Subgroups — #1693×D₇₉ #34270794

Order 20224.

758 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#461×D₇₉	C₂	1	2	yes	maximal
3	#436×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23762914	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762913	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762912	C₂	1	2	yes	maximal, complemented
7	#23762911	C₂	1	2	yes	maximal, complemented
8	#23762910	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#332×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1693	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₇₉	—	2	2	no	—
13	C₂×M₁₆×D₇₉	—	2	1	no	—
14	C₄⋊Q₈×D₇₉	C₂²	1	2	yes	—
15	C₄×D₄×D₇₉	C₂²	1	1	yes	characteristic
16	#19098968	C₂²	1	1	yes	characteristic, complemented
17	#19098967	—	2	1	no	—
18	#19098967	—	2	1	no	—
19	#19098966	C₂²	1	2	yes	complemented
20	#19098769	C₂²	1	2	yes	—
21	#19098768	C₂²	1	2	yes	—
22	#19098767	—	2	2	no	—
23	#19098766	—	2	2	no	—
24	#19098765	C₂²	1	2	yes	—
25	#19098642	C₂²	1	1	yes	characteristic
26	#19098641	C₂²	1	1	yes	characteristic
27	#19098640	C₂²	1	1	yes	characteristic
28	#19098639	—	2	1	no	—
29	#19098638	—	2	1	no	—
30	#107×D₇₉	—	2	1	no	—
31	#107×D₇₉	—	2	1	no	—
32	C₄⋊C₈×D₇₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
34	#103×D₇₉	—	2	2	no	—
35	C₂²⋊C₈×D₇₉	—	2	1	no	—
36	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
37	#19098314	C₂²	1	1	yes	characteristic, complemented
38	#19098313	C₂²	1	2	yes	complemented
39	#19098310	C₂²	1	2	yes	complemented
40	#19098309	C₂²	1	2	yes	complemented
41	#19098308	C₂²	1	2	yes	complemented
42	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#461×C₇₉	C₂²	1	2	yes	—
44	#436×C₇₉	C₂²	1	1	yes	characteristic
45	#334×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#332×C₇₉	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₇₉	—	2	2	no	—
48	C₂×D₄×D₇₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₉	—	2	1	no	—
50	C₂×#11929613	—	2	2	no	—
51	C₂×#11929612	—	2	2	no	—
52	C₂×#11929611	—	2	2	no	—
53	SD₁₆×D₇₉	—	4	8	no	—
54	C₂×#11929608	—	2	1	no	—
55	C₂×#11929607	—	2	1	no	—
56	C₂×#11929607	—	2	1	no	—
57	M₁₆×D₇₉	—	4	4	no	—
58	C₂×C₈×D₇₉	—	2	1	no	—
59	C₂×C₈×D₇₉	—	2	2	no	—
60	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
61	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
62	#14579161	C₂³	1	2	yes	—
63	#14579160	—	2	2	no	—
64	#14579160	—	2	2	no	—
65	#14579159	—	2	2	no	—
66	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
67	D₄×Dic₇₉	D₄	1	1	yes	characteristic
68	#14579123	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₇₉	—	2	1	no	—
70	(C₂²⋊D₇₉)⋊C₄	—	2	1	no	—
71	C₄⋊C₄×D₇₉	—	2	2	no	—
72	C₄⋊C₄×D₇₉	—	2	2	no	—
73	C₄⋊C₄×D₇₉	D₄	1	1	yes	characteristic
74	C₂²⋊C₄×D₇₉	—	2	1	no	—
75	C₄²×D₇₉	C₂³	1	1	yes	characteristic
76	#14579095	—	2	1	no	—
77	#14579095	—	2	1	no	—
78	#14579094	—	2	2	no	—
79	#14579094	—	2	2	no	—
80	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
