Subgroups — C₂×#554×D₇₉ #35195234

Order 20224.

8454 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099274	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19099273	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099272	C₂	1	2	yes	maximal, complemented
4	C₂×#19099271	C₂	1	2	yes	maximal, complemented
5	C₂×#19099270	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19099269	C₂	1	2	yes	maximal, complemented
7	C₂×#19099268	C₂	1	2	yes	maximal, complemented
8	C₂×#19099267	C₂	1	4	yes	maximal, complemented
9	#554×D₇₉	C₂	1	32	yes	maximal, direct product factor
10	C₂×C₄⋊Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#125×D₇₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₂²⋊Q₈×D₇₉	C₂	1	4	yes	maximal, complemented
13	C₂×C₂²⋊Q₈×D₇₉	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₄×D₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×D₄×D₇₉	C₂	1	2	yes	maximal
17	C₂²×C₄⋊C₄×D₇₉	C₂	1	2	yes	maximal, complemented
18	C₂×#554×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×Q₈×D₇₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×D₇₉	C₂²	1	2	yes	—
21	C₂²×D₄×D₇₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₇₉	C₂²	1	2	yes	—
23	C₂³×C₄×D₇₉	C₂²	1	4	yes	—
24	#19099274	C₂²	1	16	yes	complemented
25	#19099273	C₂²	1	16	yes	complemented
26	#19099272	C₂²	1	32	yes	complemented
27	#19099271	C₂²	1	32	yes	complemented
28	#19099270	C₂²	1	16	yes	complemented
29	#19099269	C₂²	1	32	yes	complemented
30	#19099268	C₂²	1	32	yes	complemented
31	#19099267	C₂²	1	64	yes	complemented
32	C₂×#14579161	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14579160	C₂²	1	2	yes	complemented
34	C₂×#14579160	C₂²	1	2	yes	complemented
35	C₂×#14579159	C₂²	1	2	yes	complemented
36	C₄⋊Q₈×D₇₉	C₂²	1	16	yes	complemented
37	C₂×#14579153	C₂²	1	2	yes	complemented
38	C₂×#14579152	C₂²	1	2	yes	complemented
39	C₂×#14579152	C₂²	1	2	yes	complemented
40	C₂×#14579151	C₂²	1	4	yes	complemented
41	C₂×#14579151	C₂²	1	4	yes	complemented
42	#125×D₇₉	C₂²	1	32	yes	complemented
43	C₂×#14579141	C₂²	1	2	yes	complemented
44	C₂×#14579141	C₂²	1	4	yes	complemented
45	C₂×#14579140	C₂²	1	2	yes	complemented
46	C₂×#14579140	C₂²	1	4	yes	complemented
47	C₂×#14579139	C₂²	1	4	yes	complemented
48	C₂×#14579139	C₂²	1	4	yes	complemented
49	C₂×#14579139	C₂²	1	4	yes	complemented
50	C₂×#14579138	C₂²	1	4	yes	complemented
51	C₂×#14579138	C₂²	1	4	yes	complemented
52	C₂×#14579138	C₂²	1	4	yes	complemented
53	C₂×#14579137	C₂²	1	4	yes	complemented
54	C₂×#14579137	C₂²	1	2	yes	complemented
55	C₂²⋊Q₈×D₇₉	C₂²	1	32	yes	complemented
56	C₂²⋊Q₈×D₇₉	C₂²	1	64	yes	complemented
57	C₂×Q₈×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
59	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14579126	C₂²	1	2	yes	complemented
61	C₂×#14579126	C₂²	1	1	yes	characteristic, complemented
62	C₄×Q₈×D₇₉	C₂²	1	16	yes	complemented
63	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
64	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
65	C₂×D₄×Dic₇₉	C₂²	1	2	yes	—
66	C₂×D₄×Dic₇₉	C₂²	1	1	yes	characteristic
67	C₂×#14579123	C₂²	1	1	yes	characteristic
68	C₂×#14579123	C₂²	1	2	yes	—
69	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	—
70	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
71	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
72	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	—
73	C₄×D₄×D₇₉	C₂²	1	16	yes	—
74	C₄×D₄×D₇₉	C₂²	1	32	yes	—
75	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
76	C₂²×Dic₇₉⋊C₄	C₂²	1	4	yes	complemented
77	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
78	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
79	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
83	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
84	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	complemented
85	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
86	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
87	C₂×C₄⋊C₄×D₇₉	C₂²	1	32	yes	complemented
88	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
89	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
90	C₂×C₄²×D₇₉	C₂²	1	2	yes	—
91	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
92	#554×C₇₉	C₂²	1	16	yes	complemented
93	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₇₉	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	4	yes	complemented
96	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
97	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
