Subgroups — C₇₉×#25808 #34137497

Order 20224.

1424 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#497×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#473×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#456×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#455×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2005	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#2003	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×H(5,𝔽₂)×C₇₉	C₂²	1	1	yes	characteristic
18	#577×C₇₉	—	2	4	no	—
19	#577×C₇₉	—	2	4	no	—
20	C₂×#137×C₇₉	—	2	1	no	—
21	C₂×#137×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#137×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#137×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#137×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#137×C₇₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
27	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#135×C₇₉	—	2	1	no	—
29	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₇₉	—	2	1	no	—
33	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
34	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
36	#536×C₇₉	C₂²	1	1	yes	characteristic
37	#536×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₇₉	C₂²	1	1	yes	characteristic
40	#497×C₇₉	—	2	4	no	—
41	#497×C₇₉	—	2	1	no	—
42	#497×C₇₉	—	2	1	no	—
43	#495×C₇₉	—	2	1	no	—
44	#494×C₇₉	—	2	1	no	—
45	#473×C₇₉	—	2	4	no	—
46	#456×C₇₉	—	2	4	no	—
47	#455×C₇₉	—	2	4	no	—
48	#452×C₇₉	—	2	2	no	—
49	#452×C₇₉	—	2	2	no	—
50	#451×C₇₉	—	2	2	no	—
51	#450×C₇₉	—	2	2	no	—
52	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	#419×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	#418×C₇₉	C₂²	1	1	yes	characteristic
58	#416×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#101×C₇₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×#101×C₇₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×#101×C₇₉	C₂²	1	1	yes	characteristic, complemented
62	C₂×#100×C₇₉	C₂²	1	1	yes	characteristic
63	#408×C₇₉	C₂²	1	1	yes	characteristic
64	#408×C₇₉	C₂²	1	1	yes	characteristic, complemented
65	#405×C₇₉	C₂²	1	1	yes	characteristic, complemented
66	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic, complemented
67	#341×C₇₉	C₂²	1	1	yes	characteristic, complemented
68	#339×C₇₉	C₂²	1	1	yes	characteristic, complemented
69	2₋¹⁺⁴×C₇₉	—	2	2	no	—
70	2₋¹⁺⁴×C₇₉	—	2	2	no	—
71	2₋¹⁺⁴×C₇₉	—	2	2	no	—
72	2₋¹⁺⁴×C₇₉	—	4	1	no	—
73	H(5,𝔽₂)×C₇₉	—	2	2	no	—
74	H(5,𝔽₂)×C₇₉	—	2	2	no	—
75	H(5,𝔽₂)×C₇₉	—	2	2	no	—
76	H(5,𝔽₂)×C₇₉	—	4	1	no	—
77	C₂×#41×C₇₉	—	2	1	no	—
78	C₂×#41×C₇₉	—	2	1	no	—
79	C₂×#41×C₇₉	—	2	1	no	—
80	C₂×#41×C₇₉	—	2	1	no	—
81	C₂×#41×C₇₉	—	4	1	no	—
82	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₇₉	—	2	1	no	—
86	C₂²×Q₈×C₇₉	—	2	1	no	—
87	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₇₉	—	2	1	no	—
91	C₂²×D₄×C₇₉	—	2	1	no	—
92	C₂²×D₄×C₇₉	—	4	1	no	—
93	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
94	#137×C₇₉	—	2	8	no	—
95	#137×C₇₉	—	2	2	no	—
96	#137×C₇₉	—	2	2	no	—
97	#137×C₇₉	—	2	2	no	—