82	Dic₇₉⋊C₈	—	2	1	no	—
83	Dic₇₉⋊C₈	—	2	2	no	—
84	#14579086	—	2	2	no	—
85	#14579085	—	2	2	no	—
86	#14579084	—	2	2	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
88	(C₂×D₇₉)⋊C₈	—	2	1	no	—
89	(C₂×D₇₉)⋊C₈	—	2	1	no	—
90	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₇₉	D₄	1	1	yes	characteristic
92	C₈×Dic₇₉	D₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₇₉	—	2	2	no	—
94	C₂×M₁₆×C₇₉	—	2	1	no	—
95	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
96	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
97	#107×C₇₉	—	2	1	no	—
98	#107×C₇₉	—	2	1	no	—
99	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
101	#103×C₇₉	—	2	2	no	—
102	C₂²⋊C₈×C₇₉	—	2	1	no	—
103	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₂³×D₇₉	—	2	1	no	—
105	C₂×Dic₁₅₈	—	2	2	no	—
106	C₂×Dic₁₅₈	—	4	2	no	—
107	Q₈×D₇₉	—	4	4	no	—
108	Q₈×D₇₉	—	4	4	no	—
109	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₇₉	—	2	1	no	—
111	D₄×D₇₉	—	2	4	no	—
112	C₂²×Dic₇₉	—	2	1	no	—
113	C₂×C₄×D₇₉	—	2	1	no	—
114	C₂×C₄×D₇₉	—	2	1	no	—
115	C₂×C₄×D₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	4	2	no	—
117	C₂×C₄×D₇₉	—	4	2	no	—
118	C₂×C₄×D₇₉	—	4	2	no	—
119	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₇₉	#41	1	1	yes	characteristic
122	#11929613	—	4	4	no	—
123	#11929612	—	4	4	no	—
124	#11929611	—	4	4	no	—
125	#11929608	—	4	2	no	—
126	#11929607	—	4	2	no	—
127	#11929607	—	4	2	no	—
128	C₂×C₇₉⋊C₈	—	2	1	no	—
129	C₂×C₇₉⋊C₈	—	2	2	no	—
130	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
132	C₈×D₇₉	—	2	2	no	—
133	C₈×D₇₉	—	4	2	no	—
134	C₈×D₇₉	—	4	4	no	—
135	C₈×D₇₉	SD₁₆	1	4	yes	complemented
136	C₄⋊Dic₇₉	—	2	2	no	—
137	C₄⋊Dic₇₉	—	2	2	no	—
138	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
139	Dic₇₉⋊C₄	—	2	1	no	—
140	Dic₇₉⋊C₄	—	4	2	no	—
141	Dic₇₉⋊C₄	—	4	2	no	—
142	C₂²⋊Dic₇₉	—	2	1	no	—
143	(C₂×D₇₉)⋊C₄	—	2	1	no	—
144	(C₂×D₇₉)⋊C₄	—	2	1	no	—
145	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₇₉	#41	1	1	yes	characteristic
148	C₂×Q₈×C₇₉	—	2	2	no	—
149	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	SD₁₆×C₇₉	—	4	4	no	—
152	M₁₆×C₇₉	—	4	2	no	—
153	C₂×C₈×C₇₉	—	2	1	no	—
154	C₂×C₈×C₇₉	—	2	2	no	—
155	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₇₉	—	2	1	no	—
161	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₂³×C₇₉	—	2	1	no	—
163	C₂²×D₇₉	—	2	1	no	—
164	C₂²×D₇₉	—	4	2	no	—
165	C₂²×D₇₉	—	4	2	no	—
166	C₂²×D₇₉	—	4	2	no	—
167	C₂²×D₇₉	#121	1	1	yes	characteristic
168	Q₈×C₇₉	—	4	2	no	—
169	Q₈×C₇₉	—	4	2	no	—
170	D₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	4	1	no	—
173	C₂×C₄×C₇₉	—	4	1	no	—
174	C₂×C₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₇₉	—	4	2	no	—
179	C₂×Dic₇₉	—	2	1	no	—
180	C₂×Dic₇₉	—	4	2	no	—
181	C₂×Dic₇₉	—	4	2	no	—
182	C₂×Dic₇₉	#121	1	1	yes	characteristic
183	C₂×Dic₇₉	#121	1	1	yes	characteristic
184	C₂×Dic₇₉	#121	1	1	yes	characteristic
185	D₃₁₆	—	2	2	no	—