99	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
100	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	complemented
101	C₂⁴×D₇₉	C₂³	1	2	yes	—
102	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
103	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
104	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
105	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
106	C₂×Q₈×D₇₉	—	2	8	no	—
107	C₂×Q₈×D₇₉	—	4	8	no	—
108	C₂×Q₈×D₇₉	C₂³	1	8	yes	—
109	C₂×Q₈×D₇₉	C₂³	1	16	yes	—
110	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
111	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
112	C₂×D₄×D₇₉	Q₈	1	16	yes	complemented
113	C₂×D₄×D₇₉	C₂³	1	8	yes	—
114	C₂³×Dic₇₉	C₂³	1	2	yes	—
115	C₂³×Dic₇₉	C₂³	1	4	yes	—
116	C₂²×C₄×D₇₉	—	2	16	no	—
117	C₂²×C₄×D₇₉	—	4	16	no	—
118	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
119	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
121	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
122	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
123	C₂²×C₄×D₇₉	C₂³	1	16	yes	—
124	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
125	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
126	C₂²×C₄×D₇₉	C₂³	1	32	yes	—
127	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
128	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
129	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
131	#14579161	C₂³	1	8	yes	complemented
132	#14579160	C₂³	1	16	yes	complemented
133	#14579160	C₂³	1	16	yes	complemented
134	#14579159	C₂³	1	16	yes	complemented
135	#14579153	C₂³	1	16	yes	complemented
136	#14579152	C₂³	1	16	yes	complemented
137	#14579152	C₂³	1	16	yes	complemented
138	#14579151	C₂³	1	32	yes	complemented
139	#14579151	C₂³	1	32	yes	complemented
140	#14579141	C₂³	1	16	yes	complemented
141	#14579141	C₂³	1	32	yes	complemented
142	#14579140	C₂³	1	16	yes	complemented
143	#14579140	C₂³	1	32	yes	complemented
144	#14579139	C₂³	1	32	yes	complemented
145	#14579139	C₂³	1	32	yes	complemented
146	#14579139	C₂³	1	32	yes	complemented
147	#14579138	C₂³	1	32	yes	complemented
148	#14579138	C₂³	1	32	yes	complemented
149	#14579138	C₂³	1	32	yes	complemented
150	#14579137	C₂³	1	32	yes	complemented
151	#14579137	C₂³	1	16	yes	complemented
152	Q₈×Dic₇₉	C₂³	1	8	yes	complemented
153	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
154	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
155	#14579126	C₂³	1	16	yes	complemented
156	#14579126	C₂³	1	8	yes	complemented
157	C₄×D₃₁₆	C₂³	1	16	yes	—
158	C₄×D₃₁₆	C₂³	1	8	yes	—
159	D₄×Dic₇₉	C₂³	1	16	yes	—
160	D₄×Dic₇₉	C₂³	1	8	yes	—
161	#14579123	C₂³	1	8	yes	—
162	#14579123	C₂³	1	16	yes	—
163	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	—
164	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	—
165	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	—
166	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	—
167	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
169	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
170	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
174	C₂×C₄⋊Dic₇₉	C₂³	1	16	yes	complemented
175	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
176	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
177	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
178	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
179	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
180	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
181	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
182	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
183	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
185	C₂×Dic₇₉⋊C₄	C₂³	1	32	yes	complemented
186	C₄⋊C₄×D₇₉	C₂³	1	8	yes	—
187	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
188	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
189	C₄⋊C₄×D₇₉	C₂³	1	8	yes	—
190	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
191	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
192	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
193	C₄⋊C₄×D₇₉	C₂³	1	32	yes	complemented
194	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
195	C₄⋊C₄×D₇₉	C₂³	1	16	yes	complemented
196	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊Dic₇₉	C₂³	1	4	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	4	yes	—
201	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
202	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
203	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
