Subgroups — #3177×D₇₉ #35158105

Order 20224.

1842 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#541×D₇₉	C₂	1	2	yes	maximal
2	#23774060	C₂	1	1	yes	maximal, characteristic, complemented
3	#23774059	C₂	1	1	yes	maximal, characteristic, complemented
4	#23774058	C₂	1	2	yes	maximal, complemented
5	#23774057	C₂	1	2	yes	maximal, complemented
6	#23774056	C₂	1	1	yes	maximal, characteristic, complemented
7	#23774055	C₂	1	2	yes	maximal, complemented
8	#23774054	C₂	1	2	yes	maximal, complemented
9	#23774053	C₂	1	2	yes	maximal, complemented
10	#23774052	C₂	1	2	yes	maximal, complemented
11	#499×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#494×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#491×D₇₉	C₂	1	2	yes	maximal, complemented
14	#470×D₇₉	C₂	1	2	yes	maximal
15	#467×D₇₉	C₂	1	2	yes	maximal
16	#441×D₇₉	C₂	1	2	yes	maximal, complemented
17	C₄×Q₁₆×D₇₉	C₂	1	2	yes	maximal, complemented
18	#405×D₇₉	C₂	1	1	yes	maximal, characteristic
19	C₇₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	—
21	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	—
22	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
24	#19099176	C₂²	1	2	yes	—
25	#19099175	C₂²	1	2	yes	—
26	#19099174	C₂²	1	2	yes	—
27	#19099173	C₂²	1	4	yes	—
28	#19099172	—	2	4	no	—
29	#19099171	C₂²	1	4	yes	—
30	#19099170	—	2	4	no	—
31	C₄⋊Q₈×D₇₉	C₂²	1	2	yes	—
32	#126×D₇₉	—	2	4	no	—
33	#125×D₇₉	—	2	4	no	—
34	#125×D₇₉	C₂²	1	2	yes	—
35	C₂²⋊Q₈×D₇₉	C₂²	1	4	yes	—
36	C₄×Q₈×D₇₉	C₂²	1	4	yes	—
37	#117×D₇₉	C₂²	1	1	yes	characteristic
38	#19098965	C₂²	1	1	yes	characteristic, complemented
39	#19098964	C₂²	1	2	yes	complemented
40	#19098963	C₂²	1	2	yes	complemented
41	#19098962	C₂²	1	2	yes	complemented
42	#19098943	C₂²	1	1	yes	characteristic, complemented
43	#19098942	C₂²	1	2	yes	complemented
44	#19098941	C₂²	1	2	yes	complemented
45	#19098941	C₂²	1	2	yes	complemented
46	#19098933	C₂²	1	2	yes	complemented
47	#19098932	C₂²	1	2	yes	complemented
48	#19098931	C₂²	1	2	yes	complemented
49	#19098930	C₂²	1	4	yes	complemented
50	#19098930	C₂²	1	4	yes	complemented
51	#19098822	C₂²	1	2	yes	—
52	#19098821	C₂²	1	2	yes	—
53	#19098820	C₂²	1	4	yes	—
54	#19098819	C₂²	1	4	yes	—
55	#19098818	C₂²	1	2	yes	—
56	#19098805	C₂²	1	2	yes	—
57	#19098804	C₂²	1	2	yes	—
58	#19098803	C₂²	1	4	yes	—
59	#19098802	C₂²	1	4	yes	—
60	#19098801	C₂²	1	2	yes	—
61	#19098671	C₂²	1	2	yes	complemented
62	#19098670	C₂²	1	2	yes	complemented
63	#19098669	C₂²	1	2	yes	complemented
64	#19098668	C₂²	1	4	yes	complemented
65	#19098667	C₂²	1	4	yes	complemented
66	C₄×Dic₃₁₆	C₂²	1	2	yes	complemented
67	Q₁₆×Dic₇₉	C₂²	1	2	yes	complemented
68	#19098657	C₂²	1	2	yes	complemented
69	C₄×#11929614	C₂²	1	4	yes	complemented
70	#19098655	C₂²	1	4	yes	complemented
71	#107×D₇₉	C₂²	1	2	yes	—
72	#106×D₇₉	C₂²	1	2	yes	—
73	#103×D₇₉	C₂²	1	4	yes	—
74	#103×D₇₉	C₂²	1	4	yes	—
75	#19098521	C₂²	1	1	yes	characteristic
