Subgroups — C₇₉×#25666 #34137355

Order 20224.

1092 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3511	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2868	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2039	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1859	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#556×C₇₉	—	2	1	no	—
11	#555×C₇₉	—	2	1	no	—
12	#554×C₇₉	—	2	1	no	—
13	#553×C₇₉	—	2	2	no	—
14	#548×C₇₉	—	2	2	no	—
15	#547×C₇₉	—	2	1	no	—
16	#542×C₇₉	—	2	2	no	—
17	#537×C₇₉	C₂²	1	2	yes	—
18	#533×C₇₉	—	2	1	no	—
19	#532×C₇₉	—	2	1	no	—
20	#532×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₇₉	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	#520×C₇₉	C₂²	1	2	yes	—
25	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
26	#489×C₇₉	—	2	2	no	—
27	#487×C₇₉	—	2	1	no	—
28	#486×C₇₉	—	2	1	no	—
29	#477×C₇₉	—	2	1	no	—
30	#476×C₇₉	—	2	1	no	—
31	#475×C₇₉	—	2	1	no	—
32	#474×C₇₉	—	2	1	no	—
33	#428×C₇₉	C₂²	1	2	yes	—
34	#423×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#104×C₇₉	C₂²	1	2	yes	—
36	C₂×#104×C₇₉	C₂²	1	4	yes	—
37	#417×C₇₉	C₂²	1	2	yes	—
38	#417×C₇₉	C₂²	1	4	yes	—
39	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
40	#384×C₇₉	—	2	2	no	—
41	#384×C₇₉	C₂²	1	4	yes	—
42	C₄³×C₇₉	C₂²	1	1	yes	characteristic
43	#343×C₇₉	C₂²	1	4	yes	—
44	#339×C₇₉	C₂²	1	2	yes	—
45	C₂×#41×C₇₉	—	2	2	no	—
46	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
47	C₂×#41×C₇₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₇₉	—	2	1	no	—
49	C₂²×Q₈×C₇₉	D₄	1	2	yes	—
50	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
51	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₇₉	—	2	1	no	—
53	C₄⋊Q₈×C₇₉	—	2	1	no	—
54	C₄⋊Q₈×C₇₉	—	2	1	no	—
55	C₄⋊Q₈×C₇₉	—	2	1	no	—
56	C₄⋊Q₈×C₇₉	—	2	1	no	—
57	C₄⋊Q₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	4	8	no	—
61	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
62	#127×C₇₉	D₄	1	1	yes	characteristic
63	#126×C₇₉	—	2	4	no	—
64	#125×C₇₉	—	2	2	no	—
65	#124×C₇₉	—	2	2	no	—
66	#124×C₇₉	—	2	4	no	—
67	#124×C₇₉	D₄	1	2	yes	—
68	#123×C₇₉	—	2	4	no	—
69	C₂²⋊Q₈×C₇₉	—	2	2	no	—
70	C₂²⋊Q₈×C₇₉	—	2	4	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	#121×C₇₉	—	2	2	no	—
74	#121×C₇₉	—	2	2	no	—
75	#121×C₇₉	—	2	2	no	—
76	#121×C₇₉	—	2	1	no	—
77	#121×C₇₉	—	2	1	no	—
78	#121×C₇₉	—	2	4	no	—
79	C₄×Q₈×C₇₉	—	2	2	no	—
80	C₄×Q₈×C₇₉	—	2	2	no	—
81	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
83	C₄×D₄×C₇₉	—	2	2	no	—
84	C₄×D₄×C₇₉	—	2	2	no	—
85	C₄×D₄×C₇₉	—	2	1	no	—
86	C₄×D₄×C₇₉	—	2	1	no	—
87	C₄×D₄×C₇₉	—	2	4	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
91	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
92	#117×C₇₉	—	2	2	no	—
93	#117×C₇₉	—	2	2	no	—
94	#117×C₇₉	—	2	1	no	—
95	#117×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	#107×C₇₉	—	2	2	no	—
108	#106×C₇₉	—	2	2	no	—
109	C₄⋊C₈×C₇₉	—	2	1	no	—
110	C₄⋊C₈×C₇₉	—	2	1	no	—
111	#104×C₇₉	—	2	4	no	—
112	#104×C₇₉	—	2	8	no	—
113	#103×C₇₉	—	2	2	no	—
