Subgroups — C₇₉×#25803 #34137492

Order 20224.

1434 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#495×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#472×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#454×C₇₉	C₂	1	2	yes	maximal, complemented
6	C₇₉×#3010	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2019	C₂	1	2	yes	maximal, complemented
8	C₇₉×#2004	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₉	C₂²	1	2	yes	—
13	#578×C₇₉	—	2	4	no	—
14	#578×C₇₉	—	2	4	no	—
15	C₂×#137×C₇₉	—	2	2	no	—
16	C₂×#137×C₇₉	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	2	yes	—
18	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	2	yes	—
19	C₂×#135×C₇₉	—	2	1	no	—
20	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₇₉	—	2	1	no	—
22	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
24	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
26	#535×C₇₉	C₂²	1	2	yes	—
27	C₂×#124×C₇₉	C₂²	1	2	yes	—
28	#496×C₇₉	—	2	2	no	—
29	#495×C₇₉	—	2	1	no	—
30	#495×C₇₉	—	2	4	no	—
31	#493×C₇₉	—	2	1	no	—
32	#472×C₇₉	—	2	4	no	—
33	#454×C₇₉	—	2	8	no	—
34	#449×C₇₉	—	2	4	no	—
35	#448×C₇₉	—	2	4	no	—
36	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#104×C₇₉	C₂²	1	2	yes	—
38	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
39	#419×C₇₉	C₂²	1	2	yes	—
40	#416×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#101×C₇₉	C₂²	1	2	yes	—
42	C₂×#100×C₇₉	C₂²	1	2	yes	—
43	#408×C₇₉	C₂²	1	2	yes	—
44	#405×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
46	#341×C₇₉	C₂²	1	1	yes	characteristic
47	#339×C₇₉	C₂²	1	1	yes	characteristic
48	2₋¹⁺⁴×C₇₉	—	2	4	no	—
49	2₋¹⁺⁴×C₇₉	—	2	4	no	—
50	2₋¹⁺⁴×C₇₉	—	2	4	no	—
51	2₋¹⁺⁴×C₇₉	—	4	2	no	—
52	C₂×#41×C₇₉	—	2	2	no	—
53	C₂×#41×C₇₉	—	2	2	no	—
54	C₂×#41×C₇₉	—	4	2	no	—
55	C₂×#41×C₇₉	C₂³	1	2	yes	—
56	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₇₉	—	2	2	no	—
58	C₂²×Q₈×C₇₉	—	2	2	no	—
59	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
61	#137×C₇₉	—	2	16	no	—
62	#137×C₇₉	—	2	4	no	—
63	#137×C₇₉	—	2	4	no	—
64	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
65	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
66	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
67	AGL(1,ℤ/8)×C₇₉	—	4	2	no	—
68	#135×C₇₉	—	2	8	no	—
69	#135×C₇₉	—	2	2	no	—
70	#135×C₇₉	—	2	2	no	—
71	C₂×Q₁₆×C₇₉	—	2	8	no	—
72	C₂×Q₁₆×C₇₉	—	2	2	no	—
73	C₂×Q₁₆×C₇₉	—	2	1	no	—
74	C₂×Q₁₆×C₇₉	—	2	1	no	—
75	C₂×Q₁₆×C₇₉	—	2	2	no	—
76	C₂×Q₁₆×C₇₉	D₄	1	1	yes	characteristic
77	C₂×Q₁₆×C₇₉	D₄	1	4	yes	complemented
78	C₂×SD₁₆×C₇₉	—	2	2	no	—
79	C₂×SD₁₆×C₇₉	—	2	2	no	—
80	C₂×SD₁₆×C₇₉	—	2	4	no	—
81	C₂×SD₁₆×C₇₉	—	2	2	no	—
82	C₂×SD₁₆×C₇₉	—	2	4	no	—
