Subgroups — #34260025

Order 20224.

722 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773975	C₂	1	1	yes	maximal, characteristic
2	#23772146	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762283	C₂	1	2	yes	maximal, complemented
4	#23762229	C₂	1	2	yes	maximal, complemented
5	#23762227	C₂	1	2	yes	maximal, complemented
6	C₈×#11929609	C₂	1	2	yes	maximal, complemented
7	C₂×#19098315	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761799	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761798	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579169	—	2	1	no	—
13	#19099113	C₂²	1	1	yes	characteristic
14	#19098966	C₄	1	1	yes	characteristic
15	#19098939	C₄	1	1	yes	characteristic
16	#19098911	C₄	1	1	yes	characteristic
17	#19098909	C₄	1	1	yes	characteristic
18	#19098797	C₄	1	2	yes	—
19	#19098797	C₄	1	2	yes	—
20	C₄×#11929609	C₂²	1	2	yes	—
21	C₄×#11929609	C₂²	1	2	yes	—
22	#19098642	C₂²	1	2	yes	—
23	#19098636	—	2	2	no	—
24	C₈×D₃₁₆	C₂²	1	2	yes	—
25	#19098616	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#19098531	—	2	1	no	—
28	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
29	#19098315	C₂²	1	1	yes	characteristic
30	#19098315	C₂²	1	1	yes	characteristic
31	#19098315	C₂²	1	1	yes	characteristic
32	#19098315	C₂²	1	1	yes	characteristic
33	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
35	#19098290	C₂²	1	2	yes	—
36	#19098290	C₂²	1	2	yes	—
37	#19098284	C₂²	1	2	yes	—
38	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
39	C₂×#131×C₇₉	—	2	1	no	—
40	#532×C₇₉	C₂²	1	1	yes	characteristic
41	#436×C₇₉	C₂²	1	2	yes	—
42	#435×C₇₉	—	2	2	no	—
43	C₈×D₄×C₇₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	#408×C₇₉	—	2	1	no	—
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	—	2	1	no	—
48	C₂×#11929609	C₂×C₄	1	2	yes	—
49	C₂×#11929609	C₂×C₄	1	2	yes	—
50	#14579169	—	4	4	no	—
51	C₂×#11929607	—	2	2	no	—
52	C₂²×C₇₉⋊C₈	—	2	1	no	—
53	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇₉	—	2	2	no	—
56	#14579161	C₂×C₄	1	1	yes	characteristic
57	#14579158	C₂×C₄	1	1	yes	characteristic
58	#14579149	—	2	1	no	—
59	#14579135	—	2	1	no	—
60	#14579135	C₂×C₄	1	2	yes	—
61	C₄×D₃₁₆	—	2	1	no	—
62	C₄×D₃₁₆	C₂³	1	2	yes	—
63	#14579094	C₂×C₄	1	2	yes	—
64	#14579094	C₂×C₄	1	2	yes	—
65	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
69	#14579082	C₂×C₄	1	2	yes	—
70	#14579082	C₂×C₄	1	2	yes	—
71	#14579081	C₂×C₄	1	2	yes	—
72	#14579081	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
74	(C₂×D₇₉)⋊C₈	—	2	2	no	—
75	(C₂×D₇₉)⋊C₈	—	2	2	no	—
76	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
79	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×#41×C₇₉	—	2	1	no	—
82	#131×C₇₉	—	4	4	no	—
83	C₂×M₁₆×C₇₉	—	2	2	no	—
84	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₇₉	—	2	1	no	—
87	C₂²×C₈×C₇₉	—	2	2	no	—
88	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
89	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
90	#124×C₇₉	—	2	1	no	—
91	#121×C₇₉	—	2	1	no	—
92	#121×C₇₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₇₉	—	2	1	no	—
94	C₄×D₄×C₇₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	—	2	1	no	—
