Subgroups — C₇₉×#25745 #34137434

Order 20224.

1522 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#454×C₇₉	C₂	1	4	yes	maximal, complemented
5	C₇₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2003	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#104×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₇₉	C₂²	1	2	yes	—
11	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	2	yes	—
12	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	4	yes	—
13	D₄×Q₈×C₇₉	—	2	2	no	—
14	#547×C₇₉	—	2	2	no	—
15	#547×C₇₉	—	2	4	no	—
16	#536×C₇₉	—	2	2	no	—
17	#536×C₇₉	C₂²	1	2	yes	—
18	#532×C₇₉	—	2	1	no	—
19	#532×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
21	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₇₉	C₂²	1	4	yes	—
24	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
25	#496×C₇₉	—	2	2	no	—
26	#493×C₇₉	—	2	1	no	—
27	#492×C₇₉	—	2	1	no	—
28	#460×C₇₉	—	2	2	no	—
29	#459×C₇₉	—	2	2	no	—
30	#454×C₇₉	—	2	16	no	—
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#104×C₇₉	C₂²	1	4	yes	—
33	C₂×#104×C₇₉	C₂²	1	2	yes	—
34	#418×C₇₉	C₂²	1	2	yes	—
35	C₂×#101×C₇₉	C₂²	1	4	yes	—
36	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
37	#390×C₇₉	—	2	4	no	—
38	C₄³×C₇₉	C₂²	1	1	yes	characteristic
39	#339×C₇₉	C₂²	1	2	yes	—
40	2₋¹⁺⁴×C₇₉	—	2	8	no	—
41	2₋¹⁺⁴×C₇₉	—	4	4	no	—
42	C₂×#41×C₇₉	—	2	2	no	—
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	—	2	4	no	—
45	C₂×#41×C₇₉	C₂³	1	2	yes	—
46	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₇₉	—	2	2	no	—
48	C₂²×Q₈×C₇₉	—	2	2	no	—
49	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
50	C₂²×D₄×C₇₉	—	2	2	no	—
51	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
52	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
53	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
54	AGL(1,ℤ/8)×C₇₉	—	4	4	no	—
55	C₂×SD₁₆×C₇₉	—	2	2	no	—
56	C₂×SD₁₆×C₇₉	—	2	4	no	—
57	C₂×D₈×C₇₉	—	2	2	no	—
58	C₂×D₈×C₇₉	—	2	4	no	—
59	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
60	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₇₉	—	2	4	no	—
62	C₄⋊Q₈×C₇₉	—	2	2	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	2	no	—
66	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
67	#127×C₇₉	—	2	2	no	—
68	#127×C₇₉	—	2	1	no	—
69	#127×C₇₉	—	2	1	no	—
70	#127×C₇₉	D₄	1	1	yes	characteristic
71	#124×C₇₉	—	2	2	no	—
72	#124×C₇₉	—	2	8	no	—
73	#124×C₇₉	—	4	4	no	—
74	#124×C₇₉	D₄	1	2	yes	—
75	#123×C₇₉	—	2	8	no	—
76	#123×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	8	no	—
78	C₂²⋊Q₈×C₇₉	—	2	4	no	—
79	#121×C₇₉	—	2	4	no	—
80	#121×C₇₉	—	2	2	no	—
81	C₄×Q₈×C₇₉	D₄	1	2	yes	—
82	C₄×D₄×C₇₉	—	2	4	no	—
83	C₄×D₄×C₇₉	—	2	2	no	—
84	C₄×D₄×C₇₉	—	2	2	no	—
85	C₄×D₄×C₇₉	D₄	1	2	yes	—
86	#117×C₇₉	—	2	1	no	—
87	#117×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₇₉	D₄	1	4	yes	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
91	C₂×C₄²×C₇₉	—	2	1	no	—
92	C₂×C₄²×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₉	—	2	2	no	—
96	#104×C₇₉	—	2	8	no	—
97	#104×C₇₉	D₄	1	8	yes	complemented
98	#102×C₇₉	—	2	4	no	—
99	#101×C₇₉	—	2	8	no	—
100	#97×C₇₉	—	2	1	no	—
101	C₄×C₈×C₇₉	—	2	1	no	—