98	#137×C₇₉	—	2	2	no	—
99	#137×C₇₉	—	2	2	no	—
100	#137×C₇₉	—	2	2	no	—
101	#137×C₇₉	—	2	2	no	—
102	#137×C₇₉	—	2	2	no	—
103	#137×C₇₉	—	4	1	no	—
104	#137×C₇₉	—	4	1	no	—
105	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
106	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
107	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
108	#135×C₇₉	—	2	8	no	—
109	#135×C₇₉	—	2	2	no	—
110	#135×C₇₉	—	2	2	no	—
111	C₂×Q₁₆×C₇₉	—	2	1	no	—
112	C₂×Q₁₆×C₇₉	—	2	1	no	—
113	C₂×Q₁₆×C₇₉	—	2	1	no	—
114	C₂×Q₁₆×C₇₉	—	2	1	no	—
115	C₂×Q₁₆×C₇₉	—	2	1	no	—
116	C₂×Q₁₆×C₇₉	—	2	2	no	—
117	C₂×Q₁₆×C₇₉	—	2	2	no	—
118	C₂×Q₁₆×C₇₉	—	2	2	no	—
119	C₂×Q₁₆×C₇₉	—	2	1	no	—
120	C₂×Q₁₆×C₇₉	—	2	1	no	—
121	C₂×Q₁₆×C₇₉	—	2	2	no	—
122	C₂×Q₁₆×C₇₉	—	4	1	no	—
123	C₂×Q₁₆×C₇₉	D₄	1	1	yes	characteristic
124	C₂×SD₁₆×C₇₉	—	2	8	no	—
125	C₂×SD₁₆×C₇₉	—	2	1	no	—
126	C₂×SD₁₆×C₇₉	—	2	1	no	—
127	C₂×SD₁₆×C₇₉	—	2	1	no	—
128	C₂×SD₁₆×C₇₉	—	2	1	no	—
129	C₂×SD₁₆×C₇₉	—	2	1	no	—
130	C₂×SD₁₆×C₇₉	—	2	1	no	—
131	C₂×SD₁₆×C₇₉	—	2	2	no	—
132	C₂×SD₁₆×C₇₉	—	2	1	no	—
133	C₂×SD₁₆×C₇₉	—	2	1	no	—
134	C₂×SD₁₆×C₇₉	—	2	2	no	—
135	C₂×SD₁₆×C₇₉	—	2	2	no	—
136	C₂×SD₁₆×C₇₉	—	4	1	no	—
137	C₂×SD₁₆×C₇₉	D₄	1	1	yes	characteristic
138	C₂×SD₁₆×C₇₉	D₄	1	4	yes	—
139	C₂×SD₁₆×C₇₉	D₄	1	1	yes	characteristic
140	C₂×D₈×C₇₉	—	2	1	no	—
141	C₂×D₈×C₇₉	D₄	1	1	yes	characteristic
142	#131×C₇₉	—	2	2	no	—
143	#131×C₇₉	D₄	1	4	yes	—
144	C₂×M₁₆×C₇₉	—	2	1	no	—
145	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₇₉	—	2	1	no	—
150	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₇₉	—	2	1	no	—
153	C₄⋊Q₈×C₇₉	—	2	1	no	—
154	C₄⋊Q₈×C₇₉	—	2	2	no	—
155	C₄⋊Q₈×C₇₉	—	2	2	no	—
156	#124×C₇₉	—	2	1	no	—
157	#124×C₇₉	—	2	1	no	—
158	#124×C₇₉	—	2	2	no	—
159	#124×C₇₉	—	2	2	no	—
160	#123×C₇₉	—	4	1	no	—
161	#123×C₇₉	—	4	1	no	—
162	C₂²⋊Q₈×C₇₉	—	2	2	no	—
163	C₂²⋊Q₈×C₇₉	—	2	2	no	—
164	#117×C₇₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
166	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
167	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
168	#108×C₇₉	—	2	2	no	—
169	#104×C₇₉	—	2	2	no	—
170	#104×C₇₉	—	2	2	no	—
171	#104×C₇₉	D₄	1	4	yes	—
172	#103×C₇₉	—	2	2	no	—
173	#103×C₇₉	D₄	1	2	yes	—
174	#102×C₇₉	—	2	2	no	—
175	#102×C₇₉	D₄	1	2	yes	—
176	#101×C₇₉	—	2	2	no	—
177	#101×C₇₉	—	2	2	no	—
178	#101×C₇₉	—	2	2	no	—
179	#100×C₇₉	—	2	2	no	—
180	C₂²⋊C₈×C₇₉	—	2	2	no	—
181	C₂²⋊C₈×C₇₉	—	2	2	no	—
182	#97×C₇₉	—	2	2	no	—
183	#97×C₇₉	—	2	1	no	—
184	C₄×C₈×C₇₉	—	2	1	no	—
185	C₂⁴×C₇₉	—	2	1	no	—
186	C₂⁴×C₇₉	—	4	1	no	—
187	#41×C₇₉	—	2	1	no	—
188	#41×C₇₉	—	2	1	no	—
189	#41×C₇₉	—	2	4	no	—
190	#41×C₇₉	—	2	4	no	—
191	#41×C₇₉	—	2	1	no	—
192	#41×C₇₉	—	2	1	no	—
193	#41×C₇₉	—	2	1	no	—
194	#41×C₇₉	—	2	1	no	—
195	#41×C₇₉	—	2	1	no	—
196	#41×C₇₉	—	2	1	no	—
197	#41×C₇₉	—	2	1	no	—
198	#41×C₇₉	—	2	1	no	—
199	#41×C₇₉	—	4	2	no	—
200	#41×C₇₉	—	4	4	no	—
201	#41×C₇₉	—	4	2	no	—
202	#41×C₇₉	—	4	2	no	—
203	#41×C₇₉	—	4	2	no	—
204	#41×C₇₉	—	4	4	no	—
205	#41×C₇₉	—	4	2	no	—
206	#41×C₇₉	—	4	2	no	—
207	#41×C₇₉	C₂×D₄	1	2	yes	—
208	#41×C₇₉	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₇₉	—	2	1	no	—