76	#19098520	C₂²	1	1	yes	characteristic
77	#19098520	C₂²	1	1	yes	characteristic
78	#19098519	C₂²	1	1	yes	characteristic
79	#19098518	C₂²	1	1	yes	characteristic
80	#19098517	C₂²	1	1	yes	characteristic
81	#19098517	C₂²	1	1	yes	characteristic
82	#97×D₇₉	C₂²	1	1	yes	characteristic
83	#97×D₇₉	C₂²	1	1	yes	characteristic
84	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
85	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
86	#541×C₇₉	C₂²	1	2	yes	—
87	#499×C₇₉	C₂²	1	1	yes	characteristic, complemented
88	#494×C₇₉	C₂²	1	1	yes	characteristic, complemented
89	#491×C₇₉	C₂²	1	2	yes	complemented
90	#470×C₇₉	C₂²	1	2	yes	—
91	#467×C₇₉	C₂²	1	2	yes	—
92	#441×C₇₉	C₂²	1	2	yes	complemented
93	C₄×Q₁₆×C₇₉	C₂²	1	2	yes	complemented
94	#405×C₇₉	C₂²	1	1	yes	characteristic
95	C₂×Q₈×D₇₉	C₂³	1	4	yes	—
96	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
97	C₂×Dic₃₁₆	C₂³	1	2	yes	—
98	C₂×Dic₃₁₆	C₂³	1	2	yes	—
99	C₂×#11929614	C₂³	1	4	yes	—
100	C₂×#11929614	C₂³	1	4	yes	—
101	Q₁₆×D₇₉	—	2	8	no	—
102	Q₁₆×D₇₉	—	2	8	no	—
103	C₂×#11929608	C₂³	1	1	yes	characteristic
104	C₂×#11929607	C₂³	1	1	yes	characteristic
105	C₂×#11929607	C₂³	1	1	yes	characteristic
106	M₁₆×D₇₉	—	2	4	no	—
107	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
108	C₂×C₈×D₇₉	—	2	4	no	—
109	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
110	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
112	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
115	#14579161	C₂³	1	2	yes	—
116	#14579160	—	2	4	no	—
117	#14579159	C₂³	1	4	yes	—
118	#14579156	—	2	4	no	—
119	#14579156	—	2	4	no	—
120	#14579156	—	2	4	no	—
121	#14579155	—	2	4	no	—
122	#14579154	—	2	4	no	—
123	#14579154	—	2	4	no	—
124	#14579154	—	2	4	no	—
125	#14579153	—	2	4	no	—
126	#14579153	C₂³	1	2	yes	—
127	#14579152	—	2	4	no	—
128	#14579152	—	2	4	no	—
129	#14579152	C₂³	1	4	yes	—
130	#14579151	—	2	4	no	—
131	#14579151	—	2	4	no	—
132	#14579151	—	2	4	no	—
133	#14579151	—	2	4	no	—
134	#14579151	—	2	4	no	—
135	#14579141	C₂³	1	4	yes	—
136	#14579140	C₂³	1	4	yes	—
137	#14579139	—	2	4	no	—
138	#14579138	—	2	4	no	—
139	#14579137	C₂³	1	4	yes	—
140	Q₈×Dic₇₉	C₂³	1	4	yes	—
141	C₄×Dic₁₅₈	—	2	4	no	—
142	C₄×Dic₁₅₈	C₂³	1	4	yes	—
143	#14579126	—	2	4	no	—
144	#14579126	C₂³	1	4	yes	—
145	#14579120	C₂³	1	1	yes	characteristic
146	#14579119	D₄	1	2	yes	—
147	#14579118	C₂³	1	1	yes	characteristic
148	#14579118	C₂³	1	1	yes	characteristic
149	#14579117	D₄	1	2	yes	—
150	C₄⋊C₄×D₇₉	—	2	4	no	—
151	C₄⋊C₄×D₇₉	—	2	4	no	—
152	C₄⋊C₄×D₇₉	—	2	4	no	—
153	C₄⋊C₄×D₇₉	—	2	4	no	—
154	C₄⋊C₄×D₇₉	D₄	1	2	yes	—
155	C₄⋊C₄×D₇₉	C₂³	1	4	yes	—
156	C₂²⋊C₄×D₇₉	—	2	4	no	—
157	C₂²⋊C₄×D₇₉	D₄	1	2	yes	—
158	C₄²×D₇₉	—	2	4	no	—
159	C₄²×D₇₉	C₂³	1	1	yes	characteristic
160	C₄²×D₇₉	C₂³	1	1	yes	characteristic
161	#14579095	C₂³	1	2	yes	—
162	#14579094	C₂³	1	4	yes	—
163	#14579093	C₂³	1	2	yes	—
164	#14579092	C₂³	1	4	yes	—
165	#14579086	C₂³	1	4	yes	—