102	C₂⁴×C₇₉	—	2	2	no	—
103	#41×C₇₉	—	2	2	no	—
104	#41×C₇₉	—	2	4	no	—
105	#41×C₇₉	—	2	4	no	—
106	#41×C₇₉	—	4	8	no	—
107	#41×C₇₉	—	4	16	no	—
108	#41×C₇₉	—	4	4	no	—
109	#41×C₇₉	—	4	4	no	—
110	#41×C₇₉	C₂×D₄	1	4	yes	—
111	C₂×Q₈×C₇₉	—	2	4	no	—
112	C₂×Q₈×C₇₉	—	2	4	no	—
113	C₂×Q₈×C₇₉	—	2	2	no	—
114	C₂×Q₈×C₇₉	—	2	2	no	—
115	C₂×Q₈×C₇₉	—	2	4	no	—
116	C₂×Q₈×C₇₉	—	4	8	no	—
117	C₂×Q₈×C₇₉	—	4	4	no	—
118	C₂×Q₈×C₇₉	—	4	4	no	—
119	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₇₉	—	2	1	no	—
122	C₂×D₄×C₇₉	—	2	4	no	—
123	C₂×D₄×C₇₉	—	2	2	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	4	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	2	4	no	—
129	C₂×D₄×C₇₉	—	4	8	no	—
130	C₂×D₄×C₇₉	—	4	2	no	—
131	C₂×D₄×C₇₉	—	4	2	no	—
132	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	4	no	—
136	C₂²×C₄×C₇₉	—	2	4	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
143	SD₁₆×C₇₉	—	4	8	no	—
144	SD₁₆×C₇₉	—	4	4	no	—
145	D₈×C₇₉	—	4	8	no	—
146	D₈×C₇₉	—	4	4	no	—
147	M₁₆×C₇₉	—	2	4	no	—
148	M₁₆×C₇₉	—	2	2	no	—
149	M₁₆×C₇₉	C₂×D₄	1	4	yes	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₄⋊C₄×C₇₉	—	2	8	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	4	no	—
155	C₄⋊C₄×C₇₉	—	2	4	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₇₉	—	2	8	no	—
159	C₂²⋊C₄×C₇₉	—	2	1	no	—
160	C₂²⋊C₄×C₇₉	—	2	2	no	—
161	C₂²⋊C₄×C₇₉	—	2	4	no	—
162	C₂²⋊C₄×C₇₉	—	4	16	no	—
163	C₄²×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	2	1	no	—
165	C₄²×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	4	4	no	—
167	C₄²×C₇₉	C₂×D₄	1	4	yes	—
168	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂×D₄	1	2	yes	—
171	C₂³×C₇₉	—	2	1	no	—
172	C₂³×C₇₉	—	2	2	no	—
173	C₂³×C₇₉	—	4	8	no	—
174	C₂³×C₇₉	—	4	2	no	—
175	C₂³×C₇₉	—	4	4	no	—
176	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₇₉	—	2	1	no	—
178	Q₈×C₇₉	—	2	4	no	—
179	Q₈×C₇₉	—	4	8	no	—
180	Q₈×C₇₉	—	4	2	no	—
181	Q₈×C₇₉	—	4	2	no	—
182	Q₈×C₇₉	—	4	4	no	—
183	Q₈×C₇₉	#127	1	2	yes	—
184	D₄×C₇₉	—	2	4	no	—
185	D₄×C₇₉	—	2	1	no	—
186	D₄×C₇₉	—	2	4	no	—
187	D₄×C₇₉	—	4	8	no	—
188	D₄×C₇₉	—	4	4	no	—
189	D₄×C₇₉	—	4	2	no	—
190	D₄×C₇₉	—	4	2	no	—
191	D₄×C₇₉	—	4	4	no	—
192	D₄×C₇₉	—	4	4	no	—
193	D₄×C₇₉	—	8	4	no	—
194	D₄×C₇₉	—	8	4	no	—
195	D₄×C₇₉	#127	1	2	yes	—
196	C₂×C₄×C₇₉	—	2	1	no	—
197	C₂×C₄×C₇₉	—	2	4	no	—
198	C₂×C₄×C₇₉	—	2	4	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	4	no	—
202	C₂×C₄×C₇₉	—	2	4	no	—
203	C₂×C₄×C₇₉	—	2	8	no	—
204	C₂×C₄×C₇₉	—	4	8	no	—
205	C₂×C₄×C₇₉	—	4	4	no	—
206	C₂×C₄×C₇₉	—	4	8	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	4	no	—
210	C₂×C₄×C₇₉	#120	1	2	yes	—
211	C₂×C₄×C₇₉	#120	1	2	yes	—
212	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
216	C₈×C₇₉	—	2	4	no	—
217	C₈×C₇₉	—	4	2	no	—
218	C₂²×C₇₉	—	2	2	no	—
219	C₂²×C₇₉	—	2	2	no	—
220	C₂²×C₇₉	—	4	2	no	—
221	C₂²×C₇₉	—	4	2	no	—
222	C₂²×C₇₉	—	4	4	no	—
223	C₂²×C₇₉	—	8	8	no	—
224	C₂²×C₇₉	—	8	2	no	—
225	C₂²×C₇₉	—	8	4	no	—
226	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
227	C₂²×C₇₉	D₄²	1	2	yes	—
228	C₄×C₇₉	—	2	2	no	—
229	C₄×C₇₉	—	2	2	no	—
230	C₄×C₇₉	—	4	4	no	—
231	C₄×C₇₉	—	4	4	no	—
232	C₄×C₇₉	—	4	2	no	—
