Subgroups — #34270737

Order 20224.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773454	C₂	1	2	yes	maximal, complemented
2	C₈×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762813	C₂	1	2	yes	maximal, complemented
4	#23762806	C₂	1	2	yes	maximal, complemented
5	#23762801	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762796	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762757	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762752	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762148	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762062	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11929624	C₂²	1	1	yes	characteristic
13	#19098884	—	2	2	no	—
14	#19098855	C₂²	1	2	yes	—
15	#19098850	C₂²	1	2	yes	—
16	#19098760	C₂²	1	2	yes	—
17	#19098755	C₂²	1	2	yes	—
18	#19098706	—	2	2	no	—
19	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
21	C₄×#11929612	—	2	2	no	—
22	C₄×#11929609	—	2	2	no	—
23	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
24	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₇₉	—	2	1	no	—
26	C₈×C₂²⋊D₇₉	—	2	1	no	—
27	#19098616	C₂²	1	2	yes	—
28	#19098616	C₂²	1	1	yes	characteristic
29	#19098614	—	2	1	no	—
30	C₄×C₈×D₇₉	—	2	1	no	—
31	#19098316	C₂²	1	1	yes	characteristic
32	#19098316	C₂²	1	1	yes	characteristic
33	#19098314	C₂²	1	2	yes	—
34	#19098312	C₂²	1	2	yes	—
35	#19098312	C₂²	1	2	yes	—
36	#19098307	C₂²	1	2	yes	—
37	#19098307	C₂²	1	2	yes	—
38	#532×C₇₉	C₂²	1	2	yes	—
39	#500×C₇₉	C₂²	1	1	yes	characteristic
40	#493×C₇₉	C₂²	1	1	yes	characteristic
41	#486×C₇₉	C₂²	1	2	yes	—
42	#466×C₇₉	—	2	1	no	—
43	#466×C₇₉	—	2	1	no	—
44	C₄×D₈×C₇₉	—	2	1	no	—
45	C₄×D₈×C₇₉	—	2	1	no	—
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	D₄	1	1	yes	characteristic
48	C₂×#11929612	—	2	2	no	—
49	C₂×#11929609	—	2	2	no	—
50	C₂×C₈×D₇₉	—	2	1	no	—
51	C₂×C₈×D₇₉	—	2	1	no	—
52	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
53	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
54	C₄×D₃₁₆	D₄	1	1	yes	characteristic
55	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₇₉	—	2	1	no	—
57	C₄×C₂²⋊D₇₉	—	2	1	no	—
58	#14579120	D₄	1	1	yes	characteristic
59	#14579118	—	2	1	no	—
60	C₄²×D₇₉	—	2	1	no	—
61	#14579094	—	2	2	no	—
62	#14579092	—	2	2	no	—
63	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₇₉⋊C₈	—	2	1	no	—
68	Dic₇₉⋊C₈	—	2	1	no	—
69	#14579084	—	2	2	no	—
70	#14579082	—	2	2	no	—
71	#14579082	—	2	2	no	—
72	#14579081	—	2	2	no	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
75	(C₂×D₇₉)⋊C₈	—	2	1	no	—
76	(C₂×D₇₉)⋊C₈	—	2	1	no	—
77	C₄×C₇₉⋊C₈	—	2	2	no	—
78	C₄×C₇₉⋊C₈	—	2	1	no	—
79	C₈×Dic₇₉	—	2	1	no	—
80	C₈×Dic₇₉	—	2	1	no	—
81	C₂×#41×C₇₉	—	2	2	no	—
82	C₂×D₈×C₇₉	—	2	1	no	—
83	C₂×D₈×C₇₉	—	2	1	no	—
84	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
86	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
87	#127×C₇₉	C₂³	1	2	yes	—
88	#124×C₇₉	—	2	2	no	—
89	#121×C₇₉	—	2	2	no	—
90	#121×C₇₉	—	2	2	no	—
91	C₄×D₄×C₇₉	—	2	2	no	—
92	C₄×D₄×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
94	#107×C₇₉	—	2	1	no	—