186	C₄×D₇₉	—	2	2	no	—
187	C₄×D₇₉	—	4	2	no	—
188	C₄×D₇₉	—	4	1	no	—
189	C₄×D₇₉	—	4	1	no	—
190	C₄×D₇₉	—	4	2	no	—
191	C₄×D₇₉	—	8	4	no	—
192	C₄×D₇₉	C₂×SD₁₆	1	2	yes	—
193	C₄×D₇₉	AGL(1,ℤ/8)	1	4	yes	—
194	C₄×D₇₉	#137	1	2	yes	—
195	Dic₁₅₈	—	4	2	no	—
196	Dic₁₅₈	—	4	2	no	—
197	Dic₁₅₈	—	8	4	no	—
198	C₈×C₇₉	—	2	1	no	—
199	C₈×C₇₉	—	4	1	no	—
200	C₈×C₇₉	—	4	2	no	—
201	C₈×C₇₉	C₂×SD₁₆	1	2	yes	complemented
202	C₇₉⋊C₈	—	2	1	no	—
203	C₇₉⋊C₈	—	4	1	no	—
204	C₇₉⋊C₈	—	4	2	no	—
205	C₇₉⋊C₈	C₂×SD₁₆	1	2	yes	complemented
206	C₂²×C₇₉	—	4	1	no	—
207	C₂²×C₇₉	—	4	1	no	—
208	C₂²×C₇₉	—	4	1	no	—
209	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
210	C₂×D₇₉	—	4	1	no	—
211	C₂×D₇₉	—	4	1	no	—
212	C₂×D₇₉	—	4	1	no	—
213	C₂×D₇₉	—	8	4	no	—
214	C₂×D₇₉	#461	1	2	yes	—
215	C₂×D₇₉	#469	1	2	yes	—
216	C₂×D₇₉	#473	1	2	yes	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	—	4	1	no	—
219	C₄×C₇₉	—	8	2	no	—
220	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
221	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
222	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
223	Dic₇₉	—	2	1	no	—
224	Dic₇₉	—	4	1	no	—
225	Dic₇₉	—	8	2	no	—
226	Dic₇₉	#461	1	2	yes	—
227	Dic₇₉	#469	1	2	yes	—
228	C₂×#1693	—	79	1	no	maximal, Sylow
229	C₂×C₇₉	—	8	1	no	—
230	C₂×C₇₉	C₂×#461	1	1	yes	characteristic
231	C₂×C₇₉	C₂×#469	1	1	yes	characteristic
232	C₂×C₇₉	C₂×#473	1	1	yes	characteristic
233	D₇₉	—	8	1	no	—
234	D₇₉	#1693	1	4	yes	direct product factor
235	C₂×#500	—	79	1	no	—
236	C₂×#461	—	79	2	no	—
237	C₂×#436	—	79	1	no	—
238	#1693	—	79	1	no	—
239	#1693	—	79	2	no	—
240	#1693	—	79	1	no	—
241	#1693	—	79	1	no	—
242	#1693	—	79	2	no	—
243	#1693	D₇₉	1	1	yes	characteristic, direct product factor
244	C₂×#334	—	79	1	no	—
245	C₂×#332	—	79	2	no	—
246	C₇₉	C₂×#1693	1	1	yes	characteristic, complemented, Sylow
247	C₂²×SD₁₆	—	158	2	no	—
248	C₂²×M₁₆	—	158	1	no	—
249	C₂×C₄⋊Q₈	—	79	2	no	—
250	C₂×C₄×D₄	—	79	1	no	—
251	#500	—	79	2	no	—
252	#500	—	79	1	no	—
253	#500	—	158	1	no	—
254	#500	—	158	1	no	—
255	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
256	#461	—	79	2	no	—
257	#461	—	79	2	no	—
258	#461	—	79	2	no	—
259	#461	—	158	2	no	—
260	#461	—	158	2	no	—
261	#461	C₂×D₇₉	1	2	yes	—
262	#436	—	79	1	no	—
263	#436	—	79	1	no	—
264	#436	—	79	1	no	—
265	#436	—	158	1	no	—
266	#436	—	158	1	no	—
267	#436	C₂×D₇₉	1	1	yes	characteristic
268	C₂×#107	—	158	1	no	—
269	C₂×#107	—	158	1	no	—
270	C₂×C₄⋊C₈	—	79	1	no	—
271	C₂×C₄⋊C₈	—	79	2	no	—
272	C₂×#103	—	158	2	no	—
273	C₂×C₂²⋊C₈	—	158	1	no	—
274	C₂×C₄×C₈	—	79	1	no	—
275	#334	—	79	2	no	—
276	#334	—	79	1	no	—
277	#334	C₂×D₇₉	1	1	yes	characteristic, complemented
278	#332	—	79	2	no	—
279	#332	—	79	2	no	—
280	#332	—	79	2	no	—
281	#332	C₂×D₇₉	1	2	yes	complemented
282	C₂²×Q₈	—	158	2	no	—
283	C₂²×D₄	—	79	1	no	—
284	C₂³×C₄	—	158	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	316	8	no	—
287	C₂×SD₁₆	—	158	2	no	—
288	C₂×SD₁₆	—	158	2	no	—
