Subgroups — C₇₉×#25747 #34137436

Order 20224.

1866 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3498	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×#453×C₇₉	C₂	1	4	yes	maximal, complemented
5	C₇₉×#2867	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2002	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1965	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×H(5,𝔽₂)×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	complemented
13	#550×C₇₉	—	2	2	no	—
14	D₄²×C₇₉	—	2	4	no	—
15	D₄²×C₇₉	—	2	2	no	—
16	#535×C₇₉	—	2	2	no	—
17	#535×C₇₉	C₂²	1	2	yes	—
18	#532×C₇₉	—	2	1	no	—
19	#532×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₉	—	2	1	no	—
21	C₂×#127×C₇₉	—	2	4	no	—
22	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₇₉	C₂²	1	4	yes	complemented
24	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
25	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
26	#496×C₇₉	—	2	2	no	—
27	#493×C₇₉	—	2	1	no	—
28	#492×C₇₉	—	2	1	no	—
29	#460×C₇₉	—	2	2	no	—
30	#459×C₇₉	—	2	2	no	—
31	#453×C₇₉	—	2	16	no	—
32	#423×C₇₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#104×C₇₉	C₂²	1	2	yes	—
34	C₂×#104×C₇₉	C₂²	1	4	yes	complemented
35	#418×C₇₉	C₂²	1	2	yes	complemented
36	C₂×#100×C₇₉	C₂²	1	4	yes	complemented
37	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₄³×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#339×C₇₉	C₂²	1	2	yes	complemented
40	H(5,𝔽₂)×C₇₉	—	2	8	no	—
41	H(5,𝔽₂)×C₇₉	—	4	4	no	—
42	C₂×#41×C₇₉	—	2	2	no	—
43	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	C₂³	1	2	yes	—
45	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₇₉	—	2	4	no	—
47	C₂²×D₄×C₇₉	—	2	4	no	—
48	C₂²×D₄×C₇₉	—	2	2	no	—
49	C₂²×D₄×C₇₉	—	2	2	no	—
50	C₂²×D₄×C₇₉	—	2	8	no	—
51	C₂²×D₄×C₇₉	—	2	2	no	—
52	C₂²×D₄×C₇₉	D₄	1	4	yes	—
53	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
55	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
56	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
57	AGL(1,ℤ/8)×C₇₉	—	4	4	no	—
58	C₂×SD₁₆×C₇₉	—	2	2	no	—
59	C₂×SD₁₆×C₇₉	—	2	4	no	—
60	C₂×D₈×C₇₉	—	2	2	no	—
61	C₂×D₈×C₇₉	—	2	4	no	—
62	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
63	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic, complemented
65	#127×C₇₉	—	2	4	no	—
66	#127×C₇₉	—	2	2	no	—
67	#127×C₇₉	—	2	1	no	—
68	#127×C₇₉	—	2	1	no	—
69	#127×C₇₉	—	2	2	no	—
70	#127×C₇₉	—	2	2	no	—
71	#127×C₇₉	—	2	1	no	—
72	#127×C₇₉	—	2	1	no	—
73	#127×C₇₉	—	2	8	no	—
74	#127×C₇₉	—	4	4	no	—
75	#127×C₇₉	—	4	16	no	—
76	#127×C₇₉	D₄	1	1	yes	characteristic, complemented
77	#124×C₇₉	—	2	2	no	—
78	#124×C₇₉	D₄	1	2	yes	complemented
79	#121×C₇₉	—	2	4	no	—
80	#121×C₇₉	—	2	8	no	—
81	#121×C₇₉	—	2	2	no	—
82	#121×C₇₉	—	2	4	no	—
83	#120×C₇₉	—	2	8	no	—
84	#120×C₇₉	—	2	4	no	—
85	C₄×Q₈×C₇₉	D₄	1	2	yes	complemented
86	C₄×D₄×C₇₉	—	2	4	no	—
87	C₄×D₄×C₇₉	—	2	2	no	—
88	C₄×D₄×C₇₉	—	2	2	no	—
89	C₄×D₄×C₇₉	D₄	1	2	yes	complemented
90	#117×C₇₉	—	2	1	no	—
91	#117×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	—	2	2	no	—
