Subgroups — #2207×D₇₉ #34442509

Order 20224.

806 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₇₉	C₂	1	2	yes	maximal, complemented
2	#493×D₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765441	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765440	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765439	C₂	1	2	yes	maximal, complemented
7	#23765438	C₂	1	2	yes	maximal, complemented
8	#23765437	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₉	C₂²	1	1	yes	characteristic
13	C₂×D₈×D₇₉	—	2	1	no	—
14	C₂×D₈×D₇₉	C₂²	1	2	yes	—
15	#127×D₇₉	—	2	1	no	—
16	C₄×Q₈×D₇₉	—	2	1	no	—
17	C₂×#14579106	C₂²	1	2	yes	complemented
18	C₂×#14579105	C₂²	1	2	yes	complemented
19	C₂×#14579104	C₂²	1	2	yes	complemented
20	SD₃₂×D₇₉	—	2	8	no	—
21	C₂×C₁₆×D₇₉	C₂²	1	2	yes	—
22	#19098940	C₂²	1	1	yes	characteristic
23	#19098939	—	2	1	no	—
24	#19098938	—	2	1	no	—
25	#19098938	C₂²	1	2	yes	—
26	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic, complemented
27	Q₁₆×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
28	#19098657	C₂²	1	1	yes	characteristic, complemented
29	C₄×#11929614	—	2	1	no	—
30	#19098655	—	2	1	no	—
31	#107×D₇₉	C₂²	1	1	yes	characteristic
32	#103×D₇₉	—	2	1	no	—
33	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
34	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
35	Dic₇₉⋊C₁₆	C₂²	1	2	yes	complemented
36	#19098365	C₂²	1	2	yes	complemented
37	#19098364	C₂²	1	2	yes	complemented
38	#19098363	C₂²	1	2	yes	complemented
39	C₂×SD₃₂×C₇₉	C₂²	1	2	yes	complemented
40	#493×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#357×C₇₉	C₂²	1	2	yes	complemented
44	C₂×Q₈×D₇₉	—	2	1	no	—
45	C₂×D₄×D₇₉	—	2	2	no	—
46	C₂×D₄×D₇₉	—	4	1	no	—
47	C₂×D₄×D₇₉	—	4	1	no	—
48	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
49	C₂×#11929614	—	2	1	no	—
50	Q₁₆×D₇₉	—	2	2	no	—
51	Q₁₆×D₇₉	D₄	1	4	yes	complemented
52	C₂×D₆₃₂	—	2	1	no	—
53	C₂×D₆₃₂	C₂³	1	2	yes	—
54	C₂×#11929609	—	2	2	no	—
55	C₂×#11929609	—	2	2	no	—
56	D₈×D₇₉	—	2	4	no	—
57	D₈×D₇₉	—	2	4	no	—
58	D₈×D₇₉	—	4	4	no	—
59	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
60	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
61	#14579158	—	2	1	no	—
62	#14579157	—	2	2	no	—
63	#14579157	—	4	1	no	—
64	#14579157	—	4	1	no	—
65	Q₈×Dic₇₉	—	2	1	no	—
66	C₄×Dic₁₅₈	—	2	1	no	—
67	C₄×Dic₁₅₈	—	4	1	no	—
68	#14579126	—	2	1	no	—
69	#14579126	—	4	1	no	—
70	C₄⋊C₄×D₇₉	—	2	1	no	—
71	C₄⋊C₄×D₇₉	—	4	1	no	—
72	C₄²×D₇₉	—	4	1	no	—
73	C₄²×D₇₉	D₄	1	1	yes	characteristic
74	#14579106	—	2	4	no	—
75	#14579105	—	2	4	no	—
76	#14579104	—	2	4	no	—
77	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
78	C₁₆×D₇₉	—	2	4	no	—
79	#14579095	C₂³	1	1	yes	characteristic
80	#14579094	—	2	1	no	—
81	#14579086	—	2	1	no	—
82	#14579085	—	2	1	no	—
83	#14579084	—	2	1	no	—
84	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
85	C₈×Dic₇₉	D₄	1	1	yes	characteristic