289	C₂×SD₁₆	—	158	2	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	316	4	no	—
292	C₂×M₁₆	—	158	1	no	—
293	C₂×M₁₆	—	158	1	no	—
294	C₂×M₁₆	—	158	1	no	—
295	C₂²×C₈	—	79	1	no	—
296	C₂²×C₈	—	79	1	no	—
297	C₂²×C₈	—	158	1	no	—
298	C₂²×C₈	—	158	2	no	—
299	C₄⋊Q₈	—	79	2	no	—
300	C₄⋊Q₈	—	158	2	no	—
301	C₄⋊Q₈	—	158	2	no	—
302	C₄⋊Q₈	—	158	2	no	—
303	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
304	C₄×D₄	—	79	1	no	—
305	C₄×D₄	—	79	1	no	—
306	C₄×D₄	—	79	1	no	—
307	C₄×D₄	—	158	1	no	—
308	C₄×D₄	—	158	1	no	—
309	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	79	1	no	—
311	C₂×C₄⋊C₄	—	158	2	no	—
312	C₂×C₄⋊C₄	—	158	2	no	—
313	C₂×C₂²⋊C₄	—	158	1	no	—
314	C₂×C₄²	—	79	1	no	—
315	#107	—	2	1	no	—
316	#107	—	2	1	no	—
317	#107	—	158	2	no	—
318	#107	—	158	2	no	—
319	#107	—	158	1	no	—
320	#107	—	158	1	no	—
321	C₄⋊C₈	—	79	1	no	—
322	C₄⋊C₈	—	79	2	no	—
323	C₄⋊C₈	—	158	1	no	—
324	C₄⋊C₈	—	158	2	no	—
325	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
326	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
327	#103	—	2	2	no	—
328	#103	—	158	2	no	—
329	#103	—	158	2	no	—
330	#103	—	158	2	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	158	1	no	—
333	C₂²⋊C₈	—	158	1	no	—
334	C₂²⋊C₈	—	158	1	no	—
335	C₄×C₈	—	79	1	no	—
336	C₄×C₈	—	79	1	no	—
337	C₄×C₈	—	79	1	no	—
338	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
339	C₂⁴	—	158	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	316	2	no	—
342	C₂×Q₈	—	316	4	no	—
343	C₂×Q₈	—	316	4	no	—
344	C₂×Q₈	—	158	2	no	—
345	C₂×D₄	—	79	1	no	—
346	C₂×D₄	—	158	4	no	—
347	C₂×D₄	—	158	1	no	—
348	C₂×D₄	D₄×D₇₉	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	316	2	no	—
351	C₂²×C₄	—	316	2	no	—
352	C₂²×C₄	—	316	2	no	—
353	C₂²×C₄	—	79	1	no	—
354	C₂²×C₄	—	79	1	no	—
355	C₂²×C₄	—	79	1	no	—
356	C₂²×C₄	—	158	1	no	—
357	C₂²×C₄	—	158	1	no	—
358	C₂²×C₄	—	158	1	no	—
359	C₂²×C₄	—	158	1	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	316	4	no	—
362	SD₁₆	—	316	4	no	—
363	SD₁₆	—	316	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	316	2	no	—
366	M₁₆	—	316	2	no	—
367	M₁₆	—	316	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	316	2	no	—
371	C₂×C₈	—	316	4	no	—
372	C₂×C₈	—	79	1	no	—
373	C₂×C₈	—	79	4	no	—
374	C₂×C₈	—	79	1	no	—
375	C₂×C₈	—	158	2	no	—
376	C₂×C₈	—	158	1	no	—
377	C₂×C₈	—	158	2	no	—
378	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
379	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	316	2	no	—
383	C₄⋊C₄	—	316	2	no	—
384	C₄⋊C₄	—	79	1	no	—
385	C₄⋊C₄	—	158	1	no	—
386	C₄⋊C₄	—	158	2	no	—
387	C₄⋊C₄	—	158	2	no	—
388	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	158	1	no	—
391	C₂²⋊C₄	—	158	1	no	—
392	C₂²⋊C₄	—	158	1	no	—
393	C₄²	—	79	1	no	—
394	C₄²	—	79	1	no	—
395	C₄²	—	79	1	no	—
396	C₄²	C₂³×D₇₉	1	1	yes	characteristic
397	C₂³	—	2	1	no	—
398	C₂³	—	316	2	no	—
399	C₂³	—	316	2	no	—
400	C₂³	—	316	2	no	—
401	C₂³	—	79	1	no	—
