Subgroups — #3584×D₇₉ #35202096

Order 20224.

10858 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#585×D₇₉	C₂	1	2	yes	maximal, complemented
2	#23778174	C₂	1	1	yes	maximal, characteristic, complemented
3	#23778173	C₂	1	6	yes	maximal, complemented
4	#23778172	C₂	1	8	yes	maximal, complemented
5	#23778171	C₂	1	2	yes	maximal, complemented
6	#23778170	C₂	1	4	yes	maximal, complemented
7	#23778169	C₂	1	6	yes	maximal, complemented
8	#23778168	C₂	1	4	yes	maximal, complemented
9	#578×D₇₉	C₂	1	4	yes	maximal, complemented
10	#577×D₇₉	C₂	1	8	yes	maximal, complemented
11	#576×D₇₉	C₂	1	4	yes	maximal, complemented
12	#575×D₇₉	C₂	1	6	yes	maximal, complemented
13	C₂×#135×D₇₉	C₂	1	6	yes	maximal, complemented
14	C₂×#131×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3584	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099400	—	2	2	no	—
17	#19099400	C₂²	1	8	yes	complemented
18	#19099399	—	2	8	no	—
19	#19099399	C₂²	1	2	yes	complemented
20	#19099399	C₂²	1	12	yes	complemented
21	#19099398	—	2	6	no	—
22	#19099398	C₂²	1	8	yes	complemented
23	2₋¹⁺⁴×D₇₉	—	2	2	no	—
24	2₋¹⁺⁴×D₇₉	C₂²	1	8	yes	complemented
25	H(5,𝔽₂)×D₇₉	—	2	6	no	—
26	H(5,𝔽₂)×D₇₉	C₂²	1	8	yes	complemented
27	C₂×#41×D₇₉	—	2	8	no	—
28	C₂×#41×D₇₉	C₂²	1	1	yes	characteristic
29	C₂×#41×D₇₉	C₂²	1	12	yes	complemented
30	#19099380	C₂²	1	4	yes	complemented
31	#19099379	C₂²	1	24	yes	complemented
32	#19099378	C₂²	1	8	yes	complemented
33	#19099377	C₂²	1	12	yes	complemented
34	#19099376	C₂²	1	12	yes	complemented
35	#19099375	C₂²	1	8	yes	complemented
36	#19099374	C₂²	1	8	yes	complemented
37	#19099373	C₂²	1	24	yes	complemented
38	#19099372	C₂²	1	24	yes	complemented
39	#19099371	C₂²	1	8	yes	complemented
40	#19099370	C₂²	1	24	yes	complemented
41	#19099369	C₂²	1	24	yes	complemented
42	#19099368	C₂²	1	4	yes	complemented
43	#19099367	C₂²	1	24	yes	complemented
44	#19099366	C₂²	1	8	yes	complemented
45	#19099365	C₂²	1	12	yes	complemented
46	#19099364	C₂²	1	12	yes	complemented
47	#19099363	C₂²	1	6	yes	complemented
48	#19099362	C₂²	1	24	yes	complemented
49	#19099361	C₂²	1	12	yes	complemented
50	#19099360	C₂²	1	24	yes	complemented
51	#19099359	C₂²	1	24	yes	complemented
52	#137×D₇₉	C₂²	1	24	yes	complemented
53	AGL(1,ℤ/8)×D₇₉	C₂²	1	24	yes	complemented
54	C₂×#14579184	C₂²	1	6	yes	complemented
55	C₂×#14579183	C₂²	1	6	yes	complemented
56	C₂×#14579182	C₂²	1	12	yes	complemented
57	C₂×#14579181	C₂²	1	12	yes	complemented
58	C₂×#14579180	C₂²	1	6	yes	complemented
59	#135×D₇₉	C₂²	1	4	yes	complemented
60	#135×D₇₉	C₂²	1	12	yes	complemented
61	#135×D₇₉	C₂²	1	12	yes	complemented
62	#135×D₇₉	C₂²	1	12	yes	complemented
63	#135×D₇₉	C₂²	1	12	yes	complemented
64	#135×D₇₉	C₂²	1	12	yes	complemented
65	#135×D₇₉	C₂²	1	12	yes	complemented
66	#135×D₇₉	C₂²	1	12	yes	complemented
67	C₂×Q₁₆×D₇₉	C₂²	1	6	yes	complemented
68	C₂×SD₁₆×D₇₉	C₂²	1	12	yes	complemented
69	C₂×D₈×D₇₉	C₂²	1	6	yes	complemented
70	C₂×#14579169	C₂²	1	3	yes	complemented
71	C₂×#14579168	C₂²	1	1	yes	characteristic, complemented
72	C₂×#14579167	C₂²	1	3	yes	complemented
73	#131×D₇₉	C₂²	1	4	yes	complemented
74	#131×D₇₉	C₂²	1	4	yes	complemented
75	#131×D₇₉	C₂²	1	4	yes	complemented
76	#131×D₇₉	C₂²	1	4	yes	complemented
77	C₂×M₁₆×D₇₉	C₂²	1	3	yes	complemented
78	C₂²×C₈×D₇₉	C₂²	1	3	yes	complemented
79	#585×C₇₉	C₂²	1	2	yes	complemented
80	#578×C₇₉	C₂²	1	4	yes	complemented
81	#577×C₇₉	C₂²	1	8	yes	complemented
82	#576×C₇₉	C₂²	1	4	yes	complemented
83	#575×C₇₉	C₂²	1	6	yes	complemented
84	C₂×#135×C₇₉	C₂²	1	6	yes	complemented
85	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic, complemented
86	#14579209	—	2	2	no	—
87	#14579209	—	2	8	no	—
88	#14579209	—	2	8	no	—
89	#14579209	C₂³	1	24	yes	complemented
90	#14579208	—	2	24	no	—
91	#14579208	—	2	12	no	—
92	#14579208	—	2	8	no	—
93	#14579208	C₂³	1	8	yes	complemented
94	#14579208	C₂³	1	24	yes	complemented
95	#14579207	—	2	8	no	—
96	#14579207	—	2	12	no	—
97	#14579207	—	2	24	no	—
98	#14579207	C₂³	1	8	yes	complemented
99	#14579207	C₂³	1	24	yes	complemented
100	#14579206	—	2	6	no	—
101	#14579206	—	2	24	no	—
102	#14579206	—	2	24	no	—
103	#14579206	—	2	24	no	—
104	#14579206	C₂³	1	24	yes	complemented
105	C₂×#11929625	—	2	8	no	—
106	C₂×#11929625	D₄	1	1	yes	characteristic
107	C₂×#11929625	C₂³	1	12	yes	complemented
