Subgroups — C₂×#540×D₇₉ #35195040

Order 20224.

8838 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19099168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099166	C₂	1	2	yes	maximal, complemented
5	C₂×#19099165	C₂	1	4	yes	maximal, complemented
6	C₂×#19099164	C₂	1	2	yes	maximal, complemented
7	C₂×#19099163	C₂	1	4	yes	maximal, complemented
8	#540×D₇₉	C₂	1	32	yes	maximal, direct product factor
9	C₂×#127×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#125×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#123×D₇₉	C₂	1	4	yes	maximal, complemented
12	C₂×#121×D₇₉	C₂	1	4	yes	maximal, complemented
13	C₂×#121×D₇₉	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×D₄×D₇₉	C₂	1	2	yes	maximal, complemented
15	C₂×#117×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#540×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×D₄×D₇₉	C₂²	1	2	yes	—
18	C₂²×D₄×D₇₉	C₂²	1	4	yes	—
19	C₂²×D₄×D₇₉	C₂²	1	4	yes	—
20	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₇₉	C₂²	1	4	yes	—
22	#19099169	C₂²	1	16	yes	complemented
23	#19099168	C₂²	1	16	yes	complemented
24	#19099167	C₂²	1	16	yes	complemented
25	#19099166	C₂²	1	32	yes	complemented
26	#19099165	C₂²	1	64	yes	complemented
27	#19099164	C₂²	1	32	yes	complemented
28	#19099163	C₂²	1	64	yes	complemented
29	C₂×#14579158	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14579157	C₂²	1	4	yes	complemented
31	C₂×#14579157	C₂²	1	2	yes	complemented
32	#127×D₇₉	C₂²	1	16	yes	complemented
33	C₂×#14579153	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14579152	C₂²	1	2	yes	complemented
35	C₂×#14579151	C₂²	1	4	yes	complemented
36	#125×D₇₉	C₂²	1	16	yes	complemented
37	C₂×#14579146	C₂²	1	4	yes	complemented
38	C₂×#14579146	C₂²	1	4	yes	complemented
39	C₂×#14579145	C₂²	1	4	yes	complemented
40	C₂×#14579144	C₂²	1	4	yes	complemented
41	C₂×#14579143	C₂²	1	4	yes	complemented
42	C₂×#14579143	C₂²	1	4	yes	complemented
43	C₂×#14579142	C₂²	1	4	yes	complemented
44	#123×D₇₉	C₂²	1	64	yes	complemented
45	C₂×#14579136	C₂²	1	2	yes	complemented
46	C₂×#14579136	C₂²	1	4	yes	complemented
47	C₂×#14579135	C₂²	1	4	yes	complemented
48	C₂×#14579135	C₂²	1	2	yes	complemented
49	C₂×#14579134	C₂²	1	4	yes	complemented
50	C₂×#14579134	C₂²	1	4	yes	complemented
51	C₂×#14579134	C₂²	1	4	yes	complemented
52	C₂×#14579133	C₂²	1	4	yes	complemented
53	C₂×#14579133	C₂²	1	4	yes	complemented
54	C₂×#14579133	C₂²	1	4	yes	complemented
55	C₂×#14579132	C₂²	1	4	yes	complemented
56	C₂×#14579132	C₂²	1	2	yes	complemented
57	#121×D₇₉	C₂²	1	64	yes	complemented
58	#121×D₇₉	C₂²	1	32	yes	complemented
59	C₂×C₄×D₃₁₆	C₂²	1	2	yes	complemented
60	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
61	C₂×#14579123	C₂²	1	2	yes	complemented
62	C₂×C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
63	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
64	C₄×D₄×D₇₉	C₂²	1	32	yes	complemented
65	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
66	C₂×#14579119	C₂²	1	2	yes	complemented
67	C₂×#14579118	C₂²	1	1	yes	characteristic, complemented
68	C₂×#14579118	C₂²	1	1	yes	characteristic, complemented
69	C₂×#14579117	C₂²	1	2	yes	complemented
70	#117×D₇₉	C₂²	1	16	yes	complemented
71	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
72	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
73	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
74	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
75	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
76	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
77	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
78	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
79	#540×C₇₉	C₂²	1	16	yes	complemented
80	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
82	C₂×#123×C₇₉	C₂²	1	4	yes	complemented
83	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
84	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
85	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
86	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