86	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×D₈×C₇₉	—	2	1	no	—
89	C₂×D₈×C₇₉	C₂³	1	2	yes	—
90	#127×C₇₉	—	2	1	no	—
91	C₄×Q₈×C₇₉	—	2	1	no	—
92	SD₃₂×C₇₉	—	2	4	no	—
93	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
94	#107×C₇₉	C₂³	1	1	yes	characteristic
95	#103×C₇₉	—	2	1	no	—
96	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂³×D₇₉	—	4	2	no	—
98	C₂×Dic₁₅₈	—	2	1	no	—
99	C₂×Dic₁₅₈	—	4	1	no	—
100	Q₈×D₇₉	—	2	4	no	—
101	Q₈×D₇₉	—	4	2	no	—
102	C₂×D₃₁₆	—	2	2	no	—
103	C₂×D₃₁₆	—	4	1	no	—
104	C₂×D₃₁₆	—	4	1	no	—
105	C₂×C₂²⋊D₇₉	—	4	2	no	—
106	C₂×C₂²⋊D₇₉	—	4	2	no	—
107	C₂×C₂²⋊D₇₉	—	4	2	no	—
108	D₄×D₇₉	—	4	4	no	—
109	D₄×D₇₉	—	4	4	no	—
110	D₄×D₇₉	—	8	4	no	—
111	D₄×D₇₉	—	8	4	no	—
112	C₂×C₄×D₇₉	—	4	1	no	—
113	C₂×C₄×D₇₉	—	4	1	no	—
114	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
115	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
116	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
117	Dic₃₁₆	—	2	1	no	—
118	Dic₃₁₆	C₂×D₄	1	2	yes	complemented
119	#11929614	—	2	4	no	—
120	D₆₃₂	—	2	2	no	—
121	D₆₃₂	—	2	2	no	—
122	D₆₃₂	—	4	2	no	—
123	#11929609	—	4	4	no	—
124	#11929609	—	4	4	no	—
125	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
127	C₈×D₇₉	—	2	2	no	—
128	C₈×D₇₉	C₂×D₄	1	2	yes	—
129	C₈×D₇₉	#41	1	2	yes	—
130	C₄⋊Dic₇₉	—	2	1	no	—
131	C₄⋊Dic₇₉	—	4	1	no	—
132	Dic₇₉⋊C₄	—	4	1	no	—
133	Dic₇₉⋊C₄	—	4	1	no	—
134	Dic₇₉⋊C₄	—	4	1	no	—
135	C₄×Dic₇₉	—	4	1	no	—
136	C₄×Dic₇₉	—	4	1	no	—
137	C₄×Dic₇₉	—	4	1	no	—
138	C₄×Dic₇₉	D₈	1	1	yes	characteristic
139	C₄×Dic₇₉	D₈	1	1	yes	characteristic
140	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
141	C₇₉⋊C₁₆	—	2	2	no	—
142	C₂×Q₈×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	—	2	2	no	—
144	C₂×D₄×C₇₉	—	4	1	no	—
145	C₂×D₄×C₇₉	—	4	1	no	—
146	Q₁₆×C₇₉	—	2	1	no	—
147	Q₁₆×C₇₉	C₂×D₄	1	2	yes	complemented
148	D₈×C₇₉	—	2	2	no	—
149	D₈×C₇₉	—	2	2	no	—
150	D₈×C₇₉	—	4	2	no	—
151	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	4	1	no	—
155	C₄²×C₇₉	—	4	1	no	—
156	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	4	2	no	—
159	C₂²×D₇₉	—	4	2	no	—
160	C₂²×D₇₉	—	8	4	no	—
161	C₂²×D₇₉	—	8	4	no	—
162	C₂²×D₇₉	—	8	4	no	—
163	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
164	Q₈×C₇₉	—	2	2	no	—
165	Q₈×C₇₉	—	4	1	no	—
166	D₄×C₇₉	—	4	2	no	—
167	D₄×C₇₉	—	4	2	no	—
168	D₄×C₇₉	—	8	2	no	—
169	D₄×C₇₉	—	8	2	no	—
170	C₂×C₄×C₇₉	—	4	1	no	—
171	C₂×C₄×C₇₉	—	4	1	no	—
172	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂²⋊D₇₉	—	8	4	no	—
176	C₂²⋊D₇₉	—	8	4	no	—
177	C₂²⋊D₇₉	—	8	4	no	—
178	C₂×Dic₇₉	—	4	1	no	—
179	C₂×Dic₇₉	—	4	1	no	—
180	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
181	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
182	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
183	D₃₁₆	—	4	2	no	—
184	D₃₁₆	—	4	2	no	—
185	D₃₁₆	—	8	2	no	—
186	D₃₁₆	—	8	2	no	—
187	C₄×D₇₉	—	2	2	no	—
188	C₄×D₇₉	—	4	4	no	—