97	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₇₉	—	2	2	no	—
100	C₂²⋊C₈×C₇₉	—	2	2	no	—
101	#97×C₇₉	D₄	1	2	yes	—
102	C₄×C₈×C₇₉	C₂³	1	2	yes	—
103	#11929624	—	4	2	no	—
104	#11929624	—	4	2	no	—
105	C₂×Dic₁₅₈	—	2	1	no	—
106	C₂×D₃₁₆	—	2	1	no	—
107	C₂×D₃₁₆	—	2	1	no	—
108	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
109	C₂×C₂²⋊D₇₉	—	2	2	no	—
110	C₂×C₄×D₇₉	—	2	2	no	—
111	#11929609	—	2	4	no	—
112	#11929609	—	4	2	no	—
113	#11929607	—	4	4	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	1	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	4	1	no	—
119	C₂×C₇₉⋊C₈	—	4	2	no	—
120	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₇₉	—	4	4	no	—
125	C₄⋊Dic₇₉	—	2	1	no	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
127	(C₂×D₇₉)⋊C₄	—	2	2	no	—
128	(C₂×D₇₉)⋊C₄	—	2	2	no	—
129	#41×C₇₉	—	4	2	no	—
130	#41×C₇₉	—	4	2	no	—
131	C₂×Q₈×C₇₉	—	2	1	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	2	1	no	—
134	C₂×D₄×C₇₉	—	2	1	no	—
135	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
140	M₁₆×C₇₉	—	2	2	no	—
141	M₁₆×C₇₉	—	4	4	no	—
142	M₁₆×C₇₉	D₈	1	4	yes	complemented
143	C₂×C₈×C₇₉	—	2	1	no	—
144	C₂×C₈×C₇₉	—	2	1	no	—
145	C₂×C₈×C₇₉	—	4	4	no	—
146	C₂×C₈×C₇₉	—	4	2	no	—
147	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
151	C₂²⋊C₄×C₇₉	—	2	2	no	—
152	C₂²⋊C₄×C₇₉	—	2	2	no	—
153	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₉	#41	1	1	yes	characteristic
156	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₇₉	—	2	2	no	—
160	Q₈×C₇₉	—	4	2	no	—
161	D₄×C₇₉	—	2	2	no	—
162	D₄×C₇₉	—	2	2	no	—
163	D₄×C₇₉	—	4	4	no	—
164	D₄×C₇₉	—	4	2	no	—
165	D₄×C₇₉	—	8	1	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₇₉	#135	1	2	yes	—
177	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₇₉	—	4	4	no	—
181	C₂×Dic₇₉	—	2	2	no	—
182	D₃₁₆	—	2	2	no	—
183	D₃₁₆	—	2	2	no	—
184	D₃₁₆	—	4	2	no	—
185	D₃₁₆	—	8	1	no	—
186	C₄×D₇₉	—	4	2	no	—
187	C₄×D₇₉	—	4	2	no	—
188	Dic₁₅₈	—	4	2	no	—
189	C₈×C₇₉	—	2	2	no	—
190	C₈×C₇₉	—	4	1	no	—
191	C₈×C₇₉	—	4	1	no	—
192	C₈×C₇₉	C₂×D₈	1	4	yes	—
193	C₇₉⋊C₈	—	2	1	no	—
194	C₇₉⋊C₈	—	2	1	no	—
195	C₇₉⋊C₈	—	2	1	no	—
196	C₇₉⋊C₈	—	4	2	no	—
197	C₇₉⋊C₈	—	4	1	no	—
198	C₇₉⋊C₈	—	4	1	no	—
199	C₇₉⋊C₈	#131	1	2	yes	complemented
200	C₂²×C₇₉	—	2	1	no	—
201	C₂²×C₇₉	—	2	1	no	—
202	C₂²×C₇₉	—	4	2	no	—
203	C₂²×C₇₉	—	4	2	no	—
204	C₂²×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	C₄×D₈	1	2	yes	—
206	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂×D₇₉	—	4	2	no	—
208	C₂×D₇₉	—	4	2	no	—
209	C₂×D₇₉	—	4	2	no	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	—	2	1	no	—
212	C₄×C₇₉	—	2	1	no	—
213	C₄×C₇₉	—	4	2	no	—
214	C₄×C₇₉	C₄×D₈	1	2	yes	—
215	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
216	C₄×C₇₉	#568	1	1	yes	characteristic
217	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
219	Dic₇₉	—	4	2	no	—
220	#18066	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	2	2	no	—
222	C₂×C₇₉	—	8	2	no	—
223	C₂×C₇₉	#2935	1	1	yes	characteristic
224	C₂×C₇₉	C₂×C₄×D₈	1	1	yes	characteristic
225	C₂×C₇₉	#2957	1	1	yes	characteristic
226	D₇₉	—	8	2	no	—
227	#3169	—	79	1	no	—
228	#2935	—	79	1	no	—