166	#14579086	C₂³	1	4	yes	—
167	#14579085	C₂³	1	4	yes	—
168	#14579085	C₂³	1	4	yes	—
169	#14579084	C₂³	1	4	yes	—
170	#14579084	C₂³	1	4	yes	—
171	#14579072	C₂³	1	1	yes	characteristic
172	#14579072	C₂³	1	1	yes	characteristic
173	#14579071	C₂³	1	1	yes	characteristic
174	#14579071	C₂³	1	1	yes	characteristic
175	#14579071	C₂³	1	1	yes	characteristic
176	#14579071	C₂³	1	1	yes	characteristic
177	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
178	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
179	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
180	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
181	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
182	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
183	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
184	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
185	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
187	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
188	#126×C₇₉	—	2	4	no	—
189	#125×C₇₉	—	2	4	no	—
190	#125×C₇₉	C₂³	1	2	yes	—
191	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
192	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
193	#117×C₇₉	C₂³	1	1	yes	characteristic
194	#107×C₇₉	C₂³	1	2	yes	—
195	#106×C₇₉	C₂³	1	2	yes	—
196	#103×C₇₉	C₂³	1	4	yes	—
197	#103×C₇₉	C₂³	1	4	yes	—
198	#97×C₇₉	C₂³	1	1	yes	characteristic
199	#97×C₇₉	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
202	C₂³×D₇₉	C₂×D₄	1	1	yes	characteristic
203	C₂×Dic₁₅₈	—	2	4	no	—
204	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
205	Q₈×D₇₉	—	2	8	no	—
206	Q₈×D₇₉	—	2	8	no	—
207	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×D₇₉	—	2	2	no	—
209	C₂×C₄×D₇₉	—	2	2	no	—
210	C₂×C₄×D₇₉	—	2	4	no	—
211	C₂×C₄×D₇₉	—	2	4	no	—
212	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
213	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
214	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
215	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
216	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
218	Dic₃₁₆	—	2	4	no	—
219	Dic₃₁₆	—	2	4	no	—
220	#11929614	—	2	8	no	—
221	#11929614	—	2	8	no	—
222	#11929608	—	2	2	no	—
223	#11929607	—	2	2	no	—
224	#11929607	—	2	2	no	—
225	C₂×C₇₉⋊C₈	—	2	2	no	—
226	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
227	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
228	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
229	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
230	C₈×D₇₉	—	2	2	no	—
231	C₈×D₇₉	—	2	2	no	—
232	C₈×D₇₉	—	2	2	no	—
233	C₈×D₇₉	—	2	2	no	—
234	C₈×D₇₉	#41	1	4	yes	—
235	C₈×D₇₉	#41	1	4	yes	—
236	C₄⋊Dic₇₉	—	2	4	no	—
237	C₄⋊Dic₇₉	—	2	4	no	—
238	C₄⋊Dic₇₉	—	2	4	no	—
239	C₄⋊Dic₇₉	—	2	4	no	—
240	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
241	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
242	Dic₇₉⋊C₄	—	2	4	no	—