189	C₄×D₇₉	—	8	2	no	—
190	C₄×D₇₉	SD₃₂	1	4	yes	complemented
191	C₄×D₇₉	#121	1	2	yes	—
192	C₄×D₇₉	AGL(1,ℤ/8)	1	2	yes	—
193	Dic₁₅₈	—	2	2	no	—
194	Dic₁₅₈	—	4	1	no	—
195	Dic₁₅₈	—	4	4	no	—
196	C₈×C₇₉	—	2	1	no	—
197	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
199	C₇₉⋊C₈	—	2	1	no	—
200	C₇₉⋊C₈	#121	1	2	yes	—
201	C₂²×C₇₉	—	8	2	no	—
202	C₂²×C₇₉	—	8	2	no	—
203	C₂²×C₇₉	—	8	2	no	—
204	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
205	C₂×D₇₉	—	8	2	no	—
206	C₂×D₇₉	—	8	2	no	—
207	C₂×D₇₉	—	8	2	no	—
208	C₂×D₇₉	—	16	8	no	—
209	C₂×D₇₉	#459	1	2	yes	—
210	C₂×D₇₉	C₂×SD₃₂	1	2	yes	—
211	C₂×D₇₉	#509	1	2	yes	—
212	C₄×C₇₉	—	2	1	no	—
213	C₄×C₇₉	—	4	2	no	—
214	C₄×C₇₉	—	8	1	no	—
215	C₄×C₇₉	C₂×SD₃₂	1	2	yes	complemented
216	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
217	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	Dic₇₉	—	2	1	no	—
219	Dic₇₉	—	4	2	no	—
220	Dic₇₉	—	8	1	no	—
221	Dic₇₉	#459	1	2	yes	—
222	Dic₇₉	C₂×SD₃₂	1	2	yes	complemented
223	C₂×#2207	—	79	1	no	maximal, Sylow
224	C₂×C₇₉	—	16	2	no	—
225	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
226	C₂×C₇₉	C₂²×SD₃₂	1	1	yes	characteristic
227	C₂×C₇₉	C₂×#509	1	1	yes	characteristic
228	D₇₉	—	16	2	no	—
229	D₇₉	#2207	1	4	yes	direct product factor
230	C₂²×SD₃₂	—	79	2	no	—
231	C₂×#493	—	79	1	no	—
232	C₂×C₄×Q₁₆	—	79	1	no	—
233	#2207	—	79	2	no	—
234	#2207	—	79	1	no	—
235	#2207	—	79	1	no	—
236	#2207	—	79	1	no	—
237	#2207	—	79	2	no	—
238	#2207	D₇₉	1	1	yes	characteristic, direct product factor
239	C₂×C₄⋊C₁₆	—	79	1	no	—
240	C₂×#357	—	79	2	no	—
241	C₇₉	C₂×#2207	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₁₆	—	79	1	no	—
243	C₂²×D₈	—	79	2	no	—
244	C₂²×D₈	—	158	1	no	—
245	C₂×#127	—	158	1	no	—
246	C₂×C₄×Q₈	—	158	1	no	—
247	C₂×SD₃₂	—	79	2	no	—
248	C₂×SD₃₂	—	79	2	no	—
249	C₂×SD₃₂	—	79	2	no	—
250	C₂×SD₃₂	—	158	8	no	—
251	C₂×SD₃₂	C₂×D₇₉	1	2	yes	complemented
252	C₂²×C₁₆	—	79	2	no	—
253	#493	—	79	2	no	—
254	#493	—	79	1	no	—
255	#493	—	158	1	no	—
256	#493	—	158	1	no	—
257	#493	C₂×D₇₉	1	1	yes	characteristic
258	C₄×Q₁₆	—	79	1	no	—
259	C₄×Q₁₆	—	79	1	no	—
260	C₄×Q₁₆	—	79	1	no	—
261	C₄×Q₁₆	—	158	1	no	—
262	C₄×Q₁₆	—	158	1	no	—
263	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
264	C₂×#107	—	79	1	no	—
265	C₂×#103	—	158	1	no	—
266	C₂×C₄×C₈	—	79	1	no	—
267	C₄⋊C₁₆	—	79	2	no	—
268	C₄⋊C₁₆	—	79	1	no	—
269	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
270	#357	—	79	2	no	—
271	#357	—	79	2	no	—
272	#357	—	79	2	no	—
273	#357	C₂×D₇₉	1	2	yes	complemented
274	C₂²×Q₈	—	158	1	no	—
275	C₂²×D₄	—	316	1	no	—
276	C₂²×D₄	—	316	1	no	—
277	C₂²×D₄	—	158	2	no	—
278	C₂×Q₁₆	—	79	4	no	—
279	C₂×Q₁₆	—	79	1	no	—
280	C₂×Q₁₆	—	158	2	no	—
281	C₂×Q₁₆	—	158	1	no	—
282	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	316	4	no	—
285	C₂×D₈	—	79	2	no	—
286	C₂×D₈	—	158	4	no	—
287	C₂×D₈	—	158	4	no	—
288	C₂×D₈	—	158	2	no	—
289	C₂×D₈	—	158	2	no	—