210	C₂×Q₈×C₇₉	—	2	4	no	—
211	C₂×Q₈×C₇₉	—	2	1	no	—
212	C₂×Q₈×C₇₉	—	2	1	no	—
213	C₂×Q₈×C₇₉	—	2	1	no	—
214	C₂×Q₈×C₇₉	—	2	1	no	—
215	C₂×Q₈×C₇₉	—	2	1	no	—
216	C₂×Q₈×C₇₉	—	2	1	no	—
217	C₂×Q₈×C₇₉	—	2	1	no	—
218	C₂×Q₈×C₇₉	—	2	1	no	—
219	C₂×Q₈×C₇₉	—	2	1	no	—
220	C₂×Q₈×C₇₉	—	2	1	no	—
221	C₂×Q₈×C₇₉	—	2	1	no	—
222	C₂×Q₈×C₇₉	—	2	1	no	—
223	C₂×Q₈×C₇₉	—	2	1	no	—
224	C₂×Q₈×C₇₉	—	2	1	no	—
225	C₂×Q₈×C₇₉	—	2	1	no	—
226	C₂×Q₈×C₇₉	—	2	1	no	—
227	C₂×Q₈×C₇₉	—	4	1	no	—
228	C₂×Q₈×C₇₉	—	4	2	no	—
229	C₂×Q₈×C₇₉	—	4	2	no	—
230	C₂×Q₈×C₇₉	—	4	2	no	—
231	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
232	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
233	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
234	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
235	C₂×D₄×C₇₉	—	2	1	no	—
236	C₂×D₄×C₇₉	—	2	4	no	—
237	C₂×D₄×C₇₉	—	2	1	no	—
238	C₂×D₄×C₇₉	—	2	1	no	—
239	C₂×D₄×C₇₉	—	2	1	no	—
240	C₂×D₄×C₇₉	—	2	1	no	—
241	C₂×D₄×C₇₉	—	2	1	no	—
242	C₂×D₄×C₇₉	—	2	1	no	—
243	C₂×D₄×C₇₉	—	2	1	no	—
244	C₂×D₄×C₇₉	—	4	2	no	—
245	C₂×D₄×C₇₉	—	4	1	no	—
246	C₂×D₄×C₇₉	—	4	1	no	—
247	C₂×D₄×C₇₉	—	4	2	no	—
248	C₂×D₄×C₇₉	—	4	4	no	—
249	C₂×D₄×C₇₉	—	4	4	no	—
250	C₂×D₄×C₇₉	—	4	1	no	—
251	C₂×D₄×C₇₉	—	4	2	no	—
252	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇₉	—	2	1	no	—
257	C₂²×C₄×C₇₉	—	2	1	no	—
258	C₂²×C₄×C₇₉	—	2	1	no	—
259	C₂²×C₄×C₇₉	—	2	1	no	—
260	C₂²×C₄×C₇₉	—	2	1	no	—
261	C₂²×C₄×C₇₉	—	2	1	no	—
262	C₂²×C₄×C₇₉	—	2	1	no	—
263	C₂²×C₄×C₇₉	—	4	1	no	—
264	C₂²×C₄×C₇₉	—	4	1	no	—
265	C₂²×C₄×C₇₉	—	4	1	no	—
266	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
267	Q₁₆×C₇₉	—	2	4	no	—
268	Q₁₆×C₇₉	—	2	2	no	—
269	Q₁₆×C₇₉	—	4	4	no	—
270	Q₁₆×C₇₉	—	4	2	no	—
271	Q₁₆×C₇₉	—	4	2	no	—
272	Q₁₆×C₇₉	—	4	2	no	—
273	Q₁₆×C₇₉	—	4	2	no	—
274	Q₁₆×C₇₉	—	4	2	no	—
275	Q₁₆×C₇₉	—	4	2	no	—
276	SD₁₆×C₇₉	—	2	4	no	—
277	SD₁₆×C₇₉	—	2	4	no	—
278	SD₁₆×C₇₉	—	2	2	no	—
279	SD₁₆×C₇₉	—	2	4	no	—
280	SD₁₆×C₇₉	—	2	4	no	—
281	SD₁₆×C₇₉	—	2	2	no	—
282	SD₁₆×C₇₉	—	4	4	no	—
283	SD₁₆×C₇₉	—	4	2	no	—
284	SD₁₆×C₇₉	—	4	2	no	—
285	SD₁₆×C₇₉	—	4	2	no	—
286	SD₁₆×C₇₉	—	4	2	no	—
287	D₈×C₇₉	—	2	4	no	—
288	D₈×C₇₉	—	2	2	no	—
289	M₁₆×C₇₉	—	2	4	no	—
290	M₁₆×C₇₉	—	2	1	no	—
291	M₁₆×C₇₉	—	2	1	no	—
292	M₁₆×C₇₉	—	2	1	no	—
293	M₁₆×C₇₉	—	2	1	no	—
294	M₁₆×C₇₉	—	2	1	no	—
295	M₁₆×C₇₉	—	2	1	no	—
296	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
297	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
298	C₂×C₈×C₇₉	—	2	4	no	—
299	C₂×C₈×C₇₉	—	2	1	no	—
300	C₂×C₈×C₇₉	—	2	1	no	—
301	C₂×C₈×C₇₉	—	2	1	no	—
302	C₂×C₈×C₇₉	—	2	1	no	—
303	C₂×C₈×C₇₉	—	2	1	no	—
304	C₂×C₈×C₇₉	—	2	1	no	—
305	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
306	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
307	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
309	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
310	C₄⋊C₄×C₇₉	—	4	4	no	—
311	C₄⋊C₄×C₇₉	—	4	2	no	—
312	C₄⋊C₄×C₇₉	—	4	2	no	—
313	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₇₉	—	2	1	no	—
315	C₂²⋊C₄×C₇₉	—	4	4	no	—
316	C₂²⋊C₄×C₇₉	—	4	2	no	—