83	C₂×SD₁₆×C₇₉	—	4	2	no	—
84	C₂×SD₁₆×C₇₉	D₄	1	2	yes	—
85	C₂×D₈×C₇₉	—	2	2	no	—
86	C₂×D₈×C₇₉	—	2	2	no	—
87	C₂×D₈×C₇₉	—	2	2	no	—
88	C₂×D₈×C₇₉	—	2	1	no	—
89	C₂×D₈×C₇₉	—	2	2	no	—
90	C₂×D₈×C₇₉	—	2	1	no	—
91	C₂×D₈×C₇₉	D₄	1	1	yes	characteristic
92	#131×C₇₉	—	2	2	no	—
93	#131×C₇₉	D₄	1	4	yes	complemented
94	C₂×M₁₆×C₇₉	—	2	1	no	—
95	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
96	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	—	2	1	no	—
99	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	#127×C₇₉	—	2	2	no	—
102	#124×C₇₉	—	2	4	no	—
103	#124×C₇₉	—	2	2	no	—
104	#124×C₇₉	—	2	4	no	—
105	#121×C₇₉	—	2	4	no	—
106	#120×C₇₉	—	4	2	no	—
107	#117×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₇₉	—	4	2	no	—
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	#108×C₇₉	—	2	2	no	—
111	#104×C₇₉	—	2	4	no	—
112	#104×C₇₉	D₄	1	4	yes	complemented
113	#103×C₇₉	—	2	4	no	—
114	#103×C₇₉	D₄	1	2	yes	—
115	#102×C₇₉	D₄	1	2	yes	—
116	#101×C₇₉	—	2	4	no	—
117	#100×C₇₉	—	2	4	no	—
118	C₂²⋊C₈×C₇₉	—	2	4	no	—
119	#97×C₇₉	—	2	1	no	—
120	C₄×C₈×C₇₉	—	2	1	no	—
121	C₄×C₈×C₇₉	—	2	2	no	—
122	C₂⁴×C₇₉	—	2	2	no	—
123	#41×C₇₉	—	2	1	no	—
124	#41×C₇₉	—	2	1	no	—
125	#41×C₇₉	—	2	8	no	—
126	#41×C₇₉	—	2	2	no	—
127	#41×C₇₉	—	2	2	no	—
128	#41×C₇₉	—	2	2	no	—
129	#41×C₇₉	—	2	2	no	—
130	#41×C₇₉	—	4	4	no	—
131	#41×C₇₉	—	4	8	no	—
132	#41×C₇₉	—	4	4	no	—
133	#41×C₇₉	—	4	8	no	—
134	#41×C₇₉	—	4	4	no	—
135	#41×C₇₉	C₂×D₄	1	2	yes	—
136	#41×C₇₉	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₇₉	—	2	2	no	—
138	C₂×Q₈×C₇₉	—	2	8	no	—
139	C₂×Q₈×C₇₉	—	2	2	no	—
140	C₂×Q₈×C₇₉	—	2	2	no	—
141	C₂×Q₈×C₇₉	—	2	2	no	—
142	C₂×Q₈×C₇₉	—	2	2	no	—
143	C₂×Q₈×C₇₉	—	4	2	no	—
144	C₂×Q₈×C₇₉	—	4	4	no	—
145	C₂×Q₈×C₇₉	—	4	4	no	—
146	C₂×Q₈×C₇₉	—	4	4	no	—
147	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
149	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₇₉	—	2	1	no	—
151	C₂×D₄×C₇₉	—	2	2	no	—
152	C₂×D₄×C₇₉	—	2	2	no	—
153	C₂×D₄×C₇₉	—	2	2	no	—
154	C₂×D₄×C₇₉	—	2	2	no	—
155	C₂×D₄×C₇₉	—	2	2	no	—
156	C₂×D₄×C₇₉	—	2	2	no	—
157	C₂×D₄×C₇₉	—	2	2	no	—
158	C₂×D₄×C₇₉	—	4	4	no	—
159	C₂×D₄×C₇₉	—	4	2	no	—
160	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
161	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₉	—	2	1	no	—
163	C₂²×C₄×C₇₉	—	2	1	no	—
164	C₂²×C₄×C₇₉	—	2	2	no	—
165	C₂²×C₄×C₇₉	—	2	2	no	—
166	C₂²×C₄×C₇₉	—	4	2	no	—
167	C₂²×C₄×C₇₉	—	4	2	no	—
168	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₇₉	—	2	8	no	—
170	Q₁₆×C₇₉	—	2	2	no	—
171	Q₁₆×C₇₉	—	2	4	no	—
172	Q₁₆×C₇₉	—	2	4	no	—
173	SD₁₆×C₇₉	—	2	8	no	—
174	SD₁₆×C₇₉	—	2	4	no	—
175	SD₁₆×C₇₉	—	4	8	no	—
176	SD₁₆×C₇₉	—	4	4	no	—