97	#104×C₇₉	—	2	8	no	—
98	#104×C₇₉	D₄	1	8	yes	complemented
99	#102×C₇₉	—	2	4	no	—
100	#100×C₇₉	—	2	8	no	—
101	#97×C₇₉	—	2	1	no	—
102	C₄×C₈×C₇₉	—	2	1	no	—
103	C₂⁴×C₇₉	—	2	4	no	—
104	C₂⁴×C₇₉	—	2	2	no	—
105	C₂⁴×C₇₉	C₂×D₄	1	4	yes	—
106	#41×C₇₉	—	2	2	no	—
107	#41×C₇₉	—	2	4	no	—
108	#41×C₇₉	—	2	4	no	—
109	#41×C₇₉	—	4	8	no	—
110	#41×C₇₉	—	4	4	no	—
111	#41×C₇₉	—	4	4	no	—
112	#41×C₇₉	C₂×D₄	1	4	yes	—
113	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
114	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₇₉	—	2	1	no	—
116	C₂×D₄×C₇₉	—	2	4	no	—
117	C₂×D₄×C₇₉	—	2	4	no	—
118	C₂×D₄×C₇₉	—	2	2	no	—
119	C₂×D₄×C₇₉	—	2	8	no	—
120	C₂×D₄×C₇₉	—	2	4	no	—
121	C₂×D₄×C₇₉	—	2	2	no	—
122	C₂×D₄×C₇₉	—	2	4	no	—
123	C₂×D₄×C₇₉	—	2	4	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	2	4	no	—
129	C₂×D₄×C₇₉	—	2	4	no	—
130	C₂×D₄×C₇₉	—	2	4	no	—
131	C₂×D₄×C₇₉	—	4	8	no	—
132	C₂×D₄×C₇₉	—	4	8	no	—
133	C₂×D₄×C₇₉	—	4	16	no	—
134	C₂×D₄×C₇₉	—	4	32	no	—
135	C₂×D₄×C₇₉	—	4	8	no	—
136	C₂×D₄×C₇₉	—	4	16	no	—
137	C₂×D₄×C₇₉	—	4	4	no	—
138	C₂×D₄×C₇₉	—	4	4	no	—
139	C₂×D₄×C₇₉	—	4	2	no	—
140	C₂×D₄×C₇₉	—	4	2	no	—
141	C₂×D₄×C₇₉	—	8	8	no	—
142	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	—	2	4	no	—
147	C₂²×C₄×C₇₉	—	2	2	no	—
148	C₂²×C₄×C₇₉	—	2	2	no	—
149	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	SD₁₆×C₇₉	—	4	8	no	—
152	SD₁₆×C₇₉	—	4	4	no	—
153	D₈×C₇₉	—	4	8	no	—
154	D₈×C₇₉	—	4	4	no	—
155	M₁₆×C₇₉	—	2	4	no	—
156	M₁₆×C₇₉	—	2	2	no	—
157	M₁₆×C₇₉	C₂×D₄	1	4	yes	complemented
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
163	C₂²⋊C₄×C₇₉	—	2	8	no	—
164	C₂²⋊C₄×C₇₉	—	2	1	no	—
165	C₂²⋊C₄×C₇₉	—	2	2	no	—
166	C₂²⋊C₄×C₇₉	—	2	4	no	—
167	C₄²×C₇₉	—	2	8	no	—
168	C₄²×C₇₉	—	2	2	no	—
169	C₄²×C₇₉	—	2	1	no	—
170	C₄²×C₇₉	—	2	2	no	—
171	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂×D₄	1	2	yes	—
174	C₄²×C₇₉	C₂×D₄	1	4	yes	complemented
175	C₂³×C₇₉	—	2	1	no	—
176	C₂³×C₇₉	—	2	4	no	—
177	C₂³×C₇₉	—	2	2	no	—
178	C₂³×C₇₉	—	2	8	no	—
179	C₂³×C₇₉	—	4	8	no	—
180	C₂³×C₇₉	—	4	8	no	—
181	C₂³×C₇₉	—	4	8	no	—
182	C₂³×C₇₉	—	4	2	no	—
183	C₂³×C₇₉	—	4	4	no	—
184	C₂³×C₇₉	—	8	8	no	—
185	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₇₉	—	2	1	no	—
187	Q₈×C₇₉	—	2	4	no	—
188	Q₈×C₇₉	#127	1	2	yes	complemented
189	D₄×C₇₉	—	2	4	no	—
190	D₄×C₇₉	—	2	1	no	—
191	D₄×C₇₉	—	2	4	no	—
192	D₄×C₇₉	—	4	8	no	—
193	D₄×C₇₉	—	4	8	no	—
194	D₄×C₇₉	—	4	4	no	—
195	D₄×C₇₉	—	4	2	no	—
196	D₄×C₇₉	—	4	2	no	—
197	D₄×C₇₉	—	4	2	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	4	4	no	—
200	D₄×C₇₉	—	4	4	no	—
201	D₄×C₇₉	—	4	8	no	—
202	D₄×C₇₉	—	4	4	no	—
203	D₄×C₇₉	—	8	4	no	—
204	D₄×C₇₉	—	8	32	no	—
205	D₄×C₇₉	—	8	4	no	—
206	D₄×C₇₉	—	8	8	no	—
207	D₄×C₇₉	—	8	4	no	—
208	D₄×C₇₉	#127	1	2	yes	complemented
209	C₂×C₄×C₇₉	—	2	8	no	—
210	C₂×C₄×C₇₉	—	2	1	no	—
211	C₂×C₄×C₇₉	—	2	4	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	4	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	4	8	no	—
217	C₂×C₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	4	no	—