108	C₂×#11929624	—	2	24	no	—
109	C₂×#11929624	—	2	12	no	—
110	C₂×#11929624	C₂³	1	3	yes	—
111	C₂×#11929624	C₂³	1	12	yes	complemented
112	C₂×#11929623	—	2	24	no	—
113	C₂×#11929623	—	2	12	no	—
114	C₂×#11929623	D₄	1	3	yes	—
115	C₂×#11929623	C₂³	1	12	yes	complemented
116	#41×D₇₉	—	2	8	no	—
117	#41×D₇₉	—	2	8	no	—
118	#41×D₇₉	—	2	24	no	—
119	#41×D₇₉	—	2	24	no	—
120	#41×D₇₉	—	2	8	no	—
121	#41×D₇₉	—	2	24	no	—
122	#41×D₇₉	—	2	12	no	—
123	#41×D₇₉	—	2	12	no	—
124	#41×D₇₉	—	2	12	no	—
125	#41×D₇₉	—	2	12	no	—
126	#41×D₇₉	D₄	1	4	yes	—
127	#41×D₇₉	D₄	1	4	yes	—
128	#41×D₇₉	C₂³	1	24	yes	—
129	#41×D₇₉	C₂³	1	8	yes	—
130	#41×D₇₉	C₂³	1	4	yes	—
131	#41×D₇₉	C₂³	1	4	yes	—
132	#41×D₇₉	C₂³	1	24	yes	complemented
133	#41×D₇₉	C₂³	1	24	yes	complemented
134	C₂×Q₈×D₇₉	—	2	8	no	—
135	C₂×Q₈×D₇₉	D₄	1	1	yes	characteristic
136	C₂×Q₈×D₇₉	C₂³	1	12	yes	—
137	C₂×D₄×D₇₉	—	2	12	no	—
138	C₂×D₄×D₇₉	—	2	24	no	—
139	C₂×D₄×D₇₉	D₄	1	3	yes	—
140	C₂×D₄×D₇₉	C₂³	1	12	yes	—
141	C₂²×C₄×D₇₉	—	2	12	no	—
142	C₂²×C₄×D₇₉	C₂³	1	3	yes	—
143	#14579194	C₂³	1	24	yes	complemented
144	#14579193	C₂³	1	48	yes	complemented
145	#14579192	C₂³	1	24	yes	complemented
146	#14579191	C₂³	1	24	yes	complemented
147	#14579190	C₂³	1	48	yes	complemented
148	#14579189	C₂³	1	24	yes	complemented
149	#14579188	C₂³	1	48	yes	complemented
150	#14579187	C₂³	1	24	yes	complemented
151	#14579186	C₂³	1	24	yes	complemented
152	#14579185	C₂³	1	48	yes	complemented
153	#14579184	C₂³	1	4	yes	complemented
154	#14579184	C₂³	1	12	yes	complemented
155	#14579184	C₂³	1	12	yes	complemented
156	#14579184	C₂³	1	12	yes	complemented
157	#14579183	C₂³	1	4	yes	complemented
158	#14579183	C₂³	1	12	yes	complemented
159	#14579183	C₂³	1	12	yes	complemented
160	#14579183	C₂³	1	12	yes	complemented
161	#14579182	C₂³	1	8	yes	complemented
162	#14579182	C₂³	1	24	yes	complemented
163	#14579182	C₂³	1	24	yes	complemented
164	#14579182	C₂³	1	24	yes	complemented
165	#14579181	C₂³	1	8	yes	complemented
166	#14579181	C₂³	1	24	yes	complemented
167	#14579181	C₂³	1	24	yes	complemented
168	#14579181	C₂³	1	24	yes	complemented
169	#14579180	C₂³	1	4	yes	complemented
170	#14579180	C₂³	1	12	yes	complemented
171	#14579180	C₂³	1	12	yes	complemented
172	#14579180	C₂³	1	12	yes	complemented
173	C₂×Dic₃₁₆	C₂³	1	6	yes	complemented
174	C₂×#11929614	C₂³	1	12	yes	complemented
175	Q₁₆×D₇₉	C₂³	1	4	yes	—
176	Q₁₆×D₇₉	C₂³	1	12	yes	—
177	Q₁₆×D₇₉	C₂³	1	12	yes	complemented
178	Q₁₆×D₇₉	C₂³	1	12	yes	complemented
179	C₂×#11929613	C₂³	1	12	yes	complemented
180	C₂×#11929612	C₂³	1	12	yes	complemented
181	C₂×#11929611	C₂³	1	12	yes	complemented
182	SD₁₆×D₇₉	C₂³	1	8	yes	—
183	SD₁₆×D₇₉	C₂³	1	24	yes	—
184	SD₁₆×D₇₉	C₂³	1	24	yes	complemented
185	SD₁₆×D₇₉	C₂³	1	24	yes	complemented
186	C₂×D₆₃₂	C₂³	1	6	yes	complemented
187	C₂×#11929609	C₂³	1	12	yes	complemented
188	D₈×D₇₉	C₂³	1	4	yes	—
189	D₈×D₇₉	C₂³	1	12	yes	—
190	D₈×D₇₉	C₂³	1	12	yes	complemented
191	D₈×D₇₉	C₂³	1	12	yes	complemented
192	#14579169	C₂³	1	12	yes	complemented
193	#14579169	C₂³	1	12	yes	complemented
194	#14579168	C₂³	1	4	yes	complemented
195	#14579168	C₂³	1	4	yes	complemented
196	#14579167	C₂³	1	12	yes	complemented
197	#14579167	C₂³	1	12	yes	complemented
198	C₂×#11929608	C₂³	1	3	yes	complemented
199	C₂×#11929607	C₂³	1	6	yes	complemented
200	M₁₆×D₇₉	C₂³	1	12	yes	—
201	M₁₆×D₇₉	C₂³	1	12	yes	complemented
202	C₂²×C₇₉⋊C₈	C₂³	1	3	yes	complemented
203	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
204	C₂×C₈×D₇₉	C₂³	1	3	yes	—
205	C₂×C₈×D₇₉	C₂³	1	6	yes	—
206	C₂×C₈×D₇₉	C₂³	1	6	yes	—
207	C₂×C₈×D₇₉	C₂³	1	6	yes	complemented
208	C₂×C₈×D₇₉	C₂³	1	6	yes	complemented
209	C₂×C₈×D₇₉	C₂³	1	3	yes	complemented
210	C₂×C₈×D₇₉	C₂³	1	3	yes	complemented
211	2₋¹⁺⁴×C₇₉	—	2	2	no	—
212	2₋¹⁺⁴×C₇₉	C₂³	1	8	yes	complemented
213	H(5,𝔽₂)×C₇₉	—	2	6	no	—
214	H(5,𝔽₂)×C₇₉	C₂³	1	8	yes	complemented
215	C₂×#41×C₇₉	—	2	8	no	—
216	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
217	C₂×#41×C₇₉	C₂³	1	12	yes	complemented
218	#137×C₇₉	C₂³	1	24	yes	complemented
219	AGL(1,ℤ/8)×C₇₉	C₂³	1	24	yes	complemented
220	#135×C₇₉	C₂³	1	4	yes	complemented
221	#135×C₇₉	C₂³	1	12	yes	complemented
222	#135×C₇₉	C₂³	1	12	yes	complemented
223	#135×C₇₉	C₂³	1	12	yes	complemented
224	C₂×Q₁₆×C₇₉	C₂³	1	6	yes	complemented
225	C₂×SD₁₆×C₇₉	C₂³	1	12	yes	complemented
226	C₂×D₈×C₇₉	C₂³	1	6	yes	complemented