317	C₂²⋊C₄×C₇₉	—	4	2	no	—
318	C₄²×C₇₉	—	2	1	no	—
319	C₄²×C₇₉	—	2	1	no	—
320	C₄²×C₇₉	C₂×D₄	1	2	yes	—
321	C₂³×C₇₉	—	2	1	no	—
322	C₂³×C₇₉	—	2	1	no	—
323	C₂³×C₇₉	—	2	1	no	—
324	C₂³×C₇₉	—	2	2	no	—
325	C₂³×C₇₉	—	4	4	no	—
326	C₂³×C₇₉	—	4	1	no	—
327	C₂³×C₇₉	—	4	1	no	—
328	C₂³×C₇₉	—	8	2	no	—
329	C₂³×C₇₉	—	16	2	no	—
330	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
331	Q₈×C₇₉	—	2	1	no	—
332	Q₈×C₇₉	—	2	1	no	—
333	Q₈×C₇₉	—	2	2	no	—
334	Q₈×C₇₉	—	2	1	no	—
335	Q₈×C₇₉	—	2	2	no	—
336	Q₈×C₇₉	—	2	1	no	—
337	Q₈×C₇₉	—	2	1	no	—
338	Q₈×C₇₉	—	4	4	no	—
339	Q₈×C₇₉	—	4	1	no	—
340	Q₈×C₇₉	—	4	1	no	—
341	Q₈×C₇₉	—	4	1	no	—
342	Q₈×C₇₉	—	4	1	no	—
343	Q₈×C₇₉	—	4	1	no	—
344	Q₈×C₇₉	—	4	1	no	—
345	Q₈×C₇₉	—	4	1	no	—
346	Q₈×C₇₉	—	4	1	no	—
347	Q₈×C₇₉	—	4	1	no	—
348	Q₈×C₇₉	—	4	1	no	—
349	Q₈×C₇₉	#127	1	2	yes	—
350	D₄×C₇₉	—	2	2	no	—
351	D₄×C₇₉	—	2	2	no	—
352	D₄×C₇₉	—	2	1	no	—
353	D₄×C₇₉	—	2	2	no	—
354	D₄×C₇₉	—	2	1	no	—
355	D₄×C₇₉	—	2	1	no	—
356	D₄×C₇₉	—	2	2	no	—
357	D₄×C₇₉	—	2	1	no	—
358	D₄×C₇₉	—	2	1	no	—
359	D₄×C₇₉	—	4	4	no	—
360	D₄×C₇₉	—	4	4	no	—
361	D₄×C₇₉	—	4	4	no	—
362	D₄×C₇₉	—	4	1	no	—
363	D₄×C₇₉	—	4	1	no	—
364	D₄×C₇₉	—	4	1	no	—
365	D₄×C₇₉	—	4	1	no	—
366	D₄×C₇₉	—	4	1	no	—
367	D₄×C₇₉	—	4	1	no	—
368	D₄×C₇₉	#127	1	2	yes	—
369	C₂×C₄×C₇₉	—	2	1	no	—
370	C₂×C₄×C₇₉	—	2	2	no	—
371	C₂×C₄×C₇₉	—	2	2	no	—
372	C₂×C₄×C₇₉	—	2	2	no	—
373	C₂×C₄×C₇₉	—	2	2	no	—
374	C₂×C₄×C₇₉	—	2	2	no	—
375	C₂×C₄×C₇₉	—	2	1	no	—
376	C₂×C₄×C₇₉	—	2	1	no	—
377	C₂×C₄×C₇₉	—	4	4	no	—
378	C₂×C₄×C₇₉	—	4	4	no	—
379	C₂×C₄×C₇₉	—	4	2	no	—
380	C₂×C₄×C₇₉	—	4	4	no	—
381	C₂×C₄×C₇₉	—	4	1	no	—
382	C₂×C₄×C₇₉	—	4	1	no	—
383	C₂×C₄×C₇₉	—	4	1	no	—
384	C₂×C₄×C₇₉	—	4	1	no	—
385	C₂×C₄×C₇₉	—	4	1	no	—
386	C₂×C₄×C₇₉	—	4	1	no	—
387	C₂×C₄×C₇₉	—	4	1	no	—
388	C₂×C₄×C₇₉	—	4	1	no	—
389	C₂×C₄×C₇₉	—	4	1	no	—
390	C₂×C₄×C₇₉	—	4	1	no	—
391	C₂×C₄×C₇₉	—	4	1	no	—
392	C₂×C₄×C₇₉	—	4	1	no	—
393	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
399	C₈×C₇₉	—	2	2	no	—
400	C₈×C₇₉	—	2	2	no	—
401	C₈×C₇₉	—	2	2	no	—
402	C₈×C₇₉	—	4	1	no	—
403	C₈×C₇₉	—	4	1	no	—
404	C₈×C₇₉	#120	1	2	yes	—
405	C₈×C₇₉	#120	1	2	yes	—
406	C₂²×C₇₉	—	2	2	no	—
407	C₂²×C₇₉	—	2	2	no	—
408	C₂²×C₇₉	—	4	2	no	—
409	C₂²×C₇₉	—	4	1	no	—
410	C₂²×C₇₉	—	4	1	no	—
411	C₂²×C₇₉	—	4	2	no	—
412	C₂²×C₇₉	—	4	2	no	—
413	C₂²×C₇₉	—	4	2	no	—
414	C₂²×C₇₉	—	8	2	no	—
415	C₂²×C₇₉	—	8	2	no	—
416	C₂²×C₇₉	—	16	1	no	—
417	C₂²×C₇₉	—	16	4	no	—
418	C₂²×C₇₉	#535	1	1	yes	characteristic
419	C₂²×C₇₉	D₄²	1	1	yes	characteristic
420	C₂²×C₇₉	D₄²	1	1	yes	characteristic
421	C₄×C₇₉	—	2	2	no	—
422	C₄×C₇₉	—	4	2	no	—
423	C₄×C₇₉	—	4	1	no	—
424	C₄×C₇₉	—	4	2	no	—
425	C₄×C₇₉	—	4	1	no	—
426	C₄×C₇₉	—	4	2	no	—
427	C₄×C₇₉	—	8	1	no	—
428	C₄×C₇₉	—	8	1	no	—
429	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
430	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
431	C₄×C₇₉	D₄²	1	1	yes	characteristic
432	C₄×C₇₉	D₄²	1	1	yes	characteristic
433	#25808	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₇₉	—	2	1	no	—
435	C₂×C₇₉	—	2	1	no	—
436	C₂×C₇₉	—	4	2	no	—
437	C₂×C₇₉	—	8	1	no	—
438	C₂×C₇₉	—	8	1	no	—
