Subgroups — #34302194

Order 20224.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773881	C₂	1	1	yes	maximal, characteristic
2	#23772318	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764311	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764296	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763932	C₂	1	2	yes	maximal, complemented
6	#23763924	C₂	1	2	yes	maximal, complemented
7	#23763887	C₂	1	2	yes	maximal, complemented
8	#23763877	C₂	1	2	yes	maximal, complemented
9	#23763523	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579187	C₂²	1	2	yes	—
13	C₂×#14579183	C₂²	1	1	yes	characteristic
14	#19099329	C₂²	1	2	yes	—
15	#19099130	C₂²	1	2	yes	—
16	#19098951	C₄	1	4	yes	complemented
17	#19098946	C₄	1	2	yes	complemented
18	#19098938	C₄	1	2	yes	complemented
19	#19098686	—	2	2	no	—
20	#19098681	—	2	2	no	—
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	#19098581	C₂²	1	2	yes	—
23	#19098581	C₂²	1	2	yes	—
24	#19098568	C₂²	1	2	yes	—
25	C₂×#14579078	C₂²	1	2	yes	—
26	#19098536	C₂²	1	2	yes	—
27	#19098518	C₂²	1	1	yes	characteristic
28	#19098518	C₂²	1	1	yes	characteristic
29	#19098333	C₂²	1	2	yes	—
30	C₇₉⋊#338	C₂²	1	1	yes	characteristic
31	#19098320	C₂²	1	1	yes	characteristic
32	#19098319	C₂²	1	2	yes	—
33	#19098319	C₂²	1	1	yes	characteristic
34	#19098319	C₂²	1	1	yes	characteristic
35	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
36	#518×C₇₉	C₂²	1	2	yes	—
37	#442×C₇₉	—	2	2	no	—
38	C₄×D₈×C₇₉	—	2	2	no	—
39	#427×C₇₉	C₂²	1	1	yes	characteristic
40	#418×C₇₉	C₂²	1	2	yes	—
41	#405×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#11929624	C₂³	1	2	yes	—
43	#14579187	—	4	2	no	—
44	#14579187	—	4	2	no	—
45	#14579183	—	2	1	no	—
46	#14579183	—	2	1	no	—
47	#14579183	—	2	1	no	—
48	#14579183	—	2	1	no	—
49	C₂×Dic₃₁₆	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#11929613	C₂×C₄	1	2	yes	complemented
51	C₂×#11929612	C₂×C₄	1	4	yes	complemented
52	C₂×D₆₃₂	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂×#11929609	C₂×C₄	1	4	yes	complemented
54	#14579169	—	4	2	no	—
55	#14579167	—	2	4	no	—
56	C₂×#11929608	C₂³	1	1	yes	characteristic
57	C₂×#11929608	C₂³	1	2	yes	—
58	C₂×#11929608	C₂³	1	1	yes	characteristic
59	M₁₆×D₇₉	—	4	2	no	—
60	#14579157	C₂×C₄	1	4	yes	complemented
61	#14579148	C₂×C₄	1	4	yes	complemented
62	#14579132	—	4	2	no	—
63	#14579130	—	4	2	no	—
64	#14579120	C₂³	1	1	yes	characteristic
65	#14579120	C₂³	1	1	yes	characteristic
66	#14579097	—	2	1	no	—
67	#14579097	—	2	1	no	—
68	#14579089	—	2	4	no	—
69	#14579089	—	4	2	no	—
70	#14579082	—	4	2	no	—
71	#14579078	—	4	2	no	—
72	#14579075	—	4	2	no	—
73	#14579071	—	2	1	no	—
74	#14579071	C₂×C₄	1	2	yes	complemented
75	C₈×Dic₇₉	—	2	1	no	—
76	C₈×Dic₇₉	C₂×C₄	1	2	yes	complemented
77	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
78	C₂×D₈×C₇₉	—	2	1	no	—
79	C₂×D₈×C₇₉	—	2	1	no	—
80	C₂×D₈×C₇₉	—	2	1	no	—
81	C₂×D₈×C₇₉	—	2	1	no	—
82	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
83	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₇₉	—	2	4	no	—
87	C₄×D₄×C₇₉	—	4	2	no	—
88	#117×C₇₉	C₂³	1	2	yes	—
89	#117×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₇₉	—	4	2	no	—
91	#107×C₇₉	—	2	1	no	—
92	#106×C₇₉	—	2	1	no	—
93	#102×C₇₉	—	2	4	no	—
94	#97×C₇₉	D₄	1	2	yes	complemented
95	C₄×C₈×C₇₉	D₄	1	2	yes	complemented
96	#11929624	—	2	2	no	—
97	#11929624	—	2	2	no	—
