	8	no	—
755	C₂×D₄	—	316	8	no	—
756	C₂×D₄	—	316	8	no	—
757	C₂×D₄	—	79	16	no	—
758	C₂×D₄	—	79	16	no	—
759	C₂×D₄	—	79	16	no	—
760	C₂×D₄	—	79	16	no	—
761	C₂×D₄	—	79	8	no	—
762	C₂×D₄	—	79	8	no	—
763	C₂×D₄	—	79	16	no	—
764	C₂×D₄	—	79	4	no	—
765	C₂×D₄	—	79	8	no	—
766	C₂×D₄	—	79	4	no	—
767	C₂×D₄	—	79	4	no	—
768	C₂×D₄	—	158	32	no	—
769	C₂×D₄	—	158	8	no	—
770	C₂×D₄	—	158	64	no	—
771	C₂×D₄	—	158	16	no	—
772	C₂×D₄	—	158	8	no	—
773	C₂×D₄	—	158	4	no	—
774	C₂×D₄	—	158	4	no	—
775	C₂×D₄	C₂³×D₇₉	1	8	yes	—
776	C₂×D₄	C₂³×D₇₉	1	16	yes	—
777	C₂×D₄	C₂³×D₇₉	1	8	yes	—
778	C₂×D₄	C₂³×D₇₉	1	8	yes	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	4	8	no	—
783	C₂²×C₄	—	316	4	no	—
784	C₂²×C₄	—	316	4	no	—
785	C₂²×C₄	—	316	8	no	—
786	C₂²×C₄	—	316	32	no	—
787	C₂²×C₄	—	316	4	no	—
788	C₂²×C₄	—	316	8	no	—
789	C₂²×C₄	—	79	8	no	—
790	C₂²×C₄	—	79	16	no	—
791	C₂²×C₄	—	79	8	no	—
792	C₂²×C₄	—	79	16	no	—
793	C₂²×C₄	—	79	8	no	—
794	C₂²×C₄	—	79	2	no	—
795	C₂²×C₄	—	79	2	no	—
796	C₂²×C₄	—	79	2	no	—
797	C₂²×C₄	—	79	2	no	—
798	C₂²×C₄	—	79	2	no	—
799	C₂²×C₄	—	79	8	no	—
800	C₂²×C₄	—	79	8	no	—
801	C₂²×C₄	—	79	8	no	—
802	C₂²×C₄	—	158	8	no	—
803	C₂²×C₄	—	158	8	no	—
804	C₂²×C₄	—	158	8	no	—
805	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
806	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
807	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
808	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
809	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
810	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
811	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
812	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
813	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
814	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
815	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
816	C₄⋊C₄	—	79	16	no	—
817	C₄⋊C₄	—	79	8	no	—
818	C₄⋊C₄	—	79	8	no	—
819	C₄⋊C₄	—	79	8	no	—
820	C₄⋊C₄	—	79	8	no	—
821	C₄⋊C₄	—	79	4	no	—
822	C₄⋊C₄	—	79	4	no	—
823	C₄⋊C₄	—	79	4	no	—
824	C₄⋊C₄	—	79	8	no	—
825	C₄⋊C₄	—	79	4	no	—
826	C₄⋊C₄	—	79	16	no	—
827	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
828	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
829	C₂²⋊C₄	—	79	16	no	—
830	C₂²⋊C₄	—	79	8	no	—
831	C₂²⋊C₄	—	79	16	no	—
832	C₂²⋊C₄	—	79	8	no	—
833	C₂²⋊C₄	—	79	8	no	—
834	C₂²⋊C₄	—	79	16	no	—
835	C₂²⋊C₄	—	79	8	no	—
836	C₂²⋊C₄	—	79	16	no	—
837	C₂²⋊C₄	—	79	8	no	—
838	C₂²⋊C₄	—	79	8	no	—
839	C₂²⋊C₄	—	79	8	no	—
840	C₂²⋊C₄	—	79	16	no	—
841	C₂²⋊C₄	—	79	8	no	—
842	C₂²⋊C₄	—	79	8	no	—
843	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
844	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
845	C₄²	—	79	16	no	—
846	C₄²	—	79	8	no	—
847	C₄²	C₂³×D₇₉	1	4	yes	—
848	C₄²	C₂³×D₇₉	1	4	yes	—
849	C₄²	C₂³×D₇₉	1	4	yes	—
850	C₄²	C₂³×D₇₉	1	4	yes	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	8	no	—
854	C₂³	—	2	8	no	—
855	C₂³	—	2	8	no	—
856	C₂³	—	316	32	no	—
857	C₂³	—	316	8	no	—
858	C₂³	—	316	16	no	—
859	C₂³	—	316	16	no	—
860	C₂³	—	79	4	no	—
861	C₂³	—	79	8	no	—
862	C₂³	—	79	4	no	—
863	C₂³	—	79	4	no	—
864	C₂³	—	632	32	no	—
865	C₂³	—	158	16	no	—