229	#2935	D₇₉	1	1	yes	characteristic, complemented
230	#1589	—	79	2	no	—
231	#1581	—	79	2	no	—
232	#1581	—	79	2	no	—
233	C₈×D₈	—	79	2	no	—
234	C₂×#335	—	79	1	no	—
235	#1480	—	79	1	no	—
236	#1480	—	79	1	no	—
237	C₈×M₁₆	—	79	1	no	—
238	C₇₉	#18066	1	1	yes	characteristic, complemented, Sylow
239	C₂×#131	—	2	1	no	—
240	C₂×#131	—	158	1	no	—
241	#532	—	79	1	no	—
242	#532	C₂×D₇₉	1	1	yes	characteristic
243	#500	—	79	1	no	—
244	#493	—	79	1	no	—
245	#486	—	79	1	no	—
246	#486	—	79	1	no	—
247	#466	—	79	2	no	—
248	#466	—	79	2	no	—
249	C₄×D₈	—	79	2	no	—
250	C₄×D₈	—	79	2	no	—
251	#436	—	79	2	no	—
252	#436	C₂×D₇₉	1	2	yes	—
253	#435	—	2	2	no	—
254	#435	—	158	2	no	—
255	C₈×D₄	—	79	2	no	—
256	C₈×D₄	C₂×D₇₉	1	2	yes	—
257	#431	—	79	1	no	—
258	C₂×C₄⋊C₈	—	79	1	no	—
259	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
260	#408	—	2	1	no	—
261	#408	—	158	1	no	—
262	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
263	C₂×C₄×C₈	—	79	1	no	—
264	#335	—	79	1	no	—
265	#335	—	79	1	no	—
266	#335	—	79	1	no	—
267	#335	—	79	1	no	—
268	D₄⋊C₈	—	79	2	no	—
269	D₄⋊C₈	—	79	2	no	—
270	D₄⋊C₈	—	79	2	no	—
271	D₄⋊C₈	—	79	2	no	—
272	#322	—	79	2	no	—
273	C₈²	—	79	2	no	—
274	C₂×#41	—	2	1	no	—
275	C₂×#41	—	158	1	no	—
276	C₂×D₈	—	79	2	no	—
277	C₂×D₈	—	79	2	no	—
278	#131	—	4	4	no	—
279	#131	—	316	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	158	2	no	—
282	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
283	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	79	1	no	—
287	C₂²×C₈	—	79	1	no	—
288	C₂²×C₈	—	158	1	no	—
289	C₂²×C₈	—	158	2	no	—
290	C₄⋊Q₈	—	79	1	no	—
291	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
292	#127	—	79	1	no	—
293	#127	C₄×D₇₉	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	158	1	no	—
296	#121	—	2	1	no	—
297	#121	—	79	2	no	—
298	#121	—	158	1	no	—
299	#121	C₄×D₇₉	1	2	yes	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	79	2	no	—
302	C₄×D₄	—	158	1	no	—
303	C₄×D₄	C₂²×D₇₉	1	2	yes	—
304	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
305	#107	—	79	2	no	—
306	#107	—	79	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	79	1	no	—
309	C₄⋊C₈	—	79	1	no	—
310	C₄⋊C₈	—	158	1	no	—
311	C₄⋊C₈	—	158	1	no	—
312	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
314	#102	—	79	2	no	—
315	#102	—	79	2	no	—
316	#102	—	79	2	no	—
317	#102	—	79	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	158	1	no	—
321	C₂²⋊C₈	—	158	2	no	—
322	C₂²⋊C₈	—	158	2	no	—
323	#97	C₂²⋊D₇₉	1	2	yes	—
324	C₄×C₈	—	79	1	no	—
325	C₄×C₈	—	79	1	no	—
326	C₄×C₈	—	79	1	no	—
327	C₄×C₈	—	79	1	no	—
328	C₄×C₈	—	79	2	no	—
329	C₄×C₈	C₂²×D₇₉	1	2	yes	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	316	2	no	—
333	#41	—	316	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	158	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	79	2	no	—
340	C₂×D₄	—	158	2	no	—
341	C₂×D₄	—	158	1	no	—
342	C₂×D₄	—	158	1	no	—
343	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	158	2	no	—
346	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
348	C₂²×C₄	#11929624	1	1	yes	characteristic
349	D₈	—	316	2	no	—