87	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
88	C₂⁴×D₇₉	C₂³	1	4	yes	—
89	C₂²×D₃₁₆	C₂³	1	2	yes	—
90	C₂²×D₃₁₆	C₂³	1	4	yes	—
91	C₂²×D₃₁₆	C₂³	1	4	yes	—
92	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
93	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
94	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
95	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
96	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
97	C₂×D₄×D₇₉	—	2	16	no	—
98	C₂×D₄×D₇₉	—	4	16	no	—
99	C₂×D₄×D₇₉	—	4	16	no	—
100	C₂×D₄×D₇₉	C₂³	1	16	yes	—
101	C₂×D₄×D₇₉	C₂³	1	32	yes	—
102	C₂×D₄×D₇₉	C₂³	1	32	yes	—
103	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
104	C₂³×Dic₇₉	C₂³	1	4	yes	—
105	C₂²×C₄×D₇₉	—	2	8	no	—
106	C₂²×C₄×D₇₉	—	4	16	no	—
107	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
108	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
109	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
111	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
112	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
113	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×D₇₉	C₂³	1	32	yes	—
115	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
116	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
117	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
118	#14579158	C₂³	1	8	yes	complemented
119	#14579157	C₂³	1	32	yes	complemented
120	#14579157	C₂³	1	16	yes	complemented
121	#14579153	C₂³	1	8	yes	complemented
122	#14579152	C₂³	1	16	yes	complemented
123	#14579151	C₂³	1	32	yes	complemented
124	#14579146	C₂³	1	32	yes	complemented
125	#14579146	C₂³	1	32	yes	complemented
126	#14579145	C₂³	1	32	yes	complemented
127	#14579144	C₂³	1	32	yes	complemented
128	#14579143	C₂³	1	32	yes	complemented
129	#14579143	C₂³	1	32	yes	complemented
130	#14579142	C₂³	1	32	yes	complemented
131	#14579136	C₂³	1	16	yes	complemented
132	#14579136	C₂³	1	32	yes	complemented
133	#14579135	C₂³	1	32	yes	complemented
134	#14579135	C₂³	1	16	yes	complemented
135	#14579134	C₂³	1	32	yes	complemented
136	#14579134	C₂³	1	32	yes	complemented
137	#14579134	C₂³	1	32	yes	complemented
138	#14579133	C₂³	1	32	yes	complemented
139	#14579133	C₂³	1	32	yes	complemented
140	#14579133	C₂³	1	32	yes	complemented
141	#14579132	C₂³	1	32	yes	complemented
142	#14579132	C₂³	1	16	yes	complemented
143	C₄×D₃₁₆	C₂³	1	16	yes	complemented
144	D₄×Dic₇₉	C₂³	1	16	yes	complemented
145	#14579123	C₂³	1	16	yes	complemented
146	C₄×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
147	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
148	#14579120	C₂³	1	8	yes	complemented
149	#14579119	C₂³	1	16	yes	complemented
150	#14579118	C₂³	1	8	yes	complemented
151	#14579118	C₂³	1	8	yes	complemented
152	#14579117	C₂³	1	16	yes	complemented
153	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
154	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
155	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
156	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
157	C₂×Dic₇₉⋊C₄	C₂³	1	2	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	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
162	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
163	C₄⋊C₄×D₇₉	C₂³	1	32	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	2	yes	—
168	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	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	16	yes	—
174	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
175	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
176	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
177	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
178	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
179	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
180	C₄²×D₇₉	C₂³	1	8	yes	—
181	C₄²×D₇₉	C₂³	1	8	yes	—
182	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
183	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