290	C₂×D₈	—	158	1	no	—
291	C₂×D₈	C₂²×D₇₉	1	2	yes	—
292	C₂²×C₈	—	79	1	no	—
293	C₂²×C₈	—	79	1	no	—
294	#127	—	2	1	no	—
295	#127	—	316	1	no	—
296	#127	—	316	1	no	—
297	#127	—	158	2	no	—
298	#127	—	158	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	316	1	no	—
301	C₄×Q₈	—	316	1	no	—
302	C₄×Q₈	—	158	1	no	—
303	C₄×Q₈	—	158	1	no	—
304	C₄×Q₈	—	158	1	no	—
305	C₂×C₄⋊C₄	—	316	1	no	—
306	C₂×C₄⋊C₄	—	158	1	no	—
307	C₂×C₄²	—	316	1	no	—
308	C₂×C₄²	—	79	1	no	—
309	SD₃₂	—	2	4	no	—
310	SD₃₂	—	158	4	no	—
311	SD₃₂	—	158	4	no	—
312	SD₃₂	—	158	4	no	—
313	C₂×C₁₆	—	79	2	no	—
314	C₂×C₁₆	—	158	4	no	—
315	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
316	#107	—	79	1	no	—
317	#107	—	158	1	no	—
318	#107	C₂²×D₇₉	1	1	yes	characteristic
319	#103	—	2	1	no	—
320	#103	—	158	1	no	—
321	#103	—	158	1	no	—
322	#103	—	158	1	no	—
323	C₄×C₈	—	79	1	no	—
324	C₄×C₈	—	79	1	no	—
325	C₄×C₈	—	79	1	no	—
326	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₂⁴	—	316	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	316	1	no	—
330	C₂×Q₈	—	316	2	no	—
331	C₂×Q₈	—	158	4	no	—
332	C₂×Q₈	—	158	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	316	4	no	—
337	C₂×D₄	—	316	4	no	—
338	C₂×D₄	—	316	2	no	—
339	C₂×D₄	—	316	2	no	—
340	C₂×D₄	—	316	2	no	—
341	C₂×D₄	—	316	1	no	—
342	C₂×D₄	—	316	1	no	—
343	C₂×D₄	—	632	4	no	—
344	C₂×D₄	—	632	4	no	—
345	C₂×D₄	—	158	2	no	—
346	C₂²×C₄	—	316	1	no	—
347	C₂²×C₄	—	316	1	no	—
348	C₂²×C₄	—	79	1	no	—
349	C₂²×C₄	—	79	1	no	—
350	C₂²×C₄	—	79	1	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	79	2	no	—
353	Q₁₆	—	158	4	no	—
354	Q₁₆	—	158	1	no	—
355	Q₁₆	D₄×D₇₉	1	2	yes	complemented
356	D₈	—	2	2	no	—
357	D₈	—	2	2	no	—
358	D₈	—	4	2	no	—
359	D₈	—	316	2	no	—
360	D₈	—	316	4	no	—
361	D₈	—	316	4	no	—
362	D₈	—	158	2	no	—
363	D₈	—	158	2	no	—
364	C₂×C₈	—	79	1	no	—
365	C₂×C₈	—	79	2	no	—
366	C₂×C₈	—	79	2	no	—
367	C₂×C₈	—	79	1	no	—
368	C₂×C₈	—	158	2	no	—
369	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
370	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	316	1	no	—
374	C₄⋊C₄	—	316	1	no	—
375	C₄⋊C₄	—	316	1	no	—
376	C₄⋊C₄	—	316	1	no	—
377	C₄⋊C₄	—	158	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	316	1	no	—
380	C₄²	—	316	1	no	—
381	C₄²	—	316	1	no	—
382	C₄²	—	79	1	no	—
383	C₄²	—	79	1	no	—
384	C₄²	—	79	1	no	—
385	C₄²	D₄×D₇₉	1	1	yes	characteristic
386	C₁₆	—	2	2	no	—
387	C₁₆	—	158	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	316	2	no	—
390	C₂³	—	79	1	no	—
391	C₂³	—	632	4	no	—
392	C₂³	—	632	4	no	—
393	C₂³	—	632	4	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	316	4	no	—
397	Q₈	—	316	1	no	—
398	Q₈	—	158	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	316	2	no	—
404	D₄	—	316	2	no	—
405	D₄	—	632	2	no	—
406	D₄	—	632	4	no	—
407	D₄	—	632	4	no	—
408	D₄	—	632	4	no	—
409	D₄	—	632	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	316	4	no	—