402	C₂³	—	158	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	316	2	no	—
406	Q₈	—	316	2	no	—
407	Q₈	—	632	4	no	—
408	D₄	—	2	2	no	—
409	D₄	—	316	2	no	—
410	D₄	—	158	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	316	2	no	—
416	C₂×C₄	—	316	2	no	—
417	C₂×C₄	—	316	2	no	—
418	C₂×C₄	—	316	1	no	—
419	C₂×C₄	—	316	1	no	—
420	C₂×C₄	—	316	2	no	—
421	C₂×C₄	—	79	1	no	—
422	C₂×C₄	—	79	1	no	—
423	C₂×C₄	—	79	2	no	—
424	C₂×C₄	—	79	4	no	—
425	C₂×C₄	—	79	2	no	—
426	C₂×C₄	—	79	1	no	—
427	C₂×C₄	—	632	4	no	—
428	C₂×C₄	—	158	2	no	—
429	C₂×C₄	—	158	1	no	—
430	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
432	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	316	1	no	—
437	C₈	—	316	2	no	—
438	C₈	—	79	2	no	—
439	C₈	—	158	1	no	—
440	C₈	SD₁₆×D₇₉	1	2	yes	complemented
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	316	1	no	—
445	C₂²	—	316	1	no	—
446	C₂²	—	316	1	no	—
447	C₂²	—	79	2	no	—
448	C₂²	—	79	2	no	—
449	C₂²	—	79	2	no	—
450	C₂²	—	632	4	no	—
451	C₂²	#121×D₇₉	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	316	1	no	—
456	C₄	—	79	2	no	—
457	C₄	—	79	2	no	—
458	C₄	—	632	2	no	—
459	C₄	—	158	1	no	—
460	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
461	C₄	AGL(1,ℤ/8)×D₇₉	1	2	yes	—
462	C₄	#137×D₇₉	1	1	yes	characteristic
463	C₂	—	8	1	no	—
464	C₂	—	79	4	no	—
465	C₂	—	632	1	no	—
466	C₂	#461×D₇₉	1	1	yes	characteristic
467	C₂	#469×D₇₉	1	1	yes	characteristic
468	C₂	#473×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₉
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1693	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂×D₄×D₇₉	D₄
hypercenter	#1693	D₇₉
hypocenter	C₇₉	C₂×#1693
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1693

Complements

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

N	H ≅ G/N	type
1. #500×D₇₉	C₂	semidirect
4. #23762914	C₂	semidirect
5. #23762913	C₂	semidirect
6. #23762912	C₂	semidirect
7. #23762911	C₂	semidirect
8. #23762910	C₂	semidirect
9. #334×D₇₉	C₂	semidirect
10. #332×D₇₉	C₂	semidirect
11. C₇₉×#1693	C₂	semidirect
16. #19098968	C₂²	semidirect
19. #19098966	C₂²	semidirect
37. #19098314	C₂²	semidirect
38. #19098313	C₂²	semidirect
39. #19098310	C₂²	semidirect
40. #19098309	C₂²	semidirect
41. #19098308	C₂²	semidirect
42. #500×C₇₉	C₂²	semidirect
45. #334×C₇₉	C₂²	semidirect
46. #332×C₇₉	C₂²	semidirect
135. C₈×D₇₉	SD₁₆	semidirect
201. C₈×C₇₉	C₂×SD₁₆	semidirect
205. C₇₉⋊C₈	C₂×SD₁₆	semidirect
234. D₇₉	#1693	direct (N × H)
243. #1693	D₇₉	direct (N × H)
246. C₇₉	C₂×#1693	semidirect
255. #500	C₂×D₇₉	semidirect
277. #334	C₂×D₇₉	semidirect
281. #332	C₂×D₇₉	semidirect
440. C₈	SD₁₆×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₇₉	2
#461×D₇₉	2
#436×D₇₉	2
#23762914	2
#23762913	2
#23762912	2
#23762911	2
#23762910	2
#334×D₇₉	2
#332×D₇₉	2
C₇₉×#1693	2
C₂×#1693	79

Subgroups — #1693×D79 #34270794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1693×D₇₉ #34270794