184	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
185	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
186	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
187	#127×C₇₉	C₂³	1	8	yes	complemented
188	#125×C₇₉	C₂³	1	8	yes	complemented
189	#123×C₇₉	C₂³	1	32	yes	complemented
190	#121×C₇₉	C₂³	1	32	yes	complemented
191	#121×C₇₉	C₂³	1	16	yes	complemented
192	C₄×D₄×C₇₉	C₂³	1	16	yes	complemented
193	#117×C₇₉	C₂³	1	8	yes	complemented
194	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
197	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
200	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
202	C₂³×D₇₉	—	2	4	no	—
203	C₂³×D₇₉	—	2	16	no	—
204	C₂³×D₇₉	—	2	16	no	—
205	C₂³×D₇₉	—	2	8	no	—
206	C₂³×D₇₉	—	2	16	no	—
207	C₂³×D₇₉	C₂⁴	1	4	yes	—
208	C₂³×D₇₉	C₂⁴	1	16	yes	—
209	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
210	C₂³×D₇₉	C₂⁴	1	4	yes	—
211	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
212	C₂×D₃₁₆	—	2	8	no	—
213	C₂×D₃₁₆	—	4	8	no	—
214	C₂×D₃₁₆	—	4	8	no	—
215	C₂×D₃₁₆	C₂⁴	1	8	yes	—
216	C₂×D₃₁₆	C₂⁴	1	16	yes	—
217	C₂×D₃₁₆	C₂⁴	1	16	yes	—
218	C₂×C₂²⋊D₇₉	—	2	16	no	—
219	C₂×C₂²⋊D₇₉	—	4	8	no	—
220	C₂×C₂²⋊D₇₉	—	4	8	no	—
221	C₂×C₂²⋊D₇₉	—	4	8	no	—
222	C₂×C₂²⋊D₇₉	—	4	8	no	—
223	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
224	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
225	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
226	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
227	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
228	D₄×D₇₉	—	2	64	no	—
229	D₄×D₇₉	—	4	64	no	—
230	D₄×D₇₉	—	4	64	no	—
231	C₂²×Dic₇₉	—	2	4	no	—
232	C₂²×Dic₇₉	—	4	8	no	—
233	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
234	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
235	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
236	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
237	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
238	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
239	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×D₇₉	—	2	4	no	—
241	C₂×C₄×D₇₉	—	2	32	no	—
242	C₂×C₄×D₇₉	—	2	4	no	—
243	C₂×C₄×D₇₉	—	2	8	no	—
244	C₂×C₄×D₇₉	—	2	16	no	—
245	C₂×C₄×D₇₉	—	2	8	no	—
246	C₂×C₄×D₇₉	—	2	4	no	—
247	C₂×C₄×D₇₉	—	4	8	no	—
248	C₂×C₄×D₇₉	—	4	8	no	—
249	C₂×C₄×D₇₉	—	4	64	no	—
250	C₂×C₄×D₇₉	#41	1	8	yes	—
251	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
252	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
253	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
254	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
255	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
256	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
257	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
258	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
259	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
260	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
261	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
262	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
263	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
264	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
265	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
266	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
267	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
268	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
269	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
270	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
271	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
272	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
273	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
274	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
275	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
276	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
277	C₄×Dic₇₉	C₂⁴	1	8	yes	—
278	C₄×Dic₇₉	C₂⁴	1	8	yes	—
279	C₄×Dic₇₉	C₂⁴	1	4	yes	—
280	C₄×Dic₇₉	C₂⁴	1	4	yes	—
