Subgroups — C₇₉×#25802 #34137491

Order 20224.

1476 conjugacy classes of subgroups.

The subgroup lattice has 900 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, complemented
2	C₇₉×#3154	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#492×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#471×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#456×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#453×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2019	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×#2002	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1764	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, complemented
24	C₂×AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	1	yes	characteristic
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×SD₁₆×C₇₉	—	2	1	no	—
31	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
34	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
36	#536×C₇₉	C₂²	1	1	yes	characteristic
37	#535×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
40	#497×C₇₉	—	2	1	no	—
41	#496×C₇₉	—	2	1	no	—
42	#495×C₇₉	—	2	1	no	—
43	#492×C₇₉	—	2	4	no	—
44	#492×C₇₉	—	2	1	no	—
45	#471×C₇₉	—	2	4	no	—
46	#456×C₇₉	—	2	4	no	—
47	#453×C₇₉	—	2	4	no	—
48	#452×C₇₉	—	2	2	no	—
49	#450×C₇₉	—	2	2	no	—
50	#449×C₇₉	—	2	2	no	—
51	#448×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×#100×C₇₉	C₂²	1	1	yes	characteristic
62	C₂×#100×C₇₉	C₂²	1	1	yes	characteristic, complemented
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×C₄×C₈×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×D₄×C₇₉	—	2	1	no	—
90	C₂²×D₄×C₇₉	—	2	1	no	—
91	C₂²×D₄×C₇₉	—	4	1	no	—
92	C₂²×D₄×C₇₉	—	4	1	no	—
93	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
95	#137×C₇₉	—	2	8	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	—	4	1	no	—
102	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
103	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
104	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
105	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
106	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
107	AGL(1,ℤ/8)×C₇₉	—	2	2	no	—
108	AGL(1,ℤ/8)×C₇₉	—	4	1	no	—
109	#135×C₇₉	—	2	8	no	—
110	#135×C₇₉	—	2	2	no	—
111	#135×C₇₉	—	2	2	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	D₄	1	1	yes	characteristic, complemented
116	C₂×SD₁₆×C₇₉	—	2	8	no	—
117	C₂×SD₁₆×C₇₉	—	2	1	no	—
118	C₂×SD₁₆×C₇₉	—	2	1	no	—
119	C₂×SD₁₆×C₇₉	—	2	1	no	—
120	C₂×SD₁₆×C₇₉	—	2	2	no	—
121	C₂×SD₁₆×C₇₉	—	2	1	no	—
122	C₂×SD₁₆×C₇₉	—	2	1	no	—
123	C₂×SD₁₆×C₇₉	—	2	2	no	—
124	C₂×SD₁₆×C₇₉	—	2	1	no	—
125	C₂×SD₁₆×C₇₉	—	2	1	no	—
126	C₂×SD₁₆×C₇₉	—	2	1	no	—
127	C₂×SD₁₆×C₇₉	—	2	2	no	—
128	C₂×SD₁₆×C₇₉	—	2	2	no	—
129	C₂×SD₁₆×C₇₉	—	2	2	no	—
130	C₂×SD₁₆×C₇₉	—	2	2	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	—	4	1	no	—