204	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
205	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
206	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
207	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
208	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
209	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
210	C₄²×D₇₉	C₂³	1	16	yes	—
211	C₄²×D₇₉	C₂³	1	8	yes	—
212	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
213	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
214	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
215	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
216	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
217	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
218	#125×C₇₉	C₂³	1	16	yes	complemented
219	C₂²⋊Q₈×C₇₉	C₂³	1	32	yes	complemented
220	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	complemented
221	C₄×Q₈×C₇₉	C₂³	1	8	yes	complemented
222	C₄×D₄×C₇₉	C₂³	1	8	yes	—
223	C₄×D₄×C₇₉	C₂³	1	16	yes	—
224	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
226	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
231	C₂×C₄⋊C₄×C₇₉	C₂³	1	16	yes	complemented
232	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
234	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
235	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
236	C₂³×D₇₉	—	2	8	no	—
237	C₂³×D₇₉	—	2	8	no	—
238	C₂³×D₇₉	C₂×Q₈	1	16	yes	—
239	C₂³×D₇₉	C₂⁴	1	8	yes	—
240	C₂³×D₇₉	C₂⁴	1	2	yes	—
241	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₅₈	—	2	8	no	—
243	C₂×Dic₁₅₈	—	2	4	no	—
244	C₂×Dic₁₅₈	—	4	8	no	—
245	C₂×Dic₁₅₈	—	4	4	no	—
246	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
247	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
248	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
249	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
250	Q₈×D₇₉	—	2	32	no	—
251	Q₈×D₇₉	—	4	32	no	—
252	C₂×D₃₁₆	C₂×Q₈	1	8	yes	complemented
253	C₂×D₃₁₆	C₂⁴	1	4	yes	—
254	C₂×C₂²⋊D₇₉	C₂×Q₈	1	16	yes	complemented
255	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
256	D₄×D₇₉	C₂×Q₈	1	64	yes	complemented
257	C₂²×Dic₇₉	—	2	8	no	—
258	C₂²×Dic₇₉	—	4	8	no	—
259	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
260	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
261	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
262	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
263	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
264	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
266	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
267	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×D₇₉	—	2	8	no	—
269	C₂×C₄×D₇₉	—	2	64	no	—
270	C₂×C₄×D₇₉	—	2	8	no	—
271	C₂×C₄×D₇₉	—	2	8	no	—
272	C₂×C₄×D₇₉	—	2	4	no	—
273	C₂×C₄×D₇₉	—	2	16	no	—
274	C₂×C₄×D₇₉	—	2	8	no	—
275	C₂×C₄×D₇₉	—	2	8	no	—
276	C₂×C₄×D₇₉	—	4	8	no	—
277	C₂×C₄×D₇₉	—	4	8	no	—
278	C₂×C₄×D₇₉	—	4	64	no	—
279	C₂×C₄×D₇₉	C₂×Q₈	1	8	yes	—
280	C₂×C₄×D₇₉	#41	1	8	yes	—
281	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
282	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
283	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
284	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
285	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
286	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
287	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
288	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
289	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
290	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
291	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
292	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
293	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
294	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
295	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
296	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
297	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
298	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
299	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
300	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
301	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
302	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
303	Dic₇₉⋊C₄	C₂⁴	1	8	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	16	yes	—
308	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
309	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