227	#131×C₇₉	C₂³	1	4	yes	complemented
228	#131×C₇₉	C₂³	1	4	yes	complemented
229	C₂×M₁₆×C₇₉	C₂³	1	3	yes	complemented
230	C₂²×C₈×C₇₉	C₂³	1	3	yes	complemented
231	C₂³×D₇₉	—	2	12	no	—
232	C₂³×D₇₉	C₂×D₄	1	3	yes	—
233	#11929625	—	2	24	no	—
234	#11929625	—	2	12	no	—
235	#11929625	—	2	12	no	—
236	#11929625	—	2	8	no	—
237	#11929625	C₂×D₄	1	4	yes	—
238	#11929625	C₂×D₄	1	4	yes	—
239	#11929625	C₂⁴	1	8	yes	—
240	#11929625	C₂⁴	1	24	yes	—
241	#11929624	—	2	24	no	—
242	#11929624	—	2	8	no	—
243	#11929624	—	2	24	no	—
244	#11929624	—	2	24	no	—
245	#11929624	—	2	24	no	—
246	#11929624	—	2	24	no	—
247	#11929624	—	2	12	no	—
248	#11929624	—	2	12	no	—
249	#11929624	—	2	48	no	—
250	#11929624	C₂×D₄	1	12	yes	—
251	#11929624	C₂⁴	1	8	yes	—
252	#11929624	C₂⁴	1	24	yes	—
253	#11929624	C₂⁴	1	12	yes	—
254	#11929623	—	2	8	no	—
255	#11929623	—	2	24	no	—
256	#11929623	—	2	24	no	—
257	#11929623	—	2	24	no	—
258	#11929623	—	2	12	no	—
259	#11929623	—	2	12	no	—
260	#11929623	—	2	24	no	—
261	#11929623	—	2	24	no	—
262	#11929623	—	2	48	no	—
263	#11929623	C₂×D₄	1	12	yes	—
264	#11929623	C₂×D₄	1	12	yes	—
265	#11929623	C₂⁴	1	8	yes	—
266	#11929623	C₂⁴	1	24	yes	—
267	C₂×Dic₁₅₈	—	2	12	no	—
268	C₂×Dic₁₅₈	—	2	24	no	—
269	C₂×Dic₁₅₈	C₂×D₄	1	3	yes	—
270	C₂×Dic₁₅₈	C₂⁴	1	12	yes	—
271	Q₈×D₇₉	—	2	12	no	—
272	Q₈×D₇₉	—	2	12	no	—
273	Q₈×D₇₉	—	2	24	no	—
274	Q₈×D₇₉	—	2	8	no	—
275	Q₈×D₇₉	C₂×D₄	1	4	yes	—
276	Q₈×D₇₉	C₂×D₄	1	4	yes	—
277	Q₈×D₇₉	C₂⁴	1	8	yes	—
278	Q₈×D₇₉	C₂⁴	1	24	yes	—
279	C₂×D₃₁₆	—	2	24	no	—
280	C₂×D₃₁₆	—	2	12	no	—
281	C₂×D₃₁₆	C₂×D₄	1	3	yes	—
282	C₂×D₃₁₆	C₂⁴	1	12	yes	—
283	C₂×C₂²⋊D₇₉	—	2	12	no	—
284	C₂×C₂²⋊D₇₉	—	2	12	no	—
285	C₂×C₂²⋊D₇₉	—	2	12	no	—
286	C₂×C₂²⋊D₇₉	—	2	48	no	—
287	C₂×C₂²⋊D₇₉	C₂×D₄	1	6	yes	—
288	D₄×D₇₉	—	2	24	no	—
289	D₄×D₇₉	—	2	12	no	—
290	D₄×D₇₉	—	2	12	no	—
291	D₄×D₇₉	—	2	24	no	—
292	D₄×D₇₉	—	2	8	no	—
293	D₄×D₇₉	—	2	24	no	—
294	D₄×D₇₉	—	2	24	no	—
295	D₄×D₇₉	—	2	24	no	—
296	D₄×D₇₉	—	2	48	no	—
297	D₄×D₇₉	C₂×D₄	1	12	yes	—
298	D₄×D₇₉	C₂×D₄	1	12	yes	—
299	D₄×D₇₉	C₂⁴	1	8	yes	—
300	D₄×D₇₉	C₂⁴	1	24	yes	—
301	C₂²×Dic₇₉	—	2	12	no	—
302	C₂²×Dic₇₉	C₂×D₄	1	3	yes	—
303	C₂×C₄×D₇₉	—	2	12	no	—
304	C₂×C₄×D₇₉	—	2	24	no	—
305	C₂×C₄×D₇₉	—	2	8	no	—
306	C₂×C₄×D₇₉	—	2	24	no	—
307	C₂×C₄×D₇₉	—	2	24	no	—
308	C₂×C₄×D₇₉	—	2	12	no	—
309	C₂×C₄×D₇₉	—	2	12	no	—
310	C₂×C₄×D₇₉	C₂×D₄	1	3	yes	—
311	C₂×C₄×D₇₉	C₂×D₄	1	3	yes	—
312	C₂×C₄×D₇₉	C₂×D₄	1	6	yes	—
313	C₂×C₄×D₇₉	C₂×D₄	1	6	yes	—
314	C₂×C₄×D₇₉	C₂⁴	1	6	yes	—
315	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
316	C₂×C₄×D₇₉	C₂⁴	1	6	yes	—
317	C₂×C₄×D₇₉	C₂⁴	1	3	yes	—
318	Dic₃₁₆	C₂⁴	1	4	yes	—
319	Dic₃₁₆	C₂⁴	1	12	yes	—
320	#11929614	C₂⁴	1	8	yes	—
321	#11929614	C₂⁴	1	24	yes	—
322	#11929613	C₂⁴	1	8	yes	—
323	#11929613	C₂⁴	1	24	yes	—
324	#11929612	C₂⁴	1	8	yes	—
325	#11929612	C₂⁴	1	24	yes	—
326	#11929611	C₂⁴	1	8	yes	—
327	#11929611	C₂⁴	1	24	yes	—
328	D₆₃₂	C₂⁴	1	4	yes	—
329	D₆₃₂	C₂⁴	1	12	yes	—
330	#11929609	C₂⁴	1	8	yes	—
331	#11929609	C₂⁴	1	24	yes	—
332	#11929608	C₂⁴	1	12	yes	—
333	#11929607	C₂⁴	1	24	yes	—
334	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
335	C₂×C₇₉⋊C₈	C₂⁴	1	3	yes	—
336	C₂×C₇₉⋊C₈	C₂⁴	1	6	yes	—
337	C₂×C₇₉⋊C₈	C₂⁴	1	6	yes	—
338	C₈×D₇₉	C₂⁴	1	1	yes	characteristic
339	C₈×D₇₉	C₂⁴	1	1	yes	characteristic
340	C₈×D₇₉	C₂⁴	1	6	yes	—
341	C₈×D₇₉	C₂⁴	1	1	yes	characteristic
342	C₈×D₇₉	C₂⁴	1	1	yes	characteristic
343	C₈×D₇₉	C₂⁴	1	6	yes	—
344	C₈×D₇₉	C₂⁴	1	6	yes	—
345	C₈×D₇₉	C₂⁴	1	6	yes	—
346	C₈×D₇₉	C₂⁴	1	6	yes	—
347	C₈×D₇₉	C₂⁴	1	6	yes	—
348	#41×C₇₉	—	2	8	no	—
349	#41×C₇₉	—	2	24	no	—
350	#41×C₇₉	—	2	12	no	—
351	#41×C₇₉	—	2	12	no	—
352	#41×C₇₉	C₂×D₄	1	4	yes	—
353	#41×C₇₉	C₂⁴	1	8	yes	—
354	#41×C₇₉	C₂⁴	1	24	yes	—
355	#41×C₇₉	C₂⁴	1	4	yes	—
356	C₂×Q₈×C₇₉	—	2	8	no	—
357	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₇₉	C₂⁴	1	12	yes	—
359	C₂×D₄×C₇₉	—	2	12	no	—
360	C₂×D₄×C₇₉	—	2	24	no	—
361	C₂×D₄×C₇₉	C₂×D₄	1	3	yes	—
362	C₂×D₄×C₇₉	C₂⁴	1	12	yes	—
363	C₂²×C₄×C₇₉	—	2	12	no	—
364	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
365	Q₁₆×C₇₉	C₂⁴	1	4	yes	—
366	Q₁₆×C₇₉	C₂⁴	1	12	yes	—
367	SD₁₆×C₇₉	C₂⁴	1	8	yes	—
368	SD₁₆×C₇₉	C₂⁴	1	24	yes	—
369	D₈×C₇₉	C₂⁴	1	4	yes	—
370	D₈×C₇₉	C₂⁴	1	12	yes	—
371	M₁₆×C₇₉	C₂⁴	1	12	yes	—
372	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₇₉	C₂⁴	1	3	yes	—
374	C₂×C₈×C₇₉	C₂⁴	1	6	yes	—