281	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
282	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
283	C₂×D₄×C₇₉	—	2	8	no	—
284	C₂×D₄×C₇₉	—	4	8	no	—
285	C₂×D₄×C₇₉	—	4	8	no	—
286	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
287	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
288	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
289	C₂²×C₄×C₇₉	—	2	4	no	—
290	C₂²×C₄×C₇₉	—	4	8	no	—
291	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	—
297	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
301	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
303	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
304	C₄²×C₇₉	C₂⁴	1	4	yes	—
305	C₄²×C₇₉	C₂⁴	1	4	yes	—
306	C₂³×C₇₉	—	2	2	no	—
307	C₂³×C₇₉	—	2	8	no	—
308	C₂³×C₇₉	—	2	8	no	—
309	C₂³×C₇₉	—	2	4	no	—
310	C₂³×C₇₉	—	2	8	no	—
311	C₂³×C₇₉	C₂⁵	1	8	yes	—
312	C₂³×C₇₉	C₂⁵	1	2	yes	—
313	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
314	C₂²×D₇₉	—	2	2	no	—
315	C₂²×D₇₉	—	2	8	no	—
316	C₂²×D₇₉	—	2	8	no	—
317	C₂²×D₇₉	—	2	4	no	—
318	C₂²×D₇₉	—	2	8	no	—
319	C₂²×D₇₉	—	2	8	no	—
320	C₂²×D₇₉	—	2	32	no	—
321	C₂²×D₇₉	—	2	32	no	—
322	C₂²×D₇₉	—	2	16	no	—
323	C₂²×D₇₉	—	2	32	no	—
324	C₂²×D₇₉	—	4	16	no	—
325	C₂²×D₇₉	—	4	64	no	—
326	C₂²×D₇₉	C₂×#41	1	4	yes	—
327	C₂²×D₇₉	H(5,𝔽₂)	1	8	yes	—
328	C₂²×D₇₉	C₂⁵	1	8	yes	—
329	C₂²×D₇₉	C₂⁵	1	2	yes	—
330	C₂²×D₇₉	C₂⁵	1	2	yes	—
331	D₄×C₇₉	—	2	16	no	—
332	D₄×C₇₉	—	4	16	no	—
333	D₄×C₇₉	—	4	16	no	—
334	C₂×C₄×C₇₉	—	2	2	no	—
335	C₂×C₄×C₇₉	—	2	4	no	—
336	C₂×C₄×C₇₉	—	2	8	no	—
337	C₂×C₄×C₇₉	—	2	4	no	—
338	C₂×C₄×C₇₉	—	2	8	no	—
339	C₂×C₄×C₇₉	—	4	16	no	—
340	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
341	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
342	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
343	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
344	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
345	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
346	C₂²⋊D₇₉	—	2	32	no	—
347	C₂²⋊D₇₉	—	4	16	no	—
348	C₂²⋊D₇₉	—	4	16	no	—
349	C₂²⋊D₇₉	—	4	16	no	—
350	C₂²⋊D₇₉	—	4	16	no	—
351	C₂×Dic₇₉	—	2	2	no	—
352	C₂×Dic₇₉	—	2	4	no	—
353	C₂×Dic₇₉	—	2	8	no	—
354	C₂×Dic₇₉	—	2	4	no	—
355	C₂×Dic₇₉	—	2	8	no	—
356	C₂×Dic₇₉	—	4	16	no	—
357	C₂×Dic₇₉	C₂×#41	1	4	yes	—
358	C₂×Dic₇₉	C₂⁵	1	4	yes	—
359	C₂×Dic₇₉	C₂⁵	1	4	yes	—
360	C₂×Dic₇₉	C₂⁵	1	2	yes	—
361	C₂×Dic₇₉	C₂⁵	1	8	yes	—
362	C₂×Dic₇₉	C₂⁵	1	2	yes	—
363	D₃₁₆	—	2	16	no	—
364	D₃₁₆	—	4	16	no	—
365	D₃₁₆	—	4	16	no	—
366	C₄×D₇₉	—	2	8	no	—
367	C₄×D₇₉	—	2	16	no	—
368	C₄×D₇₉	—	2	32	no	—
369	C₄×D₇₉	—	2	16	no	—
370	C₄×D₇₉	—	2	8	no	—
371	C₄×D₇₉	—	2	8	no	—
372	C₄×D₇₉	—	4	16	no	—
373	C₄×D₇₉	—	4	16	no	—
374	C₄×D₇₉	C₂×#41	1	16	yes	—
375	C₂²×C₇₉	—	2	8	no	—
376	C₂²×C₇₉	—	2	2	no	—
377	C₂²×C₇₉	—	2	8	no	—
378	C₂²×C₇₉	—	2	4	no	—
379	C₂²×C₇₉	—	2	8	no	—
380	C₂²×C₇₉	—	4	4	no	—
381	C₂²×C₇₉	—	4	16	no	—
382	C₂²×C₇₉	C₂²×#41	1	2	yes	—
383	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
384	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
385	C₂×D₇₉	—	2	8	no	—
386	C₂×D₇₉	—	2	2	no	—
387	C₂×D₇₉	—	2	8	no	—
388	C₂×D₇₉	—	2	4	no	—
389	C₂×D₇₉	—	2	8	no	—
390	C₂×D₇₉	—	4	4	no	—
391	C₂×D₇₉	—	4	16	no	—
392	C₂×D₇₉	—	4	16	no	—
393	C₂×D₇₉	—	4	64	no	—
394	C₂×D₇₉	#540	1	16	yes	direct product factor
395	C₂×D₇₉	C₂²×#41	1	4	yes	—
396	C₂×D₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
397	C₄×C₇₉	—	2	2	no	—
398	C₄×C₇₉	—	2	4	no	—
399	C₄×C₇₉	—	2	8	no	—
400	C₄×C₇₉	—	2	4	no	—
401	C₄×C₇₉	C₂²×#41	1	4	yes	—
402	Dic₇₉	—	2	2	no	—
403	Dic₇₉	—	2	4	no	—
404	Dic₇₉	—	2	8	no	—
405	Dic₇₉	—	2	4	no	—
406	Dic₇₉	C₂²×#41	1	4	yes	—
407	C₂²×#540	—	79	1	no	maximal, Sylow
408	C₂×C₇₉	—	4	8	no	—
409	C₂×C₇₉	—	4	2	no	—
410	C₂×C₇₉	C₂×#540	1	4	yes	complemented
411	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
412	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
413	D₇₉	—	4	8	no	—
414	D₇₉	—	4	2	no	—
415	D₇₉	C₂×#540	1	8	yes	direct product factor
416	C₂×#540	—	79	32	no	—
417	C₂×#540	—	79	1	no	—
418	C₂×#540	—	79	1	no	—
419	C₂×#540	—	79	4	no	—