220	C₂×C₄×C₇₉	#120	1	2	yes	—
221	C₂×C₄×C₇₉	#120	1	2	yes	—
222	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₇₉	—	2	4	no	—
227	C₈×C₇₉	—	4	2	no	—
228	C₂²×C₇₉	—	2	2	no	—
229	C₂²×C₇₉	—	2	2	no	—
230	C₂²×C₇₉	—	4	2	no	—
231	C₂²×C₇₉	—	4	2	no	—
232	C₂²×C₇₉	—	4	4	no	—
233	C₂²×C₇₉	—	4	8	no	—
234	C₂²×C₇₉	—	4	4	no	—
235	C₂²×C₇₉	—	8	8	no	—
236	C₂²×C₇₉	—	8	8	no	—
237	C₂²×C₇₉	—	8	2	no	—
238	C₂²×C₇₉	—	8	4	no	—
239	C₂²×C₇₉	—	16	8	no	—
240	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
241	C₂²×C₇₉	D₄²	1	2	yes	—
242	C₄×C₇₉	—	2	8	no	—
243	C₄×C₇₉	—	2	2	no	—
244	C₄×C₇₉	—	2	2	no	—
245	C₄×C₇₉	—	4	2	no	—
246	C₄×C₇₉	—	4	2	no	—
247	C₄×C₇₉	#453	1	4	yes	complemented
248	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
249	C₄×C₇₉	#535	1	1	yes	characteristic
250	C₄×C₇₉	D₄²	1	2	yes	—
251	#25747	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂×C₇₉	—	2	2	no	—
253	C₂×C₇₉	—	4	2	no	—
254	C₂×C₇₉	—	8	4	no	—
255	C₂×C₇₉	—	8	2	no	—
256	C₂×C₇₉	—	16	2	no	—
257	C₂×C₇₉	#2433	1	1	yes	characteristic
258	C₂×C₇₉	C₂×#453	1	2	yes	—
259	#3498	C₂×C₇₉	1	1	yes	characteristic, complemented
260	#3151	C₂×C₇₉	1	1	yes	characteristic, complemented
261	#3038	C₂×C₇₉	1	1	yes	characteristic, complemented
262	C₂×#453	C₂×C₇₉	1	4	yes	complemented
263	#2867	C₂×C₇₉	1	1	yes	characteristic, complemented
264	#2002	C₂×C₇₉	1	4	yes	complemented
265	#1965	C₂×C₇₉	1	1	yes	characteristic, complemented
266	#1962	C₂×C₇₉	1	1	yes	characteristic, complemented
267	C₄×#104	C₂×C₇₉	1	1	yes	characteristic, complemented
268	C₇₉	#25747	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×H(5,𝔽₂)	C₂²×C₇₉	1	2	yes	—
270	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	2	yes	—
271	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	4	yes	complemented
272	#550	—	2	2	no	—
273	D₄²	—	2	4	no	—
274	D₄²	—	2	2	no	—
275	#535	—	2	2	no	—
276	#535	C₂²×C₇₉	1	2	yes	—
277	#532	—	2	1	no	—
278	#532	C₂²×C₇₉	1	1	yes	characteristic
279	C₂×#127	—	2	1	no	—
280	C₂×#127	—	2	4	no	—
281	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
282	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic, complemented
283	C₂×#127	C₂²×C₇₉	1	4	yes	complemented
284	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
285	#496	—	2	2	no	—
286	#493	—	2	1	no	—
287	#492	—	2	1	no	—
288	#460	—	2	2	no	—
289	#459	—	2	2	no	—
290	#453	—	2	16	no	—
291	#423	C₂²×C₇₉	1	1	yes	characteristic, complemented
292	C₂×#104	C₂²×C₇₉	1	2	yes	—
293	C₂×#104	C₂²×C₇₉	1	4	yes	complemented
294	#418	C₂²×C₇₉	1	2	yes	complemented
295	C₂×#100	C₂²×C₇₉	1	4	yes	complemented
296	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
297	C₄³	C₂²×C₇₉	1	1	yes	characteristic, complemented
298	#339	C₂²×C₇₉	1	2	yes	complemented
299	H(5,𝔽₂)	—	2	8	no	—
300	H(5,𝔽₂)	—	4	4	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	C₂³×C₇₉	1	2	yes	—
304	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
305	C₂²×D₄	—	2	4	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	8	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	D₄×C₇₉	1	4	yes	—