135	C₂×SD₁₆×C₇₉	—	4	1	no	—
136	C₂×SD₁₆×C₇₉	D₄	1	4	yes	complemented
137	C₂×SD₁₆×C₇₉	D₄	1	1	yes	characteristic, complemented
138	C₂×SD₁₆×C₇₉	D₄	1	1	yes	characteristic, complemented
139	C₂×D₈×C₇₉	—	2	1	no	—
140	C₂×D₈×C₇₉	—	2	1	no	—
141	C₂×D₈×C₇₉	—	2	1	no	—
142	C₂×D₈×C₇₉	D₄	1	1	yes	characteristic, complemented
143	#131×C₇₉	—	2	2	no	—
144	#131×C₇₉	D₄	1	4	yes	complemented
145	C₂×M₁₆×C₇₉	—	2	1	no	—
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	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₇₉	—	2	1	no	—
151	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₇₉	—	2	2	no	—
154	C₄⋊Q₈×C₇₉	—	2	1	no	—
155	C₄⋊Q₈×C₇₉	—	2	2	no	—
156	#127×C₇₉	—	2	2	no	—
157	#127×C₇₉	—	2	1	no	—
158	#127×C₇₉	—	2	2	no	—
159	#124×C₇₉	—	2	1	no	—
160	#124×C₇₉	—	2	1	no	—
161	#123×C₇₉	—	4	1	no	—
162	C₂²⋊Q₈×C₇₉	—	2	2	no	—
163	#121×C₇₉	—	2	2	no	—
164	#120×C₇₉	—	4	1	no	—
165	#117×C₇₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊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	complemented
172	#103×C₇₉	—	2	2	no	—
173	#103×C₇₉	D₄	1	2	yes	complemented
174	#102×C₇₉	—	2	2	no	—
175	#102×C₇₉	D₄	1	2	yes	complemented
176	#101×C₇₉	—	2	2	no	—
177	#101×C₇₉	—	2	2	no	—
178	#100×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	1	no	—
183	C₄×C₈×C₇₉	—	2	2	no	—
184	C₄×C₈×C₇₉	—	2	1	no	—
185	C₂⁴×C₇₉	—	2	1	no	—
186	C₂⁴×C₇₉	—	2	1	no	—
187	C₂⁴×C₇₉	—	4	1	no	—
188	#41×C₇₉	—	2	1	no	—
189	#41×C₇₉	—	2	1	no	—
190	#41×C₇₉	—	2	4	no	—
191	#41×C₇₉	—	2	4	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	—	2	1	no	—
200	#41×C₇₉	—	4	2	no	—
201	#41×C₇₉	—	4	4	no	—
202	#41×C₇₉	—	4	2	no	—
203	#41×C₇₉	—	4	2	no	—
204	#41×C₇₉	—	4	2	no	—
205	#41×C₇₉	—	4	4	no	—
206	#41×C₇₉	—	4	2	no	—
207	#41×C₇₉	—	4	2	no	—
208	#41×C₇₉	C₂×D₄	1	2	yes	—
209	#41×C₇₉	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₇₉	—	2	1	no	—
211	C₂×Q₈×C₇₉	—	2	4	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	—	4	1	no	—
223	C₂×Q₈×C₇₉	—	4	2	no	—
224	C₂×Q₈×C₇₉	—	4	2	no	—
225	C₂×Q₈×C₇₉	—	4	2	no	—
226	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
229	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
230	C₂×D₄×C₇₉	—	2	1	no	—
231	C₂×D₄×C₇₉	—	2	4	no	—
232	C₂×D₄×C₇₉	—	2	1	no	—
233	C₂×D₄×C₇₉	—	2	1	no	—
234	C₂×D₄×C₇₉	—	2	1	no	—
235	C₂×D₄×C₇₉	—	2	1	no	—
236	C₂×D₄×C₇₉	—	2	1	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	—	2	1	no	—
245	C₂×D₄×C₇₉	—	4	2	no	—
246	C₂×D₄×C₇₉	—	4	1	no	—
247	C₂×D₄×C₇₉	—	4	1	no	—
248	C₂×D₄×C₇₉	—	4	4	no	—
249	C₂×D₄×C₇₉	—	4	2	no	—
250	C₂×D₄×C₇₉	—	4	2	no	—
251	C₂×D₄×C₇₉	—	4	4	no	—
252	C₂×D₄×C₇₉	—	4	4	no	—
253	C₂×D₄×C₇₉	—	4	1	no	—
254	C₂×D₄×C₇₉	—	4	2	no	—
255	C₂×D₄×C₇₉	—	8	4	no	—
256	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
264	C₂²×C₄×C₇₉	—	2	1	no	—
265	C₂²×C₄×C₇₉	—	2	1	no	—
266	C₂²×C₄×C₇₉	—	4	1	no	—
267	C₂²×C₄×C₇₉	—	4	1	no	—
268	C₂²×C₄×C₇₉	—	4	1	no	—