420	C₂×#540	—	79	4	no	—
421	C₂×#540	—	79	2	no	—
422	C₂×#540	—	79	2	no	—
423	C₂×#540	—	79	1	no	—
424	C₂×#540	D₇₉	1	1	yes	characteristic, direct product factor
425	C₂²×#127	—	79	1	no	—
426	C₂²×#125	—	79	1	no	—
427	C₂²×#123	—	79	4	no	—
428	C₂²×#121	—	79	4	no	—
429	C₂²×#121	—	79	2	no	—
430	C₂²×C₄×D₄	—	79	2	no	—
431	C₂²×#117	—	79	1	no	—
432	C₇₉	C₂²×#540	1	1	yes	characteristic, complemented, Sylow
433	C₂³×D₄	—	79	4	no	—
434	C₂³×D₄	—	79	4	no	—
435	C₂³×D₄	—	79	2	no	—
436	C₂⁴×C₄	—	79	4	no	—
437	C₂⁴×C₄	—	79	1	no	—
438	#540	—	79	16	no	—
439	#540	—	79	16	no	—
440	#540	—	79	64	no	—
441	#540	—	79	64	no	—
442	#540	—	79	32	no	—
443	#540	—	79	32	no	—
444	#540	—	79	16	no	—
445	#540	C₂×D₇₉	1	16	yes	direct product factor
446	C₂×#127	—	79	2	no	—
447	C₂×#127	—	79	4	no	—
448	C₂×#127	—	79	16	no	—
449	C₂×#127	—	79	1	no	—
450	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
451	C₂×#125	—	79	16	no	—
452	C₂×#125	—	79	4	no	—
453	C₂×#125	—	79	2	no	—
454	C₂×#125	—	79	1	no	—
455	C₂×#125	C₂×D₇₉	1	1	yes	characteristic, complemented
456	C₂×#123	—	79	4	no	—
457	C₂×#123	—	79	4	no	—
458	C₂×#123	—	79	64	no	—
459	C₂×#123	—	79	4	no	—
460	C₂×#123	—	79	4	no	—
461	C₂×#123	—	79	4	no	—
462	C₂×#123	—	79	4	no	—
463	C₂×#123	—	79	4	no	—
464	C₂×#123	C₂×D₇₉	1	4	yes	complemented
465	C₂×#121	—	79	4	no	—
466	C₂×#121	—	79	2	no	—
467	C₂×#121	—	79	4	no	—
468	C₂×#121	—	79	4	no	—
469	C₂×#121	—	79	4	no	—
470	C₂×#121	—	79	4	no	—
471	C₂×#121	—	79	2	no	—
472	C₂×#121	—	79	64	no	—
473	C₂×#121	—	79	32	no	—
474	C₂×#121	—	79	4	no	—
475	C₂×#121	—	79	2	no	—
476	C₂×#121	—	79	4	no	—
477	C₂×#121	—	79	4	no	—
478	C₂×#121	—	79	4	no	—
479	C₂×#121	C₂×D₇₉	1	4	yes	complemented
480	C₂×#121	C₂×D₇₉	1	2	yes	complemented
481	C₂×C₄×D₄	—	79	2	no	—
482	C₂×C₄×D₄	—	79	4	no	—
483	C₂×C₄×D₄	—	79	32	no	—
484	C₂×C₄×D₄	—	79	2	no	—
485	C₂×C₄×D₄	—	79	4	no	—
486	C₂×C₄×D₄	—	79	2	no	—
487	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	complemented
488	C₂×#117	—	79	1	no	—
489	C₂×#117	—	79	16	no	—
490	C₂×#117	—	79	2	no	—
491	C₂×#117	—	79	2	no	—
492	C₂×#117	—	79	1	no	—
493	C₂×#117	—	79	1	no	—
494	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
495	C₂²×C₄⋊C₄	—	79	2	no	—
496	C₂²×C₄⋊C₄	—	79	2	no	—
497	C₂²×C₄⋊C₄	—	79	4	no	—
498	C₂²×C₂²⋊C₄	—	79	2	no	—
499	C₂²×C₂²⋊C₄	—	79	4	no	—
500	C₂²×C₂²⋊C₄	—	79	4	no	—
501	C₂²×C₄²	—	79	1	no	—
502	C₂²×C₄²	—	79	1	no	—
503	C₂⁵	—	79	4	no	—
504	C₂⁵	—	79	1	no	—
505	C₂²×D₄	—	316	16	no	—
506	C₂²×D₄	—	316	16	no	—
507	C₂²×D₄	—	79	4	no	—
508	C₂²×D₄	—	79	4	no	—
509	C₂²×D₄	—	79	4	no	—
510	C₂²×D₄	—	79	4	no	—
511	C₂²×D₄	—	79	32	no	—
512	C₂²×D₄	—	79	32	no	—
513	C₂²×D₄	—	79	4	no	—
514	C₂²×D₄	—	79	16	no	—
515	C₂²×D₄	—	79	4	no	—
516	C₂²×D₄	—	79	4	no	—
517	C₂²×D₄	—	79	2	no	—
518	C₂²×D₄	—	158	16	no	—
519	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
520	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
521	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
522	C₂³×C₄	—	316	16	no	—
523	C₂³×C₄	—	79	4	no	—
524	C₂³×C₄	—	79	4	no	—
525	C₂³×C₄	—	79	4	no	—
526	C₂³×C₄	—	79	32	no	—
527	C₂³×C₄	—	79	1	no	—
528	C₂³×C₄	—	79	1	no	—
529	C₂³×C₄	—	79	1	no	—
530	C₂³×C₄	—	79	2	no	—
531	C₂³×C₄	—	79	4	no	—
532	C₂³×C₄	—	79	2	no	—
533	C₂³×C₄	—	79	1	no	—
534	C₂³×C₄	—	79	8	no	—
535	C₂³×C₄	—	79	1	no	—
536	C₂³×C₄	—	158	8	no	—
537	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
538	C₂³×C₄	C₂²×D₇₉	1	4	yes	—
539	#127	—	79	16	no	—
540	#127	—	79	32	no	—
541	#127	—	79	8	no	—
542	#127	C₂²×D₇₉	1	8	yes	complemented
543	#125	—	79	32	no	—
544	#125	—	79	16	no	—
545	#125	—	79	8	no	—
546	#125	C₂²×D₇₉	1	8	yes	complemented
547	#123	—	79	32	no	—
548	#123	—	79	32	no	—
549	#123	—	79	32	no	—
550	#123	—	79	32	no	—
551	#123	—	79	32	no	—
552	#123	—	79	32	no	—
553	#123	—	79	32	no	—
554	#123	C₂²×D₇₉	1	32	yes	complemented
555	#121	—	79	32	no	—
556	#121	—	79	16	no	—
557	#121	—	79	32	no	—
558	#121	—	79	32	no	—
559	#121	—	79	32	no	—
560	#121	—	79	32	no	—
561	#121	—	79	16	no	—
562	#121	—	79	32	no	—
563	#121	—	79	16	no	—
564	#121	—	79	32	no	—