95	#107×C₇₉	—	2	1	no	—
96	#102×C₇₉	—	2	2	no	—
97	#102×C₇₉	—	2	2	no	—
98	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	#11929624	—	2	2	no	—
103	#11929624	—	2	2	no	—
104	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₉	—	2	1	no	—
107	C₂×C₄×D₇₉	—	2	1	no	—
108	C₂×C₄×D₇₉	—	2	1	no	—
109	C₂×C₄×D₇₉	—	2	1	no	—
110	#11929612	—	4	4	no	—
111	#11929609	—	4	4	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₈×D₇₉	—	4	2	no	—
117	C₈×D₇₉	—	4	2	no	—
118	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
120	Dic₇₉⋊C₄	—	2	1	no	—
121	Dic₇₉⋊C₄	—	2	1	no	—
122	C₂²⋊Dic₇₉	—	2	1	no	—
123	(C₂×D₇₉)⋊C₄	—	2	1	no	—
124	(C₂×D₇₉)⋊C₄	—	2	1	no	—
125	C₄×Dic₇₉	—	2	1	no	—
126	C₄×Dic₇₉	—	2	1	no	—
127	C₄×Dic₇₉	—	2	1	no	—
128	#41×C₇₉	—	8	4	no	—
129	C₂×Q₈×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	4	2	no	—
134	C₂²×C₄×C₇₉	—	4	2	no	—
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
138	D₈×C₇₉	—	4	2	no	—
139	D₈×C₇₉	—	4	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	4	1	no	—
142	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₇₉	—	2	2	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₂²⋊C₄×C₇₉	—	4	2	no	—
149	C₂²⋊C₄×C₇₉	—	4	2	no	—
150	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₉	#41	1	1	yes	characteristic
153	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₇₉	—	4	2	no	—
155	C₂³×C₇₉	#121	1	1	yes	characteristic
156	C₂²×D₇₉	—	2	1	no	—
157	Q₈×C₇₉	—	8	2	no	—
158	D₄×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	4	2	no	—
160	D₄×C₇₉	—	4	2	no	—
161	D₄×C₇₉	—	4	2	no	—
162	D₄×C₇₉	—	8	2	no	—
163	D₄×C₇₉	—	8	4	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	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	2	no	—
170	C₂×C₄×C₇₉	—	8	4	no	—
171	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₇₉	—	2	4	no	—
178	C₂×Dic₇₉	—	2	1	no	—
179	C₂×Dic₇₉	—	2	1	no	—
180	C₂×Dic₇₉	—	2	1	no	—
181	D₃₁₆	—	2	1	no	—
182	D₃₁₆	#135	1	2	yes	—
183	C₄×D₇₉	—	2	4	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	1	no	—
186	C₄×D₇₉	—	4	2	no	—
187	Dic₁₅₈	—	2	1	no	—
188	Dic₁₅₈	#135	1	2	yes	—
189	C₈×C₇₉	—	2	1	no	—
190	C₈×C₇₉	—	2	1	no	—
191	C₈×C₇₉	—	2	1	no	—
192	C₈×C₇₉	#135	1	2	yes	—
193	C₇₉⋊C₈	—	4	1	no	—
194	C₇₉⋊C₈	—	4	2	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₇₉⋊C₈	—	4	1	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	2	1	no	—
199	C₂²×C₇₉	—	2	1	no	—
200	C₂²×C₇₉	—	8	2	no	—
201	C₂²×C₇₉	—	8	2	no	—
202	C₂²×C₇₉	—	8	2	no	—
203	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
204	C₂×D₇₉	—	2	2	no	—
205	C₂×D₇₉	—	4	1	no	—
206	C₂×D₇₉	—	4	1	no	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	8	2	no	—
211	C₄×C₇₉	#472	1	2	yes	—
212	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
213	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
214	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
215	C₄×C₇₉	#575	1	1	yes	characteristic
216	Dic₇₉	—	2	2	no	—
217	Dic₇₉	—	4	1	no	—
218	Dic₇₉	—	4	1	no	—
219	#19128	—	79	1	no	maximal, Sylow
220	C₂×C₇₉	—	4	1	no	—
221	C₂×C₇₉	—	16	2	no	—
222	C₂×C₇₉	#3035	1	1	yes	characteristic