98	#11929624	—	2	2	no	—
99	#11929624	—	2	2	no	—
100	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
101	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₇₉	—	2	2	no	—
103	C₂×C₂²⋊D₇₉	—	4	4	no	—
104	C₂×C₄×D₇₉	—	2	2	no	—
105	Dic₃₁₆	—	2	1	no	—
106	Dic₃₁₆	—	2	1	no	—
107	#11929613	—	2	2	no	—
108	#11929613	—	2	2	no	—
109	#11929612	—	4	4	no	—
110	D₆₃₂	—	2	1	no	—
111	D₆₃₂	—	2	1	no	—
112	#11929609	—	4	4	no	—
113	#11929608	—	2	2	no	—
114	#11929608	—	2	1	no	—
115	#11929608	—	2	1	no	—
116	#11929608	—	2	1	no	—
117	#11929608	—	2	2	no	—
118	#11929608	—	2	1	no	—
119	#11929607	—	4	4	no	—
120	C₂×C₇₉⋊C₈	—	2	1	no	—
121	C₂×C₇₉⋊C₈	—	2	2	no	—
122	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
123	C₈×D₇₉	—	4	4	no	—
124	C₄⋊Dic₇₉	—	2	1	no	—
125	C₄⋊Dic₇₉	—	2	1	no	—
126	C₂²⋊Dic₇₉	—	2	1	no	—
127	C₂²⋊Dic₇₉	—	2	1	no	—
128	C₂²⋊Dic₇₉	—	4	4	no	—
129	C₄×Dic₇₉	—	2	1	no	—
130	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
131	C₂⁴×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	—	2	2	no	—
135	C₂×D₄×C₇₉	—	2	2	no	—
136	C₂×D₄×C₇₉	—	2	2	no	—
137	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₇₉	—	4	4	no	—
139	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
140	D₈×C₇₉	—	2	2	no	—
141	D₈×C₇₉	—	2	2	no	—
142	D₈×C₇₉	—	2	2	no	—
143	D₈×C₇₉	—	2	2	no	—
144	M₁₆×C₇₉	—	2	1	no	—
145	M₁₆×C₇₉	—	2	1	no	—
146	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
152	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₂²⋊C₄×C₇₉	—	2	1	no	—
156	C₂²⋊C₄×C₇₉	—	2	2	no	—
157	C₂²⋊C₄×C₇₉	—	4	4	no	—
158	C₄²×C₇₉	—	2	2	no	—
159	C₄²×C₇₉	C₂×D₄	1	2	yes	—
160	C₂³×C₇₉	—	2	4	no	—
161	C₂³×C₇₉	—	4	2	no	—
162	C₂³×C₇₉	—	4	2	no	—
163	C₂³×C₇₉	—	16	2	no	—
164	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂²×D₇₉	—	2	2	no	—
166	D₄×C₇₉	—	2	4	no	—
167	D₄×C₇₉	—	2	4	no	—
168	D₄×C₇₉	—	4	2	no	—
169	D₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	16	4	no	—
173	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂²⋊D₇₉	—	4	2	no	—
180	C₂²⋊D₇₉	—	4	2	no	—
181	C₂²⋊D₇₉	—	16	4	no	—
182	C₂×Dic₇₉	—	2	2	no	—
183	C₂×Dic₇₉	—	2	2	no	—
184	C₂×Dic₇₉	—	4	1	no	—
185	D₃₁₆	—	2	2	no	—
186	D₃₁₆	—	2	2	no	—
187	C₄×D₇₉	—	4	2	no	—
188	C₄×D₇₉	—	4	2	no	—
189	Dic₁₅₈	—	2	2	no	—
190	Dic₁₅₈	—	2	2	no	—
191	C₈×C₇₉	—	2	2	no	—
192	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
193	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
194	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
195	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
196	C₇₉⋊C₈	—	2	2	no	—
197	C₇₉⋊C₈	—	4	2	no	—
198	C₇₉⋊C₈	—	4	1	no	—
199	C₂²×C₇₉	—	4	1	no	—
200	C₂²×C₇₉	—	4	4	no	—
201	C₂²×C₇₉	—	8	4	no	—
202	C₂²×C₇₉	—	8	4	no	—
203	C₂²×C₇₉	—	16	2	no	—
204	C₂²×C₇₉	#518	1	1	yes	characteristic
205	C₂²×C₇₉	#535	1	1	yes	characteristic
206	C₂²×C₇₉	#540	1	1	yes	characteristic
207	C₂×D₇₉	—	4	2	no	—
208	C₂×D₇₉	—	8	2	no	—
209	C₄×C₇₉	—	4	2	no	—
210	C₄×C₇₉	—	8	2	no	—
211	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₇₉	#518	1	1	yes	characteristic
213	C₄×C₇₉	#535	1	1	yes	characteristic
214	C₄×C₇₉	#540	1	1	yes	characteristic
215	Dic₇₉	—	4	2	no	—
216	Dic₇₉	—	4	2	no	—
217	Dic₇₉	—	8	1	no	—
218	#22286	—	79	1	no	maximal, Sylow
219	C₂×C₇₉	—	2	1	no	—
220	C₂×C₇₉	—	2	1	no	—
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	8	4	no	—
223	C₂×C₇₉	#2328	1	1	yes	characteristic
224	D₇₉	—	8	2	no	—
225	#3155	—	79	1	no	—
226	#2957	—	79	1	no	—