439	C₂×C₇₉	—	8	2	no	—
440	C₂×C₇₉	#2433	1	1	yes	characteristic
441	C₂×C₇₉	#3289	1	2	yes	—
442	C₂×#577	C₂×C₇₉	1	1	yes	characteristic
443	#3156	C₂×C₇₉	1	1	yes	characteristic, complemented
444	C₂×#497	C₂×C₇₉	1	1	yes	characteristic, complemented
445	C₂×#473	C₂×C₇₉	1	1	yes	characteristic, complemented
446	C₂×#456	C₂×C₇₉	1	1	yes	characteristic, complemented
447	C₂×#455	C₂×C₇₉	1	1	yes	characteristic, complemented
448	#3011	C₂×C₇₉	1	1	yes	characteristic, complemented
449	#3009	C₂×C₇₉	1	1	yes	characteristic, complemented
450	#2020	C₂×C₇₉	1	1	yes	characteristic, complemented
451	#2019	C₂×C₇₉	1	1	yes	characteristic, complemented
452	#2005	C₂×C₇₉	1	1	yes	characteristic, complemented
453	#2003	C₂×C₇₉	1	1	yes	characteristic, complemented
454	#1977	C₂×C₇₉	1	1	yes	characteristic, complemented
455	#1975	C₂×C₇₉	1	1	yes	characteristic, complemented
456	#1765	C₂×C₇₉	1	1	yes	characteristic, complemented
457	C₇₉	#25808	1	1	yes	characteristic, direct product factor, Sylow
458	C₂×2₋¹⁺⁴	C₂²×C₇₉	1	1	yes	characteristic
459	C₂×H(5,𝔽₂)	C₂²×C₇₉	1	1	yes	characteristic
460	#577	—	2	4	no	—
461	#577	—	2	4	no	—
462	C₂×#137	—	2	1	no	—
463	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
464	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
465	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
466	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
467	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic, complemented
468	C₂×AGL(1,ℤ/8)	—	2	1	no	—
469	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	1	yes	characteristic
470	C₂×#135	—	2	1	no	—
471	C₂×#135	C₂²×C₇₉	1	1	yes	characteristic
472	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
473	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
474	C₂²×SD₁₆	—	2	1	no	—
475	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
476	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
477	C₂×#131	C₂²×C₇₉	1	1	yes	characteristic
478	#536	C₂²×C₇₉	1	1	yes	characteristic
479	#536	C₂²×C₇₉	1	1	yes	characteristic, complemented
480	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
481	C₂×#124	C₂²×C₇₉	1	1	yes	characteristic
482	#497	—	2	4	no	—
483	#497	—	2	1	no	—
484	#497	—	2	1	no	—
485	#495	—	2	1	no	—
486	#494	—	2	1	no	—
487	#473	—	2	4	no	—
488	#456	—	2	4	no	—
489	#455	—	2	4	no	—
490	#452	—	2	2	no	—
491	#452	—	2	2	no	—
492	#451	—	2	2	no	—
493	#450	—	2	2	no	—
494	C₂×#108	C₂²×C₇₉	1	1	yes	characteristic, complemented
495	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic
496	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic
497	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic, complemented
498	#419	C₂²×C₇₉	1	1	yes	characteristic, complemented
499	#418	C₂²×C₇₉	1	1	yes	characteristic
500	#416	C₂²×C₇₉	1	1	yes	characteristic
501	C₂×#101	C₂²×C₇₉	1	1	yes	characteristic, complemented
502	C₂×#101	C₂²×C₇₉	1	1	yes	characteristic, complemented
503	C₂×#101	C₂²×C₇₉	1	1	yes	characteristic, complemented
504	C₂×#100	C₂²×C₇₉	1	1	yes	characteristic
505	#408	C₂²×C₇₉	1	1	yes	characteristic