177	SD₁₆×C₇₉	—	4	4	no	—
178	D₈×C₇₉	—	2	2	no	—
179	D₈×C₇₉	—	4	4	no	—
180	D₈×C₇₉	—	4	2	no	—
181	D₈×C₇₉	—	4	2	no	—
182	D₈×C₇₉	—	4	4	no	—
183	M₁₆×C₇₉	—	2	4	no	—
184	M₁₆×C₇₉	—	2	1	no	—
185	M₁₆×C₇₉	—	2	2	no	—
186	M₁₆×C₇₉	—	2	2	no	—
187	M₁₆×C₇₉	—	2	1	no	—
188	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
189	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₇₉	—	2	4	no	—
191	C₂×C₈×C₇₉	—	2	1	no	—
192	C₂×C₈×C₇₉	—	2	1	no	—
193	C₂×C₈×C₇₉	—	2	1	no	—
194	C₂×C₈×C₇₉	—	2	2	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
197	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
199	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
202	C₂²⋊C₄×C₇₉	—	2	1	no	—
203	C₂²⋊C₄×C₇₉	—	4	8	no	—
204	C₂²⋊C₄×C₇₉	—	4	4	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	C₂×D₄	1	2	yes	—
208	C₂³×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	2	2	no	—
210	C₂³×C₇₉	—	4	2	no	—
211	C₂³×C₇₉	—	4	2	no	—
212	C₂³×C₇₉	—	4	2	no	—
213	C₂³×C₇₉	—	8	4	no	—
214	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
215	Q₈×C₇₉	—	2	1	no	—
216	Q₈×C₇₉	—	2	4	no	—
217	Q₈×C₇₉	—	2	2	no	—
218	Q₈×C₇₉	—	2	4	no	—
219	Q₈×C₇₉	—	2	2	no	—
220	Q₈×C₇₉	—	4	8	no	—
221	Q₈×C₇₉	—	4	2	no	—
222	Q₈×C₇₉	—	4	2	no	—
223	Q₈×C₇₉	#127	1	2	yes	—
224	D₄×C₇₉	—	2	2	no	—
225	D₄×C₇₉	—	2	2	no	—
226	D₄×C₇₉	—	2	2	no	—
227	D₄×C₇₉	—	2	1	no	—
228	D₄×C₇₉	—	2	2	no	—
229	D₄×C₇₉	—	4	8	no	—
230	D₄×C₇₉	—	4	2	no	—
231	D₄×C₇₉	—	4	2	no	—
232	D₄×C₇₉	—	4	2	no	—
233	D₄×C₇₉	—	4	2	no	—
234	D₄×C₇₉	—	4	2	no	—
235	D₄×C₇₉	—	4	2	no	—
236	D₄×C₇₉	—	16	4	no	—
237	D₄×C₇₉	#127	1	2	yes	—
238	C₂×C₄×C₇₉	—	2	1	no	—
239	C₂×C₄×C₇₉	—	2	2	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	2	2	no	—
242	C₂×C₄×C₇₉	—	2	4	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	4	8	no	—
246	C₂×C₄×C₇₉	—	4	2	no	—
247	C₂×C₄×C₇₉	—	4	8	no	—
248	C₂×C₄×C₇₉	—	4	2	no	—
249	C₂×C₄×C₇₉	—	4	2	no	—
250	C₂×C₄×C₇₉	—	4	2	no	—
251	C₂×C₄×C₇₉	—	4	2	no	—
252	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
258	C₈×C₇₉	—	2	2	no	—
259	C₈×C₇₉	—	2	2	no	—
260	C₈×C₇₉	—	2	2	no	—
261	C₈×C₇₉	—	4	2	no	—
262	C₈×C₇₉	#120	1	2	yes	—
263	C₈×C₇₉	#120	1	2	yes	—
264	C₂²×C₇₉	—	2	2	no	—
265	C₂²×C₇₉	—	2	2	no	—
266	C₂²×C₇₉	—	4	2	no	—
267	C₂²×C₇₉	—	4	2	no	—
268	C₂²×C₇₉	—	4	4	no	—
269	C₂²×C₇₉	—	8	4	no	—
270	C₂²×C₇₉	—	8	2	no	—
271	C₂²×C₇₉	—	8	4	no	—
272	C₂²×C₇₉	—	16	2	no	—
273	C₂²×C₇₉	#535	1	1	yes	characteristic
274	C₂²×C₇₉	D₄²	1	1	yes	characteristic
275	C₂²×C₇₉	D₄²	1	1	yes	characteristic
276	C₄×C₇₉	—	2	2	no	—
277	C₄×C₇₉	—	4	2	no	—
278	C₄×C₇₉	—	4	4	no	—
279	C₄×C₇₉	—	4	2	no	—
280	C₄×C₇₉	—	4	2	no	—
281	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