233	C₄×C₇₉	—	4	2	no	—
234	C₄×C₇₉	#454	1	4	yes	complemented
235	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
236	C₄×C₇₉	#535	1	1	yes	characteristic
237	C₄×C₇₉	D₄²	1	2	yes	—
238	#25745	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₇₉	—	2	2	no	—
240	C₂×C₇₉	—	4	2	no	—
241	C₂×C₇₉	—	8	2	no	—
242	C₂×C₇₉	—	16	2	no	—
243	C₂×C₇₉	#2433	1	1	yes	characteristic
244	C₂×C₇₉	C₂×#454	1	2	yes	—
245	#3499	C₂×C₇₉	1	1	yes	characteristic, complemented
246	#3151	C₂×C₇₉	1	1	yes	characteristic, complemented
247	#3038	C₂×C₇₉	1	1	yes	characteristic, complemented
248	C₂×#454	C₂×C₇₉	1	4	yes	complemented
249	#2858	C₂×C₇₉	1	1	yes	characteristic, complemented
250	#2003	C₂×C₇₉	1	4	yes	complemented
251	#1966	C₂×C₇₉	1	1	yes	characteristic, complemented
252	#1962	C₂×C₇₉	1	1	yes	characteristic, complemented
253	C₄×#104	C₂×C₇₉	1	1	yes	characteristic, complemented
254	C₇₉	#25745	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×2₋¹⁺⁴	C₂²×C₇₉	1	2	yes	—
256	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	2	yes	—
257	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	4	yes	—
258	D₄×Q₈	—	2	2	no	—
259	#547	—	2	2	no	—
260	#547	—	2	4	no	—
261	#536	—	2	2	no	—
262	#536	C₂²×C₇₉	1	2	yes	—
263	#532	—	2	1	no	—
264	#532	C₂²×C₇₉	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
267	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
268	C₂×#124	C₂²×C₇₉	1	4	yes	—
269	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
270	#496	—	2	2	no	—
271	#493	—	2	1	no	—
272	#492	—	2	1	no	—
273	#460	—	2	2	no	—
274	#459	—	2	2	no	—
275	#454	—	2	16	no	—
276	#423	C₂²×C₇₉	1	1	yes	characteristic
277	C₂×#104	C₂²×C₇₉	1	4	yes	—
278	C₂×#104	C₂²×C₇₉	1	2	yes	—
279	#418	C₂²×C₇₉	1	2	yes	—
280	C₂×#101	C₂²×C₇₉	1	4	yes	—
281	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
282	#390	—	2	4	no	—
283	C₄³	C₂²×C₇₉	1	1	yes	characteristic
284	#339	C₂²×C₇₉	1	2	yes	—
285	2₋¹⁺⁴	—	2	8	no	—
286	2₋¹⁺⁴	—	4	4	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	4	no	—
290	C₂×#41	C₂³×C₇₉	1	2	yes	—
291	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
297	AGL(1,ℤ/8)	—	2	8	no	—
298	AGL(1,ℤ/8)	—	2	8	no	—
299	AGL(1,ℤ/8)	—	4	4	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	4	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	—	2	4	no	—
304	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
305	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
312	#127	—	2	2	no	—
313	#127	—	2	1	no	—
314	#127	—	2	1	no	—
315	#127	D₄×C₇₉	1	1	yes	characteristic
316	#124	—	2	2	no	—
317	#124	—	2	8	no	—
318	#124	—	4	4	no	—
319	#124	D₄×C₇₉	1	2	yes	—
320	#123	—	2	8	no	—
321	#123	—	2	4	no	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	#121	—	2	4	no	—
325	#121	—	2	2	no	—
326	C₄×Q₈	D₄×C₇₉	1	2	yes	—
327	C₄×D₄	—	2	4	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	D₄×C₇₉	1	2	yes	—
331	#117	—	2	1	no	—
332	#117	C₂³×C₇₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	D₄×C₇₉	1	4	yes	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
339	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
340	C₄⋊C₈	—	2	2	no	—
341	#104	—	2	8	no	—
342	#104	D₄×C₇₉	1	8	yes	complemented