866	C₂³	—	158	32	no	—
867	C₂³	—	158	16	no	—
868	C₂³	—	158	4	no	—
869	C₂³	—	158	4	no	—
870	C₂³	—	158	4	no	—
871	C₂³	—	158	4	no	—
872	C₂³	—	158	4	no	—
873	C₂³	—	158	4	no	—
874	C₂³	—	158	4	no	—
875	C₂³	—	158	4	no	—
876	C₂³	#14579206	1	4	yes	—
877	C₂³	C₂⁴×D₇₉	1	8	yes	—
878	C₂³	C₂⁴×D₇₉	1	2	yes	—
879	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
880	Q₈	—	4	8	no	—
881	Q₈	—	158	8	no	—
882	D₄	—	2	32	no	—
883	D₄	—	2	16	no	—
884	D₄	—	2	16	no	—
885	D₄	—	4	8	no	—
886	D₄	—	316	16	no	—
887	D₄	—	316	16	no	—
888	D₄	—	316	16	no	—
889	D₄	—	316	16	no	—
890	D₄	—	79	16	no	—
891	D₄	—	158	16	no	—
892	D₄	—	158	32	no	—
893	D₄	—	158	16	no	—
894	D₄	—	158	8	no	—
895	D₄	—	158	8	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	8	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	8	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	4	16	no	—
905	C₂×C₄	—	316	8	no	—
906	C₂×C₄	—	316	8	no	—
907	C₂×C₄	—	316	16	no	—
908	C₂×C₄	—	316	8	no	—
909	C₂×C₄	—	316	16	no	—
910	C₂×C₄	—	79	4	no	—
911	C₂×C₄	—	79	4	no	—
912	C₂×C₄	—	79	4	no	—
913	C₂×C₄	—	79	4	no	—
914	C₂×C₄	—	79	4	no	—
915	C₂×C₄	—	158	4	no	—
916	C₂×C₄	—	158	4	no	—
917	C₂×C₄	—	158	4	no	—
918	C₂×C₄	—	158	4	no	—
919	C₂×C₄	—	158	4	no	—
920	C₂×C₄	—	158	16	no	—
921	C₂×C₄	—	158	16	no	—
922	C₂×C₄	—	158	16	no	—
923	C₂×C₄	#41×D₇₉	1	4	yes	—
924	C₂×C₄	#14579207	1	4	yes	—
925	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
926	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
927	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
928	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
929	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
930	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
931	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
932	C₂²	—	2	8	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	8	no	—
936	C₂²	—	2	8	no	—
937	C₂²	—	2	8	no	—
938	C₂²	—	4	16	no	—
939	C₂²	—	316	32	no	—
940	C₂²	—	316	8	no	—
941	C₂²	—	316	8	no	—
942	C₂²	—	79	8	no	—
943	C₂²	—	632	32	no	—
944	C₂²	—	158	4	no	—
945	C₂²	—	158	4	no	—
946	C₂²	—	158	4	no	—
947	C₂²	—	158	4	no	—
948	C₂²	—	158	4	no	—
949	C₂²	—	158	4	no	—
950	C₂²	—	158	16	no	—
951	C₂²	—	158	4	no	—
952	C₂²	—	158	4	no	—
953	C₂²	C₂×#41×D₇₉	1	2	yes	—
954	C₂²	C₂×#14579206	1	4	yes	—
955	C₂²	C₂×#14579206	1	2	yes	—
956	C₂²	C₂×#14579207	1	2	yes	—
957	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	8	no	—
962	C₄	—	2	2	no	—
963	C₄	—	158	4	no	—
964	C₄	—	158	4	no	—
965	C₄	—	158	4	no	—
966	C₄	—	158	4	no	—
967	C₄	—	158	4	no	—
968	C₄	C₂×#41×D₇₉	1	4	yes	—
969	C₄	C₂×#14579207	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	4	8	no	—
972	C₂	—	316	4	no	—
973	C₂	—	316	4	no	—
974	C₂	—	158	8	no	—
975	C₂	#23777427	1	4	yes	direct product factor
976	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
977	C₂	C₂²×#14579206	1	1	yes	characteristic
978	C₂	C₂²×#14579207	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#532×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#532	D₇₉
hypocenter	C₇₉	C₂×#3519
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #23777427	C₂	direct (N × H)
2. C₂×#19099279	C₂	semidirect