375	C₂×C₈×C₇₉	C₂⁴	1	6	yes	—
376	C₂³×C₇₉	—	2	12	no	—
377	C₂³×C₇₉	C₂²×D₄	1	3	yes	—
378	C₂²×D₇₉	—	2	12	no	—
379	C₂²×D₇₉	—	2	8	no	—
380	C₂²×D₇₉	—	2	24	no	—
381	C₂²×D₇₉	—	4	6	no	—
382	C₂²×D₇₉	—	8	24	no	—
383	C₂²×D₇₉	C₂²×D₄	1	6	yes	—
384	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
385	C₂²×D₇₉	C₂²×D₄	1	3	yes	—
386	C₂²×D₇₉	C₂²×D₄	1	6	yes	—
387	Q₈×C₇₉	—	2	12	no	—
388	Q₈×C₇₉	C₂²×D₄	1	4	yes	—
389	Q₈×C₇₉	C₂⁵	1	8	yes	—
390	D₄×C₇₉	—	2	8	no	—
391	D₄×C₇₉	—	2	24	no	—
392	D₄×C₇₉	—	2	12	no	—
393	D₄×C₇₉	C₂²×D₄	1	12	yes	—
394	D₄×C₇₉	C₂⁵	1	8	yes	—
395	C₂×C₄×C₇₉	—	2	12	no	—
396	C₂×C₄×C₇₉	—	2	8	no	—
397	C₂×C₄×C₇₉	—	2	24	no	—
398	C₂×C₄×C₇₉	C₂²×D₄	1	6	yes	—
399	C₂×C₄×C₇₉	C₂²×D₄	1	3	yes	—
400	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
401	C₂×C₄×C₇₉	C₂⁵	1	6	yes	—
402	C₂²⋊D₇₉	—	2	8	no	—
403	C₂²⋊D₇₉	—	2	24	no	—
404	C₂²⋊D₇₉	—	2	8	no	—
405	C₂²⋊D₇₉	—	2	24	no	—
406	C₂²⋊D₇₉	—	2	8	no	—
407	C₂²⋊D₇₉	—	2	24	no	—
408	C₂²⋊D₇₉	C₂²×D₄	1	24	yes	—
409	C₂×Dic₇₉	—	2	12	no	—
410	C₂×Dic₇₉	—	2	8	no	—
411	C₂×Dic₇₉	—	2	24	no	—
412	C₂×Dic₇₉	C₂²×D₄	1	6	yes	—
413	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
414	C₂×Dic₇₉	C₂²×D₄	1	6	yes	—
415	C₂×Dic₇₉	C₂²×D₄	1	3	yes	—
416	D₃₁₆	—	2	8	no	—
417	D₃₁₆	—	2	24	no	—
418	D₃₁₆	—	2	12	no	—
419	D₃₁₆	C₂²×D₄	1	12	yes	—
420	D₃₁₆	C₂⁵	1	8	yes	—
421	C₄×D₇₉	—	2	8	no	—
422	C₄×D₇₉	—	2	24	no	—
423	C₄×D₇₉	—	2	8	no	—
424	C₄×D₇₉	—	2	24	no	—
425	C₄×D₇₉	—	2	8	no	—
426	C₄×D₇₉	—	2	24	no	—
427	C₄×D₇₉	C₂²×D₄	1	1	yes	characteristic
428	C₄×D₇₉	C₂²×D₄	1	6	yes	—
429	C₄×D₇₉	C₂²×D₄	1	6	yes	—
430	C₄×D₇₉	C₂²×D₄	1	6	yes	—
431	C₄×D₇₉	C₂²×D₄	1	1	yes	characteristic
432	C₄×D₇₉	C₂²×D₄	1	6	yes	—
433	C₄×D₇₉	C₂²×D₄	1	6	yes	—
434	C₄×D₇₉	C₂⁵	1	1	yes	characteristic
435	C₄×D₇₉	C₂⁵	1	1	yes	characteristic
436	C₄×D₇₉	C₂⁵	1	6	yes	—
437	Dic₁₅₈	—	2	12	no	—
438	Dic₁₅₈	—	2	8	no	—
439	Dic₁₅₈	—	2	24	no	—
440	Dic₁₅₈	C₂²×D₄	1	12	yes	—
441	Dic₁₅₈	C₂⁵	1	8	yes	—
442	C₈×C₇₉	C₂⁵	1	1	yes	characteristic
443	C₈×C₇₉	C₂⁵	1	1	yes	characteristic
444	C₈×C₇₉	C₂⁵	1	6	yes	—
445	C₇₉⋊C₈	C₂⁵	1	1	yes	characteristic
446	C₇₉⋊C₈	C₂⁵	1	1	yes	characteristic
447	C₇₉⋊C₈	C₂⁵	1	6	yes	—
448	C₂²×C₇₉	—	2	8	no	—
449	C₂²×C₇₉	—	4	3	no	—
450	C₂²×C₇₉	—	8	12	no	—
451	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
452	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
453	C₂×D₇₉	—	2	2	no	—
454	C₂×D₇₉	—	2	12	no	—
455	C₂×D₇₉	—	2	8	no	—
456	C₂×D₇₉	—	4	6	no	—
457	C₂×D₇₉	—	4	3	no	—
458	C₂×D₇₉	—	4	16	no	—
459	C₂×D₇₉	—	8	24	no	—
460	C₂×D₇₉	—	8	12	no	—
461	C₂×D₇₉	C₂³×D₄	1	1	yes	characteristic
462	C₂×D₇₉	C₂³×D₄	1	6	yes	—
463	C₂×D₇₉	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₇₉	—	2	8	no	—
465	C₄×C₇₉	C₂³×D₄	1	6	yes	—
466	C₄×C₇₉	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₇₉	C₂⁶	1	1	yes	characteristic
468	Dic₇₉	—	2	8	no	—
469	Dic₇₉	C₂³×D₄	1	1	yes	characteristic
470	Dic₇₉	C₂³×D₄	1	6	yes	—
471	Dic₇₉	C₂³×D₄	1	1	yes	characteristic
472	C₂×#3584	—	79	1	no	maximal, Sylow
473	C₂×C₇₉	—	2	1	no	—
474	C₂×C₇₉	—	2	6	no	—
475	C₂×C₇₉	—	4	8	no	—
476	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
477	D₇₉	—	2	1	no	—
478	D₇₉	—	2	6	no	—
479	D₇₉	—	4	8	no	—
480	D₇₉	#3584	1	2	yes	direct product factor
481	C₂×#585	—	79	2	no	—
482	#3584	—	79	2	no	—
483	#3584	—	79	4	no	—
484	#3584	—	79	8	no	—
485	#3584	—	79	4	no	—
486	#3584	—	79	6	no	—
487	#3584	—	79	6	no	—
488	#3584	—	79	1	no	—
489	#3584	D₇₉	1	1	yes	characteristic, direct product factor
490	C₂×#578	—	79	4	no	—
491	C₂×#577	—	79	8	no	—
492	C₂×#576	—	79	4	no	—
493	C₂×#575	—	79	6	no	—
494	C₂²×#135	—	79	6	no	—
495	C₂²×#131	—	79	1	no	—
496	C₇₉	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
497	#585	—	79	8	no	—
498	#585	—	79	8	no	—
499	#585	—	79	2	no	—
500	#585	—	79	12	no	—
501	#585	—	158	8	no	—
502	#585	—	158	6	no	—
503	#585	—	158	2	no	—
504	#585	C₂×D₇₉	1	2	yes	complemented
505	C₂×2₋¹⁺⁴	—	79	8	no	—
506	C₂×2₋¹⁺⁴	—	158	2	no	—
507	C₂×H(5,𝔽₂)	—	79	8	no	—
508	C₂×H(5,𝔽₂)	—	158	6	no	—
509	C₂²×#41	—	79	1	no	—
510	C₂²×#41	—	79	12	no	—
511	C₂²×#41	—	158	8	no	—
512	#578	—	79	8	no	—
513	#578	—	79	24	no	—
514	#578	—	79	12	no	—
515	#578	—	79	12	no	—
516	#578	—	79	4	no	—
517	#578	C₂×D₇₉	1	4	yes	complemented
518	#577	—	79	8	no	—
519	#577	—	79	8	no	—
520	#577	—	79	24	no	—
521	#577	—	79	24	no	—
522	#577	—	79	24	no	—
523	#577	—	79	24	no	—
524	#577	—	79	8	no	—