114	#103×C₇₉	—	2	4	no	—
115	#102×C₇₉	—	2	2	no	—
116	#102×C₇₉	—	2	4	no	—
117	#97×C₇₉	—	2	1	no	—
118	C₄×C₈×C₇₉	—	2	1	no	—
119	#41×C₇₉	—	2	4	no	—
120	#41×C₇₉	—	2	2	no	—
121	#41×C₇₉	—	2	4	no	—
122	#41×C₇₉	—	2	2	no	—
123	#41×C₇₉	—	8	4	no	—
124	C₂×Q₈×C₇₉	—	2	2	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	4	4	no	—
127	C₂×Q₈×C₇₉	—	4	4	no	—
128	C₂×Q₈×C₇₉	—	4	1	no	—
129	C₂×Q₈×C₇₉	—	4	1	no	—
130	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₇₉	—	2	1	no	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	—	2	4	no	—
135	C₂×D₄×C₇₉	—	2	1	no	—
136	C₂×D₄×C₇₉	—	2	1	no	—
137	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	4	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	—	2	2	no	—
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₇₉	—	2	4	no	—
151	M₁₆×C₇₉	—	2	2	no	—
152	M₁₆×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	2	no	—
154	C₂×C₈×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	4	no	—
156	C₄⋊C₄×C₇₉	—	2	4	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	2	1	no	—
160	C₄⋊C₄×C₇₉	—	2	1	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	4	16	no	—
168	C₄⋊C₄×C₇₉	—	4	1	no	—
169	C₄⋊C₄×C₇₉	—	4	1	no	—
170	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₇₉	—	2	4	no	—
173	C₂²⋊C₄×C₇₉	—	2	4	no	—
174	C₂²⋊C₄×C₇₉	—	2	4	no	—
175	C₂²⋊C₄×C₇₉	—	2	1	no	—
176	C₂²⋊C₄×C₇₉	—	2	1	no	—
177	C₂²⋊C₄×C₇₉	—	2	1	no	—
178	C₂²⋊C₄×C₇₉	—	2	2	no	—
179	C₂²⋊C₄×C₇₉	—	2	2	no	—
180	C₄²×C₇₉	—	2	4	no	—
181	C₄²×C₇₉	—	2	4	no	—
182	C₄²×C₇₉	—	2	4	no	—
183	C₄²×C₇₉	—	2	1	no	—
184	C₄²×C₇₉	—	2	1	no	—
185	C₄²×C₇₉	—	2	1	no	—
186	C₄²×C₇₉	—	2	2	no	—
187	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇₉	#41	1	4	yes	complemented
192	C₂³×C₇₉	—	2	1	no	—
193	C₂³×C₇₉	—	2	2	no	—
194	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₇₉	—	2	1	no	—
196	Q₈×C₇₉	—	2	1	no	—
197	Q₈×C₇₉	—	2	4	no	—
198	Q₈×C₇₉	—	4	4	no	—
199	Q₈×C₇₉	—	8	2	no	—
200	Q₈×C₇₉	—	8	2	no	—
201	Q₈×C₇₉	—	8	2	no	—
202	D₄×C₇₉	—	2	1	no	—
203	D₄×C₇₉	—	2	1	no	—
204	D₄×C₇₉	—	2	4	no	—
205	D₄×C₇₉	—	4	4	no	—
206	D₄×C₇₉	—	4	2	no	—
207	D₄×C₇₉	—	4	2	no	—
208	D₄×C₇₉	—	4	2	no	—
209	D₄×C₇₉	—	8	4	no	—
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	4	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	1	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	4	no	—
220	C₂×C₄×C₇₉	—	4	2	no	—
221	C₂×C₄×C₇₉	—	4	2	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	2	no	—
225	C₂×C₄×C₇₉	—	4	4	no	—
226	C₂×C₄×C₇₉	—	4	4	no	—
227	C₂×C₄×C₇₉	—	4	2	no	—
228	C₂×C₄×C₇₉	—	8	4	no	—
229	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
237	C₈×C₇₉	—	4	2	no	—
238	C₈×C₇₉	—	4	2	no	—
239	C₂²×C₇₉	—	2	1	no	—
240	C₂²×C₇₉	—	2	1	no	—
241	C₂²×C₇₉	—	4	2	no	—
242	C₂²×C₇₉	—	4	1	no	—
243	C₂²×C₇₉	—	4	1	no	—
244	C₂²×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	4	1	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
248	C₂²×C₇₉	#548	1	2	yes	—
249	C₄×C₇₉	—	2	8	no	—
250	C₄×C₇₉	—	2	1	no	—
251	C₄×C₇₉	—	2	1	no	—