506	#408	C₂²×C₇₉	1	1	yes	characteristic, complemented
507	#405	C₂²×C₇₉	1	1	yes	characteristic, complemented
508	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic, complemented
509	#341	C₂²×C₇₉	1	1	yes	characteristic, complemented
510	#339	C₂²×C₇₉	1	1	yes	characteristic, complemented
511	2₋¹⁺⁴	—	2	2	no	—
512	2₋¹⁺⁴	—	2	2	no	—
513	2₋¹⁺⁴	—	2	2	no	—
514	2₋¹⁺⁴	—	4	1	no	—
515	H(5,𝔽₂)	—	2	2	no	—
516	H(5,𝔽₂)	—	2	2	no	—
517	H(5,𝔽₂)	—	2	2	no	—
518	H(5,𝔽₂)	—	4	1	no	—
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	2	1	no	—
522	C₂×#41	—	2	1	no	—
523	C₂×#41	—	4	1	no	—
524	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
525	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
526	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	4	1	no	—
535	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
536	#137	—	2	8	no	—
537	#137	—	2	2	no	—
538	#137	—	2	2	no	—
539	#137	—	2	2	no	—
540	#137	—	2	2	no	—
541	#137	—	2	2	no	—
542	#137	—	2	2	no	—
543	#137	—	2	2	no	—
544	#137	—	2	2	no	—
545	#137	—	4	1	no	—
546	#137	—	4	1	no	—
547	AGL(1,ℤ/8)	—	2	8	no	—
548	AGL(1,ℤ/8)	—	2	2	no	—
549	AGL(1,ℤ/8)	—	2	2	no	—
550	#135	—	2	8	no	—
551	#135	—	2	2	no	—
552	#135	—	2	2	no	—
553	C₂×Q₁₆	—	2	1	no	—
554	C₂×Q₁₆	—	2	2	no	—
555	C₂×Q₁₆	—	2	1	no	—
556	C₂×Q₁₆	—	2	1	no	—
557	C₂×Q₁₆	—	2	1	no	—
558	C₂×Q₁₆	—	2	1	no	—
559	C₂×Q₁₆	—	2	2	no	—
560	C₂×Q₁₆	—	2	2	no	—
561	C₂×Q₁₆	—	2	1	no	—
562	C₂×Q₁₆	—	2	1	no	—
563	C₂×Q₁₆	—	2	2	no	—
564	C₂×Q₁₆	—	4	1	no	—
565	C₂×Q₁₆	D₄×C₇₉	1	1	yes	characteristic
566	C₂×SD₁₆	—	2	8	no	—
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	—	2	1	no	—
569	C₂×SD₁₆	—	2	2	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	2	no	—
577	C₂×SD₁₆	—	2	2	no	—
578	C₂×SD₁₆	—	4	1	no	—
579	C₂×SD₁₆	D₄×C₇₉	1	1	yes	characteristic
580	C₂×SD₁₆	D₄×C₇₉	1	4	yes	—
581	C₂×SD₁₆	D₄×C₇₉	1	1	yes	characteristic
582	C₂×D₈	—	2	1	no	—
583	C₂×D₈	D₄×C₇₉	1	1	yes	characteristic
584	#131	—	2	2	no	—
585	#131	D₄×C₇₉	1	4	yes	—
586	C₂×M₁₆	—	2	1	no	—
587	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
589	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
590	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
591	C₂²×C₈	—	2	1	no	—
592	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	2	no	—
598	#124	—	2	2	no	—
599	#124	—	2	1	no	—
600	#124	—	2	1	no	—
601	#124	—	2	2	no	—
602	#123	—	4	1	no	—
603	#123	—	4	1	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	#117	C₂³×C₇₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₂²⋊C₄	—	4	1	no	—
609	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
610	#108	—	2	2	no	—
611	#104	—	2	2	no	—
612	#104	—	2	2	no	—
613	#104	D₄×C₇₉	1	4	yes	—
614	#103	—	2	2	no	—
615	#103	D₄×C₇₉	1	2	yes	—
616	#102	—	2	2	no	—
617	#102	D₄×C₇₉	1	2	yes	—
618	#101	—	2	2	no	—
619	#101	—	2	2	no	—
620	#101	—	2	2	no	—
621	#100	—	2	2	no	—
622	C₂²⋊C₈	—	2	2	no	—
623	C₂²⋊C₈	—	2	2	no	—
624	#97	—	2	2	no	—
625	#97	—	2	1	no	—
626	C₄×C₈	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	4	1	no	—
629	#41	—	2	1	no	—
630	#41	—	2	1	no	—