525	#577	C₂×D₇₉	1	8	yes	complemented
526	#576	—	79	8	no	—
527	#576	—	79	24	no	—
528	#576	—	79	12	no	—
529	#576	—	79	12	no	—
530	#576	—	79	4	no	—
531	#576	C₂×D₇₉	1	4	yes	complemented
532	#575	—	79	12	no	—
533	#575	—	79	24	no	—
534	#575	—	79	24	no	—
535	#575	—	79	24	no	—
536	#575	—	79	6	no	—
537	#575	C₂×D₇₉	1	6	yes	complemented
538	C₂×#137	—	79	24	no	—
539	C₂×AGL(1,ℤ/8)	—	79	24	no	—
540	C₂×#135	—	79	12	no	—
541	C₂×#135	—	79	12	no	—
542	C₂×#135	—	79	12	no	—
543	C₂×#135	—	79	12	no	—
544	C₂×#135	—	79	12	no	—
545	C₂×#135	—	79	4	no	—
546	C₂×#135	—	79	12	no	—
547	C₂×#135	—	79	12	no	—
548	C₂×#135	—	79	12	no	—
549	C₂×#135	—	79	6	no	—
550	C₂×#135	—	79	12	no	—
551	C₂×#135	—	79	6	no	—
552	C₂×#135	—	79	6	no	—
553	C₂×#135	C₂×D₇₉	1	6	yes	complemented
554	C₂²×Q₁₆	—	79	6	no	—
555	C₂²×SD₁₆	—	79	12	no	—
556	C₂²×D₈	—	79	6	no	—
557	C₂×#131	—	79	1	no	—
558	C₂×#131	—	79	4	no	—
559	C₂×#131	—	79	4	no	—
560	C₂×#131	—	79	4	no	—
561	C₂×#131	—	79	4	no	—
562	C₂×#131	—	79	3	no	—
563	C₂×#131	—	79	3	no	—
564	C₂×#131	C₂×D₇₉	1	1	yes	characteristic, complemented
565	C₂²×M₁₆	—	79	3	no	—
566	C₂³×C₈	—	79	3	no	—
567	2₋¹⁺⁴	—	2	2	no	—
568	2₋¹⁺⁴	—	79	24	no	—
569	2₋¹⁺⁴	—	79	8	no	—
570	2₋¹⁺⁴	—	79	24	no	—
571	2₋¹⁺⁴	—	158	8	no	—
572	2₋¹⁺⁴	—	158	8	no	—
573	2₋¹⁺⁴	—	158	8	no	—
574	2₋¹⁺⁴	—	158	12	no	—
575	2₋¹⁺⁴	—	158	24	no	—
576	2₋¹⁺⁴	—	158	2	no	—
577	2₋¹⁺⁴	C₂²×D₇₉	1	8	yes	complemented
578	H(5,𝔽₂)	—	2	6	no	—
579	H(5,𝔽₂)	—	79	24	no	—
580	H(5,𝔽₂)	—	79	8	no	—
581	H(5,𝔽₂)	—	79	24	no	—
582	H(5,𝔽₂)	—	158	24	no	—
583	H(5,𝔽₂)	—	158	24	no	—
584	H(5,𝔽₂)	—	158	24	no	—
585	H(5,𝔽₂)	—	158	24	no	—
586	H(5,𝔽₂)	—	158	12	no	—
587	H(5,𝔽₂)	—	158	8	no	—
588	H(5,𝔽₂)	—	158	6	no	—
589	H(5,𝔽₂)	C₂²×D₇₉	1	8	yes	complemented
590	C₂×#41	—	2	8	no	—
591	C₂×#41	—	79	4	no	—
592	C₂×#41	—	79	4	no	—
593	C₂×#41	—	79	4	no	—
594	C₂×#41	—	79	4	no	—
595	C₂×#41	—	79	1	no	—
596	C₂×#41	—	79	3	no	—
597	C₂×#41	—	79	3	no	—
598	C₂×#41	—	79	8	no	—
599	C₂×#41	—	79	24	no	—
600	C₂×#41	—	79	24	no	—
601	C₂×#41	—	79	24	no	—
602	C₂×#41	—	79	12	no	—
603	C₂×#41	—	79	12	no	—
604	C₂×#41	—	79	12	no	—
605	C₂×#41	—	158	12	no	—
606	C₂×#41	—	158	24	no	—
607	C₂×#41	—	158	12	no	—
608	C₂×#41	—	158	12	no	—
609	C₂×#41	—	158	12	no	—
610	C₂×#41	—	158	12	no	—
611	C₂×#41	—	158	12	no	—
612	C₂×#41	—	158	24	no	—
613	C₂×#41	—	158	24	no	—
614	C₂×#41	—	158	8	no	—
615	C₂×#41	—	158	8	no	—
616	C₂×#41	—	158	8	no	—
617	C₂×#41	—	158	24	no	—
618	C₂×#41	—	158	24	no	—
619	C₂×#41	—	158	8	no	—
620	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
621	C₂×#41	C₂²×D₇₉	1	12	yes	complemented
622	C₂²×Q₈	—	79	1	no	—
623	C₂²×Q₈	—	79	12	no	—
624	C₂²×Q₈	—	158	8	no	—
625	C₂²×D₄	—	79	3	no	—
626	C₂²×D₄	—	79	12	no	—
627	C₂²×D₄	—	158	24	no	—
628	C₂²×D₄	—	158	12	no	—
629	C₂³×C₄	—	79	3	no	—
630	C₂³×C₄	—	158	12	no	—
631	#137	—	79	24	no	—
632	#137	—	79	24	no	—
633	#137	—	79	48	no	—
634	#137	—	79	48	no	—
635	#137	—	79	24	no	—
636	#137	C₂²×D₇₉	1	24	yes	complemented
637	AGL(1,ℤ/8)	—	79	24	no	—
638	AGL(1,ℤ/8)	—	79	24	no	—
639	AGL(1,ℤ/8)	—	79	48	no	—
640	AGL(1,ℤ/8)	—	79	48	no	—
641	AGL(1,ℤ/8)	—	79	24	no	—
642	AGL(1,ℤ/8)	C₂²×D₇₉	1	24	yes	complemented
643	#135	—	79	8	no	—
644	#135	—	79	24	no	—
645	#135	—	79	24	no	—
646	#135	—	79	24	no	—
647	#135	—	79	4	no	—
648	#135	—	79	12	no	—
649	#135	—	79	12	no	—
650	#135	—	79	12	no	—
651	#135	—	79	8	no	—
652	#135	—	79	24	no	—
653	#135	—	79	24	no	—
654	#135	—	79	24	no	—
655	#135	—	79	4	no	—
656	#135	—	79	12	no	—
657	#135	—	79	12	no	—
658	#135	—	79	12	no	—
659	#135	—	79	4	no	—
660	#135	—	79	12	no	—
661	#135	—	79	12	no	—
662	#135	—	79	12	no	—
663	#135	C₂²×D₇₉	1	4	yes	complemented
664	#135	C₂²×D₇₉	1	12	yes	complemented
665	#135	C₂²×D₇₉	1	12	yes	complemented
666	#135	C₂²×D₇₉	1	12	yes	complemented
667	C₂×Q₁₆	—	79	12	no	—
668	C₂×Q₁₆	—	79	4	no	—
669	C₂×Q₁₆	—	79	12	no	—
670	C₂×Q₁₆	—	79	12	no	—
671	C₂×Q₁₆	—	79	12	no	—
672	C₂×Q₁₆	—	79	6	no	—
673	C₂×Q₁₆	C₂²×D₇₉	1	6	yes	complemented
674	C₂×SD₁₆	—	79	12	no	—
675	C₂×SD₁₆	—	79	12	no	—
676	C₂×SD₁₆	—	79	8	no	—
677	C₂×SD₁₆	—	79	24	no	—
678	C₂×SD₁₆	—	79	24	no	—
679	C₂×SD₁₆	—	79	24	no	—
680	C₂×SD₁₆	—	79	12	no	—
681	C₂×SD₁₆	C₂²×D₇₉	1	12	yes	complemented
682	C₂×D₈	—	79	12	no	—
683	C₂×D₈	—	79	4	no	—
684	C₂×D₈	—	79	12	no	—
685	C₂×D₈	—	79	12	no	—
686	C₂×D₈	—	79	12	no	—
687	C₂×D₈	—	79	6	no	—