3. C₂×#19099274	C₂	semidirect
4. C₂×#19099265	C₂	semidirect
5. C₂×#19099263	C₂	semidirect
6. C₂×#19099233	C₂	semidirect
7. C₂×#19099208	C₂	semidirect
8. C₂×#19099201	C₂	semidirect
9. C₂×#19099198	C₂	semidirect
10. C₂×#19099197	C₂	semidirect
11. C₂×#19099164	C₂	semidirect
12. C₂×#19099147	C₂	semidirect
13. C₂×#19099097	C₂	semidirect
14. C₂×#19099073	C₂	semidirect
15. C₂×#121×D₇₉	C₂	semidirect
16. C₂×#19099035	C₂	semidirect
17. C₂²×C₄×D₃₁₆	C₂	semidirect
18. C₂×#532×C₇₉	C₂	semidirect
19. C₂²×#11929623	C₂²	semidirect
22. C₂²×D₄×D₇₉	C₂²	semidirect
23. C₂²×D₄×D₇₉	C₂²	semidirect
24. C₂³×C₄×D₇₉	C₂²	semidirect
25. #19099279	C₂²	semidirect
26. #19099274	C₂²	semidirect
27. #19099265	C₂²	semidirect
28. #19099263	C₂²	semidirect
29. #19099233	C₂²	semidirect
30. #19099208	C₂²	semidirect
31. #19099201	C₂²	semidirect
32. #19099198	C₂²	semidirect
33. #19099197	C₂²	semidirect
34. #19099164	C₂²	semidirect
35. #19099147	C₂²	semidirect
36. C₂×#14579157	C₂²	semidirect
37. #19099097	C₂²	semidirect
38. C₂×#14579155	C₂²	semidirect
39. C₂×#14579154	C₂²	semidirect
40. C₂×#14579153	C₂²	semidirect
41. C₂×#14579152	C₂²	semidirect
42. C₂×#14579150	C₂²	semidirect
43. C₂×#14579149	C₂²	semidirect
44. #19099073	C₂²	semidirect
45. C₂×#14579145	C₂²	semidirect
46. C₂×#14579144	C₂²	semidirect
47. C₂×#14579144	C₂²	semidirect
48. C₂×#14579143	C₂²	semidirect
49. C₂×#14579141	C₂²	semidirect
50. C₂×#14579140	C₂²	semidirect
51. C₂×#14579137	C₂²	semidirect
52. C₂×#14579136	C₂²	semidirect
53. C₂×#14579136	C₂²	semidirect
55. C₂×#14579135	C₂²	semidirect
56. C₂×#14579134	C₂²	semidirect
57. C₂×#14579134	C₂²	semidirect
58. C₂×#14579133	C₂²	semidirect
59. C₂×#14579133	C₂²	semidirect
60. C₂×#14579132	C₂²	semidirect
61. C₂×#14579132	C₂²	semidirect
62. C₂×#14579132	C₂²	semidirect
63. #121×D₇₉	C₂²	semidirect
64. C₂×#14579131	C₂²	semidirect
65. C₂×#14579129	C₂²	semidirect
66. C₂×#14579129	C₂²	semidirect
67. #19099035	C₂²	semidirect
68. C₂×C₄×Dic₁₅₈	C₂²	semidirect
71. C₂×C₄×D₃₁₆	C₂²	semidirect
72. C₂×C₄×D₃₁₆	C₂²	semidirect
73. C₂×C₄×D₃₁₆	C₂²	semidirect
74. C₂×C₄×D₃₁₆	C₂²	semidirect
75. C₂×C₄×D₃₁₆	C₂²	semidirect
76. C₂×C₄×D₃₁₆	C₂²	semidirect
77. C₂×D₄×Dic₇₉	C₂²	semidirect
78. C₂×D₄×Dic₇₉	C₂²	semidirect
80. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
81. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
82. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
83. C₂×#14579119	C₂²	semidirect
84. C₂×#14579119	C₂²	semidirect
85. C₂×#14579118	C₂²	semidirect
86. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
87. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
88. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
89. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
90. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
91. C₂²×#41×C₇₉	C₂²	semidirect
92. #532×C₇₉	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
94. C₂×#127×C₇₉	C₂²	semidirect
95. C₂×#124×C₇₉	C₂²	semidirect
96. C₂×#121×C₇₉	C₂²	semidirect
97. C₂×#121×C₇₉	C₂²	semidirect
98. C₂×C₄×D₄×C₇₉	C₂²	semidirect
99. C₂×C₄×D₄×C₇₉	C₂²	semidirect
100. C₂²×C₄²×C₇₉	C₂²	semidirect