243	Dic₇₉⋊C₄	—	2	4	no	—
244	Dic₇₉⋊C₄	—	2	4	no	—
245	Dic₇₉⋊C₄	—	2	4	no	—
246	Dic₇₉⋊C₄	—	2	4	no	—
247	Dic₇₉⋊C₄	—	2	4	no	—
248	Dic₇₉⋊C₄	—	2	4	no	—
249	Dic₇₉⋊C₄	—	2	4	no	—
250	Dic₇₉⋊C₄	—	2	4	no	—
251	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
252	Dic₇₉⋊C₄	C₂×D₄	1	2	yes	—
253	C₂²⋊Dic₇₉	—	2	4	no	—
254	C₂²⋊Dic₇₉	C₂×D₄	1	2	yes	—
255	(C₂×D₇₉)⋊C₄	—	2	4	no	—
256	(C₂×D₇₉)⋊C₄	—	2	4	no	—
257	(C₂×D₇₉)⋊C₄	C₂×D₄	1	2	yes	—
258	(C₂×D₇₉)⋊C₄	C₂×D₄	1	2	yes	—
259	C₄×Dic₇₉	—	2	4	no	—
260	C₄×Dic₇₉	—	2	4	no	—
261	C₄×Dic₇₉	—	2	4	no	—
262	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
263	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
264	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
265	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
266	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₇₉	—	2	4	no	—
269	Q₁₆×C₇₉	—	2	4	no	—
270	M₁₆×C₇₉	—	2	2	no	—
271	C₂×C₈×C₇₉	—	2	2	no	—
272	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₇₉	—	2	4	no	—
277	C₄⋊C₄×C₇₉	—	2	4	no	—
278	C₄⋊C₄×C₇₉	—	2	4	no	—
279	C₄⋊C₄×C₇₉	—	2	4	no	—
280	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
282	C₂²⋊C₄×C₇₉	—	2	4	no	—
283	C₂²⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
284	C₄²×C₇₉	—	2	4	no	—
285	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
286	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
287	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
288	C₂²×D₇₉	—	2	2	no	—
289	C₂²×D₇₉	—	2	4	no	—
290	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
291	C₂²×D₇₉	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₇₉	—	2	4	no	—
293	Q₈×C₇₉	—	2	4	no	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	1	no	—
296	C₂×C₄×C₇₉	—	2	4	no	—
297	C₂×C₄×C₇₉	—	2	4	no	—
298	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
302	C₂×Dic₇₉	—	2	2	no	—
303	C₂×Dic₇₉	—	2	4	no	—
304	C₂×Dic₇₉	—	2	4	no	—
305	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
306	C₂×Dic₇₉	C₂²×D₄	1	2	yes	—
307	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×Dic₇₉	C₂²×D₄	1	1	yes	characteristic
309	C₄×D₇₉	—	2	2	no	—
310	C₄×D₇₉	—	2	4	no	—
311	C₄×D₇₉	—	2	4	no	—
312	C₄×D₇₉	—	2	1	no	—
313	C₄×D₇₉	—	2	1	no	—
314	C₄×D₇₉	—	2	2	no	—
315	C₄×D₇₉	—	4	8	no	—
316	C₄×D₇₉	—	4	8	no	—
317	C₄×D₇₉	C₂×#41	1	2	yes	—
318	C₄×D₇₉	C₂×#41	1	2	yes	—
319	Dic₁₅₈	—	2	4	no	—
320	Dic₁₅₈	—	2	4	no	—
321	Dic₁₅₈	—	4	8	no	—
322	C₈×C₇₉	—	2	1	no	—
323	C₈×C₇₉	—	2	1	no	—
324	C₈×C₇₉	C₂×#41	1	2	yes	—
325	C₈×C₇₉	C₂×#41	1	2	yes	—
326	C₇₉⋊C₈	—	2	1	no	—
327	C₇₉⋊C₈	—	2	1	no	—
328	C₇₉⋊C₈	C₂×#41	1	2	yes	—
329	C₇₉⋊C₈	C₂×#41	1	2	yes	—
330	C₂²×C₇₉	—	2	1	no	—
331	C₂²×C₇₉	—	2	2	no	—
332	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
333	C₂×D₇₉	—	2	1	no	—
334	C₂×D₇₉	—	2	2	no	—
335	C₂×D₇₉	—	4	4	no	—
336	C₂×D₇₉	#532	1	2	yes	—
337	C₂×D₇₉	#578	1	4	yes	—
338	C₄×C₇₉	—	2	1	no	—
339	C₄×C₇₉	—	2	2	no	—
340	C₄×C₇₉	—	2	2	no	—
341	C₄×C₇₉	—	4	4	no	—