310	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
311	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
312	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
315	C₄×Dic₇₉	C₂⁴	1	4	yes	—
316	C₄×Dic₇₉	C₂⁴	1	8	yes	—
317	C₄×Dic₇₉	C₂⁴	1	8	yes	—
318	C₄×Dic₇₉	C₂⁴	1	4	yes	—
319	C₄×Dic₇₉	C₂⁴	1	8	yes	—
320	C₄×Dic₇₉	C₂⁴	1	4	yes	—
321	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₇₉	—	2	4	no	—
323	C₂×Q₈×C₇₉	—	4	4	no	—
324	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
325	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
326	C₂×D₄×C₇₉	C₂×Q₈	1	8	yes	complemented
327	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₇₉	—	2	8	no	—
329	C₂²×C₄×C₇₉	—	4	8	no	—
330	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
337	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
340	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
341	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
342	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
343	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
344	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
347	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
348	C₄²×C₇₉	C₂⁴	1	8	yes	—
349	C₄²×C₇₉	C₂⁴	1	4	yes	—
350	C₂³×C₇₉	—	2	4	no	—
351	C₂³×C₇₉	—	2	4	no	—
352	C₂³×C₇₉	C₂²×Q₈	1	8	yes	—
353	C₂³×C₇₉	C₂⁵	1	4	yes	—
354	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
355	C₂²×D₇₉	—	2	4	no	—
356	C₂²×D₇₉	—	2	4	no	—
357	C₂²×D₇₉	—	2	64	no	—
358	C₂²×D₇₉	—	2	16	no	—
359	C₂²×D₇₉	—	2	16	no	—
360	C₂²×D₇₉	C₂²×Q₈	1	32	yes	—
361	C₂²×D₇₉	C₂²×Q₈	1	8	yes	—
362	C₂²×D₇₉	C₂²×Q₈	1	4	yes	—
363	C₂²×D₇₉	C₂×#41	1	4	yes	—
364	C₂²×D₇₉	H(5,𝔽₂)	1	4	yes	—
365	C₂²×D₇₉	C₂⁵	1	4	yes	—
366	C₂²×D₇₉	C₂⁵	1	2	yes	—
367	Q₈×C₇₉	—	2	8	no	—
368	Q₈×C₇₉	—	4	8	no	—
369	D₄×C₇₉	C₂²×Q₈	1	16	yes	complemented
370	C₂×C₄×C₇₉	—	2	4	no	—
371	C₂×C₄×C₇₉	—	2	4	no	—
372	C₂×C₄×C₇₉	—	2	4	no	—
373	C₂×C₄×C₇₉	—	2	8	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	16	no	—
376	C₂×C₄×C₇₉	—	4	16	no	—
377	C₂×C₄×C₇₉	C₂²×Q₈	1	4	yes	—
378	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
379	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
380	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
381	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
382	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
383	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
384	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
385	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
386	C₂²⋊D₇₉	C₂²×Q₈	1	32	yes	complemented
387	C₂×Dic₇₉	—	2	4	no	—
388	C₂×Dic₇₉	—	2	4	no	—
389	C₂×Dic₇₉	—	2	4	no	—
390	C₂×Dic₇₉	—	2	8	no	—
391	C₂×Dic₇₉	—	2	2	no	—
392	C₂×Dic₇₉	—	2	16	no	—
393	C₂×Dic₇₉	—	4	16	no	—
394	C₂×Dic₇₉	C₂²×Q₈	1	4	yes	—
395	C₂×Dic₇₉	C₂×#41	1	4	yes	—
396	C₂×Dic₇₉	C₂⁵	1	4	yes	—
397	C₂×Dic₇₉	C₂⁵	1	2	yes	—
398	C₂×Dic₇₉	C₂⁵	1	4	yes	—
399	C₂×Dic₇₉	C₂⁵	1	4	yes	—
400	C₂×Dic₇₉	C₂⁵	1	8	yes	—
401	C₂×Dic₇₉	C₂⁵	1	2	yes	—
402	C₂×Dic₇₉	C₂⁵	1	2	yes	—
403	D₃₁₆	C₂²×Q₈	1	16	yes	complemented
404	C₄×D₇₉	—	2	16	no	—
405	C₄×D₇₉	—	2	16	no	—
406	C₄×D₇₉	—	2	16	no	—
407	C₄×D₇₉	—	2	32	no	—
408	C₄×D₇₉	—	2	8	no	—
409	C₄×D₇₉	—	2	16	no	—
410	C₄×D₇₉	—	2	16	no	—
411	C₄×D₇₉	—	4	16	no	—
412	C₄×D₇₉	—	4	16	no	—
413	C₄×D₇₉	C₂²×Q₈	1	16	yes	—
414	C₄×D₇₉	C₂×#41	1	16	yes	—
415	Dic₁₅₈	—	2	8	no	—
416	Dic₁₅₈	—	2	16	no	—
417	Dic₁₅₈	—	4	16	no	—
418	Dic₁₅₈	—	4	8	no	—
419	C₂²×C₇₉	—	2	4	no	—
420	C₂²×C₇₉	—	2	4	no	—
421	C₂²×C₇₉	—	2	16	no	—
422	C₂²×C₇₉	C₂³×Q₈	1	8	yes	—
423	C₂²×C₇₉	C₂³×Q₈	1	2	yes	—
424	C₂²×C₇₉	C₂²×#41	1	2	yes	—
425	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
426	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
427	C₂×D₇₉	—	2	4	no	—
428	C₂×D₇₉	—	2	4	no	—
429	C₂×D₇₉	—	2	16	no	—
430	C₂×D₇₉	—	2	64	no	—
431	C₂×D₇₉	#554	1	16	yes	direct product factor
432	C₂×D₇₉	C₂³×Q₈	1	8	yes	—
433	C₂×D₇₉	C₂³×Q₈	1	4	yes	—
434	C₂×D₇₉	C₂²×#41	1	4	yes	—
435	C₂×D₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
436	C₄×C₇₉	—	2	4	no	—
437	C₄×C₇₉	—	2	4	no	—
438	C₄×C₇₉	—	2	4	no	—
439	C₄×C₇₉	—	2	8	no	—
440	C₄×C₇₉	—	2	2	no	—
441	C₄×C₇₉	C₂³×Q₈	1	4	yes	—
442	C₄×C₇₉	C₂²×#41	1	4	yes	—
443	Dic₇₉	—	2	4	no	—
444	Dic₇₉	—	2	4	no	—
445	Dic₇₉	—	2	2	no	—
446	Dic₇₉	—	2	8	no	—
447	Dic₇₉	—	2	4	no	—
448	Dic₇₉	C₂³×Q₈	1	4	yes	—
449	Dic₇₉	C₂²×#41	1	4	yes	—
450	C₂²×#554	—	79	1	no	maximal, Sylow
451	C₂×C₇₉	—	2	8	no	—
452	C₂×C₇₉	C₂×#554	1	4	yes	complemented
453	C₂×C₇₉	C₂⁴×Q₈	1	1	yes	characteristic
454	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