269	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₇₉	—	2	4	no	—
271	Q₁₆×C₇₉	—	2	2	no	—
272	Q₁₆×C₇₉	—	4	2	no	—
273	Q₁₆×C₇₉	—	4	2	no	—
274	SD₁₆×C₇₉	—	2	4	no	—
275	SD₁₆×C₇₉	—	2	4	no	—
276	SD₁₆×C₇₉	—	2	2	no	—
277	SD₁₆×C₇₉	—	2	4	no	—
278	SD₁₆×C₇₉	—	2	4	no	—
279	SD₁₆×C₇₉	—	2	2	no	—
280	SD₁₆×C₇₉	—	4	4	no	—
281	SD₁₆×C₇₉	—	4	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	SD₁₆×C₇₉	—	4	2	no	—
288	D₈×C₇₉	—	2	4	no	—
289	D₈×C₇₉	—	2	2	no	—
290	D₈×C₇₉	—	4	2	no	—
291	D₈×C₇₉	—	4	2	no	—
292	M₁₆×C₇₉	—	2	4	no	—
293	M₁₆×C₇₉	—	2	1	no	—
294	M₁₆×C₇₉	—	2	1	no	—
295	M₁₆×C₇₉	—	2	1	no	—
296	M₁₆×C₇₉	—	2	1	no	—
297	M₁₆×C₇₉	—	2	1	no	—
298	M₁₆×C₇₉	—	2	1	no	—
299	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
300	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
301	C₂×C₈×C₇₉	—	2	4	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	—	2	1	no	—
306	C₂×C₈×C₇₉	—	2	1	no	—
307	C₂×C₈×C₇₉	—	2	1	no	—
308	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
309	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
310	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
311	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
312	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₇₉	—	4	4	no	—
314	C₄⋊C₄×C₇₉	—	4	2	no	—
315	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₇₉	—	2	1	no	—
317	C₂²⋊C₄×C₇₉	—	4	2	no	—
318	C₂²⋊C₄×C₇₉	—	4	2	no	—
319	C₄²×C₇₉	—	2	1	no	—
320	C₄²×C₇₉	—	2	1	no	—
321	C₄²×C₇₉	C₂×D₄	1	2	yes	—
322	C₂³×C₇₉	—	2	1	no	—
323	C₂³×C₇₉	—	2	1	no	—
324	C₂³×C₇₉	—	2	1	no	—
325	C₂³×C₇₉	—	2	2	no	—
326	C₂³×C₇₉	—	4	4	no	—
327	C₂³×C₇₉	—	4	1	no	—
328	C₂³×C₇₉	—	4	1	no	—
329	C₂³×C₇₉	—	4	1	no	—
330	C₂³×C₇₉	—	4	1	no	—
331	C₂³×C₇₉	—	4	1	no	—
332	C₂³×C₇₉	—	8	2	no	—
333	C₂³×C₇₉	—	8	2	no	—
334	C₂³×C₇₉	—	16	2	no	—
335	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
336	Q₈×C₇₉	—	2	1	no	—
337	Q₈×C₇₉	—	2	1	no	—
338	Q₈×C₇₉	—	2	2	no	—
339	Q₈×C₇₉	—	2	1	no	—
340	Q₈×C₇₉	—	2	2	no	—
341	Q₈×C₇₉	—	2	1	no	—
342	Q₈×C₇₉	—	2	1	no	—
343	Q₈×C₇₉	—	4	4	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	—	4	1	no	—
350	Q₈×C₇₉	#127	1	2	yes	—
351	D₄×C₇₉	—	2	2	no	—
352	D₄×C₇₉	—	2	2	no	—
353	D₄×C₇₉	—	2	1	no	—
354	D₄×C₇₉	—	2	2	no	—
355	D₄×C₇₉	—	2	1	no	—
356	D₄×C₇₉	—	2	1	no	—
357	D₄×C₇₉	—	2	1	no	—
358	D₄×C₇₉	—	2	2	no	—
359	D₄×C₇₉	—	2	1	no	—
360	D₄×C₇₉	—	4	4	no	—
361	D₄×C₇₉	—	4	4	no	—
362	D₄×C₇₉	—	4	4	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	—	4	1	no	—
369	D₄×C₇₉	—	4	1	no	—
370	D₄×C₇₉	—	4	1	no	—
371	D₄×C₇₉	—	4	1	no	—
372	D₄×C₇₉	—	4	1	no	—
373	D₄×C₇₉	—	8	8	no	—
374	D₄×C₇₉	—	16	2	no	—
375	D₄×C₇₉	#127	1	2	yes	—
376	C₂×C₄×C₇₉	—	2	4	no	—
377	C₂×C₄×C₇₉	—	2	2	no	—
378	C₂×C₄×C₇₉	—	2	1	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	2	no	—
381	C₂×C₄×C₇₉	—	2	2	no	—
382	C₂×C₄×C₇₉	—	2	2	no	—
383	C₂×C₄×C₇₉	—	2	1	no	—
384	C₂×C₄×C₇₉	—	2	1	no	—
385	C₂×C₄×C₇₉	—	4	4	no	—