104. C₂×#11929623	C₂³	semidirect
122. C₂×D₄×D₇₉	C₂³	semidirect
123. C₂×D₄×D₇₉	C₂³	semidirect
133. C₂²×C₄×D₇₉	C₂³	semidirect
134. #14579157	C₂³	semidirect
135. #14579155	C₂³	semidirect
136. #14579154	C₂³	semidirect
137. #14579153	C₂³	semidirect
138. #14579152	C₂³	semidirect
139. #14579150	C₂³	semidirect
140. #14579149	C₂³	semidirect
141. #14579145	C₂³	semidirect
142. #14579144	C₂³	semidirect
143. #14579144	C₂³	semidirect
144. #14579143	C₂³	semidirect
145. #14579141	C₂³	semidirect
146. #14579140	C₂³	semidirect
147. #14579137	C₂³	semidirect
148. #14579136	C₂³	semidirect
149. #14579136	C₂³	semidirect
151. #14579135	C₂³	semidirect
152. #14579134	C₂³	semidirect
153. #14579134	C₂³	semidirect
154. #14579133	C₂³	semidirect
155. #14579133	C₂³	semidirect
156. #14579132	C₂³	semidirect
157. #14579132	C₂³	semidirect
158. #14579132	C₂³	semidirect
159. #14579131	C₂³	semidirect
160. #14579129	C₂³	semidirect
161. #14579129	C₂³	semidirect
162. C₄×Dic₁₅₈	C₂³	semidirect
165. C₄×D₃₁₆	C₂³	semidirect
166. C₄×D₃₁₆	C₂³	semidirect
167. C₄×D₃₁₆	C₂³	semidirect
168. C₄×D₃₁₆	C₂³	semidirect
169. C₄×D₃₁₆	C₂³	semidirect
170. D₄×Dic₇₉	C₂³	semidirect
171. D₄×Dic₇₉	C₂³	semidirect
173. C₄×C₂²⋊D₇₉	C₂³	semidirect
174. C₄×C₂²⋊D₇₉	C₂³	semidirect
175. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
176. #14579119	C₂³	semidirect
177. #14579119	C₂³	semidirect
178. #14579118	C₂³	semidirect
185. C₂×C₄⋊Dic₇₉	C₂³	semidirect
191. C₄⋊C₄×D₇₉	C₂³	semidirect
206. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
207. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
208. C₂²⋊C₄×D₇₉	C₂³	semidirect
212. C₂×#41×C₇₉	C₂³	semidirect
222. C₄⋊Q₈×C₇₉	C₂³	semidirect
223. #127×C₇₉	C₂³	semidirect
224. #124×C₇₉	C₂³	semidirect
225. #121×C₇₉	C₂³	semidirect
226. #121×C₇₉	C₂³	semidirect
227. C₄×D₄×C₇₉	C₂³	semidirect
228. C₄×D₄×C₇₉	C₂³	semidirect
237. C₂×C₄²×C₇₉	C₂³	semidirect
257. C₂×D₃₁₆	#41	semidirect
434. D₃₁₆	C₂×#41	semidirect
483. C₂×C₇₉	#3519	semidirect
502. C₂×#532	D₇₉	semidirect
508. C₇₉	C₂×#3519	semidirect
510. C₂²×#41	C₂×D₇₉	semidirect
527. #532	C₂×D₇₉	semidirect
528. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
530. C₂×#127	C₂×D₇₉	semidirect
538. C₂×#124	C₂×D₇₉	semidirect
559. C₂×#121	C₂×D₇₉	semidirect
560. C₂×#121	C₂×D₇₉	semidirect
580. C₂×C₄×D₄	C₂×D₇₉	semidirect
581. C₂×C₄×D₄	C₂×D₇₉	semidirect
590. C₂²×C₄²	C₂×D₇₉	semidirect
596. C₂×#41	C₂²×D₇₉	semidirect
635. C₄⋊Q₈	C₂²×D₇₉	semidirect
637. #127	C₂²×D₇₉	semidirect
644. #124	C₂²×D₇₉	semidirect
663. #121	C₂²×D₇₉	semidirect
664. #121	C₂²×D₇₉	semidirect
682. C₄×D₄	C₂²×D₇₉	semidirect
683. C₄×D₄	C₂²×D₇₉	semidirect
727. C₂×C₄²	C₂²×D₇₉	semidirect
975. C₂	#23777427	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777427	2
C₂×#19099279	2
C₂×#19099274	2
C₂×#19099265	2
C₂×#19099263	2
C₂×#19099233	2
C₂×#19099208	2
C₂×#19099201	2
C₂×#19099198	2
C₂×#19099197	2
C₂×#19099164	2
C₂×#19099147	2
C₂×#19099097	2
C₂×#19099073	2
C₂×#121×D₇₉	2
C₂×#19099035	2
C₂²×C₄×D₃₁₆	2
C₂×#532×C₇₉	2
C₂×#3519	79

Subgroups — C2×#23777427 #35196256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777427 #35196256