455	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
456	D₇₉	—	2	8	no	—
457	D₇₉	C₂×#554	1	8	yes	direct product factor
458	C₂×#554	—	79	32	no	—
459	C₂×#554	—	79	1	no	—
460	C₂×#554	—	79	2	no	—
461	C₂×#554	—	79	4	no	—
462	C₂×#554	—	79	2	no	—
463	C₂×#554	—	79	1	no	—
464	C₂×#554	—	79	1	no	—
465	C₂×#554	—	79	2	no	—
466	C₂×#554	—	79	2	no	—
467	C₂×#554	D₇₉	1	1	yes	characteristic, direct product factor
468	C₂²×C₄⋊Q₈	—	79	1	no	—
469	C₂²×#125	—	79	2	no	—
470	C₂²×C₂²⋊Q₈	—	79	4	no	—
471	C₂²×C₂²⋊Q₈	—	79	2	no	—
472	C₂²×C₄×Q₈	—	79	1	no	—
473	C₂²×C₄×D₄	—	79	1	no	—
474	C₂²×C₄×D₄	—	79	2	no	—
475	C₂³×C₄⋊C₄	—	79	2	no	—
476	C₇₉	C₂²×#554	1	1	yes	characteristic, complemented, Sylow
477	C₂³×Q₈	—	79	2	no	—
478	C₂³×Q₈	—	79	1	no	—
479	C₂³×D₄	—	79	1	no	—
480	C₂⁴×C₄	—	79	4	no	—
481	C₂⁴×C₄	—	79	2	no	—
482	#554	—	79	16	no	—
483	#554	—	79	32	no	—
484	#554	—	79	64	no	—
485	#554	—	79	32	no	—
486	#554	—	79	16	no	—
487	#554	—	79	16	no	—
488	#554	—	79	32	no	—
489	#554	—	79	32	no	—
490	#554	C₂×D₇₉	1	16	yes	direct product factor
491	C₂×C₄⋊Q₈	—	79	2	no	—
492	C₂×C₄⋊Q₈	—	79	16	no	—
493	C₂×C₄⋊Q₈	—	79	2	no	—
494	C₂×C₄⋊Q₈	—	79	2	no	—
495	C₂×C₄⋊Q₈	—	79	1	no	—
496	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
497	C₂×#125	—	79	32	no	—
498	C₂×#125	—	79	4	no	—
499	C₂×#125	—	79	4	no	—
500	C₂×#125	—	79	2	no	—
501	C₂×#125	—	79	2	no	—
502	C₂×#125	—	79	2	no	—
503	C₂×#125	C₂×D₇₉	1	2	yes	complemented
504	C₂×C₂²⋊Q₈	—	79	4	no	—
505	C₂×C₂²⋊Q₈	—	79	2	no	—
506	C₂×C₂²⋊Q₈	—	79	4	no	—
507	C₂×C₂²⋊Q₈	—	79	2	no	—
508	C₂×C₂²⋊Q₈	—	79	64	no	—
509	C₂×C₂²⋊Q₈	—	79	32	no	—
510	C₂×C₂²⋊Q₈	—	79	4	no	—
511	C₂×C₂²⋊Q₈	—	79	4	no	—
512	C₂×C₂²⋊Q₈	—	79	4	no	—
513	C₂×C₂²⋊Q₈	—	79	4	no	—
514	C₂×C₂²⋊Q₈	—	79	2	no	—
515	C₂×C₂²⋊Q₈	—	79	4	no	—
516	C₂×C₂²⋊Q₈	—	79	4	no	—
517	C₂×C₂²⋊Q₈	—	79	4	no	—
518	C₂×C₂²⋊Q₈	C₂×D₇₉	1	4	yes	complemented
519	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
520	C₂×C₄×Q₈	—	79	1	no	—
521	C₂×C₄×Q₈	—	79	16	no	—
522	C₂×C₄×Q₈	—	79	2	no	—
523	C₂×C₄×Q₈	—	79	1	no	—
524	C₂×C₄×Q₈	—	79	1	no	—
525	C₂×C₄×Q₈	—	79	2	no	—
526	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
527	C₂×C₄×D₄	—	79	2	no	—
528	C₂×C₄×D₄	—	79	1	no	—
529	C₂×C₄×D₄	—	79	4	no	—
530	C₂×C₄×D₄	—	79	2	no	—
531	C₂×C₄×D₄	—	79	32	no	—
532	C₂×C₄×D₄	—	79	16	no	—
533	C₂×C₄×D₄	—	79	2	no	—
534	C₂×C₄×D₄	—	79	1	no	—
535	C₂×C₄×D₄	—	79	4	no	—
536	C₂×C₄×D₄	—	79	2	no	—
537	C₂×C₄×D₄	—	79	2	no	—
538	C₂×C₄×D₄	—	79	1	no	—
539	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
540	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
541	C₂²×C₄⋊C₄	—	79	4	no	—
542	C₂²×C₄⋊C₄	—	79	2	no	—
543	C₂²×C₄⋊C₄	—	79	1	no	—
544	C₂²×C₄⋊C₄	—	79	4	no	—
545	C₂²×C₄⋊C₄	—	79	2	no	—
546	C₂²×C₄⋊C₄	—	79	4	no	—
547	C₂²×C₄⋊C₄	—	79	2	no	—
548	C₂²×C₄⋊C₄	—	79	2	no	—
549	C₂²×C₄⋊C₄	—	79	1	no	—
550	C₂²×C₄⋊C₄	—	79	2	no	—
551	C₂²×C₄⋊C₄	—	79	2	no	—
552	C₂²×C₄⋊C₄	—	79	4	no	—
553	C₂²×C₄⋊C₄	—	79	32	no	—
554	C₂²×C₄⋊C₄	C₂×D₇₉	1	2	yes	complemented
555	C₂²×C₂²⋊C₄	—	79	4	no	—
556	C₂²×C₂²⋊C₄	—	79	2	no	—
557	C₂²×C₄²	—	79	2	no	—
558	C₂²×C₄²	—	79	1	no	—
559	C₂⁵	—	79	2	no	—
560	C₂²×Q₈	—	316	8	no	—
561	C₂²×Q₈	—	79	16	no	—
562	C₂²×Q₈	—	79	8	no	—
563	C₂²×Q₈	—	79	4	no	—
564	C₂²×Q₈	—	79	2	no	—
565	C₂²×Q₈	—	79	2	no	—
566	C₂²×Q₈	—	79	1	no	—
567	C₂²×Q₈	—	158	8	no	—
568	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
569	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
570	C₂²×D₄	—	79	2	no	—
571	C₂²×D₄	—	79	16	no	—
572	C₂²×D₄	—	79	8	no	—
573	C₂²×D₄	—	79	1	no	—
574	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
575	C₂³×C₄	—	316	16	no	—
576	C₂³×C₄	—	79	4	no	—
577	C₂³×C₄	—	79	4	no	—
578	C₂³×C₄	—	79	4	no	—
579	C₂³×C₄	—	79	32	no	—
580	C₂³×C₄	—	79	1	no	—
581	C₂³×C₄	—	79	1	no	—
582	C₂³×C₄	—	79	2	no	—
583	C₂³×C₄	—	79	2	no	—
584	C₂³×C₄	—	79	1	no	—
585	C₂³×C₄	—	79	2	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	2	no	—
591	C₂³×C₄	—	158	16	no	—
592	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
593	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
594	C₄⋊Q₈	—	79	16	no	—
595	C₄⋊Q₈	—	79	16	no	—
596	C₄⋊Q₈	—	79	16	no	—
597	C₄⋊Q₈	—	79	8	no	—
598	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
599	#125	—	79	32	no	—
600	#125	—	79	32	no	—
601	#125	—	79	16	no	—
602	#125	—	79	16	no	—
603	#125	—	79	16	no	—
604	#125	C₂²×D₇₉	1	16	yes	complemented
605	C₂²⋊Q₈	—	79	32	no	—
606	C₂²⋊Q₈	—	79	16	no	—
607	C₂²⋊Q₈	—	79	32	no	—
608	C₂²⋊Q₈	—	79	16	no	—
609	C₂²⋊Q₈	—	79	32	no	—
610	C₂²⋊Q₈	—	79	32	no	—
611	C₂²⋊Q₈	—	79	32	no	—
612	C₂²⋊Q₈	—	79	32	no	—
613	C₂²⋊Q₈	—	79	16	no	—
614	C₂²⋊Q₈	—	79	32	no	—