565	#121	—	79	32	no	—
566	#121	—	79	32	no	—
567	#121	C₂²×D₇₉	1	32	yes	complemented
568	#121	C₂²×D₇₉	1	16	yes	complemented
569	C₄×D₄	—	79	16	no	—
570	C₄×D₄	—	79	32	no	—
571	C₄×D₄	—	79	16	no	—
572	C₄×D₄	—	79	32	no	—
573	C₄×D₄	—	79	16	no	—
574	C₄×D₄	C₂²×D₇₉	1	16	yes	complemented
575	#117	—	79	8	no	—
576	#117	—	79	16	no	—
577	#117	—	79	16	no	—
578	#117	—	79	8	no	—
579	#117	—	79	8	no	—
580	#117	C₂²×D₇₉	1	8	yes	complemented
581	C₂×C₄⋊C₄	—	79	2	no	—
582	C₂×C₄⋊C₄	—	79	2	no	—
583	C₂×C₄⋊C₄	—	79	2	no	—
584	C₂×C₄⋊C₄	—	79	4	no	—
585	C₂×C₄⋊C₄	—	79	2	no	—
586	C₂×C₄⋊C₄	—	79	4	no	—
587	C₂×C₄⋊C₄	—	79	4	no	—
588	C₂×C₄⋊C₄	—	79	4	no	—
589	C₂×C₄⋊C₄	—	79	16	no	—
590	C₂×C₄⋊C₄	—	79	16	no	—
591	C₂×C₄⋊C₄	—	79	32	no	—
592	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
595	C₂×C₂²⋊C₄	—	79	2	no	—
596	C₂×C₂²⋊C₄	—	79	4	no	—
597	C₂×C₂²⋊C₄	—	79	4	no	—
598	C₂×C₂²⋊C₄	—	79	2	no	—
599	C₂×C₂²⋊C₄	—	79	2	no	—
600	C₂×C₂²⋊C₄	—	79	4	no	—
601	C₂×C₂²⋊C₄	—	79	4	no	—
602	C₂×C₂²⋊C₄	—	79	4	no	—
603	C₂×C₂²⋊C₄	—	79	4	no	—
604	C₂×C₂²⋊C₄	—	79	16	no	—
605	C₂×C₂²⋊C₄	—	79	32	no	—
606	C₂×C₂²⋊C₄	—	79	32	no	—
607	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
610	C₂×C₄²	—	79	2	no	—
611	C₂×C₄²	—	79	1	no	—
612	C₂×C₄²	—	79	2	no	—
613	C₂×C₄²	—	79	1	no	—
614	C₂×C₄²	—	79	8	no	—
615	C₂×C₄²	—	79	8	no	—
616	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
617	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
618	C₂⁴	—	79	1	no	—
619	C₂⁴	—	79	16	no	—
620	C₂⁴	—	79	4	no	—
621	C₂⁴	—	79	4	no	—
622	C₂⁴	—	79	1	no	—
623	C₂⁴	—	158	16	no	—
624	C₂⁴	—	158	4	no	—
625	C₂⁴	—	158	16	no	—
626	C₂⁴	—	158	8	no	—
627	C₂⁴	—	158	16	no	—
628	C₂⁴	C₂³×D₇₉	1	4	yes	—
629	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
630	C₂×D₄	—	2	8	no	—
631	C₂×D₄	—	4	8	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	316	8	no	—
634	C₂×D₄	—	316	8	no	—
635	C₂×D₄	—	316	64	no	—
636	C₂×D₄	—	316	64	no	—
637	C₂×D₄	—	316	8	no	—
638	C₂×D₄	—	316	8	no	—
639	C₂×D₄	—	316	8	no	—
640	C₂×D₄	—	316	8	no	—
641	C₂×D₄	—	79	16	no	—
642	C₂×D₄	—	79	16	no	—
643	C₂×D₄	—	79	16	no	—
644	C₂×D₄	—	79	16	no	—
645	C₂×D₄	—	79	16	no	—
646	C₂×D₄	—	79	16	no	—
647	C₂×D₄	—	79	16	no	—
648	C₂×D₄	—	79	8	no	—
649	C₂×D₄	—	158	64	no	—
650	C₂×D₄	—	158	16	no	—
651	C₂×D₄	—	158	8	no	—
652	C₂×D₄	C₂³×D₇₉	1	8	yes	—
653	C₂×D₄	C₂³×D₇₉	1	16	yes	—
654	C₂×D₄	C₂³×D₇₉	1	16	yes	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	4	8	no	—
657	C₂²×C₄	—	316	8	no	—
658	C₂²×C₄	—	316	8	no	—
659	C₂²×C₄	—	316	64	no	—
660	C₂²×C₄	—	316	8	no	—
661	C₂²×C₄	—	79	16	no	—
662	C₂²×C₄	—	79	16	no	—
663	C₂²×C₄	—	79	16	no	—
664	C₂²×C₄	—	79	1	no	—
665	C₂²×C₄	—	79	8	no	—
666	C₂²×C₄	—	79	4	no	—
667	C₂²×C₄	—	79	4	no	—
668	C₂²×C₄	—	79	2	no	—
669	C₂²×C₄	—	79	2	no	—
670	C₂²×C₄	—	79	1	no	—
671	C₂²×C₄	—	79	4	no	—
672	C₂²×C₄	—	79	8	no	—
673	C₂²×C₄	—	79	8	no	—
674	C₂²×C₄	—	79	4	no	—
675	C₂²×C₄	—	79	16	no	—
676	C₂²×C₄	—	79	4	no	—
677	C₂²×C₄	—	79	4	no	—
678	C₂²×C₄	—	158	4	no	—
679	C₂²×C₄	—	158	32	no	—
680	C₂²×C₄	—	158	8	no	—
681	C₂²×C₄	—	158	16	no	—
682	C₂²×C₄	—	158	4	no	—
683	C₂²×C₄	—	158	8	no	—
684	C₂²×C₄	—	158	4	no	—
685	C₂²×C₄	—	158	4	no	—
686	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
687	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
688	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
689	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
690	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
691	C₂²×C₄	C₂³×D₇₉	1	16	yes	—
692	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
693	C₄⋊C₄	—	79	8	no	—
694	C₄⋊C₄	—	79	8	no	—
695	C₄⋊C₄	—	79	16	no	—
696	C₄⋊C₄	—	79	16	no	—
697	C₄⋊C₄	—	79	16	no	—
698	C₄⋊C₄	—	79	8	no	—
699	C₄⋊C₄	—	79	8	no	—
700	C₄⋊C₄	—	79	16	no	—
701	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
702	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
703	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
704	C₂²⋊C₄	—	79	8	no	—
705	C₂²⋊C₄	—	79	16	no	—
706	C₂²⋊C₄	—	79	16	no	—
707	C₂²⋊C₄	—	79	8	no	—
708	C₂²⋊C₄	—	79	8	no	—
709	C₂²⋊C₄	—	79	16	no	—