631	#41	—	2	4	no	—
632	#41	—	2	4	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	2	1	no	—
637	#41	—	2	1	no	—
638	#41	—	2	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	1	no	—
641	#41	—	4	2	no	—
642	#41	—	4	4	no	—
643	#41	—	4	2	no	—
644	#41	—	4	2	no	—
645	#41	—	4	2	no	—
646	#41	—	4	4	no	—
647	#41	—	4	2	no	—
648	#41	—	4	2	no	—
649	#41	C₂×D₄×C₇₉	1	2	yes	—
650	#41	C₂×D₄×C₇₉	1	2	yes	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	2	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
674	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
675	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
676	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
695	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
696	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
697	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	1	no	—
708	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
709	Q₁₆	—	2	4	no	—
710	Q₁₆	—	2	2	no	—
711	Q₁₆	—	4	4	no	—
712	Q₁₆	—	4	2	no	—
713	Q₁₆	—	4	2	no	—
714	Q₁₆	—	4	2	no	—
715	Q₁₆	—	4	2	no	—
716	Q₁₆	—	4	2	no	—
717	Q₁₆	—	4	2	no	—
718	SD₁₆	—	2	4	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	2	2	no	—
721	SD₁₆	—	2	4	no	—
722	SD₁₆	—	2	4	no	—
723	SD₁₆	—	2	2	no	—
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	2	no	—
726	SD₁₆	—	4	2	no	—
727	SD₁₆	—	4	2	no	—
728	SD₁₆	—	4	2	no	—
729	D₈	—	2	4	no	—
730	D₈	—	2	2	no	—
731	M₁₆	—	2	1	no	—
732	M₁₆	—	2	1	no	—
733	M₁₆	—	2	4	no	—
734	M₁₆	—	2	1	no	—
735	M₁₆	—	2	1	no	—
736	M₁₆	—	2	1	no	—
737	M₁₆	—	2	1	no	—
738	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
739	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	4	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
748	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
749	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
750	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
751	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
752	C₄⋊C₄	—	4	4	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	4	4	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	C₂×D₄×C₇₉	1	2	yes	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	16	2	no	—
772	C₂³	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
773	Q₈	—	2	1	no	—
774	Q₈	—	2	1	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	1	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	1	no	—
782	Q₈	—	4	1	no	—
783	Q₈	—	4	1	no	—
784	Q₈	—	4	1	no	—
785	Q₈	—	4	1	no	—
786	Q₈	—	4	1	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	4	1	no	—
791	Q₈	#127×C₇₉	1	2	yes	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	1	no	—
800	D₄	—	2	1	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	1	no	—
805	D₄	—	4	1	no	—
806	D₄	—	4	1	no	—
807	D₄	—	4	1	no	—
808	D₄	—	4	1	no	—
809	D₄	—	4	1	no	—
810	D₄	#127×C₇₉	1	2	yes	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
840	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₈	—	4	1	no	—
845	C₈	—	4	1	no	—
846	C₈	#120×C₇₉	1	2	yes	—