688	C₂×D₈	C₂²×D₇₉	1	6	yes	complemented
689	#131	—	79	4	no	—
690	#131	—	79	4	no	—
691	#131	—	79	12	no	—
692	#131	—	79	12	no	—
693	#131	—	79	12	no	—
694	#131	—	79	12	no	—
695	#131	C₂²×D₇₉	1	4	yes	complemented
696	#131	C₂²×D₇₉	1	4	yes	complemented
697	C₂×M₁₆	—	79	3	no	—
698	C₂×M₁₆	—	79	12	no	—
699	C₂×M₁₆	—	79	12	no	—
700	C₂×M₁₆	—	79	6	no	—
701	C₂×M₁₆	C₂²×D₇₉	1	3	yes	complemented
702	C₂²×C₈	—	79	3	no	—
703	C₂²×C₈	—	79	1	no	—
704	C₂²×C₈	—	79	3	no	—
705	C₂²×C₈	—	79	6	no	—
706	C₂²×C₈	—	79	6	no	—
707	C₂²×C₈	—	79	3	no	—
708	C₂²×C₈	—	79	3	no	—
709	C₂²×C₈	—	79	6	no	—
710	C₂²×C₈	—	79	6	no	—
711	C₂²×C₈	C₂²×D₇₉	1	3	yes	complemented
712	C₂⁴	—	79	3	no	—
713	C₂⁴	—	158	12	no	—
714	#41	—	2	8	no	—
715	#41	—	2	24	no	—
716	#41	—	2	12	no	—
717	#41	—	2	12	no	—
718	#41	—	79	4	no	—
719	#41	—	79	4	no	—
720	#41	—	79	12	no	—
721	#41	—	79	12	no	—
722	#41	—	79	12	no	—
723	#41	—	79	12	no	—
724	#41	—	79	8	no	—
725	#41	—	79	24	no	—
726	#41	—	79	8	no	—
727	#41	—	79	24	no	—
728	#41	—	79	8	no	—
729	#41	—	79	24	no	—
730	#41	—	158	8	no	—
731	#41	—	158	24	no	—
732	#41	—	158	24	no	—
733	#41	—	158	24	no	—
734	#41	—	158	48	no	—
735	#41	—	158	24	no	—
736	#41	—	158	24	no	—
737	#41	—	158	8	no	—
738	#41	—	158	24	no	—
739	#41	—	158	12	no	—
740	#41	—	158	24	no	—
741	#41	—	158	24	no	—
742	#41	—	158	12	no	—
743	#41	—	158	12	no	—
744	#41	—	158	12	no	—
745	#41	—	158	48	no	—
746	#41	—	158	24	no	—
747	#41	—	158	24	no	—
748	#41	—	158	8	no	—
749	#41	—	158	24	no	—
750	#41	—	158	12	no	—
751	#41	—	158	12	no	—
752	#41	D₄×D₇₉	1	4	yes	—
753	#41	C₂³×D₇₉	1	8	yes	—
754	#41	C₂³×D₇₉	1	24	yes	—
755	#41	C₂³×D₇₉	1	4	yes	—
756	C₂×Q₈	—	2	8	no	—
757	C₂×Q₈	—	79	4	no	—
758	C₂×Q₈	—	79	4	no	—
759	C₂×Q₈	—	79	3	no	—
760	C₂×Q₈	—	79	8	no	—
761	C₂×Q₈	—	79	24	no	—
762	C₂×Q₈	—	79	12	no	—
763	C₂×Q₈	—	158	12	no	—
764	C₂×Q₈	—	158	24	no	—
765	C₂×Q₈	—	158	12	no	—
766	C₂×Q₈	—	158	12	no	—
767	C₂×Q₈	—	158	24	no	—
768	C₂×Q₈	—	158	8	no	—
769	C₂×Q₈	D₄×D₇₉	1	1	yes	characteristic
770	C₂×Q₈	C₂³×D₇₉	1	12	yes	—
771	C₂×D₄	—	2	12	no	—
772	C₂×D₄	—	2	24	no	—
773	C₂×D₄	—	79	6	no	—
774	C₂×D₄	—	79	12	no	—
775	C₂×D₄	—	79	12	no	—
776	C₂×D₄	—	79	8	no	—
777	C₂×D₄	—	79	24	no	—
778	C₂×D₄	—	79	12	no	—
779	C₂×D₄	—	79	3	no	—
780	C₂×D₄	—	158	24	no	—
781	C₂×D₄	—	158	12	no	—
782	C₂×D₄	—	158	12	no	—
783	C₂×D₄	—	158	12	no	—
784	C₂×D₄	—	158	12	no	—
785	C₂×D₄	—	158	48	no	—
786	C₂×D₄	—	158	24	no	—
787	C₂×D₄	—	158	8	no	—
788	C₂×D₄	—	158	24	no	—
789	C₂×D₄	—	158	24	no	—
790	C₂×D₄	—	158	24	no	—
791	C₂×D₄	—	158	48	no	—
792	C₂×D₄	—	158	12	no	—
793	C₂×D₄	—	158	12	no	—
794	C₂×D₄	—	158	24	no	—
795	C₂×D₄	D₄×D₇₉	1	3	yes	—
796	C₂×D₄	C₂³×D₇₉	1	12	yes	—
797	C₂²×C₄	—	2	12	no	—
798	C₂²×C₄	—	79	3	no	—
799	C₂²×C₄	—	79	1	no	—
800	C₂²×C₄	—	79	6	no	—
801	C₂²×C₄	—	79	6	no	—
802	C₂²×C₄	—	79	3	no	—
803	C₂²×C₄	—	79	6	no	—
804	C₂²×C₄	—	79	3	no	—
805	C₂²×C₄	—	79	3	no	—
806	C₂²×C₄	—	79	6	no	—
807	C₂²×C₄	—	158	8	no	—
808	C₂²×C₄	—	158	24	no	—
809	C₂²×C₄	—	158	12	no	—
810	C₂²×C₄	—	158	24	no	—
811	C₂²×C₄	—	158	24	no	—
812	C₂²×C₄	—	158	12	no	—
813	C₂²×C₄	—	158	12	no	—
814	C₂²×C₄	—	158	12	no	—
815	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
816	Q₁₆	—	79	8	no	—
817	Q₁₆	—	79	24	no	—
818	Q₁₆	—	79	4	no	—
819	Q₁₆	—	79	12	no	—
820	Q₁₆	C₂³×D₇₉	1	4	yes	—
821	Q₁₆	C₂³×D₇₉	1	12	yes	—
822	SD₁₆	—	79	8	no	—
823	SD₁₆	—	79	24	no	—
824	SD₁₆	—	79	8	no	—
825	SD₁₆	—	79	24	no	—
826	SD₁₆	—	79	8	no	—
827	SD₁₆	—	79	24	no	—
828	SD₁₆	C₂³×D₇₉	1	8	yes	—
829	SD₁₆	C₂³×D₇₉	1	24	yes	—
830	D₈	—	79	8	no	—
831	D₈	—	79	24	no	—
832	D₈	—	79	4	no	—
833	D₈	—	79	12	no	—
834	D₈	C₂³×D₇₉	1	4	yes	—
835	D₈	C₂³×D₇₉	1	12	yes	—
836	M₁₆	—	79	12	no	—
837	M₁₆	—	79	24	no	—
838	M₁₆	C₂³×D₇₉	1	12	yes	—
839	C₂×C₈	—	79	1	no	—
840	C₂×C₈	—	79	3	no	—
841	C₂×C₈	—	79	6	no	—
842	C₂×C₈	—	79	6	no	—
843	C₂×C₈	—	79	1	no	—
844	C₂×C₈	—	79	1	no	—
845	C₂×C₈	—	79	1	no	—
846	C₂×C₈	—	79	1	no	—
847	C₂×C₈	—	79	6	no	—
848	C₂×C₈	—	79	6	no	—
849	C₂×C₈	—	79	6	no	—
850	C₂×C₈	—	79	6	no	—
851	C₂×C₈	—	79	6	no	—
852	C₂×C₈	—	79	6	no	—
853	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
854	C₂×C₈	C₂³×D₇₉	1	3	yes	—
855	C₂×C₈	C₂³×D₇₉	1	6	yes	—
856	C₂×C₈	C₂³×D₇₉	1	6	yes	—
857	C₂³	—	2	12	no	—
858	C₂³	—	316	6	no	—
859	C₂³	—	79	6	no	—
860	C₂³	—	79	3	no	—
861	C₂³	—	79	1	no	—
862	C₂³	—	79	6	no	—
863	C₂³	—	632	24	no	—
864	C₂³	—	158	8	no	—
865	C₂³	—	158	24	no	—