282	C₄×C₇₉	C₂×#127	1	1	yes	characteristic
283	C₄×C₇₉	D₄²	1	1	yes	characteristic
284	C₄×C₇₉	D₄²	1	1	yes	characteristic
285	#25803	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₇₉	—	2	1	no	—
287	C₂×C₇₉	—	2	1	no	—
288	C₂×C₇₉	—	4	2	no	—
289	C₂×C₇₉	—	8	2	no	—
290	C₂×C₇₉	—	16	2	no	—
291	C₂×C₇₉	#2433	1	1	yes	characteristic
292	C₂×C₇₉	#3290	1	2	yes	—
293	C₂×#578	C₂×C₇₉	1	1	yes	characteristic, complemented
294	#3155	C₂×C₇₉	1	1	yes	characteristic, complemented
295	C₂×#495	C₂×C₇₉	1	1	yes	characteristic, complemented
296	C₂×#472	C₂×C₇₉	1	1	yes	characteristic, complemented
297	C₂×#454	C₂×C₇₉	1	2	yes	complemented
298	#3010	C₂×C₇₉	1	2	yes	complemented
299	#2019	C₂×C₇₉	1	2	yes	complemented
300	#2004	C₂×C₇₉	1	2	yes	complemented
301	#1979	C₂×C₇₉	1	1	yes	characteristic, complemented
302	#1974	C₂×C₇₉	1	1	yes	characteristic, complemented
303	#1764	C₂×C₇₉	1	1	yes	characteristic, complemented
304	C₇₉	#25803	1	1	yes	characteristic, direct product factor, Sylow
305	C₂×2₋¹⁺⁴	C₂²×C₇₉	1	2	yes	—
306	#578	—	2	4	no	—
307	#578	—	2	4	no	—
308	C₂×#137	—	2	2	no	—
309	C₂×#137	C₂²×C₇₉	1	2	yes	—
310	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	2	yes	—
311	C₂×AGL(1,ℤ/8)	C₂²×C₇₉	1	2	yes	—
312	C₂×#135	—	2	1	no	—
313	C₂×#135	C₂²×C₇₉	1	1	yes	characteristic
314	C₂²×Q₁₆	—	2	1	no	—
315	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
316	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
317	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
318	C₂×#131	C₂²×C₇₉	1	1	yes	characteristic
319	#535	C₂²×C₇₉	1	2	yes	—
320	C₂×#124	C₂²×C₇₉	1	2	yes	—
321	#496	—	2	2	no	—
322	#495	—	2	1	no	—
323	#495	—	2	4	no	—
324	#493	—	2	1	no	—
325	#472	—	2	4	no	—
326	#454	—	2	8	no	—
327	#449	—	2	4	no	—
328	#448	—	2	4	no	—
329	C₂×#108	C₂²×C₇₉	1	1	yes	characteristic
330	C₂×#104	C₂²×C₇₉	1	2	yes	—
331	C₂×#104	C₂²×C₇₉	1	1	yes	characteristic
332	#419	C₂²×C₇₉	1	2	yes	—
333	#416	C₂²×C₇₉	1	1	yes	characteristic
334	C₂×#101	C₂²×C₇₉	1	2	yes	—
335	C₂×#100	C₂²×C₇₉	1	2	yes	—
336	#408	C₂²×C₇₉	1	2	yes	—
337	#405	C₂²×C₇₉	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
339	#341	C₂²×C₇₉	1	1	yes	characteristic
340	#339	C₂²×C₇₉	1	1	yes	characteristic
341	2₋¹⁺⁴	—	2	4	no	—
342	2₋¹⁺⁴	—	2	4	no	—
343	2₋¹⁺⁴	—	2	4	no	—
344	2₋¹⁺⁴	—	4	2	no	—
345	C₂×#41	—	2	2	no	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	4	2	no	—
348	C₂×#41	C₂³×C₇₉	1	2	yes	—
349	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
350	C₂²×Q₈	—	2	2	no	—
351	C₂²×Q₈	—	2	2	no	—
352	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
353	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
354	#137	—	2	16	no	—
355	#137	—	2	4	no	—