386	C₂×C₄×C₇₉	—	4	4	no	—
387	C₂×C₄×C₇₉	—	4	4	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	—	4	1	no	—
394	C₂×C₄×C₇₉	—	4	1	no	—
395	C₂×C₄×C₇₉	—	4	1	no	—
396	C₂×C₄×C₇₉	—	4	1	no	—
397	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
403	C₈×C₇₉	—	2	2	no	—
404	C₈×C₇₉	—	2	2	no	—
405	C₈×C₇₉	—	2	2	no	—
406	C₈×C₇₉	—	4	1	no	—
407	C₈×C₇₉	—	4	1	no	—
408	C₈×C₇₉	#120	1	2	yes	—
409	C₈×C₇₉	#120	1	2	yes	—
410	C₂²×C₇₉	—	2	2	no	—
411	C₂²×C₇₉	—	2	2	no	—
412	C₂²×C₇₉	—	4	2	no	—
413	C₂²×C₇₉	—	4	1	no	—
414	C₂²×C₇₉	—	4	1	no	—
415	C₂²×C₇₉	—	4	2	no	—
416	C₂²×C₇₉	—	4	2	no	—
417	C₂²×C₇₉	—	4	2	no	—
418	C₂²×C₇₉	—	8	2	no	—
419	C₂²×C₇₉	—	8	2	no	—
420	C₂²×C₇₉	—	8	2	no	—
421	C₂²×C₇₉	—	8	1	no	—
422	C₂²×C₇₉	—	8	2	no	—
423	C₂²×C₇₉	—	16	1	no	—
424	C₂²×C₇₉	—	16	1	no	—
425	C₂²×C₇₉	—	16	4	no	—
426	C₂²×C₇₉	#535	1	1	yes	characteristic
427	C₂²×C₇₉	D₄²	1	1	yes	characteristic
428	C₂²×C₇₉	D₄²	1	1	yes	characteristic
429	C₄×C₇₉	—	2	4	no	—
430	C₄×C₇₉	—	2	2	no	—
431	C₄×C₇₉	—	4	1	no	—
432	C₄×C₇₉	—	4	2	no	—
433	C₄×C₇₉	—	4	1	no	—
434	C₄×C₇₉	—	4	2	no	—
435	C₄×C₇₉	—	8	1	no	—
436	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
437	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
438	C₄×C₇₉	D₄²	1	1	yes	characteristic
439	C₄×C₇₉	D₄²	1	1	yes	characteristic
440	#25802	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₇₉	—	2	1	no	—
442	C₂×C₇₉	—	2	1	no	—
443	C₂×C₇₉	—	4	2	no	—
444	C₂×C₇₉	—	8	1	no	—
445	C₂×C₇₉	—	8	1	no	—
446	C₂×C₇₉	—	8	2	no	—
447	C₂×C₇₉	—	16	1	no	—
448	C₂×C₇₉	#2433	1	1	yes	characteristic
449	C₂×C₇₉	#3291	1	2	yes	—
450	C₂×#577	C₂×C₇₉	1	1	yes	characteristic, complemented
451	#3154	C₂×C₇₉	1	1	yes	characteristic, complemented
452	C₂×#492	C₂×C₇₉	1	1	yes	characteristic, complemented
453	C₂×#471	C₂×C₇₉	1	1	yes	characteristic, complemented
454	C₂×#456	C₂×C₇₉	1	1	yes	characteristic, complemented
455	C₂×#453	C₂×C₇₉	1	1	yes	characteristic, complemented
456	#3010	C₂×C₇₉	1	1	yes	characteristic, complemented
457	#3009	C₂×C₇₉	1	1	yes	characteristic, complemented
458	#2019	C₂×C₇₉	1	1	yes	characteristic, complemented
459	#2019	C₂×C₇₉	1	1	yes	characteristic, complemented
460	#2005	C₂×C₇₉	1	1	yes	characteristic, complemented
461	#2002	C₂×C₇₉	1	1	yes	characteristic, complemented
462	#1977	C₂×C₇₉	1	1	yes	characteristic, complemented
463	#1974	C₂×C₇₉	1	1	yes	characteristic, complemented
464	#1764	C₂×C₇₉	1	1	yes	characteristic, complemented
465	C₇₉	#25802	1	1	yes	characteristic, direct product factor, Sylow
466	C₂×2₋¹⁺⁴	C₂²×C₇₉	1	1	yes	characteristic
467	C₂×H(5,𝔽₂)	C₂²×C₇₉	1	1	yes	characteristic
468	#577	—	2	4	no	—
469	#577	—	2	4	no	—
470	C₂×#137	—	2	1	no	—
471	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
472	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic
473	C₂×#137	C₂²×C₇₉	1	1	yes	characteristic, complemented
474	C₂×AGL(1,ℤ/8)	—	2	1	no	—