615	C₂²⋊Q₈	—	79	32	no	—
616	C₂²⋊Q₈	—	79	32	no	—
617	C₂²⋊Q₈	C₂²×D₇₉	1	32	yes	complemented
618	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	complemented
619	C₄×Q₈	—	79	8	no	—
620	C₄×Q₈	—	79	16	no	—
621	C₄×Q₈	—	79	8	no	—
622	C₄×Q₈	—	79	8	no	—
623	C₄×Q₈	—	79	16	no	—
624	C₄×Q₈	C₂²×D₇₉	1	8	yes	complemented
625	C₄×D₄	—	79	16	no	—
626	C₄×D₄	—	79	8	no	—
627	C₄×D₄	—	79	32	no	—
628	C₄×D₄	—	79	16	no	—
629	C₄×D₄	—	79	16	no	—
630	C₄×D₄	—	79	8	no	—
631	C₄×D₄	—	79	32	no	—
632	C₄×D₄	—	79	16	no	—
633	C₄×D₄	—	79	16	no	—
634	C₄×D₄	—	79	8	no	—
635	C₄×D₄	C₂²×D₇₉	1	16	yes	—
636	C₄×D₄	C₂²×D₇₉	1	8	yes	—
637	C₂×C₄⋊C₄	—	79	2	no	—
638	C₂×C₄⋊C₄	—	79	1	no	—
639	C₂×C₄⋊C₄	—	79	4	no	—
640	C₂×C₄⋊C₄	—	79	4	no	—
641	C₂×C₄⋊C₄	—	79	4	no	—
642	C₂×C₄⋊C₄	—	79	4	no	—
643	C₂×C₄⋊C₄	—	79	2	no	—
644	C₂×C₄⋊C₄	—	79	32	no	—
645	C₂×C₄⋊C₄	—	79	16	no	—
646	C₂×C₄⋊C₄	—	79	2	no	—
647	C₂×C₄⋊C₄	—	79	1	no	—
648	C₂×C₄⋊C₄	—	79	4	no	—
649	C₂×C₄⋊C₄	—	79	2	no	—
650	C₂×C₄⋊C₄	—	79	2	no	—
651	C₂×C₄⋊C₄	—	79	2	no	—
652	C₂×C₄⋊C₄	—	79	2	no	—
653	C₂×C₄⋊C₄	—	79	4	no	—
654	C₂×C₄⋊C₄	—	79	4	no	—
655	C₂×C₄⋊C₄	—	79	4	no	—
656	C₂×C₄⋊C₄	—	79	8	no	—
657	C₂×C₄⋊C₄	—	79	32	no	—
658	C₂×C₄⋊C₄	—	79	16	no	—
659	C₂×C₄⋊C₄	—	79	32	no	—
660	C₂×C₄⋊C₄	—	79	16	no	—
661	C₂×C₄⋊C₄	—	79	16	no	—
662	C₂×C₄⋊C₄	—	79	8	no	—
663	C₂×C₄⋊C₄	—	79	16	no	—
664	C₂×C₄⋊C₄	—	79	16	no	—
665	C₂×C₄⋊C₄	—	79	32	no	—
666	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
668	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
669	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
673	C₂×C₄⋊C₄	C₂²×D₇₉	1	16	yes	complemented
674	C₂×C₂²⋊C₄	—	79	4	no	—
675	C₂×C₂²⋊C₄	—	79	2	no	—
676	C₂×C₂²⋊C₄	—	79	4	no	—
677	C₂×C₂²⋊C₄	—	79	2	no	—
678	C₂×C₂²⋊C₄	—	79	2	no	—
679	C₂×C₂²⋊C₄	—	79	4	no	—
680	C₂×C₂²⋊C₄	—	79	32	no	—
681	C₂×C₂²⋊C₄	—	79	16	no	—
682	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
683	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
684	C₂×C₄²	—	79	2	no	—
685	C₂×C₄²	—	79	2	no	—
686	C₂×C₄²	—	79	2	no	—
687	C₂×C₄²	—	79	1	no	—
688	C₂×C₄²	—	79	1	no	—
689	C₂×C₄²	—	79	1	no	—
690	C₂×C₄²	—	79	16	no	—
691	C₂×C₄²	—	79	8	no	—
692	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
693	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
694	C₂⁴	—	79	1	no	—
695	C₂⁴	—	79	16	no	—
696	C₂⁴	—	79	8	no	—
697	C₂⁴	—	79	2	no	—
698	C₂⁴	—	158	8	no	—
699	C₂⁴	—	158	8	no	—
700	C₂⁴	C₂³×D₇₉	1	2	yes	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	4	4	no	—
703	C₂×Q₈	—	316	8	no	—
704	C₂×Q₈	—	316	4	no	—
705	C₂×Q₈	—	316	32	no	—
706	C₂×Q₈	—	79	16	no	—
707	C₂×Q₈	—	79	8	no	—
708	C₂×Q₈	—	79	8	no	—
709	C₂×Q₈	—	79	4	no	—
710	C₂×Q₈	—	158	8	no	—
711	C₂×Q₈	—	158	32	no	—
712	C₂×Q₈	—	158	4	no	—
713	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
714	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
715	C₂×D₄	—	79	16	no	—
716	C₂×D₄	—	79	8	no	—
717	C₂×D₄	—	79	64	no	—
718	C₂×D₄	—	79	8	no	—
719	C₂×D₄	—	79	4	no	—
720	C₂×D₄	Q₈×D₇₉	1	8	yes	complemented
721	C₂×D₄	C₂³×D₇₉	1	4	yes	—
722	C₂²×C₄	—	2	8	no	—
723	C₂²×C₄	—	4	8	no	—
724	C₂²×C₄	—	316	8	no	—
725	C₂²×C₄	—	316	8	no	—
726	C₂²×C₄	—	316	64	no	—
727	C₂²×C₄	—	316	8	no	—
728	C₂²×C₄	—	79	16	no	—
729	C₂²×C₄	—	79	16	no	—
730	C₂²×C₄	—	79	16	no	—
731	C₂²×C₄	—	79	1	no	—
732	C₂²×C₄	—	79	1	no	—
733	C₂²×C₄	—	79	8	no	—
734	C₂²×C₄	—	79	8	no	—
735	C₂²×C₄	—	79	4	no	—
736	C₂²×C₄	—	79	4	no	—
737	C₂²×C₄	—	79	8	no	—
738	C₂²×C₄	—	79	2	no	—
739	C₂²×C₄	—	79	1	no	—
740	C₂²×C₄	—	79	2	no	—
741	C₂²×C₄	—	79	2	no	—
742	C₂²×C₄	—	79	4	no	—
743	C₂²×C₄	—	79	8	no	—
744	C₂²×C₄	—	79	4	no	—
745	C₂²×C₄	—	79	8	no	—
746	C₂²×C₄	—	79	8	no	—
747	C₂²×C₄	—	79	16	no	—
748	C₂²×C₄	—	79	8	no	—
749	C₂²×C₄	—	79	8	no	—
750	C₂²×C₄	—	158	8	no	—
751	C₂²×C₄	—	158	64	no	—
752	C₂²×C₄	—	158	8	no	—
753	C₂²×C₄	—	158	16	no	—
754	C₂²×C₄	—	158	8	no	—
755	C₂²×C₄	—	158	4	no	—
756	C₂²×C₄	—	158	8	no	—
757	C₂²×C₄	—	158	8	no	—
758	C₂²×C₄	—	158	8	no	—
759	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
760	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
761	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
763	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
764	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
765	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
766	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
767	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
768	C₄⋊C₄	—	79	8	no	—
769	C₄⋊C₄	—	79	16	no	—
770	C₄⋊C₄	—	79	16	no	—
771	C₄⋊C₄	—	79	16	no	—
772	C₄⋊C₄	—	79	8	no	—
773	C₄⋊C₄	—	79	16	no	—
774	C₄⋊C₄	—	79	8	no	—