866	C₂³	—	158	12	no	—
867	C₂³	C₂×D₄×D₇₉	1	3	yes	—
868	Q₈	—	2	12	no	—
869	Q₈	—	79	12	no	—
870	Q₈	—	79	8	no	—
871	Q₈	—	158	8	no	—
872	Q₈	—	158	24	no	—
873	Q₈	—	158	12	no	—
874	Q₈	C₂×D₄×D₇₉	1	4	yes	—
875	Q₈	C₂⁴×D₇₉	1	8	yes	—
876	D₄	—	2	24	no	—
877	D₄	—	2	8	no	—
878	D₄	—	2	12	no	—
879	D₄	—	79	24	no	—
880	D₄	—	79	8	no	—
881	D₄	—	79	12	no	—
882	D₄	—	158	8	no	—
883	D₄	—	158	24	no	—
884	D₄	—	158	8	no	—
885	D₄	—	158	24	no	—
886	D₄	—	158	8	no	—
887	D₄	—	158	24	no	—
888	D₄	—	158	24	no	—
889	D₄	—	158	8	no	—
890	D₄	—	158	12	no	—
891	D₄	C₂×D₄×D₇₉	1	12	yes	—
892	D₄	C₂⁴×D₇₉	1	8	yes	—
893	C₂×C₄	—	2	12	no	—
894	C₂×C₄	—	2	24	no	—
895	C₂×C₄	—	2	8	no	—
896	C₂×C₄	—	79	1	no	—
897	C₂×C₄	—	79	6	no	—
898	C₂×C₄	—	79	3	no	—
899	C₂×C₄	—	79	6	no	—
900	C₂×C₄	—	79	1	no	—
901	C₂×C₄	—	79	1	no	—
902	C₂×C₄	—	79	6	no	—
903	C₂×C₄	—	79	6	no	—
904	C₂×C₄	—	79	6	no	—
905	C₂×C₄	—	79	6	no	—
906	C₂×C₄	—	79	6	no	—
907	C₂×C₄	—	79	1	no	—
908	C₂×C₄	—	79	1	no	—
909	C₂×C₄	—	79	6	no	—
910	C₂×C₄	—	158	8	no	—
911	C₂×C₄	—	158	24	no	—
912	C₂×C₄	—	158	8	no	—
913	C₂×C₄	—	158	24	no	—
914	C₂×C₄	—	158	8	no	—
915	C₂×C₄	—	158	24	no	—
916	C₂×C₄	—	158	12	no	—
917	C₂×C₄	—	158	24	no	—
918	C₂×C₄	—	158	8	no	—
919	C₂×C₄	C₂×D₄×D₇₉	1	3	yes	—
920	C₂×C₄	C₂×D₄×D₇₉	1	6	yes	—
921	C₂×C₄	C₂⁴×D₇₉	1	6	yes	—
922	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
923	C₈	—	79	1	no	—
924	C₈	—	79	1	no	—
925	C₈	—	79	6	no	—
926	C₈	C₂⁴×D₇₉	1	1	yes	characteristic
927	C₈	C₂⁴×D₇₉	1	1	yes	characteristic
928	C₈	C₂⁴×D₇₉	1	6	yes	—
929	C₂²	—	2	8	no	—
930	C₂²	—	4	3	no	—
931	C₂²	—	8	12	no	—
932	C₂²	—	316	3	no	—
933	C₂²	—	316	6	no	—
934	C₂²	—	316	16	no	—
935	C₂²	—	79	1	no	—
936	C₂²	—	79	1	no	—
937	C₂²	—	79	6	no	—
938	C₂²	—	632	12	no	—
939	C₂²	—	632	24	no	—
940	C₂²	—	158	2	no	—
941	C₂²	—	158	12	no	—
942	C₂²	—	158	8	no	—
943	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
944	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
945	C₄	—	2	8	no	—
946	C₄	—	79	1	no	—
947	C₄	—	79	1	no	—
948	C₄	—	79	6	no	—
949	C₄	—	158	8	no	—
950	C₄	C₂²×D₄×D₇₉	1	6	yes	—
951	C₄	C₂²×D₄×D₇₉	1	1	yes	characteristic
952	C₄	C₂⁵×D₇₉	1	1	yes	characteristic
953	C₂	—	2	1	no	—
954	C₂	—	2	6	no	—
955	C₂	—	4	8	no	—
956	C₂	—	316	8	no	—
957	C₂	—	79	2	no	—
958	C₂	—	158	1	no	—
959	C₂	—	158	6	no	—
960	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₇₉
commutator, cosocle	C₄×C₇₉	C₂⁶
Frattini	C₄	C₂⁵×D₇₉
Fitting	C₇₉×#3584	C₂
socle	C₂×C₇₉	C₂⁴×D₄
hypercenter	#3584	D₇₉
hypocenter	C₇₉	C₂×#3584
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #585×D₇₉	C₂	semidirect
2. #23778174	C₂	semidirect
3. #23778173	C₂	semidirect
4. #23778172	C₂	semidirect
5. #23778171	C₂	semidirect
6. #23778170	C₂	semidirect
7. #23778169	C₂	semidirect
8. #23778168	C₂	semidirect
9. #578×D₇₉	C₂	semidirect
10. #577×D₇₉	C₂	semidirect
11. #576×D₇₉	C₂	semidirect
12. #575×D₇₉	C₂	semidirect
13. C₂×#135×D₇₉	C₂	semidirect
14. C₂×#131×D₇₉	C₂	semidirect
15. C₇₉×#3584	C₂	semidirect
17. #19099400	C₂²	semidirect
19. #19099399	C₂²	semidirect
20. #19099399	C₂²	semidirect
22. #19099398	C₂²	semidirect
24. 2₋¹⁺⁴×D₇₉	C₂²	semidirect
26. H(5,𝔽₂)×D₇₉	C₂²	semidirect
29. C₂×#41×D₇₉	C₂²	semidirect
30. #19099380	C₂²	semidirect
31. #19099379	C₂²	semidirect
32. #19099378	C₂²	semidirect
33. #19099377	C₂²	semidirect
34. #19099376	C₂²	semidirect
35. #19099375	C₂²	semidirect
36. #19099374	C₂²	semidirect
37. #19099373	C₂²	semidirect
38. #19099372	C₂²	semidirect
39. #19099371	C₂²	semidirect
40. #19099370	C₂²	semidirect
41. #19099369	C₂²	semidirect
42. #19099368	C₂²	semidirect
43. #19099367	C₂²	semidirect
44. #19099366	C₂²	semidirect
45. #19099365	C₂²	semidirect
46. #19099364	C₂²	semidirect
47. #19099363	C₂²	semidirect
48. #19099362	C₂²	semidirect
49. #19099361	C₂²	semidirect
50. #19099360	C₂²	semidirect
51. #19099359	C₂²	semidirect
52. #137×D₇₉	C₂²	semidirect
53. AGL(1,ℤ/8)×D₇₉	C₂²	semidirect
54. C₂×#14579184	C₂²	semidirect
55. C₂×#14579183	C₂²	semidirect
56. C₂×#14579182	C₂²	semidirect
57. C₂×#14579181	C₂²	semidirect
58. C₂×#14579180	C₂²	semidirect
59. #135×D₇₉	C₂²	semidirect
60. #135×D₇₉	C₂²	semidirect
61. #135×D₇₉	C₂²	semidirect
62. #135×D₇₉	C₂²	semidirect
63. #135×D₇₉	C₂²	semidirect
64. #135×D₇₉	C₂²	semidirect
65. #135×D₇₉	C₂²	semidirect
66. #135×D₇₉	C₂²	semidirect
67. C₂×Q₁₆×D₇₉	C₂²	semidirect