413	C₂×C₄	—	316	1	no	—
414	C₂×C₄	—	316	1	no	—
415	C₂×C₄	—	79	1	no	—
416	C₂×C₄	—	79	1	no	—
417	C₂×C₄	—	79	4	no	—
418	C₂×C₄	—	79	2	no	—
419	C₂×C₄	—	79	2	no	—
420	C₂×C₄	—	79	1	no	—
421	C₂×C₄	—	632	2	no	—
422	C₂×C₄	—	158	2	no	—
423	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
424	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	79	2	no	—
428	C₈	—	158	1	no	—
429	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
430	C₈	#41×D₇₉	1	1	yes	characteristic
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	79	2	no	—
435	C₂²	—	79	2	no	—
436	C₂²	—	79	2	no	—
437	C₂²	—	632	2	no	—
438	C₂²	—	632	2	no	—
439	C₂²	—	632	2	no	—
440	C₂²	—	1264	8	no	—
441	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	316	2	no	—
446	C₄	—	79	2	no	—
447	C₄	—	79	2	no	—
448	C₄	—	632	1	no	—
449	C₄	—	158	1	no	—
450	C₄	SD₃₂×D₇₉	1	2	yes	complemented
451	C₄	#121×D₇₉	1	1	yes	characteristic
452	C₄	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
453	C₂	—	16	2	no	—
454	C₂	—	79	4	no	—
455	C₂	—	1264	2	no	—
456	C₂	#459×D₇₉	1	1	yes	characteristic
457	C₂	C₂×SD₃₂×D₇₉	1	1	yes	characteristic
458	C₂	#509×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2207	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#493×D₇₉	C₂
hypercenter	#2207	D₇₉
hypocenter	C₇₉	C₂×#2207
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2207

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₇₉	C₂	semidirect
3. C₄×Q₁₆×D₇₉	C₂	semidirect
4. #23765441	C₂	semidirect
5. #23765440	C₂	semidirect
6. #23765439	C₂	semidirect
7. #23765438	C₂	semidirect
8. #23765437	C₂	semidirect
9. C₄⋊C₁₆×D₇₉	C₂	semidirect
10. #357×D₇₉	C₂	semidirect
11. C₇₉×#2207	C₂	semidirect
17. C₂×#14579106	C₂²	semidirect
18. C₂×#14579105	C₂²	semidirect
19. C₂×#14579104	C₂²	semidirect
26. C₄×Dic₃₁₆	C₂²	semidirect
27. Q₁₆×Dic₇₉	C₂²	semidirect
28. #19098657	C₂²	semidirect
34. C₄⋊(C₇₉⋊C₁₆)	C₂²	semidirect
35. Dic₇₉⋊C₁₆	C₂²	semidirect
36. #19098365	C₂²	semidirect
37. #19098364	C₂²	semidirect
38. #19098363	C₂²	semidirect
39. C₂×SD₃₂×C₇₉	C₂²	semidirect
41. C₄×Q₁₆×C₇₉	C₂²	semidirect
42. C₄⋊C₁₆×C₇₉	C₂²	semidirect
43. #357×C₇₉	C₂²	semidirect
51. Q₁₆×D₇₉	D₄	semidirect
118. Dic₃₁₆	C₂×D₄	semidirect
147. Q₁₆×C₇₉	C₂×D₄	semidirect
190. C₄×D₇₉	SD₃₂	semidirect
215. C₄×C₇₉	C₂×SD₃₂	semidirect
222. Dic₇₉	C₂×SD₃₂	semidirect
229. D₇₉	#2207	direct (N × H)
238. #2207	D₇₉	direct (N × H)
241. C₇₉	C₂×#2207	semidirect
251. C₂×SD₃₂	C₂×D₇₉	semidirect
263. C₄×Q₁₆	C₂×D₇₉	semidirect
269. C₄⋊C₁₆	C₂×D₇₉	semidirect
273. #357	C₂×D₇₉	semidirect
355. Q₁₆	D₄×D₇₉	semidirect
450. C₄	SD₃₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₇₉	2
#493×D₇₉	2
C₄×Q₁₆×D₇₉	2
#23765441	2
#23765440	2
#23765439	2
#23765438	2
#23765437	2
C₄⋊C₁₆×D₇₉	2
#357×D₇₉	2
C₇₉×#2207	2
C₂×#2207	79

Subgroups — #2207×D79 #34442509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2207×D₇₉ #34442509