342	C₄×C₇₉	—	4	4	no	—
343	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
344	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
345	Dic₇₉	—	2	1	no	—
346	Dic₇₉	—	2	2	no	—
347	Dic₇₉	—	2	2	no	—
348	Dic₇₉	—	4	4	no	—
349	Dic₇₉	—	4	4	no	—
350	Dic₇₉	#532	1	2	yes	—
351	C₂×#3177	—	79	1	no	maximal, Sylow
352	C₂×C₇₉	—	4	1	no	—
353	C₂×C₇₉	C₂×#532	1	1	yes	characteristic
354	C₂×C₇₉	C₂×#578	1	2	yes	—
355	D₇₉	—	4	1	no	—
356	D₇₉	#3177	1	4	yes	direct product factor
357	C₂×#541	—	79	2	no	—
358	#3177	—	79	1	no	—
359	#3177	—	79	1	no	—
360	#3177	—	79	2	no	—
361	#3177	—	79	2	no	—
362	#3177	—	79	2	no	—
363	#3177	—	79	2	no	—
364	#3177	—	79	2	no	—
365	#3177	—	79	1	no	—
366	#3177	—	79	2	no	—
367	#3177	D₇₉	1	1	yes	characteristic, direct product factor
368	C₂×#499	—	79	1	no	—
369	C₂×#494	—	79	1	no	—
370	C₂×#491	—	79	2	no	—
371	C₂×#470	—	79	2	no	—
372	C₂×#467	—	79	2	no	—
373	C₂×#441	—	79	2	no	—
374	C₂×C₄×Q₁₆	—	79	2	no	—
375	C₂×#405	—	79	1	no	—
376	C₇₉	C₂×#3177	1	1	yes	characteristic, complemented, Sylow
377	C₂²×Q₁₆	—	79	2	no	—
378	C₂²×Q₁₆	—	79	2	no	—
379	C₂²×M₁₆	—	79	1	no	—
380	C₂³×C₈	—	79	1	no	—
381	#541	—	79	2	no	—
382	#541	—	79	2	no	—
383	#541	—	79	4	no	—
384	#541	—	79	4	no	—
385	#541	—	79	2	no	—
386	#541	—	158	4	no	—
387	#541	—	158	4	no	—
388	#541	C₂×D₇₉	1	2	yes	—
389	C₂×C₄⋊Q₈	—	79	2	no	—
390	C₂×#126	—	158	4	no	—
391	C₂×#125	—	79	2	no	—
392	C₂×#125	—	158	4	no	—
393	C₂×C₂²⋊Q₈	—	79	4	no	—
394	C₂×C₄×Q₈	—	79	4	no	—
395	C₂×#117	—	79	1	no	—
396	#499	—	79	2	no	—
397	#499	—	79	2	no	—
398	#499	—	79	2	no	—
399	#499	—	79	1	no	—
400	#499	C₂×D₇₉	1	1	yes	characteristic, complemented
401	#494	—	79	2	no	—
402	#494	—	79	2	no	—
403	#494	—	79	2	no	—
404	#494	—	79	1	no	—
405	#494	C₂×D₇₉	1	1	yes	characteristic, complemented
406	#491	—	79	2	no	—
407	#491	—	79	2	no	—
408	#491	—	79	4	no	—
409	#491	—	79	4	no	—
410	#491	—	79	2	no	—
411	#491	C₂×D₇₉	1	2	yes	complemented
412	#470	—	79	2	no	—
413	#470	—	79	2	no	—
414	#470	—	79	4	no	—
415	#470	—	79	2	no	—
416	#470	—	79	4	no	—
417	#470	C₂×D₇₉	1	2	yes	—
418	#467	—	79	2	no	—
419	#467	—	79	2	no	—
420	#467	—	79	4	no	—
421	#467	—	79	2	no	—
422	#467	—	79	4	no	—
423	#467	C₂×D₇₉	1	2	yes	—
424	#441	—	79	2	no	—
425	#441	—	79	4	no	—
426	#441	—	79	2	no	—
427	#441	—	79	4	no	—
428	#441	—	79	2	no	—
429	#441	C₂×D₇₉	1	2	yes	complemented
430	C₄×Q₁₆	—	79	2	no	—
431	C₄×Q₁₆	—	79	4	no	—
432	C₄×Q₁₆	—	79	2	no	—
433	C₄×Q₁₆	—	79	4	no	—
434	C₄×Q₁₆	—	79	2	no	—
435	C₄×Q₁₆	C₂×D₇₉	1	2	yes	complemented
436	C₂×#107	—	79	2	no	—
437	C₂×#106	—	79	2	no	—
438	C₂×#103	—	79	4	no	—
439	C₂×#103	—	79	4	no	—
440	#405	—	79	1	no	—
441	#405	—	79	1	no	—
442	#405	—	79	1	no	—
443	#405	—	79	1	no	—
444	#405	—	79	1	no	—
445	#405	—	79	1	no	—
446	#405	—	79	1	no	—
447	#405	C₂×D₇₉	1	1	yes	characteristic
448	C₂×#97	—	79	1	no	—
449	C₂×#97	—	79	1	no	—
450	C₂×C₄×C₈	—	79	1	no	—
451	C₂×C₄×C₈	—	79	1	no	—
452	C₂²×Q₈	—	79	4	no	—