252	C₄×C₇₉	—	4	2	no	—
253	C₄×C₇₉	—	4	1	no	—
254	C₄×C₇₉	—	4	1	no	—
255	C₄×C₇₉	—	4	4	no	—
256	C₄×C₇₉	—	4	1	no	—
257	C₄×C₇₉	—	8	2	no	—
258	C₄×C₇₉	#453	1	2	yes	—
259	C₄×C₇₉	#456	1	2	yes	—
260	C₄×C₇₉	#532	1	1	yes	characteristic
261	C₄×C₇₉	#536	1	1	yes	characteristic
262	C₄×C₇₉	#547	1	2	yes	—
263	#25666	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂×C₇₉	—	2	2	no	—
265	C₂×C₇₉	—	8	1	no	—
266	C₂×C₇₉	—	8	2	no	—
267	C₂×C₇₉	#2432	1	1	yes	characteristic
268	C₂×C₇₉	C₂×#453	1	1	yes	characteristic
269	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
270	#3511	C₂×C₇₉	1	1	yes	characteristic
271	#3141	C₂×C₇₉	1	1	yes	characteristic, complemented
272	#3079	C₂×C₇₉	1	1	yes	characteristic, complemented
273	#2868	C₂×C₇₉	1	1	yes	characteristic, complemented
274	#2039	C₂×C₇₉	1	4	yes	complemented
275	#1997	C₂×C₇₉	1	1	yes	characteristic, complemented
276	#1962	C₂×C₇₉	1	1	yes	characteristic, complemented
277	#1859	C₂×C₇₉	1	4	yes	complemented
278	C₄×#104	C₂×C₇₉	1	1	yes	characteristic, complemented
279	C₇₉	#25666	1	1	yes	characteristic, direct product factor, Sylow
280	#556	—	2	1	no	—
281	#555	—	2	1	no	—
282	#554	—	2	1	no	—
283	#553	—	2	2	no	—
284	#548	—	2	2	no	—
285	#547	—	2	1	no	—
286	#542	—	2	2	no	—
287	#537	C₂²×C₇₉	1	2	yes	—
288	#533	—	2	1	no	—
289	#532	—	2	1	no	—
290	#532	C₂²×C₇₉	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	—	2	2	no	—
292	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
293	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
294	#520	C₂²×C₇₉	1	2	yes	—
295	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
296	#489	—	2	2	no	—
297	#487	—	2	1	no	—
298	#486	—	2	1	no	—
299	#477	—	2	1	no	—
300	#476	—	2	1	no	—
301	#475	—	2	1	no	—
302	#474	—	2	1	no	—
303	#428	C₂²×C₇₉	1	2	yes	—
304	#423	C₂²×C₇₉	1	1	yes	characteristic
305	C₂×#104	C₂²×C₇₉	1	4	yes	—
306	C₂×#104	C₂²×C₇₉	1	2	yes	—
307	#417	C₂²×C₇₉	1	2	yes	—
308	#417	C₂²×C₇₉	1	4	yes	—
309	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
310	#384	—	2	2	no	—
311	#384	C₂²×C₇₉	1	4	yes	—
312	C₄³	C₂²×C₇₉	1	1	yes	characteristic
313	#343	C₂²×C₇₉	1	4	yes	—
314	#339	C₂²×C₇₉	1	2	yes	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂³×C₇₉	1	1	yes	characteristic
317	C₂×#41	C₂³×C₇₉	1	2	yes	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂²×Q₈	D₄×C₇₉	1	2	yes	—
320	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
321	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	4	8	no	—
331	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
332	#127	D₄×C₇₉	1	1	yes	characteristic
333	#126	—	2	4	no	—
334	#125	—	2	2	no	—
335	#124	—	2	2	no	—
336	#124	—	2	4	no	—
337	#124	D₄×C₇₉	1	2	yes	—
338	#123	—	2	4	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	4	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
352	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
361	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
362	#117	—	2	2	no	—
363	#117	—	2	2	no	—
364	#117	—	2	1	no	—