710	C₂²⋊C₄	—	79	16	no	—
711	C₂²⋊C₄	—	79	16	no	—
712	C₂²⋊C₄	—	79	16	no	—
713	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
714	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
715	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
716	C₄²	—	79	8	no	—
717	C₄²	—	79	4	no	—
718	C₄²	—	79	8	no	—
719	C₄²	—	79	4	no	—
720	C₄²	C₂³×D₇₉	1	4	yes	—
721	C₄²	C₂³×D₇₉	1	4	yes	—
722	C₂³	—	2	8	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	8	no	—
727	C₂³	—	316	64	no	—
728	C₂³	—	316	16	no	—
729	C₂³	—	79	8	no	—
730	C₂³	—	79	2	no	—
731	C₂³	—	79	4	no	—
732	C₂³	—	79	2	no	—
733	C₂³	—	79	8	no	—
734	C₂³	—	158	32	no	—
735	C₂³	—	158	8	no	—
736	C₂³	—	158	32	no	—
737	C₂³	—	158	16	no	—
738	C₂³	—	158	32	no	—
739	C₂³	—	158	8	no	—
740	C₂³	—	158	8	no	—
741	C₂³	—	158	4	no	—
742	C₂³	—	158	2	no	—
743	C₂³	—	158	8	no	—
744	C₂³	C₂⁴×D₇₉	1	2	yes	—
745	C₂³	C₂⁴×D₇₉	1	8	yes	—
746	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
747	D₄	—	2	16	no	—
748	D₄	—	4	16	no	—
749	D₄	—	4	16	no	—
750	D₄	—	316	16	no	—
751	D₄	—	316	16	no	—
752	D₄	—	316	16	no	—
753	D₄	—	316	16	no	—
754	D₄	—	316	16	no	—
755	D₄	—	316	16	no	—
756	D₄	—	158	32	no	—
757	D₄	—	158	16	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	4	16	no	—
764	C₂×C₄	—	316	16	no	—
765	C₂×C₄	—	316	16	no	—
766	C₂×C₄	—	316	16	no	—
767	C₂×C₄	—	79	2	no	—
768	C₂×C₄	—	79	4	no	—
769	C₂×C₄	—	79	16	no	—
770	C₂×C₄	—	79	4	no	—
771	C₂×C₄	—	79	4	no	—
772	C₂×C₄	—	79	2	no	—
773	C₂×C₄	—	79	8	no	—
774	C₂×C₄	—	158	8	no	—
775	C₂×C₄	—	158	16	no	—
776	C₂×C₄	—	158	32	no	—
777	C₂×C₄	—	158	8	no	—
778	C₂×C₄	—	158	16	no	—
779	C₂×C₄	—	158	8	no	—
780	C₂×C₄	—	158	4	no	—
781	C₂×C₄	—	158	8	no	—
782	C₂×C₄	—	158	4	no	—
783	C₂×C₄	—	158	2	no	—
784	C₂×C₄	—	158	8	no	—
785	C₂×C₄	#41×D₇₉	1	4	yes	—
786	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
787	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
788	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
789	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
790	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	8	no	—
793	C₂²	—	2	8	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	2	8	no	—
796	C₂²	—	4	16	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	316	64	no	—
799	C₂²	—	316	16	no	—
800	C₂²	—	316	16	no	—
801	C₂²	—	316	4	no	—
802	C₂²	—	79	4	no	—
803	C₂²	—	79	8	no	—
804	C₂²	—	79	16	no	—
805	C₂²	—	158	2	no	—
806	C₂²	—	158	8	no	—
807	C₂²	—	158	8	no	—
808	C₂²	—	158	4	no	—
809	C₂²	—	158	8	no	—
810	C₂²	C₂×#41×D₇₉	1	2	yes	—
811	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
812	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
813	C₄	—	2	2	no	—
814	C₄	—	2	4	no	—
815	C₄	—	2	8	no	—
816	C₄	—	2	4	no	—
817	C₄	—	79	4	no	—
818	C₄	—	158	2	no	—
819	C₄	—	158	4	no	—
820	C₄	—	158	8	no	—
821	C₄	—	158	4	no	—
822	C₄	C₂×#41×D₇₉	1	4	yes	—
823	C₂	—	4	2	no	—
824	C₂	—	4	8	no	—
825	C₂	—	316	2	no	—
826	C₂	—	316	8	no	—
827	C₂	—	79	8	no	—
828	C₂	#540×D₇₉	1	4	yes	direct product factor
829	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
830	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#540×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#540	D₇₉
hypocenter	C₇₉	C₂²×#540
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#540

Complements

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

N	H ≅ G/N	type
1. C₂×#19099169	C₂	semidirect
2. C₂×#19099168	C₂	semidirect
3. C₂×#19099167	C₂	semidirect
4. C₂×#19099166	C₂	semidirect
5. C₂×#19099165	C₂	semidirect
6. C₂×#19099164	C₂	semidirect
7. C₂×#19099163	C₂	semidirect
8. #540×D₇₉	C₂	direct (N × H)
9. C₂×#127×D₇₉	C₂	semidirect
10. C₂×#125×D₇₉	C₂	semidirect
11. C₂×#123×D₇₉	C₂	semidirect
12. C₂×#121×D₇₉	C₂	semidirect
13. C₂×#121×D₇₉	C₂	semidirect
14. C₂×C₄×D₄×D₇₉	C₂	semidirect
15. C₂×#117×D₇₉	C₂	semidirect
16. C₂×#540×C₇₉	C₂	semidirect
22. #19099169	C₂²	semidirect
23. #19099168	C₂²	semidirect
24. #19099167	C₂²	semidirect
25. #19099166	C₂²	semidirect
26. #19099165	C₂²	semidirect
27. #19099164	C₂²	semidirect
28. #19099163	C₂²	semidirect