475	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	1	yes	characteristic
476	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	1	yes	characteristic
477	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	1	yes	characteristic
478	C₂×#135	—	2	1	no	—
479	C₂×#135	C₂²×C₇₉	1	1	yes	characteristic
480	C₂²×SD₁₆	—	2	1	no	—
481	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
482	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
483	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
484	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
485	C₂×#131	C₂²×C₇₉	1	1	yes	characteristic
486	#536	C₂²×C₇₉	1	1	yes	characteristic
487	#535	C₂²×C₇₉	1	1	yes	characteristic, complemented
488	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
489	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
490	#497	—	2	1	no	—
491	#496	—	2	1	no	—
492	#495	—	2	1	no	—
493	#492	—	2	4	no	—
494	#492	—	2	1	no	—
495	#471	—	2	4	no	—
496	#456	—	2	4	no	—
497	#453	—	2	4	no	—
498	#452	—	2	2	no	—
499	#450	—	2	2	no	—
500	#449	—	2	2	no	—
501	#448	—	2	2	no	—
502	C₂×#108	C₂²×C₇₉	1	1	yes	characteristic, complemented
503	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic
504	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic
505	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic, complemented
506	#419	C₂²×C₇₉	1	1	yes	characteristic, complemented
507	#418	C₂²×C₇₉	1	1	yes	characteristic
508	#416	C₂²×C₇₉	1	1	yes	characteristic
509	C₂×#101	C₂²×C₇₉	1	1	yes	characteristic, complemented
510	C₂×#101	C₂²×C₇₉	1	1	yes	characteristic, complemented
511	C₂×#100	C₂²×C₇₉	1	1	yes	characteristic
512	C₂×#100	C₂²×C₇₉	1	1	yes	characteristic, complemented
513	#408	C₂²×C₇₉	1	1	yes	characteristic
514	#408	C₂²×C₇₉	1	1	yes	characteristic, complemented
515	#405	C₂²×C₇₉	1	1	yes	characteristic, complemented
516	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
517	#341	C₂²×C₇₉	1	1	yes	characteristic, complemented
518	#339	C₂²×C₇₉	1	1	yes	characteristic, complemented
519	2₋¹⁺⁴	—	2	2	no	—
520	2₋¹⁺⁴	—	2	2	no	—
521	2₋¹⁺⁴	—	2	2	no	—
522	2₋¹⁺⁴	—	4	1	no	—
523	H(5,𝔽₂)	—	2	2	no	—
524	H(5,𝔽₂)	—	2	2	no	—
525	H(5,𝔽₂)	—	2	2	no	—
526	H(5,𝔽₂)	—	4	1	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	4	1	no	—
532	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
533	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
534	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	4	1	no	—
542	C₂²×D₄	—	4	1	no	—
543	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
545	#137	—	2	8	no	—
546	#137	—	2	2	no	—
547	#137	—	2	2	no	—
548	#137	—	2	2	no	—
549	#137	—	2	2	no	—
550	#137	—	2	2	no	—
551	#137	—	4	1	no	—
552	AGL(1,ℤ/8)	—	2	8	no	—
553	AGL(1,ℤ/8)	—	2	2	no	—
554	AGL(1,ℤ/8)	—	2	2	no	—
555	AGL(1,ℤ/8)	—	2	2	no	—
556	AGL(1,ℤ/8)	—	2	2	no	—
557	AGL(1,ℤ/8)	—	2	2	no	—
558	AGL(1,ℤ/8)	—	4	1	no	—