356	#137	—	2	4	no	—
357	AGL(1,ℤ/8)	—	2	4	no	—
358	AGL(1,ℤ/8)	—	2	4	no	—
359	AGL(1,ℤ/8)	—	2	4	no	—
360	AGL(1,ℤ/8)	—	4	2	no	—
361	#135	—	2	8	no	—
362	#135	—	2	2	no	—
363	#135	—	2	2	no	—
364	C₂×Q₁₆	—	2	8	no	—
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×Q₁₆	—	2	1	no	—
368	C₂×Q₁₆	—	2	2	no	—
369	C₂×Q₁₆	D₄×C₇₉	1	1	yes	characteristic
370	C₂×Q₁₆	D₄×C₇₉	1	4	yes	complemented
371	C₂×SD₁₆	—	2	2	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	4	no	—
376	C₂×SD₁₆	—	4	2	no	—
377	C₂×SD₁₆	D₄×C₇₉	1	2	yes	—
378	C₂×D₈	—	2	2	no	—
379	C₂×D₈	—	2	2	no	—
380	C₂×D₈	—	2	2	no	—
381	C₂×D₈	—	2	1	no	—
382	C₂×D₈	—	2	2	no	—
383	C₂×D₈	—	2	1	no	—
384	C₂×D₈	D₄×C₇₉	1	1	yes	characteristic
385	#131	—	2	2	no	—
386	#131	D₄×C₇₉	1	4	yes	complemented
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
389	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
394	#127	—	2	2	no	—
395	#124	—	2	4	no	—
396	#124	—	2	2	no	—
397	#124	—	2	4	no	—
398	#121	—	2	4	no	—
399	#120	—	4	2	no	—
400	#117	C₂³×C₇₉	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	4	2	no	—
402	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
403	#108	—	2	2	no	—
404	#104	—	2	4	no	—
405	#104	D₄×C₇₉	1	4	yes	complemented
406	#103	—	2	4	no	—
407	#103	D₄×C₇₉	1	2	yes	—
408	#102	D₄×C₇₉	1	2	yes	—
409	#101	—	2	4	no	—
410	#100	—	2	4	no	—
411	C₂²⋊C₈	—	2	4	no	—
412	#97	—	2	1	no	—
413	C₄×C₈	—	2	2	no	—
414	C₄×C₈	—	2	1	no	—
415	C₂⁴	—	2	2	no	—
416	#41	—	2	1	no	—
417	#41	—	2	1	no	—
418	#41	—	2	8	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	4	4	no	—
424	#41	—	4	8	no	—
425	#41	—	4	4	no	—
426	#41	—	4	8	no	—
427	#41	—	4	4	no	—
428	#41	C₂×D₄×C₇₉	1	2	yes	—
429	#41	C₂×D₄×C₇₉	1	2	yes	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	8	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	—	4	4	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
441	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
442	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
454	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
462	Q₁₆	—	2	8	no	—
463	Q₁₆	—	2	2	no	—
464	Q₁₆	—	2	4	no	—
465	Q₁₆	—	2	4	no	—
466	SD₁₆	—	2	8	no	—
467	SD₁₆	—	2	4	no	—
468	SD₁₆	—	4	8	no	—
469	SD₁₆	—	4	4	no	—
470	SD₁₆	—	4	4	no	—
471	D₈	—	2	2	no	—
472	D₈	—	4	4	no	—
473	D₈	—	4	4	no	—
474	D₈	—	4	2	no	—
475	D₈	—	4	2	no	—
476	M₁₆	—	2	1	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	4	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
482	M₁₆	C₂×D₄×C₇₉	1	2	yes	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
490	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
492	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