223	C₂×C₇₉	#3050	1	1	yes	characteristic
224	C₂×C₇₉	C₂×#472	1	1	yes	characteristic
225	D₇₉	—	4	2	no	—
226	#3169	D₇₉	1	1	yes	characteristic, complemented
227	#3106	—	79	2	no	—
228	C₈×#41	—	79	1	no	—
229	#1678	—	79	2	no	—
230	#1677	—	79	2	no	—
231	#1676	—	79	1	no	—
232	#1675	—	79	1	no	—
233	#1668	—	79	1	no	—
234	#1667	—	79	1	no	—
235	#1564	—	79	1	no	—
236	#1543	—	79	2	no	—
237	C₇₉	#19128	1	1	yes	characteristic, complemented, Sylow
238	#532	C₂×D₇₉	1	2	yes	—
239	C₄×#41	—	79	1	no	—
240	#500	C₂×D₇₉	1	1	yes	characteristic
241	#493	C₂×D₇₉	1	1	yes	characteristic
242	#486	C₂×D₇₉	1	2	yes	—
243	#482	—	158	2	no	—
244	#477	—	79	2	no	—
245	#476	—	79	2	no	—
246	#466	—	2	1	no	—
247	#466	—	2	1	no	—
248	#460	—	79	2	no	—
249	#459	—	79	2	no	—
250	#449	—	158	2	no	—
251	C₈×Q₈	—	79	1	no	—
252	C₈×Q₈	—	79	1	no	—
253	C₄×SD₁₆	—	158	2	no	—
254	C₄×D₈	—	2	1	no	—
255	C₄×D₈	—	2	1	no	—
256	C₄×D₈	—	158	2	no	—
257	C₈×D₄	—	79	1	no	—
258	C₈×D₄	—	79	1	no	—
259	C₈×D₄	—	158	1	no	—
260	C₈×D₄	—	158	1	no	—
261	#431	—	79	1	no	—
262	#431	—	79	2	no	—
263	#431	—	158	1	no	—
264	C₂×C₄×C₈	—	158	1	no	—
265	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
266	#335	—	79	1	no	—
267	#335	—	79	1	no	—
268	#334	—	79	2	no	—
269	#333	—	79	2	no	—
270	#333	—	79	2	no	—
271	#331	—	79	2	no	—
272	#331	—	79	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	79	1	no	—
275	C₂×SD₁₆	—	158	2	no	—
276	C₂×D₈	—	2	1	no	—
277	C₂×D₈	—	2	1	no	—
278	C₂×D₈	—	158	2	no	—
279	C₂²×C₈	—	158	1	no	—
280	C₂²×C₈	—	158	1	no	—
281	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
283	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
284	#127	C₂²×D₇₉	1	2	yes	—
285	#124	—	2	2	no	—
286	#121	—	2	2	no	—
287	#121	—	2	2	no	—
288	C₄×Q₈	—	79	1	no	—
289	C₄×Q₈	—	79	1	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	—	79	1	no	—
293	C₄×D₄	—	79	1	no	—
294	C₄×D₄	—	158	1	no	—
295	C₄×D₄	—	158	1	no	—
296	#117	—	79	1	no	—
297	#117	—	158	1	no	—
298	C₂×C₄²	—	158	1	no	—
299	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
300	#107	—	2	1	no	—
301	#107	—	2	1	no	—
302	#107	—	158	2	no	—
303	#106	—	158	2	no	—
304	C₄⋊C₈	—	79	1	no	—
305	C₄⋊C₈	—	79	1	no	—
306	C₄⋊C₈	—	79	2	no	—
307	C₄⋊C₈	—	79	2	no	—
308	C₄⋊C₈	—	158	1	no	—
309	C₄⋊C₈	—	158	1	no	—
310	#103	—	158	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	158	2	no	—
314	#102	—	158	2	no	—
315	#102	—	158	2	no	—
316	C₂²⋊C₈	—	158	2	no	—
317	C₂²⋊C₈	—	158	1	no	—
318	C₂²⋊C₈	—	158	1	no	—
319	C₂²⋊C₈	—	158	1	no	—
320	C₄×C₈	—	158	1	no	—
321	C₄×C₈	—	158	1	no	—
322	C₄×C₈	—	158	2	no	—
323	C₄×C₈	—	158	1	no	—
324	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
325	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
328	#41	—	8	4	no	—
329	#41	—	158	2	no	—
330	#41	—	158	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	79	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	79	1	no	—
338	C₂×D₄	—	158	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	158	1	no	—
341	C₂²×C₄	—	158	1	no	—
342	C₂²×C₄	—	158	1	no	—
343	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