312	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
313	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
314	AGL(1,ℤ/8)	—	2	8	no	—
315	AGL(1,ℤ/8)	—	2	8	no	—
316	AGL(1,ℤ/8)	—	4	4	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	4	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	4	no	—
321	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
322	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
323	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic, complemented
324	#127	—	2	4	no	—
325	#127	—	2	2	no	—
326	#127	—	2	1	no	—
327	#127	—	2	1	no	—
328	#127	—	2	2	no	—
329	#127	—	2	2	no	—
330	#127	—	2	1	no	—
331	#127	—	2	1	no	—
332	#127	—	2	8	no	—
333	#127	—	4	4	no	—
334	#127	—	4	16	no	—
335	#127	D₄×C₇₉	1	1	yes	characteristic, complemented
336	#124	—	2	2	no	—
337	#124	D₄×C₇₉	1	2	yes	complemented
338	#121	—	2	4	no	—
339	#121	—	2	8	no	—
340	#121	—	2	2	no	—
341	#121	—	2	4	no	—
342	#120	—	2	8	no	—
343	#120	—	2	4	no	—
344	C₄×Q₈	D₄×C₇₉	1	2	yes	complemented
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	D₄×C₇₉	1	2	yes	complemented
349	#117	—	2	1	no	—
350	#117	C₂³×C₇₉	1	1	yes	characteristic
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
354	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
355	C₄⋊C₈	—	2	2	no	—
356	#104	—	2	8	no	—
357	#104	D₄×C₇₉	1	8	yes	complemented
358	#102	—	2	4	no	—
359	#100	—	2	8	no	—
360	#97	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	C₂×D₄×C₇₉	1	4	yes	—
365	#41	—	2	2	no	—
366	#41	—	2	4	no	—
367	#41	—	2	4	no	—
368	#41	—	4	8	no	—
369	#41	—	4	4	no	—
370	#41	—	4	4	no	—
371	#41	C₂×D₄×C₇₉	1	4	yes	—
372	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
373	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	8	no	—
392	C₂×D₄	—	4	16	no	—
393	C₂×D₄	—	4	32	no	—
394	C₂×D₄	—	4	8	no	—
395	C₂×D₄	—	4	16	no	—
396	C₂×D₄	—	4	4	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	8	8	no	—
401	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
402	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
410	SD₁₆	—	4	8	no	—
411	SD₁₆	—	4	4	no	—
412	D₈	—	4	8	no	—
413	D₈	—	4	4	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	4	no	—
416	M₁₆	C₂×D₄×C₇₉	1	4	yes	complemented
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	8	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
432	C₄²	C₂×D₄×C₇₉	1	2	yes	—
433	C₄²	C₂×D₄×C₇₉	1	4	yes	complemented
434	C₂³	—	2	1	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	8	8	no	—
444	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
445	Q₈	—	2	1	no	—
446	Q₈	—	2	4	no	—
447	Q₈	#127×C₇₉	1	2	yes	complemented
448	D₄	—	2	4	no	—
449	D₄	—	2	1	no	—
450	D₄	—	2	4	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	8	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	4	no	—
461	D₄	—	4	4	no	—
462	D₄	—	8	4	no	—
463	D₄	—	8	32	no	—
464	D₄	—	8	4	no	—
465	D₄	—	8	8	no	—
466	D₄	—	8	4	no	—
467	D₄	#127×C₇₉	1	2	yes	complemented