559	#135	—	2	8	no	—
560	#135	—	2	2	no	—
561	#135	—	2	2	no	—
562	C₂×Q₁₆	—	2	1	no	—
563	C₂×Q₁₆	—	2	1	no	—
564	C₂×Q₁₆	—	2	1	no	—
565	C₂×Q₁₆	D₄×C₇₉	1	1	yes	characteristic, complemented
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	2	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	—	2	2	no	—
578	C₂×SD₁₆	—	2	2	no	—
579	C₂×SD₁₆	—	2	2	no	—
580	C₂×SD₁₆	—	2	2	no	—
581	C₂×SD₁₆	—	2	2	no	—
582	C₂×SD₁₆	—	2	1	no	—
583	C₂×SD₁₆	—	2	1	no	—
584	C₂×SD₁₆	—	4	1	no	—
585	C₂×SD₁₆	—	4	1	no	—
586	C₂×SD₁₆	D₄×C₇₉	1	1	yes	characteristic, complemented
587	C₂×SD₁₆	D₄×C₇₉	1	4	yes	complemented
588	C₂×SD₁₆	D₄×C₇₉	1	1	yes	characteristic, complemented
589	C₂×D₈	—	2	1	no	—
590	C₂×D₈	—	2	1	no	—
591	C₂×D₈	—	2	1	no	—
592	C₂×D₈	D₄×C₇₉	1	1	yes	characteristic, complemented
593	#131	—	2	2	no	—
594	#131	D₄×C₇₉	1	4	yes	complemented
595	C₂×M₁₆	—	2	1	no	—
596	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
598	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
600	C₂²×C₈	—	2	1	no	—
601	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
603	C₄⋊Q₈	—	2	2	no	—
604	C₄⋊Q₈	—	2	1	no	—
605	C₄⋊Q₈	—	2	2	no	—
606	#127	—	2	2	no	—
607	#127	—	2	1	no	—
608	#127	—	2	2	no	—
609	#124	—	2	1	no	—
610	#124	—	2	1	no	—
611	#123	—	4	1	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	#121	—	2	2	no	—
614	#120	—	4	1	no	—
615	#117	C₂³×C₇₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	—	4	1	no	—
617	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
618	#108	—	2	2	no	—
619	#104	—	2	2	no	—
620	#104	—	2	2	no	—
621	#104	D₄×C₇₉	1	4	yes	complemented
622	#103	—	2	2	no	—
623	#103	D₄×C₇₉	1	2	yes	complemented
624	#102	—	2	2	no	—
625	#102	D₄×C₇₉	1	2	yes	complemented
626	#101	—	2	2	no	—
627	#101	—	2	2	no	—
628	#100	—	2	2	no	—
629	#100	—	2	2	no	—
630	C₂²⋊C₈	—	2	2	no	—
631	C₂²⋊C₈	—	2	2	no	—
632	#97	—	2	1	no	—
633	C₄×C₈	—	2	2	no	—
634	C₄×C₈	—	2	1	no	—
635	C₂⁴	—	2	1	no	—
636	C₂⁴	—	2	1	no	—
637	C₂⁴	—	4	1	no	—
638	#41	—	2	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	4	no	—
641	#41	—	2	4	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	2	1	no	—
649	#41	—	2	1	no	—
650	#41	—	4	2	no	—
651	#41	—	4	4	no	—
652	#41	—	4	2	no	—
653	#41	—	4	2	no	—
654	#41	—	4	2	no	—
655	#41	—	4	4	no	—
656	#41	—	4	2	no	—
657	#41	—	4	2	no	—
658	#41	C₂×D₄×C₇₉	1	2	yes	—
659	#41	C₂×D₄×C₇₉	1	2	yes	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	4	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	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	4	1	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
678	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
679	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	4	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	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	1	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	8	4	no	—