345	C₂²×C₄	#11929623	1	1	yes	characteristic
346	SD₁₆	—	316	4	no	—
347	D₈	—	4	2	no	—
348	D₈	—	4	2	no	—
349	D₈	—	316	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	316	2	no	—
353	C₂×C₈	—	316	2	no	—
354	C₂×C₈	—	158	2	no	—
355	C₂×C₈	—	158	2	no	—
356	C₂×C₈	—	158	1	no	—
357	C₂×C₈	—	158	1	no	—
358	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
360	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
361	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	79	1	no	—
365	C₄⋊C₄	—	79	1	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	1	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	158	1	no	—
371	C₂²⋊C₄	—	158	1	no	—
372	C₂²⋊C₄	—	158	1	no	—
373	C₄²	—	158	1	no	—
374	C₄²	—	158	1	no	—
375	C₄²	—	158	1	no	—
376	C₄²	D₄×D₇₉	1	1	yes	characteristic
377	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
378	C₄²	#11929623	1	1	yes	characteristic
379	C₄²	C₂³×D₇₉	1	1	yes	characteristic
380	C₂³	—	4	2	no	—
381	C₂³	—	158	1	no	—
382	C₂³	#14579132	1	1	yes	characteristic
383	Q₈	—	8	2	no	—
384	Q₈	—	79	2	no	—
385	Q₈	—	158	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	4	no	—
392	D₄	—	79	2	no	—
393	D₄	—	158	4	no	—
394	D₄	—	158	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	—	316	2	no	—
403	C₂×C₄	—	316	1	no	—
404	C₂×C₄	—	316	1	no	—
405	C₂×C₄	—	158	4	no	—
406	C₂×C₄	—	158	1	no	—
407	C₂×C₄	—	158	1	no	—
408	C₂×C₄	—	158	1	no	—
409	C₂×C₄	#14579132	1	1	yes	characteristic
410	C₂×C₄	#14579132	1	1	yes	characteristic
411	C₂×C₄	#14579132	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
414	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	316	2	no	—
419	C₈	—	316	2	no	—
420	C₈	—	316	1	no	—
421	C₈	—	316	1	no	—
422	C₈	#14579181	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	316	1	no	—
430	C₂²	—	316	1	no	—
431	C₂²	—	158	2	no	—
432	C₂²	C₂×#14579132	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	316	1	no	—
438	C₄	—	316	1	no	—
439	C₄	—	158	2	no	—
440	C₄	#19098830	1	2	yes	—
441	C₄	#135×D₇₉	1	1	yes	characteristic
442	C₄	#135×D₇₉	1	1	yes	characteristic
443	C₄	C₂×#14579181	1	1	yes	characteristic
444	C₄	#19099361	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	16	2	no	—
447	C₂	—	316	2	no	—
448	C₂	#23772849	1	1	yes	characteristic
449	C₂	#23772977	1	1	yes	characteristic
450	C₂	C₂×#19098830	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3169	C₂
socle	C₂²×C₇₉	C₂×#121
hypercenter	#3169	D₇₉
hypocenter	C₇₉	#19128
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #23773454	C₂	semidirect
2. C₈×#11929624	C₂	semidirect
3. #23762813	C₂	semidirect
4. #23762806	C₂	semidirect
5. #23762801	C₂	semidirect
6. #23762796	C₂	semidirect
7. #23762757	C₂	semidirect
8. #23762752	C₂	semidirect
9. #23762148	C₂	semidirect
10. #23762062	C₂	semidirect
11. C₇₉×#3169	C₂	semidirect
226. #3169	D₇₉	semidirect
237. C₇₉	#19128	semidirect

Maximal subgroups

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

subgroup	index
#23773454	2
C₈×#11929624	2
#23762813	2
#23762806	2
#23762801	2
#23762796	2
#23762757	2
#23762752	2
#23762148	2
#23762062	2
C₇₉×#3169	2
#19128	79