343	#102	—	2	4	no	—
344	#101	—	2	8	no	—
345	#97	—	2	1	no	—
346	C₄×C₈	—	2	1	no	—
347	C₂⁴	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	4	8	no	—
352	#41	—	4	16	no	—
353	#41	—	4	4	no	—
354	#41	—	4	4	no	—
355	#41	C₂×D₄×C₇₉	1	4	yes	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	4	8	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	—	4	4	no	—
364	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
365	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
378	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
388	SD₁₆	—	4	8	no	—
389	SD₁₆	—	4	4	no	—
390	D₈	—	4	8	no	—
391	D₈	—	4	4	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	4	no	—
394	M₁₆	C₂×D₄×C₇₉	1	4	yes	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	4	16	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₄²	C₂×D₄×C₇₉	1	4	yes	—
413	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₇₉	1	2	yes	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
422	Q₈	—	2	1	no	—
423	Q₈	—	2	4	no	—
424	Q₈	—	4	8	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	4	no	—
428	Q₈	#127×C₇₉	1	2	yes	—
429	D₄	—	2	4	no	—
430	D₄	—	2	1	no	—
431	D₄	—	2	4	no	—
432	D₄	—	4	8	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	4	no	—
438	D₄	—	8	4	no	—
439	D₄	—	8	4	no	—
440	D₄	#127×C₇₉	1	2	yes	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	#120×C₇₉	1	2	yes	—
456	C₂×C₄	#120×C₇₉	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
460	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
461	C₈	—	2	4	no	—
462	C₈	—	4	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	8	8	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	4	no	—
471	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
472	C₂²	D₄²×C₇₉	1	2	yes	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	#454×C₇₉	1	4	yes	complemented
480	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
481	C₄	#535×C₇₉	1	1	yes	characteristic
482	C₄	D₄²×C₇₉	1	2	yes	—
483	C₂	—	2	2	no	—
484	C₂	—	4	2	no	—
485	C₂	—	8	2	no	—
486	C₂	—	16	2	no	—
487	C₂	C₇₉×#2433	1	1	yes	characteristic
488	C₂	C₂×#454×C₇₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3499	C₂	semidirect
2. C₇₉×#3151	C₂	semidirect
3. C₇₉×#3038	C₂	semidirect
4. C₂×#454×C₇₉	C₂	semidirect
5. C₇₉×#2858	C₂	semidirect
6. C₇₉×#2003	C₂	semidirect
7. C₇₉×#1966	C₂	semidirect
8. C₇₉×#1962	C₂	semidirect
9. C₄×#104×C₇₉	C₂	semidirect
97. #104×C₇₉	D₄	semidirect
234. C₄×C₇₉	#454	semidirect
238. #25745	C₇₉	direct (N × H)
245. #3499	C₂×C₇₉	semidirect
246. #3151	C₂×C₇₉	semidirect
247. #3038	C₂×C₇₉	semidirect
248. C₂×#454	C₂×C₇₉	semidirect
249. #2858	C₂×C₇₉	semidirect
250. #2003	C₂×C₇₉	semidirect
251. #1966	C₂×C₇₉	semidirect
252. #1962	C₂×C₇₉	semidirect
253. C₄×#104	C₂×C₇₉	semidirect
254. C₇₉	#25745	direct (N × H)
342. #104	D₄×C₇₉	semidirect
479. C₄	#454×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3499	2
C₇₉×#3151	2
C₇₉×#3038	2
C₂×#454×C₇₉	2
C₇₉×#2858	2
C₇₉×#2003	2
C₇₉×#1966	2
C₇₉×#1962	2
C₄×#104×C₇₉	2
#25745	79

Subgroups — C79×#25745 #34137434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25745 #34137434