775	C₄⋊C₄	—	79	8	no	—
776	C₄⋊C₄	—	79	16	no	—
777	C₄⋊C₄	—	79	16	no	—
778	C₄⋊C₄	—	79	4	no	—
779	C₄⋊C₄	—	79	16	no	—
780	C₄⋊C₄	—	79	8	no	—
781	C₄⋊C₄	—	79	4	no	—
782	C₄⋊C₄	—	79	8	no	—
783	C₄⋊C₄	—	79	8	no	—
784	C₄⋊C₄	—	79	16	no	—
785	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
786	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
787	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
788	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
789	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
790	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
791	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
792	C₂²⋊C₄	—	79	16	no	—
793	C₂²⋊C₄	—	79	8	no	—
794	C₂²⋊C₄	—	79	16	no	—
795	C₂²⋊C₄	—	79	8	no	—
796	C₂²⋊C₄	—	79	8	no	—
797	C₂²⋊C₄	—	79	16	no	—
798	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
799	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
800	C₄²	—	79	8	no	—
801	C₄²	—	79	8	no	—
802	C₄²	—	79	8	no	—
803	C₄²	—	79	4	no	—
804	C₄²	—	79	4	no	—
805	C₄²	—	79	4	no	—
806	C₄²	C₂³×D₇₉	1	8	yes	—
807	C₄²	C₂³×D₇₉	1	4	yes	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	79	4	no	—
811	C₂³	—	79	2	no	—
812	C₂³	—	79	4	no	—
813	C₂³	—	79	4	no	—
814	C₂³	—	79	4	no	—
815	C₂³	—	79	32	no	—
816	C₂³	—	79	8	no	—
817	C₂³	—	158	16	no	—
818	C₂³	—	158	16	no	—
819	C₂³	—	158	64	no	—
820	C₂³	—	158	4	no	—
821	C₂³	—	158	4	no	—
822	C₂³	C₂×Q₈×D₇₉	1	8	yes	—
823	C₂³	C₂⁴×D₇₉	1	4	yes	—
824	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
825	Q₈	—	2	8	no	—
826	Q₈	—	4	8	no	—
827	Q₈	—	316	16	no	—
828	Q₈	—	316	8	no	—
829	Q₈	—	158	16	no	—
830	Q₈	—	158	8	no	—
831	D₄	—	79	32	no	—
832	D₄	—	79	16	no	—
833	D₄	C₂×Q₈×D₇₉	1	16	yes	complemented
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	16	no	—
840	C₂×C₄	—	4	16	no	—
841	C₂×C₄	—	316	16	no	—
842	C₂×C₄	—	316	16	no	—
843	C₂×C₄	—	316	16	no	—
844	C₂×C₄	—	79	2	no	—
845	C₂×C₄	—	79	2	no	—
846	C₂×C₄	—	79	4	no	—
847	C₂×C₄	—	79	4	no	—
848	C₂×C₄	—	79	16	no	—
849	C₂×C₄	—	79	16	no	—
850	C₂×C₄	—	79	4	no	—
851	C₂×C₄	—	79	2	no	—
852	C₂×C₄	—	79	4	no	—
853	C₂×C₄	—	79	4	no	—
854	C₂×C₄	—	79	8	no	—
855	C₂×C₄	—	158	16	no	—
856	C₂×C₄	—	158	16	no	—
857	C₂×C₄	—	158	32	no	—
858	C₂×C₄	—	158	16	no	—
859	C₂×C₄	—	158	8	no	—
860	C₂×C₄	—	158	16	no	—
861	C₂×C₄	—	158	16	no	—
862	C₂×C₄	—	158	4	no	—
863	C₂×C₄	—	158	8	no	—
864	C₂×C₄	—	158	2	no	—
865	C₂×C₄	—	158	4	no	—
866	C₂×C₄	—	158	4	no	—
867	C₂×C₄	—	158	16	no	—
868	C₂×C₄	C₂×Q₈×D₇₉	1	4	yes	—
869	C₂×C₄	#41×D₇₉	1	4	yes	—
870	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
871	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
872	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
873	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
874	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
875	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
876	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	16	no	—
880	C₂²	—	79	4	no	—
881	C₂²	—	79	4	no	—
882	C₂²	—	79	4	no	—
883	C₂²	—	79	16	no	—
884	C₂²	—	79	8	no	—
885	C₂²	—	158	64	no	—
886	C₂²	—	158	4	no	—
887	C₂²	—	158	4	no	—
888	C₂²	—	158	16	no	—
889	C₂²	C₂²×Q₈×D₇₉	1	8	yes	—
890	C₂²	C₂²×Q₈×D₇₉	1	2	yes	—
891	C₂²	C₂×#41×D₇₉	1	2	yes	—
892	C₂²	H(5,𝔽₂)×D₇₉	1	2	yes	—
893	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
894	C₄	—	2	4	no	—
895	C₄	—	2	4	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	8	no	—
898	C₄	—	2	2	no	—
899	C₄	—	79	4	no	—
900	C₄	—	79	4	no	—
901	C₄	—	158	4	no	—
902	C₄	—	158	4	no	—
903	C₄	—	158	4	no	—
904	C₄	—	158	8	no	—
905	C₄	—	158	2	no	—
906	C₄	C₂²×Q₈×D₇₉	1	4	yes	—
907	C₄	C₂×#41×D₇₉	1	4	yes	—
908	C₂	—	2	8	no	—
909	C₂	—	79	8	no	—
910	C₂	—	158	8	no	—
911	C₂	#554×D₇₉	1	4	yes	direct product factor
912	C₂	C₂³×Q₈×D₇₉	1	1	yes	characteristic
913	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
914	C₂	C₂×H(5,𝔽₂)×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#554×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
prime radical	C₂²×D₄×D₇₉	C₂²
hypercenter	C₂×#554	D₇₉
hypocenter	C₇₉	C₂²×#554
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. C₂×#19099274	C₂	semidirect
2. C₂×#19099273	C₂	semidirect
3. C₂×#19099272	C₂	semidirect
4. C₂×#19099271	C₂	semidirect
5. C₂×#19099270	C₂	semidirect
6. C₂×#19099269	C₂	semidirect
7. C₂×#19099268	C₂	semidirect
8. C₂×#19099267	C₂	semidirect
9. #554×D₇₉	C₂	direct (N × H)
10. C₂×C₄⋊Q₈×D₇₉	C₂	semidirect
11. C₂×#125×D₇₉	C₂	semidirect
12. C₂×C₂²⋊Q₈×D₇₉	C₂	semidirect
13. C₂×C₂²⋊Q₈×D₇₉	C₂	semidirect
14. C₂×C₄×Q₈×D₇₉	C₂	semidirect