350	D₈	—	158	4	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	—	316	4	no	—
354	M₁₆	#11929609	1	4	yes	complemented
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	—	316	2	no	—
360	C₂×C₈	—	316	4	no	—
361	C₂×C₈	—	316	1	no	—
362	C₂×C₈	—	79	1	no	—
363	C₂×C₈	—	79	1	no	—
364	C₂×C₈	—	79	1	no	—
365	C₂×C₈	—	79	1	no	—
366	C₂×C₈	—	158	2	no	—
367	C₂×C₈	—	158	1	no	—
368	C₂×C₈	—	158	1	no	—
369	C₂×C₈	—	158	2	no	—
370	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
371	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	79	2	no	—
374	C₄⋊C₄	—	158	1	no	—
375	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	158	2	no	—
379	C₂²⋊C₄	—	158	2	no	—
380	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
381	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
382	C₄²	#11929624	1	1	yes	characteristic
383	C₄²	C₂³×D₇₉	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	158	2	no	—
386	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
387	Q₈	—	4	2	no	—
388	Q₈	—	316	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	316	4	no	—
395	D₄	—	316	2	no	—
396	D₄	—	632	1	no	—
397	D₄	—	158	2	no	—
398	D₄	—	158	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	316	2	no	—
406	C₂×C₄	—	316	2	no	—
407	C₂×C₄	—	158	2	no	—
408	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#11929609	1	2	yes	—
412	C₂×C₄	#14579181	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
415	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	316	2	no	—
420	C₈	—	316	1	no	—
421	C₈	—	316	1	no	—
422	C₈	—	79	2	no	—
423	C₈	—	158	1	no	—
424	C₈	—	158	1	no	—
425	C₈	—	158	1	no	—
426	C₈	C₂×#11929609	1	4	yes	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	316	2	no	—
433	C₂²	—	316	2	no	—
434	C₂²	—	316	2	no	—
435	C₂²	C₄×#11929609	1	2	yes	—
436	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	316	2	no	—
442	C₄	C₄×#11929609	1	2	yes	—
443	C₄	#131×D₇₉	1	1	yes	characteristic
444	C₄	#19099328	1	1	yes	characteristic
445	C₄	C₂²×#11929609	1	1	yes	characteristic
446	C₄	C₂×#14579181	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	2	no	—
449	C₂	—	632	2	no	—
450	C₂	#23772142	1	1	yes	characteristic
451	C₂	C₂×C₄×#11929609	1	1	yes	characteristic
452	C₂	#23772315	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#2935	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773975	C₂
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#2935	D₇₉
hypocenter	C₇₉	#18066
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #23772146	C₂	semidirect
3. #23762283	C₂	semidirect
4. #23762229	C₂	semidirect
5. #23762227	C₂	semidirect
6. C₈×#11929609	C₂	semidirect
7. C₂×#19098315	C₂	semidirect
8. #23761799	C₂	semidirect
9. #23761798	C₂	semidirect
10. M₁₆×C₇₉⋊C₈	C₂	semidirect
11. C₇₉×#2935	C₂	semidirect
142. M₁₆×C₇₉	D₈	semidirect
199. C₇₉⋊C₈	#131	semidirect
229. #2935	D₇₉	semidirect
238. C₇₉	#18066	semidirect
354. M₁₆	#11929609	semidirect

Maximal subgroups

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

subgroup	index
#23773975	2
#23772146	2
#23762283	2
#23762229	2
#23762227	2
C₈×#11929609	2
C₂×#19098315	2
#23761799	2
#23761798	2
M₁₆×C₇₉⋊C₈	2
C₇₉×#2935	2
#18066	79