453	C₂³×C₄	—	79	1	no	—
454	C₂×Q₁₆	—	79	4	no	—
455	C₂×Q₁₆	—	79	4	no	—
456	C₂×Q₁₆	—	79	2	no	—
457	C₂×Q₁₆	—	79	2	no	—
458	C₂×Q₁₆	—	158	8	no	—
459	C₂×Q₁₆	—	158	8	no	—
460	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
461	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
462	C₂×M₁₆	—	79	1	no	—
463	C₂×M₁₆	—	79	1	no	—
464	C₂×M₁₆	—	79	1	no	—
465	C₂×M₁₆	—	158	4	no	—
466	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
467	C₂²×C₈	—	79	1	no	—
468	C₂²×C₈	—	79	1	no	—
469	C₂²×C₈	—	79	1	no	—
470	C₂²×C₈	—	79	1	no	—
471	C₂²×C₈	—	79	1	no	—
472	C₂²×C₈	—	79	1	no	—
473	C₂²×C₈	—	79	1	no	—
474	C₂²×C₈	—	158	4	no	—
475	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
476	C₄⋊Q₈	—	79	4	no	—
477	C₄⋊Q₈	—	79	2	no	—
478	C₄⋊Q₈	—	158	4	no	—
479	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
480	#126	—	2	4	no	—
481	#126	—	158	4	no	—
482	#126	—	158	4	no	—
483	#126	—	158	4	no	—
484	#126	—	158	4	no	—
485	#126	—	158	4	no	—
486	#126	—	158	4	no	—
487	#126	—	158	4	no	—
488	#125	—	2	4	no	—
489	#125	—	79	4	no	—
490	#125	—	79	2	no	—
491	#125	—	158	4	no	—
492	#125	—	158	4	no	—
493	#125	—	158	4	no	—
494	#125	—	158	4	no	—
495	#125	—	158	4	no	—
496	#125	—	158	4	no	—
497	#125	—	158	4	no	—
498	#125	—	158	4	no	—
499	#125	C₂²×D₇₉	1	2	yes	—
500	C₂²⋊Q₈	—	79	4	no	—
501	C₂²⋊Q₈	—	79	4	no	—
502	C₂²⋊Q₈	—	79	4	no	—
503	C₂²⋊Q₈	—	158	4	no	—
504	C₂²⋊Q₈	—	158	4	no	—
505	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
506	C₄×Q₈	—	79	4	no	—
507	C₄×Q₈	—	79	4	no	—
508	C₄×Q₈	—	79	4	no	—
509	C₄×Q₈	—	158	4	no	—
510	C₄×Q₈	—	158	4	no	—
511	C₄×Q₈	C₂²×D₇₉	1	4	yes	—
512	#117	—	79	1	no	—
513	#117	—	79	2	no	—
514	#117	—	79	2	no	—
515	#117	—	79	1	no	—
516	#117	—	79	1	no	—
517	#117	C₂²×D₇₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	—	79	2	no	—
519	C₂×C₄⋊C₄	—	79	4	no	—
520	C₂×C₄⋊C₄	—	158	4	no	—
521	C₂×C₄⋊C₄	—	158	4	no	—
522	C₂×C₄⋊C₄	—	158	4	no	—
523	C₂×C₄⋊C₄	—	158	4	no	—
524	C₂×C₂²⋊C₄	—	79	2	no	—
525	C₂×C₂²⋊C₄	—	158	4	no	—
526	C₂×C₄²	—	79	1	no	—
527	C₂×C₄²	—	79	1	no	—
528	C₂×C₄²	—	158	4	no	—
529	#107	—	79	2	no	—
530	#107	—	79	4	no	—
531	#107	C₂²×D₇₉	1	2	yes	—
532	#106	—	79	2	no	—
533	#106	—	79	4	no	—
534	#106	C₂²×D₇₉	1	2	yes	—
535	#103	—	79	4	no	—
536	#103	—	79	4	no	—
537	#103	—	79	4	no	—
538	#103	—	79	4	no	—
539	#103	—	79	4	no	—
540	#103	—	79	4	no	—
541	#103	C₂²×D₇₉	1	4	yes	—
542	#103	C₂²×D₇₉	1	4	yes	—
543	#97	—	79	1	no	—
544	#97	—	79	1	no	—
545	#97	—	79	1	no	—
546	#97	—	79	1	no	—
547	#97	—	79	1	no	—
548	#97	—	79	1	no	—
549	#97	C₂²×D₇₉	1	1	yes	characteristic
550	#97	C₂²×D₇₉	1	1	yes	characteristic
551	C₄×C₈	—	79	1	no	—
552	C₄×C₈	—	79	1	no	—
553	C₄×C₈	—	79	1	no	—
554	C₄×C₈	—	79	1	no	—
555	C₄×C₈	—	79	1	no	—
556	C₄×C₈	—	79	1	no	—
557	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
558	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
559	C₂⁴	—	79	1	no	—
560	C₂×Q₈	—	79	4	no	—
561	C₂×Q₈	—	158	4	no	—