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	#120×C₇₉	1	2	yes	—
480	C₂×C₄	#120×C₇₉	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
484	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
485	C₈	—	2	4	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	8	8	no	—
495	C₂²	—	8	8	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	4	no	—
498	C₂²	—	16	8	no	—
499	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
500	C₂²	D₄²×C₇₉	1	2	yes	—
501	C₄	—	2	8	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	#453×C₇₉	1	4	yes	complemented
507	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
508	C₄	#535×C₇₉	1	1	yes	characteristic
509	C₄	D₄²×C₇₉	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	4	no	—
513	C₂	—	8	2	no	—
514	C₂	—	16	2	no	—
515	C₂	C₇₉×#2433	1	1	yes	characteristic
516	C₂	C₂×#453×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×#3498	C₂	semidirect
2. C₇₉×#3151	C₂	semidirect
3. C₇₉×#3038	C₂	semidirect
4. C₂×#453×C₇₉	C₂	semidirect
5. C₇₉×#2867	C₂	semidirect
6. C₇₉×#2002	C₂	semidirect
7. C₇₉×#1965	C₂	semidirect
8. C₇₉×#1962	C₂	semidirect
9. C₄×#104×C₇₉	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₇₉	C₂²	semidirect
23. C₂×#127×C₇₉	C₂²	semidirect
24. C₂×#127×C₇₉	C₂²	semidirect
32. #423×C₇₉	C₂²	semidirect
34. C₂×#104×C₇₉	C₂²	semidirect
35. #418×C₇₉	C₂²	semidirect
36. C₂×#100×C₇₉	C₂²	semidirect
37. C₄×M₁₆×C₇₉	C₂²	semidirect
38. C₄³×C₇₉	C₂²	semidirect
39. #339×C₇₉	C₂²	semidirect
64. C₄⋊Q₈×C₇₉	D₄	semidirect
76. #127×C₇₉	D₄	semidirect
78. #124×C₇₉	D₄	semidirect
85. C₄×Q₈×C₇₉	D₄	semidirect
89. C₄×D₄×C₇₉	D₄	semidirect
98. #104×C₇₉	D₄	semidirect
157. M₁₆×C₇₉	C₂×D₄	semidirect
174. C₄²×C₇₉	C₂×D₄	semidirect
188. Q₈×C₇₉	#127	semidirect
208. D₄×C₇₉	#127	semidirect
247. C₄×C₇₉	#453	semidirect
251. #25747	C₇₉	direct (N × H)
259. #3498	C₂×C₇₉	semidirect
260. #3151	C₂×C₇₉	semidirect
261. #3038	C₂×C₇₉	semidirect
262. C₂×#453	C₂×C₇₉	semidirect
263. #2867	C₂×C₇₉	semidirect
264. #2002	C₂×C₇₉	semidirect
265. #1965	C₂×C₇₉	semidirect
266. #1962	C₂×C₇₉	semidirect
267. C₄×#104	C₂×C₇₉	semidirect
268. C₇₉	#25747	direct (N × H)
271. C₂×AGL(1,ℤ/8)	C₂²×C₇₉	semidirect
282. C₂×#127	C₂²×C₇₉	semidirect
283. C₂×#127	C₂²×C₇₉	semidirect
291. #423	C₂²×C₇₉	semidirect
293. C₂×#104	C₂²×C₇₉	semidirect
294. #418	C₂²×C₇₉	semidirect
295. C₂×#100	C₂²×C₇₉	semidirect
296. C₄×M₁₆	C₂²×C₇₉	semidirect
297. C₄³	C₂²×C₇₉	semidirect
298. #339	C₂²×C₇₉	semidirect
323. C₄⋊Q₈	D₄×C₇₉	semidirect
335. #127	D₄×C₇₉	semidirect
337. #124	D₄×C₇₉	semidirect
344. C₄×Q₈	D₄×C₇₉	semidirect
348. C₄×D₄	D₄×C₇₉	semidirect
357. #104	D₄×C₇₉	semidirect
416. M₁₆	C₂×D₄×C₇₉	semidirect
433. C₄²	C₂×D₄×C₇₉	semidirect
447. Q₈	#127×C₇₉	semidirect
467. D₄	#127×C₇₉	semidirect
506. C₄	#453×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3498	2
C₇₉×#3151	2
C₇₉×#3038	2
C₂×#453×C₇₉	2
C₇₉×#2867	2
C₇₉×#2002	2
C₇₉×#1965	2
C₇₉×#1962	2
C₄×#104×C₇₉	2
#25747	79

Subgroups — C79×#25747 #34137436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25747 #34137436