847	C₈	#120×C₇₉	1	2	yes	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	1	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	8	2	no	—
857	C₂²	—	8	2	no	—
858	C₂²	—	16	1	no	—
859	C₂²	—	16	4	no	—
860	C₂²	#535×C₇₉	1	1	yes	characteristic
861	C₂²	D₄²×C₇₉	1	1	yes	characteristic
862	C₂²	D₄²×C₇₉	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	8	1	no	—
870	C₄	—	8	1	no	—
871	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
872	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
873	C₄	D₄²×C₇₉	1	1	yes	characteristic
874	C₄	D₄²×C₇₉	1	1	yes	characteristic
875	C₂	—	2	1	no	—
876	C₂	—	2	1	no	—
877	C₂	—	4	2	no	—
878	C₂	—	8	1	no	—
879	C₂	—	8	1	no	—
880	C₂	—	8	2	no	—
881	C₂	C₇₉×#2433	1	1	yes	characteristic
882	C₂	C₇₉×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#577×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3156	C₂	semidirect
3. C₂×#497×C₇₉	C₂	semidirect
4. C₂×#473×C₇₉	C₂	semidirect
5. C₂×#456×C₇₉	C₂	semidirect
6. C₂×#455×C₇₉	C₂	semidirect
7. C₇₉×#3011	C₂	semidirect
8. C₇₉×#3009	C₂	semidirect
9. C₇₉×#2020	C₂	semidirect
10. C₇₉×#2019	C₂	semidirect
11. C₇₉×#2005	C₂	semidirect
12. C₇₉×#2003	C₂	semidirect
13. C₇₉×#1977	C₂	semidirect
14. C₇₉×#1975	C₂	semidirect
15. C₇₉×#1765	C₂	semidirect
25. C₂×#137×C₇₉	C₂²	semidirect
30. C₂²×Q₁₆×C₇₉	C₂²	semidirect
31. C₂²×Q₁₆×C₇₉	C₂²	semidirect
37. #536×C₇₉	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
52. C₂×#108×C₇₉	C₂²	semidirect
55. C₂×#104×C₇₉	C₂²	semidirect
56. #419×C₇₉	C₂²	semidirect
59. C₂×#101×C₇₉	C₂²	semidirect
60. C₂×#101×C₇₉	C₂²	semidirect
61. C₂×#101×C₇₉	C₂²	semidirect
64. #408×C₇₉	C₂²	semidirect
65. #405×C₇₉	C₂²	semidirect
66. C₂×#97×C₇₉	C₂²	semidirect
67. #341×C₇₉	C₂²	semidirect
68. #339×C₇₉	C₂²	semidirect
433. #25808	C₇₉	direct (N × H)
443. #3156	C₂×C₇₉	semidirect
444. C₂×#497	C₂×C₇₉	semidirect
445. C₂×#473	C₂×C₇₉	semidirect
446. C₂×#456	C₂×C₇₉	semidirect
447. C₂×#455	C₂×C₇₉	semidirect
448. #3011	C₂×C₇₉	semidirect
449. #3009	C₂×C₇₉	semidirect
450. #2020	C₂×C₇₉	semidirect
451. #2019	C₂×C₇₉	semidirect
452. #2005	C₂×C₇₉	semidirect
453. #2003	C₂×C₇₉	semidirect
454. #1977	C₂×C₇₉	semidirect
455. #1975	C₂×C₇₉	semidirect
456. #1765	C₂×C₇₉	semidirect
457. C₇₉	#25808	direct (N × H)
467. C₂×#137	C₂²×C₇₉	semidirect
472. C₂²×Q₁₆	C₂²×C₇₉	semidirect
473. C₂²×Q₁₆	C₂²×C₇₉	semidirect
479. #536	C₂²×C₇₉	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
494. C₂×#108	C₂²×C₇₉	semidirect
497. C₂×#104	C₂²×C₇₉	semidirect
498. #419	C₂²×C₇₉	semidirect
501. C₂×#101	C₂²×C₇₉	semidirect
502. C₂×#101	C₂²×C₇₉	semidirect
503. C₂×#101	C₂²×C₇₉	semidirect
506. #408	C₂²×C₇₉	semidirect
507. #405	C₂²×C₇₉	semidirect
508. C₂×#97	C₂²×C₇₉	semidirect
509. #341	C₂²×C₇₉	semidirect
510. #339	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₇₉	2
C₇₉×#3156	2
C₂×#497×C₇₉	2
C₂×#473×C₇₉	2
C₂×#456×C₇₉	2
C₂×#455×C₇₉	2
C₇₉×#3011	2
C₇₉×#3009	2
C₇₉×#2020	2
C₇₉×#2019	2
C₇₉×#2005	2
C₇₉×#2003	2
C₇₉×#1977	2
C₇₉×#1975	2
C₇₉×#1765	2
#25808	79

Subgroups — C79×#25808 #34137497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25808 #34137497