227	#2948	D₇₉	1	1	yes	characteristic, complemented
228	#1978	—	79	1	no	—
229	#1976	—	79	1	no	—
230	#1911	—	79	2	no	—
231	#1910	—	79	2	no	—
232	#1904	—	79	2	no	—
233	#1903	—	79	2	no	—
234	#1833	—	79	1	no	—
235	#1747	—	79	1	no	—
236	C₇₉	#22286	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	—	79	2	no	—
238	C₂×#135	—	79	1	no	—
239	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
240	#568	—	79	2	no	—
241	#535	—	79	2	no	—
242	#518	C₂×D₇₉	1	2	yes	—
243	#496	—	79	4	no	—
244	#495	—	79	2	no	—
245	#493	—	79	2	no	—
246	#444	—	158	2	no	—
247	#443	—	158	2	no	—
248	#442	—	2	2	no	—
249	C₄×D₈	—	2	2	no	—
250	C₂×#108	—	79	1	no	—
251	#427	C₂×D₇₉	1	1	yes	characteristic
252	#421	—	79	2	no	—
253	#421	—	79	2	no	—
254	#418	—	79	2	no	—
255	#418	C₂×D₇₉	1	2	yes	—
256	C₂×#100	—	79	2	no	—
257	#410	—	79	2	no	—
258	#405	—	79	1	no	—
259	#405	—	79	1	no	—
260	#405	C₂×D₇₉	1	1	yes	characteristic
261	#344	—	79	2	no	—
262	#338	—	79	1	no	—
263	H(3,ℤ/4)	—	79	1	no	—
264	H(3,ℤ/4)	—	79	2	no	—
265	H(3,ℤ/4)	—	79	1	no	—
266	H(3,ℤ/4)	—	79	1	no	—
267	C₂×#41	—	79	2	no	—
268	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
269	AGL(1,ℤ/8)	—	316	2	no	—
270	AGL(1,ℤ/8)	—	316	2	no	—
271	#135	—	158	1	no	—
272	#135	—	158	1	no	—
273	#135	—	158	1	no	—
274	#135	—	158	1	no	—
275	C₂×Q₁₆	—	79	1	no	—
276	C₂×SD₁₆	—	79	4	no	—
277	C₂×SD₁₆	—	79	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	79	4	no	—
283	C₂×D₈	—	79	1	no	—
284	C₂×D₈	C₄×D₇₉	1	2	yes	—
285	C₂×D₈	C₄×D₇₉	1	2	yes	—
286	#131	—	316	2	no	—
287	#131	—	158	4	no	—
288	C₂×M₁₆	—	316	2	no	—
289	C₂×M₁₆	—	79	1	no	—
290	C₂×M₁₆	—	79	2	no	—
291	C₂×M₁₆	—	79	1	no	—
292	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
294	#127	—	79	4	no	—
295	#124	—	79	4	no	—
296	#121	—	316	2	no	—
297	#120	—	316	2	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	4	2	no	—
300	#117	—	79	1	no	—
301	#117	—	79	1	no	—
302	#117	C₂²×D₇₉	1	2	yes	—
303	#117	C₂²×D₇₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	4	2	no	—
305	#108	—	158	1	no	—
306	#108	—	158	1	no	—
307	#107	—	2	1	no	—
308	#106	—	2	1	no	—
309	#104	—	316	2	no	—
310	#104	—	158	4	no	—
311	#102	—	2	4	no	—
312	#102	—	316	2	no	—
313	#100	—	316	2	no	—
314	#99	—	316	2	no	—
315	#97	—	79	2	no	—
316	#97	—	158	1	no	—
317	#97	C₂²⋊D₇₉	1	2	yes	complemented
318	C₄×C₈	—	79	2	no	—
319	C₄×C₈	—	158	1	no	—
320	C₄×C₈	C₂²⋊D₇₉	1	2	yes	complemented
321	C₂⁴	—	2	2	no	—
322	#41	—	158	2	no	—
323	#41	—	158	2	no	—
324	#41	—	158	2	no	—
325	#41	—	158	2	no	—
326	C₂×Q₈	—	79	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	316	4	no	—
333	C₂×D₄	—	79	2	no	—
334	C₂×D₄	—	158	2	no	—
335	C₂×D₄	C₂×C₄×D₇₉	1	4	yes	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	158	2	no	—
338	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
339	Q₁₆	—	158	1	no	—
340	Q₁₆	—	158	1	no	—
341	SD₁₆	—	316	4	no	—
342	SD₁₆	—	158	2	no	—
343	SD₁₆	—	158	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	316	4	no	—
349	D₈	—	158	1	no	—
350	D₈	—	158	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	316	4	no	—
354	M₁₆	—	158	1	no	—
355	M₁₆	—	158	1	no	—
356	M₁₆	—	158	2	no	—
357	M₁₆	—	158	2	no	—
358	M₁₆	—	158	1	no	—
359	M₁₆	—	158	1	no	—
360	C₂×C₈	—	316	4	no	—
361	C₂×C₈	—	79	2	no	—
362	C₂×C₈	—	158	1	no	—
363	C₂×C₈	—	158	2	no	—
364	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
366	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