68. C₂×SD₁₆×D₇₉	C₂²	semidirect
69. C₂×D₈×D₇₉	C₂²	semidirect
70. C₂×#14579169	C₂²	semidirect
71. C₂×#14579168	C₂²	semidirect
72. C₂×#14579167	C₂²	semidirect
73. #131×D₇₉	C₂²	semidirect
74. #131×D₇₉	C₂²	semidirect
75. #131×D₇₉	C₂²	semidirect
76. #131×D₇₉	C₂²	semidirect
77. C₂×M₁₆×D₇₉	C₂²	semidirect
78. C₂²×C₈×D₇₉	C₂²	semidirect
79. #585×C₇₉	C₂²	semidirect
80. #578×C₇₉	C₂²	semidirect
81. #577×C₇₉	C₂²	semidirect
82. #576×C₇₉	C₂²	semidirect
83. #575×C₇₉	C₂²	semidirect
84. C₂×#135×C₇₉	C₂²	semidirect
85. C₂×#131×C₇₉	C₂²	semidirect
89. #14579209	C₂³	semidirect
93. #14579208	C₂³	semidirect
94. #14579208	C₂³	semidirect
98. #14579207	C₂³	semidirect
99. #14579207	C₂³	semidirect
104. #14579206	C₂³	semidirect
107. C₂×#11929625	C₂³	semidirect
111. C₂×#11929624	C₂³	semidirect
115. C₂×#11929623	C₂³	semidirect
132. #41×D₇₉	C₂³	semidirect
133. #41×D₇₉	C₂³	semidirect
143. #14579194	C₂³	semidirect
144. #14579193	C₂³	semidirect
145. #14579192	C₂³	semidirect
146. #14579191	C₂³	semidirect
147. #14579190	C₂³	semidirect
148. #14579189	C₂³	semidirect
149. #14579188	C₂³	semidirect
150. #14579187	C₂³	semidirect
151. #14579186	C₂³	semidirect
152. #14579185	C₂³	semidirect
153. #14579184	C₂³	semidirect
154. #14579184	C₂³	semidirect
155. #14579184	C₂³	semidirect
156. #14579184	C₂³	semidirect
157. #14579183	C₂³	semidirect
158. #14579183	C₂³	semidirect
159. #14579183	C₂³	semidirect
160. #14579183	C₂³	semidirect
161. #14579182	C₂³	semidirect
162. #14579182	C₂³	semidirect
163. #14579182	C₂³	semidirect
164. #14579182	C₂³	semidirect
165. #14579181	C₂³	semidirect
166. #14579181	C₂³	semidirect
167. #14579181	C₂³	semidirect
168. #14579181	C₂³	semidirect
169. #14579180	C₂³	semidirect
170. #14579180	C₂³	semidirect
171. #14579180	C₂³	semidirect
172. #14579180	C₂³	semidirect
173. C₂×Dic₃₁₆	C₂³	semidirect
174. C₂×#11929614	C₂³	semidirect
177. Q₁₆×D₇₉	C₂³	semidirect
178. Q₁₆×D₇₉	C₂³	semidirect
179. C₂×#11929613	C₂³	semidirect
180. C₂×#11929612	C₂³	semidirect
181. C₂×#11929611	C₂³	semidirect
184. SD₁₆×D₇₉	C₂³	semidirect
185. SD₁₆×D₇₉	C₂³	semidirect
186. C₂×D₆₃₂	C₂³	semidirect
187. C₂×#11929609	C₂³	semidirect
190. D₈×D₇₉	C₂³	semidirect
191. D₈×D₇₉	C₂³	semidirect
192. #14579169	C₂³	semidirect
193. #14579169	C₂³	semidirect
194. #14579168	C₂³	semidirect
195. #14579168	C₂³	semidirect
196. #14579167	C₂³	semidirect
197. #14579167	C₂³	semidirect
198. C₂×#11929608	C₂³	semidirect
199. C₂×#11929607	C₂³	semidirect
201. M₁₆×D₇₉	C₂³	semidirect
202. C₂²×C₇₉⋊C₈	C₂³	semidirect
207. C₂×C₈×D₇₉	C₂³	semidirect
208. C₂×C₈×D₇₉	C₂³	semidirect
209. C₂×C₈×D₇₉	C₂³	semidirect
210. C₂×C₈×D₇₉	C₂³	semidirect
212. 2₋¹⁺⁴×C₇₉	C₂³	semidirect
214. H(5,𝔽₂)×C₇₉	C₂³	semidirect
217. C₂×#41×C₇₉	C₂³	semidirect
218. #137×C₇₉	C₂³	semidirect
219. AGL(1,ℤ/8)×C₇₉	C₂³	semidirect
220. #135×C₇₉	C₂³	semidirect
221. #135×C₇₉	C₂³	semidirect
222. #135×C₇₉	C₂³	semidirect
223. #135×C₇₉	C₂³	semidirect
224. C₂×Q₁₆×C₇₉	C₂³	semidirect
225. C₂×SD₁₆×C₇₉	C₂³	semidirect
226. C₂×D₈×C₇₉	C₂³	semidirect
227. #131×C₇₉	C₂³	semidirect
228. #131×C₇₉	C₂³	semidirect
229. C₂×M₁₆×C₇₉	C₂³	semidirect
230. C₂²×C₈×C₇₉	C₂³	semidirect
480. D₇₉	#3584	direct (N × H)
489. #3584	D₇₉	direct (N × H)
496. C₇₉	C₂×#3584	semidirect
504. #585	C₂×D₇₉	semidirect
517. #578	C₂×D₇₉	semidirect
525. #577	C₂×D₇₉	semidirect
531. #576	C₂×D₇₉	semidirect
537. #575	C₂×D₇₉	semidirect
553. C₂×#135	C₂×D₇₉	semidirect
564. C₂×#131	C₂×D₇₉	semidirect
577. 2₋¹⁺⁴	C₂²×D₇₉	semidirect
589. H(5,𝔽₂)	C₂²×D₇₉	semidirect
621. C₂×#41	C₂²×D₇₉	semidirect
636. #137	C₂²×D₇₉	semidirect
642. AGL(1,ℤ/8)	C₂²×D₇₉	semidirect
663. #135	C₂²×D₇₉	semidirect
664. #135	C₂²×D₇₉	semidirect
665. #135	C₂²×D₇₉	semidirect
666. #135	C₂²×D₇₉	semidirect
673. C₂×Q₁₆	C₂²×D₇₉	semidirect
681. C₂×SD₁₆	C₂²×D₇₉	semidirect
688. C₂×D₈	C₂²×D₇₉	semidirect
695. #131	C₂²×D₇₉	semidirect
696. #131	C₂²×D₇₉	semidirect
701. C₂×M₁₆	C₂²×D₇₉	semidirect
711. C₂²×C₈	C₂²×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#585×D₇₉	2
#23778174	2
#23778173	2
#23778172	2
#23778171	2
#23778170	2
#23778169	2
#23778168	2
#578×D₇₉	2
#577×D₇₉	2
#576×D₇₉	2
#575×D₇₉	2
C₂×#135×D₇₉	2
C₂×#131×D₇₉	2
C₇₉×#3584	2
C₂×#3584	79

Subgroups — #3584×D79 #35202096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3584×D₇₉ #35202096