562	C₂×Q₈	—	158	8	no	—
563	C₂×Q₈	—	158	8	no	—
564	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
565	C₂²×C₄	—	79	1	no	—
566	C₂²×C₄	—	79	1	no	—
567	C₂²×C₄	—	79	1	no	—
568	C₂²×C₄	—	79	2	no	—
569	C₂²×C₄	—	79	2	no	—
570	C₂²×C₄	—	79	1	no	—
571	C₂²×C₄	—	79	1	no	—
572	C₂²×C₄	—	158	4	no	—
573	C₂²×C₄	—	158	4	no	—
574	C₂²×C₄	—	158	2	no	—
575	C₂²×C₄	—	158	2	no	—
576	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	—	158	8	no	—
580	Q₁₆	—	158	8	no	—
581	Q₁₆	—	158	4	no	—
582	Q₁₆	—	158	4	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	158	2	no	—
585	M₁₆	—	158	2	no	—
586	M₁₆	—	158	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	79	1	no	—
589	C₂×C₈	—	79	1	no	—
590	C₂×C₈	—	79	4	no	—
591	C₂×C₈	—	79	4	no	—
592	C₂×C₈	—	79	1	no	—
593	C₂×C₈	—	79	1	no	—
594	C₂×C₈	—	158	2	no	—
595	C₂×C₈	—	158	2	no	—
596	C₂×C₈	—	158	2	no	—
597	C₂×C₈	—	158	2	no	—
598	C₂×C₈	—	158	2	no	—
599	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
600	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
601	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
602	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	79	2	no	—
608	C₄⋊C₄	—	79	2	no	—
609	C₄⋊C₄	—	79	2	no	—
610	C₄⋊C₄	—	79	4	no	—
611	C₄⋊C₄	—	158	4	no	—
612	C₄⋊C₄	—	158	4	no	—
613	C₄⋊C₄	—	158	4	no	—
614	C₄⋊C₄	—	158	4	no	—
615	C₄⋊C₄	—	158	4	no	—
616	C₄⋊C₄	—	158	4	no	—
617	C₄⋊C₄	—	158	4	no	—
618	C₄⋊C₄	—	158	4	no	—
619	C₄⋊C₄	—	158	4	no	—
620	C₄⋊C₄	—	158	4	no	—
621	C₄⋊C₄	—	158	4	no	—
622	C₄⋊C₄	—	158	4	no	—
623	C₄⋊C₄	—	158	4	no	—
624	C₄⋊C₄	D₄×D₇₉	1	2	yes	—
625	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	79	2	no	—
628	C₂²⋊C₄	—	79	2	no	—
629	C₂²⋊C₄	—	79	2	no	—
630	C₂²⋊C₄	—	158	4	no	—
631	C₂²⋊C₄	—	158	4	no	—
632	C₂²⋊C₄	—	158	4	no	—
633	C₂²⋊C₄	D₄×D₇₉	1	2	yes	—
634	C₄²	—	2	4	no	—
635	C₄²	—	79	1	no	—
636	C₄²	—	79	1	no	—
637	C₄²	—	79	2	no	—
638	C₄²	—	79	2	no	—
639	C₄²	—	158	4	no	—
640	C₄²	—	158	4	no	—
641	C₄²	—	158	4	no	—
642	C₄²	C₂³×D₇₉	1	1	yes	characteristic
643	C₄²	C₂³×D₇₉	1	1	yes	characteristic
644	C₂³	—	79	1	no	—
645	C₂³	—	79	1	no	—
646	C₂³	—	158	2	no	—
647	C₂³	—	158	4	no	—
648	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
649	Q₈	—	2	4	no	—
650	Q₈	—	2	4	no	—
651	Q₈	—	316	8	no	—
652	Q₈	—	158	4	no	—
653	Q₈	—	158	4	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	316	8	no	—
659	C₂×C₄	—	316	8	no	—
660	C₂×C₄	—	79	1	no	—
661	C₂×C₄	—	79	2	no	—
662	C₂×C₄	—	79	2	no	—
663	C₂×C₄	—	79	2	no	—
664	C₂×C₄	—	79	2	no	—
665	C₂×C₄	—	79	1	no	—
666	C₂×C₄	—	158	2	no	—
667	C₂×C₄	—	158	2	no	—
668	C₂×C₄	—	158	4	no	—
669	C₂×C₄	—	158	4	no	—
670	C₂×C₄	—	158	4	no	—
671	C₂×C₄	—	158	4	no	—
672	C₂×C₄	—	158	2	no	—
673	C₂×C₄	—	158	1	no	—
674	C₂×C₄	—	158	1	no	—
675	C₂×C₄	C₂×D₄×D₇₉	1	2	yes	—
676	C₂×C₄	C₂×D₄×D₇₉	1	2	yes	—
677	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
678	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
679	C₈	—	2	1	no	—
680	C₈	—	2	1	no	—