365	#117	C₂³×C₇₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	8	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
377	#107	—	2	2	no	—
378	#106	—	2	2	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	#104	—	2	8	no	—
382	#104	—	2	4	no	—
383	#103	—	2	2	no	—
384	#103	—	2	4	no	—
385	#102	—	2	2	no	—
386	#102	—	2	4	no	—
387	#97	—	2	1	no	—
388	C₄×C₈	—	2	1	no	—
389	#41	—	2	4	no	—
390	#41	—	2	2	no	—
391	#41	—	2	4	no	—
392	#41	—	2	2	no	—
393	#41	—	8	4	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	—	4	4	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
401	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
408	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
420	M₁₆	—	2	4	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	4	16	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
461	C₄²	#41×C₇₉	1	4	yes	complemented
462	C₂³	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	4	4	no	—
469	Q₈	—	8	2	no	—
470	Q₈	—	8	2	no	—
471	Q₈	—	8	2	no	—
472	D₄	—	2	1	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	4	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	4	no	—
499	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
500	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
501	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
502	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
506	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
507	C₈	—	4	2	no	—
508	C₈	—	4	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	2	no	—
517	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
518	C₂²	#548×C₇₉	1	2	yes	—
519	C₄	—	2	8	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	1	no	—
527	C₄	—	8	2	no	—
528	C₄	#453×C₇₉	1	2	yes	—
529	C₄	#456×C₇₉	1	2	yes	—
530	C₄	#532×C₇₉	1	1	yes	characteristic
531	C₄	#536×C₇₉	1	1	yes	characteristic
532	C₄	#547×C₇₉	1	2	yes	—
533	C₂	—	2	2	no	—
534	C₂	—	8	1	no	—
535	C₂	—	8	2	no	—
536	C₂	C₇₉×#2432	1	1	yes	characteristic
537	C₂	C₂×#453×C₇₉	1	1	yes	characteristic
538	C₂	C₂×#456×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#3511	C₂
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
2. C₇₉×#3141	C₂	semidirect
3. C₇₉×#3079	C₂	semidirect
4. C₇₉×#2868	C₂	semidirect
5. C₇₉×#2039	C₂	semidirect
6. C₇₉×#1997	C₂	semidirect
7. C₇₉×#1962	C₂	semidirect
8. C₇₉×#1859	C₂	semidirect
9. C₄×#104×C₇₉	C₂	semidirect
191. C₄²×C₇₉	#41	semidirect
263. #25666	C₇₉	direct (N × H)
271. #3141	C₂×C₇₉	semidirect
272. #3079	C₂×C₇₉	semidirect
273. #2868	C₂×C₇₉	semidirect
274. #2039	C₂×C₇₉	semidirect
275. #1997	C₂×C₇₉	semidirect
276. #1962	C₂×C₇₉	semidirect
277. #1859	C₂×C₇₉	semidirect
278. C₄×#104	C₂×C₇₉	semidirect
279. C₇₉	#25666	direct (N × H)
461. C₄²	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3511	2
C₇₉×#3141	2
C₇₉×#3079	2
C₇₉×#2868	2
C₇₉×#2039	2
C₇₉×#1997	2
C₇₉×#1962	2
C₇₉×#1859	2
C₄×#104×C₇₉	2
#25666	79

Subgroups — C79×#25666 #34137355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25666 #34137355