706	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
707	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
708	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
720	Q₁₆	—	2	4	no	—
721	Q₁₆	—	2	2	no	—
722	Q₁₆	—	4	2	no	—
723	Q₁₆	—	4	2	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	2	4	no	—
726	SD₁₆	—	2	2	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	2	2	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	4	no	—
733	SD₁₆	—	4	2	no	—
734	SD₁₆	—	4	2	no	—
735	SD₁₆	—	4	2	no	—
736	SD₁₆	—	4	2	no	—
737	SD₁₆	—	4	2	no	—
738	D₈	—	2	4	no	—
739	D₈	—	2	2	no	—
740	D₈	—	4	2	no	—
741	D₈	—	4	2	no	—
742	M₁₆	—	2	1	no	—
743	M₁₆	—	2	1	no	—
744	M₁₆	—	2	4	no	—
745	M₁₆	—	2	1	no	—
746	M₁₆	—	2	1	no	—
747	M₁₆	—	2	1	no	—
748	M₁₆	—	2	1	no	—
749	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
750	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	4	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
759	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
760	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
761	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
762	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
763	C₄⋊C₄	—	4	4	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	1	no	—
771	C₄²	C₂×D₄×C₇₉	1	2	yes	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	8	2	no	—
783	C₂³	—	8	2	no	—
784	C₂³	—	16	2	no	—
785	C₂³	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	1	no	—
793	Q₈	—	4	4	no	—
794	Q₈	—	4	1	no	—
795	Q₈	—	4	1	no	—
796	Q₈	—	4	1	no	—
797	Q₈	—	4	1	no	—
798	Q₈	—	4	1	no	—
799	Q₈	—	4	1	no	—
800	Q₈	#127×C₇₉	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	1	no	—
814	D₄	—	4	1	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	1	no	—
818	D₄	—	4	1	no	—
819	D₄	—	4	1	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	8	8	no	—
824	D₄	—	16	2	no	—
825	D₄	#127×C₇₉	1	2	yes	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
852	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₈	#120×C₇₉	1	2	yes	—
859	C₈	#120×C₇₉	1	2	yes	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	8	2	no	—
869	C₂²	—	8	2	no	—
870	C₂²	—	8	2	no	—
871	C₂²	—	8	2	no	—
872	C₂²	—	8	1	no	—
873	C₂²	—	16	1	no	—
874	C₂²	—	16	1	no	—
875	C₂²	—	16	4	no	—
876	C₂²	#535×C₇₉	1	1	yes	characteristic
877	C₂²	D₄²×C₇₉	1	1	yes	characteristic
878	C₂²	D₄²×C₇₉	1	1	yes	characteristic
879	C₄	—	2	4	no	—
880	C₄	—	2	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	2	no	—
885	C₄	—	8	1	no	—
886	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
887	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
888	C₄	D₄²×C₇₉	1	1	yes	characteristic
889	C₄	D₄²×C₇₉	1	1	yes	characteristic
890	C₂	—	2	1	no	—
891	C₂	—	2	1	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	1	no	—
894	C₂	—	8	1	no	—
895	C₂	—	8	2	no	—
896	C₂	—	16	1	no	—