29. C₂×#14579158	C₂²	semidirect
30. C₂×#14579157	C₂²	semidirect
31. C₂×#14579157	C₂²	semidirect
32. #127×D₇₉	C₂²	semidirect
33. C₂×#14579153	C₂²	semidirect
34. C₂×#14579152	C₂²	semidirect
35. C₂×#14579151	C₂²	semidirect
36. #125×D₇₉	C₂²	semidirect
37. C₂×#14579146	C₂²	semidirect
38. C₂×#14579146	C₂²	semidirect
39. C₂×#14579145	C₂²	semidirect
40. C₂×#14579144	C₂²	semidirect
41. C₂×#14579143	C₂²	semidirect
42. C₂×#14579143	C₂²	semidirect
43. C₂×#14579142	C₂²	semidirect
44. #123×D₇₉	C₂²	semidirect
45. C₂×#14579136	C₂²	semidirect
46. C₂×#14579136	C₂²	semidirect
47. C₂×#14579135	C₂²	semidirect
48. C₂×#14579135	C₂²	semidirect
49. C₂×#14579134	C₂²	semidirect
50. C₂×#14579134	C₂²	semidirect
51. C₂×#14579134	C₂²	semidirect
52. C₂×#14579133	C₂²	semidirect
53. C₂×#14579133	C₂²	semidirect
54. C₂×#14579133	C₂²	semidirect
55. C₂×#14579132	C₂²	semidirect
56. C₂×#14579132	C₂²	semidirect
57. #121×D₇₉	C₂²	semidirect
58. #121×D₇₉	C₂²	semidirect
59. C₂×C₄×D₃₁₆	C₂²	semidirect
60. C₂×D₄×Dic₇₉	C₂²	semidirect
61. C₂×#14579123	C₂²	semidirect
62. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
63. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
64. C₄×D₄×D₇₉	C₂²	semidirect
65. C₂×#14579120	C₂²	semidirect
66. C₂×#14579119	C₂²	semidirect
67. C₂×#14579118	C₂²	semidirect
68. C₂×#14579118	C₂²	semidirect
69. C₂×#14579117	C₂²	semidirect
70. #117×D₇₉	C₂²	semidirect
79. #540×C₇₉	C₂²	semidirect
80. C₂×#127×C₇₉	C₂²	semidirect
81. C₂×#125×C₇₉	C₂²	semidirect
82. C₂×#123×C₇₉	C₂²	semidirect
83. C₂×#121×C₇₉	C₂²	semidirect
84. C₂×#121×C₇₉	C₂²	semidirect
85. C₂×C₄×D₄×C₇₉	C₂²	semidirect
86. C₂×#117×C₇₉	C₂²	semidirect
118. #14579158	C₂³	semidirect
119. #14579157	C₂³	semidirect
120. #14579157	C₂³	semidirect
121. #14579153	C₂³	semidirect
122. #14579152	C₂³	semidirect
123. #14579151	C₂³	semidirect
124. #14579146	C₂³	semidirect
125. #14579146	C₂³	semidirect
126. #14579145	C₂³	semidirect
127. #14579144	C₂³	semidirect
128. #14579143	C₂³	semidirect
129. #14579143	C₂³	semidirect
130. #14579142	C₂³	semidirect
131. #14579136	C₂³	semidirect
132. #14579136	C₂³	semidirect
133. #14579135	C₂³	semidirect
134. #14579135	C₂³	semidirect
135. #14579134	C₂³	semidirect
136. #14579134	C₂³	semidirect
137. #14579134	C₂³	semidirect
138. #14579133	C₂³	semidirect
139. #14579133	C₂³	semidirect
140. #14579133	C₂³	semidirect
141. #14579132	C₂³	semidirect
142. #14579132	C₂³	semidirect
143. C₄×D₃₁₆	C₂³	semidirect
144. D₄×Dic₇₉	C₂³	semidirect
145. #14579123	C₂³	semidirect
146. C₄×C₂²⋊D₇₉	C₂³	semidirect
147. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
148. #14579120	C₂³	semidirect
149. #14579119	C₂³	semidirect
150. #14579118	C₂³	semidirect
151. #14579118	C₂³	semidirect
152. #14579117	C₂³	semidirect
187. #127×C₇₉	C₂³	semidirect
188. #125×C₇₉	C₂³	semidirect
189. #123×C₇₉	C₂³	semidirect
190. #121×C₇₉	C₂³	semidirect
191. #121×C₇₉	C₂³	semidirect
192. C₄×D₄×C₇₉	C₂³	semidirect
193. #117×C₇₉	C₂³	semidirect
394. C₂×D₇₉	#540	direct (N × H)
410. C₂×C₇₉	C₂×#540	semidirect
415. D₇₉	C₂×#540	direct (N × H)
424. C₂×#540	D₇₉	direct (N × H)
432. C₇₉	C₂²×#540	semidirect
445. #540	C₂×D₇₉	direct (N × H)
450. C₂×#127	C₂×D₇₉	semidirect
455. C₂×#125	C₂×D₇₉	semidirect
464. C₂×#123	C₂×D₇₉	semidirect
479. C₂×#121	C₂×D₇₉	semidirect
480. C₂×#121	C₂×D₇₉	semidirect
487. C₂×C₄×D₄	C₂×D₇₉	semidirect
494. C₂×#117	C₂×D₇₉	semidirect
542. #127	C₂²×D₇₉	semidirect
546. #125	C₂²×D₇₉	semidirect
554. #123	C₂²×D₇₉	semidirect
567. #121	C₂²×D₇₉	semidirect
568. #121	C₂²×D₇₉	semidirect
574. C₄×D₄	C₂²×D₇₉	semidirect
580. #117	C₂²×D₇₉	semidirect
828. C₂	#540×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×#19099169	2
C₂×#19099168	2
C₂×#19099167	2
C₂×#19099166	2
C₂×#19099165	2
C₂×#19099164	2
C₂×#19099163	2
#540×D₇₉	2
C₂×#127×D₇₉	2
C₂×#125×D₇₉	2
C₂×#123×D₇₉	2
C₂×#121×D₇₉	2
C₂×C₄×D₄×D₇₉	2
C₂×#117×D₇₉	2
C₂×#540×C₇₉	2
C₂²×#540	79

Subgroups — C2×#540×D79 #35195040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#540×D₇₉ #35195040