681	C₈	—	79	2	no	—
682	C₈	—	79	2	no	—
683	C₈	—	158	1	no	—
684	C₈	—	158	1	no	—
685	C₈	#41×D₇₉	1	2	yes	—
686	C₈	#41×D₇₉	1	2	yes	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	316	4	no	—
690	C₂²	—	79	4	no	—
691	C₂²	—	79	2	no	—
692	C₂²	—	158	2	no	—
693	C₂²	—	158	1	no	—
694	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	4	no	—
700	C₄	—	316	4	no	—
701	C₄	—	316	4	no	—
702	C₄	—	79	2	no	—
703	C₄	—	158	2	no	—
704	C₄	—	158	2	no	—
705	C₄	—	158	1	no	—
706	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
707	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
708	C₂	—	4	1	no	—
709	C₂	—	316	1	no	—
710	C₂	—	79	4	no	—
711	C₂	#532×D₇₉	1	1	yes	characteristic
712	C₂	#578×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#3177	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	C₂³×D₇₉	C₂×D₄
hypercenter	#3177	D₇₉
hypocenter	C₇₉	C₂×#3177
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3177

Complements

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

N	H ≅ G/N	type
2. #23774060	C₂	semidirect
3. #23774059	C₂	semidirect
4. #23774058	C₂	semidirect
5. #23774057	C₂	semidirect
6. #23774056	C₂	semidirect
7. #23774055	C₂	semidirect
8. #23774054	C₂	semidirect
9. #23774053	C₂	semidirect
10. #23774052	C₂	semidirect
11. #499×D₇₉	C₂	semidirect
12. #494×D₇₉	C₂	semidirect
13. #491×D₇₉	C₂	semidirect
16. #441×D₇₉	C₂	semidirect
17. C₄×Q₁₆×D₇₉	C₂	semidirect
19. C₇₉×#3177	C₂	semidirect
38. #19098965	C₂²	semidirect
39. #19098964	C₂²	semidirect
40. #19098963	C₂²	semidirect
41. #19098962	C₂²	semidirect
42. #19098943	C₂²	semidirect
43. #19098942	C₂²	semidirect
44. #19098941	C₂²	semidirect
45. #19098941	C₂²	semidirect
46. #19098933	C₂²	semidirect
47. #19098932	C₂²	semidirect
48. #19098931	C₂²	semidirect
49. #19098930	C₂²	semidirect
50. #19098930	C₂²	semidirect
61. #19098671	C₂²	semidirect
62. #19098670	C₂²	semidirect
63. #19098669	C₂²	semidirect
64. #19098668	C₂²	semidirect
65. #19098667	C₂²	semidirect
66. C₄×Dic₃₁₆	C₂²	semidirect
67. Q₁₆×Dic₇₉	C₂²	semidirect
68. #19098657	C₂²	semidirect
69. C₄×#11929614	C₂²	semidirect
70. #19098655	C₂²	semidirect
87. #499×C₇₉	C₂²	semidirect
88. #494×C₇₉	C₂²	semidirect
89. #491×C₇₉	C₂²	semidirect
92. #441×C₇₉	C₂²	semidirect
93. C₄×Q₁₆×C₇₉	C₂²	semidirect
356. D₇₉	#3177	direct (N × H)
367. #3177	D₇₉	direct (N × H)
376. C₇₉	C₂×#3177	semidirect
400. #499	C₂×D₇₉	semidirect
405. #494	C₂×D₇₉	semidirect
411. #491	C₂×D₇₉	semidirect
429. #441	C₂×D₇₉	semidirect
435. C₄×Q₁₆	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#541×D₇₉	2
#23774060	2
#23774059	2
#23774058	2
#23774057	2
#23774056	2
#23774055	2
#23774054	2
#23774053	2
#23774052	2
#499×D₇₉	2
#494×D₇₉	2
#491×D₇₉	2
#470×D₇₉	2
#467×D₇₉	2
#441×D₇₉	2
C₄×Q₁₆×D₇₉	2
#405×D₇₉	2
C₇₉×#3177	2
C₂×#3177	79

Subgroups — #3177×D79 #35158105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3177×D₇₉ #35158105