367	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
368	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
369	C₂×C₈	#11929624	1	1	yes	characteristic
370	C₂×C₈	#11929624	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	158	1	no	—
374	C₄⋊C₄	—	158	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	316	4	no	—
379	C₂²⋊C₄	—	158	1	no	—
380	C₂²⋊C₄	—	158	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	79	2	no	—
383	C₄²	—	158	1	no	—
384	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	—	158	2	no	—
390	C₂³	#14579206	1	1	yes	characteristic
391	Q₈	—	158	2	no	—
392	Q₈	—	158	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	316	2	no	—
398	D₄	—	316	2	no	—
399	D₄	—	158	2	no	—
400	D₄	—	158	2	no	—
401	D₄	—	1264	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	16	4	no	—
405	C₂×C₄	—	316	2	no	—
406	C₂×C₄	—	316	2	no	—
407	C₂×C₄	—	316	1	no	—
408	C₂×C₄	—	158	2	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
413	C₂×C₄	#14579206	1	1	yes	characteristic
414	C₂×C₄	#14579207	1	1	yes	characteristic
415	C₂×C₄	#14579207	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	316	1	no	—
418	C₈	—	316	2	no	—
419	C₈	—	158	2	no	—
420	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
421	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
422	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
423	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	16	2	no	—
429	C₂²	—	316	2	no	—
430	C₂²	—	632	2	no	—
431	C₂²	#19099035	1	1	yes	characteristic
432	C₂²	#19099130	1	1	yes	characteristic
433	C₂²	#19099164	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	316	2	no	—
437	C₄	—	316	2	no	—
438	C₄	—	632	1	no	—
439	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
440	C₄	#19099035	1	1	yes	characteristic
441	C₄	#19099127	1	1	yes	characteristic
442	C₄	#19099164	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	632	2	no	—
448	C₂	#23766122	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23766122
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2948	C₂
socle	C₂×C₇₉	#2328
prime radical	#23773881	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2948	D₇₉
hypocenter	C₇₉	#22286
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2948

Complements

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

N	H ≅ G/N	type
2. #23772318	C₂	semidirect
3. #23764311	C₂	semidirect
4. #23764296	C₂	semidirect
5. #23763932	C₂	semidirect
6. #23763924	C₂	semidirect
7. #23763887	C₂	semidirect
8. #23763877	C₂	semidirect
9. #23763523	C₂	semidirect
10. #23763155	C₂	semidirect
11. C₇₉×#2948	C₂	semidirect
16. #19098951	C₄	semidirect
17. #19098946	C₄	semidirect
18. #19098938	C₄	semidirect
49. C₂×Dic₃₁₆	C₂×C₄	semidirect
50. C₂×#11929613	C₂×C₄	semidirect
51. C₂×#11929612	C₂×C₄	semidirect
52. C₂×D₆₃₂	C₂×C₄	semidirect
53. C₂×#11929609	C₂×C₄	semidirect
60. #14579157	C₂×C₄	semidirect
61. #14579148	C₂×C₄	semidirect
74. #14579071	C₂×C₄	semidirect
76. C₈×Dic₇₉	C₂×C₄	semidirect
94. #97×C₇₉	D₄	semidirect
95. C₄×C₈×C₇₉	D₄	semidirect
227. #2948	D₇₉	semidirect
236. C₇₉	#22286	semidirect
317. #97	C₂²⋊D₇₉	semidirect
320. C₄×C₈	C₂²⋊D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23773881	2
#23772318	2
#23764311	2
#23764296	2
#23763932	2
#23763924	2
#23763887	2
#23763877	2
#23763523	2
#23763155	2
C₇₉×#2948	2
#22286	79