17. C₂²×C₄⋊C₄×D₇₉	C₂	semidirect
18. C₂×#554×C₇₉	C₂	semidirect
24. #19099274	C₂²	semidirect
25. #19099273	C₂²	semidirect
26. #19099272	C₂²	semidirect
27. #19099271	C₂²	semidirect
28. #19099270	C₂²	semidirect
29. #19099269	C₂²	semidirect
30. #19099268	C₂²	semidirect
31. #19099267	C₂²	semidirect
32. C₂×#14579161	C₂²	semidirect
33. C₂×#14579160	C₂²	semidirect
34. C₂×#14579160	C₂²	semidirect
35. C₂×#14579159	C₂²	semidirect
36. C₄⋊Q₈×D₇₉	C₂²	semidirect
37. C₂×#14579153	C₂²	semidirect
38. C₂×#14579152	C₂²	semidirect
39. C₂×#14579152	C₂²	semidirect
40. C₂×#14579151	C₂²	semidirect
41. C₂×#14579151	C₂²	semidirect
42. #125×D₇₉	C₂²	semidirect
43. C₂×#14579141	C₂²	semidirect
44. C₂×#14579141	C₂²	semidirect
45. C₂×#14579140	C₂²	semidirect
46. C₂×#14579140	C₂²	semidirect
47. C₂×#14579139	C₂²	semidirect
48. C₂×#14579139	C₂²	semidirect
49. C₂×#14579139	C₂²	semidirect
50. C₂×#14579138	C₂²	semidirect
51. C₂×#14579138	C₂²	semidirect
52. C₂×#14579138	C₂²	semidirect
53. C₂×#14579137	C₂²	semidirect
54. C₂×#14579137	C₂²	semidirect
55. C₂²⋊Q₈×D₇₉	C₂²	semidirect
56. C₂²⋊Q₈×D₇₉	C₂²	semidirect
57. C₂×Q₈×Dic₇₉	C₂²	semidirect
58. C₂×C₄×Dic₁₅₈	C₂²	semidirect
59. C₂×C₄×Dic₁₅₈	C₂²	semidirect
60. C₂×#14579126	C₂²	semidirect
61. C₂×#14579126	C₂²	semidirect
62. C₄×Q₈×D₇₉	C₂²	semidirect
75. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
76. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
84. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
85. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
86. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
87. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
92. #554×C₇₉	C₂²	semidirect
93. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
94. C₂×#125×C₇₉	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
97. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
100. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
112. C₂×D₄×D₇₉	Q₈	semidirect
131. #14579161	C₂³	semidirect
132. #14579160	C₂³	semidirect
133. #14579160	C₂³	semidirect
134. #14579159	C₂³	semidirect
135. #14579153	C₂³	semidirect
136. #14579152	C₂³	semidirect
137. #14579152	C₂³	semidirect
138. #14579151	C₂³	semidirect
139. #14579151	C₂³	semidirect
140. #14579141	C₂³	semidirect
141. #14579141	C₂³	semidirect
142. #14579140	C₂³	semidirect
143. #14579140	C₂³	semidirect
144. #14579139	C₂³	semidirect
145. #14579139	C₂³	semidirect
146. #14579139	C₂³	semidirect
147. #14579138	C₂³	semidirect
148. #14579138	C₂³	semidirect
149. #14579138	C₂³	semidirect
150. #14579137	C₂³	semidirect
151. #14579137	C₂³	semidirect
152. Q₈×Dic₇₉	C₂³	semidirect
153. C₄×Dic₁₅₈	C₂³	semidirect
154. C₄×Dic₁₅₈	C₂³	semidirect
155. #14579126	C₂³	semidirect
156. #14579126	C₂³	semidirect
174. C₂×C₄⋊Dic₇₉	C₂³	semidirect
185. C₂×Dic₇₉⋊C₄	C₂³	semidirect
193. C₄⋊C₄×D₇₉	C₂³	semidirect
194. C₄⋊C₄×D₇₉	C₂³	semidirect
195. C₄⋊C₄×D₇₉	C₂³	semidirect
217. C₄⋊Q₈×C₇₉	C₂³	semidirect
218. #125×C₇₉	C₂³	semidirect
219. C₂²⋊Q₈×C₇₉	C₂³	semidirect
220. C₂²⋊Q₈×C₇₉	C₂³	semidirect
221. C₄×Q₈×C₇₉	C₂³	semidirect
231. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
252. C₂×D₃₁₆	C₂×Q₈	semidirect
254. C₂×C₂²⋊D₇₉	C₂×Q₈	semidirect
256. D₄×D₇₉	C₂×Q₈	semidirect
326. C₂×D₄×C₇₉	C₂×Q₈	semidirect
369. D₄×C₇₉	C₂²×Q₈	semidirect
386. C₂²⋊D₇₉	C₂²×Q₈	semidirect
403. D₃₁₆	C₂²×Q₈	semidirect
431. C₂×D₇₉	#554	direct (N × H)
452. C₂×C₇₉	C₂×#554	semidirect
457. D₇₉	C₂×#554	direct (N × H)
467. C₂×#554	D₇₉	direct (N × H)
476. C₇₉	C₂²×#554	semidirect
490. #554	C₂×D₇₉	direct (N × H)
496. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
503. C₂×#125	C₂×D₇₉	semidirect
518. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
519. C₂×C₂²⋊Q₈	C₂×D₇₉	semidirect
526. C₂×C₄×Q₈	C₂×D₇₉	semidirect
554. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
598. C₄⋊Q₈	C₂²×D₇₉	semidirect
604. #125	C₂²×D₇₉	semidirect
617. C₂²⋊Q₈	C₂²×D₇₉	semidirect
618. C₂²⋊Q₈	C₂²×D₇₉	semidirect
624. C₄×Q₈	C₂²×D₇₉	semidirect
673. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
720. C₂×D₄	Q₈×D₇₉	semidirect
833. D₄	C₂×Q₈×D₇₉	semidirect
911. C₂	#554×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19099274	2
C₂×#19099273	2
C₂×#19099272	2
C₂×#19099271	2
C₂×#19099270	2
C₂×#19099269	2
C₂×#19099268	2
C₂×#19099267	2
#554×D₇₉	2
C₂×C₄⋊Q₈×D₇₉	2
C₂×#125×D₇₉	2
C₂×C₂²⋊Q₈×D₇₉	2
C₂×C₄×Q₈×D₇₉	2
C₂×C₄×D₄×D₇₉	2
C₂²×C₄⋊C₄×D₇₉	2
C₂×#554×C₇₉	2
C₂²×#554	79

Subgroups — C2×#554×D79 #35195234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#554×D₇₉ #35195234