897	C₂	C₇₉×#2433	1	1	yes	characteristic
898	C₂	C₇₉×#3291	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
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
1. C₂×#577×C₇₉	C₂	semidirect
2. C₇₉×#3154	C₂	semidirect
3. C₂×#492×C₇₉	C₂	semidirect
4. C₂×#471×C₇₉	C₂	semidirect
5. C₂×#456×C₇₉	C₂	semidirect
6. C₂×#453×C₇₉	C₂	semidirect
7. C₇₉×#3010	C₂	semidirect
8. C₇₉×#3009	C₂	semidirect
9. C₇₉×#2019	C₂	semidirect
10. C₇₉×#2019	C₂	semidirect
11. C₇₉×#2005	C₂	semidirect
12. C₇₉×#2002	C₂	semidirect
13. C₇₉×#1977	C₂	semidirect
14. C₇₉×#1974	C₂	semidirect
15. C₇₉×#1764	C₂	semidirect
23. C₂×#137×C₇₉	C₂²	semidirect
33. C₂²×SD₁₆×C₇₉	C₂²	semidirect
34. C₂²×SD₁₆×C₇₉	C₂²	semidirect
37. #535×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
62. C₂×#100×C₇₉	C₂²	semidirect
64. #408×C₇₉	C₂²	semidirect
65. #405×C₇₉	C₂²	semidirect
66. C₂×C₄×C₈×C₇₉	C₂²	semidirect
67. #341×C₇₉	C₂²	semidirect
68. #339×C₇₉	C₂²	semidirect
115. C₂×Q₁₆×C₇₉	D₄	semidirect
136. C₂×SD₁₆×C₇₉	D₄	semidirect
137. C₂×SD₁₆×C₇₉	D₄	semidirect
138. C₂×SD₁₆×C₇₉	D₄	semidirect
142. C₂×D₈×C₇₉	D₄	semidirect
144. #131×C₇₉	D₄	semidirect
171. #104×C₇₉	D₄	semidirect
173. #103×C₇₉	D₄	semidirect
175. #102×C₇₉	D₄	semidirect
440. #25802	C₇₉	direct (N × H)
450. C₂×#577	C₂×C₇₉	semidirect
451. #3154	C₂×C₇₉	semidirect
452. C₂×#492	C₂×C₇₉	semidirect
453. C₂×#471	C₂×C₇₉	semidirect
454. C₂×#456	C₂×C₇₉	semidirect
455. C₂×#453	C₂×C₇₉	semidirect
456. #3010	C₂×C₇₉	semidirect
457. #3009	C₂×C₇₉	semidirect
458. #2019	C₂×C₇₉	semidirect
459. #2019	C₂×C₇₉	semidirect
460. #2005	C₂×C₇₉	semidirect
461. #2002	C₂×C₇₉	semidirect
462. #1977	C₂×C₇₉	semidirect
463. #1974	C₂×C₇₉	semidirect
464. #1764	C₂×C₇₉	semidirect
465. C₇₉	#25802	direct (N × H)
473. C₂×#137	C₂²×C₇₉	semidirect
483. C₂²×SD₁₆	C₂²×C₇₉	semidirect
484. C₂²×SD₁₆	C₂²×C₇₉	semidirect
487. #535	C₂²×C₇₉	semidirect
488. C₂×C₄⋊Q₈	C₂²×C₇₉	semidirect
502. C₂×#108	C₂²×C₇₉	semidirect
505. C₂×#104	C₂²×C₇₉	semidirect
506. #419	C₂²×C₇₉	semidirect
509. C₂×#101	C₂²×C₇₉	semidirect
510. C₂×#101	C₂²×C₇₉	semidirect
512. C₂×#100	C₂²×C₇₉	semidirect
514. #408	C₂²×C₇₉	semidirect
515. #405	C₂²×C₇₉	semidirect
516. C₂×C₄×C₈	C₂²×C₇₉	semidirect
517. #341	C₂²×C₇₉	semidirect
518. #339	C₂²×C₇₉	semidirect
565. C₂×Q₁₆	D₄×C₇₉	semidirect
586. C₂×SD₁₆	D₄×C₇₉	semidirect
587. C₂×SD₁₆	D₄×C₇₉	semidirect
588. C₂×SD₁₆	D₄×C₇₉	semidirect
592. C₂×D₈	D₄×C₇₉	semidirect
594. #131	D₄×C₇₉	semidirect
621. #104	D₄×C₇₉	semidirect
623. #103	D₄×C₇₉	semidirect
625. #102	D₄×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×#3154	2
C₂×#492×C₇₉	2
C₂×#471×C₇₉	2
C₂×#456×C₇₉	2
C₂×#453×C₇₉	2
C₇₉×#3010	2
C₇₉×#3009	2
C₇₉×#2019	2
C₇₉×#2005	2
C₇₉×#2002	2
C₇₉×#1977	2
C₇₉×#1974	2
C₇₉×#1764	2
#25802	79

Subgroups — C79×#25802 #34137491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25802 #34137491