494	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	4	8	no	—
497	C₂²⋊C₄	—	4	4	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	C₂×D₄×C₇₉	1	2	yes	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	8	4	no	—
507	C₂³	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
508	Q₈	—	2	1	no	—
509	Q₈	—	2	4	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	4	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	4	8	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	2	no	—
516	Q₈	#127×C₇₉	1	2	yes	—
517	D₄	—	2	2	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	8	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	16	4	no	—
530	D₄	#127×C₇₉	1	2	yes	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
550	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	4	2	no	—
555	C₈	#120×C₇₉	1	2	yes	—
556	C₈	#120×C₇₉	1	2	yes	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	8	4	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	16	2	no	—
566	C₂²	#535×C₇₉	1	1	yes	characteristic
567	C₂²	D₄²×C₇₉	1	1	yes	characteristic
568	C₂²	D₄²×C₇₉	1	1	yes	characteristic
569	C₄	—	2	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
575	C₄	C₂×#127×C₇₉	1	1	yes	characteristic
576	C₄	D₄²×C₇₉	1	1	yes	characteristic
577	C₄	D₄²×C₇₉	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	2	no	—
582	C₂	—	16	2	no	—
583	C₂	C₇₉×#2433	1	1	yes	characteristic
584	C₂	C₇₉×#3290	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×#578×C₇₉	C₂	semidirect
2. C₇₉×#3155	C₂	semidirect
3. C₂×#495×C₇₉	C₂	semidirect
4. C₂×#472×C₇₉	C₂	semidirect
5. C₂×#454×C₇₉	C₂	semidirect
6. C₇₉×#3010	C₂	semidirect
7. C₇₉×#2019	C₂	semidirect
8. C₇₉×#2004	C₂	semidirect
9. C₇₉×#1979	C₂	semidirect
10. C₇₉×#1974	C₂	semidirect
11. C₇₉×#1764	C₂	semidirect
77. C₂×Q₁₆×C₇₉	D₄	semidirect
93. #131×C₇₉	D₄	semidirect
112. #104×C₇₉	D₄	semidirect
285. #25803	C₇₉	direct (N × H)
293. C₂×#578	C₂×C₇₉	semidirect
294. #3155	C₂×C₇₉	semidirect
295. C₂×#495	C₂×C₇₉	semidirect
296. C₂×#472	C₂×C₇₉	semidirect
297. C₂×#454	C₂×C₇₉	semidirect
298. #3010	C₂×C₇₉	semidirect
299. #2019	C₂×C₇₉	semidirect
300. #2004	C₂×C₇₉	semidirect
301. #1979	C₂×C₇₉	semidirect
302. #1974	C₂×C₇₉	semidirect
303. #1764	C₂×C₇₉	semidirect
304. C₇₉	#25803	direct (N × H)
370. C₂×Q₁₆	D₄×C₇₉	semidirect
386. #131	D₄×C₇₉	semidirect
405. #104	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×#578×C₇₉	2
C₇₉×#3155	2
C₂×#495×C₇₉	2
C₂×#472×C₇₉	2
C₂×#454×C₇₉	2
C₇₉×#3010	2
C₇₉×#2019	2
C₇₉×#2004	2
C₇₉×#1979	2
C₇₉×#1974	2
C₇₉×#1764	2
#25803	79

Subgroups — C79×#25803 #34137492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25803 #34137492