Subgroups — #34302201

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	#23773887	C₂	1	1	yes	maximal, characteristic
2	#23772253	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764308	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764299	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763929	C₂	1	2	yes	maximal, complemented
6	#23763927	C₂	1	2	yes	maximal, complemented
7	#23763884	C₂	1	2	yes	maximal, complemented
8	#23763880	C₂	1	2	yes	maximal, complemented
9	#23763525	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579186	C₂²	1	2	yes	—
13	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
14	#19099127	C₂²	1	2	yes	—
15	#19099037	C₂²	1	2	yes	—
16	#19098949	C₄	1	4	yes	complemented
17	#19098948	C₄	1	2	yes	complemented
18	#19098938	C₄	1	2	yes	complemented
19	#19098676	—	2	2	no	—
20	C₄×D₆₃₂	—	2	2	no	—
21	#19098601	C₂²	1	1	yes	characteristic
22	#19098580	C₂²	1	2	yes	—
23	#19098569	C₂²	1	2	yes	—
24	#19098569	C₂²	1	2	yes	—
25	C₂×#14579077	C₂²	1	2	yes	—
26	#19098537	C₂²	1	2	yes	—
27	#19098518	C₂²	1	1	yes	characteristic
28	#19098518	C₂²	1	1	yes	characteristic
29	#19098335	C₂²	1	2	yes	—
30	C₇₉⋊#338	C₂²	1	1	yes	characteristic
31	#19098320	C₂²	1	2	yes	—
32	#19098320	C₂²	1	1	yes	characteristic
33	#19098319	C₂²	1	1	yes	characteristic
34	#19098319	C₂²	1	1	yes	characteristic
35	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
36	#568×C₇₉	C₂²	1	2	yes	—
37	#444×C₇₉	—	2	2	no	—
38	#443×C₇₉	—	2	2	no	—
39	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
40	#421×C₇₉	C₂²	1	2	yes	—
41	#405×C₇₉	C₂²	1	1	yes	characteristic
42	C₂²×D₃₁₆	C₂³	1	2	yes	—
43	#14579186	—	4	2	no	—
44	#14579186	—	4	2	no	—
45	C₂×#11929611	C₂×C₄	1	4	yes	complemented
46	C₂×D₆₃₂	—	2	1	no	—
47	C₂×D₆₃₂	—	2	1	no	—
48	C₂×D₆₃₂	—	2	1	no	—
49	C₂×D₆₃₂	—	2	1	no	—
50	C₂×D₆₃₂	C₂×C₄	1	2	yes	—
51	C₂×D₆₃₂	C₂×C₄	1	2	yes	—
52	C₂×#11929609	C₂×C₄	1	4	yes	complemented
53	C₂×#11929608	C₂³	1	1	yes	characteristic
54	C₂×#11929608	C₂³	1	1	yes	characteristic
55	#14579157	C₂×C₄	1	4	yes	complemented
56	#14579150	C₂×C₄	1	4	yes	complemented
57	#14579135	—	4	2	no	—
58	#14579129	—	4	2	no	—
59	C₄×D₃₁₆	—	2	4	no	—
60	#14579123	—	4	2	no	—
61	#14579120	C₂³	1	1	yes	characteristic
62	#14579120	C₂³	1	2	yes	—
63	#14579120	C₂³	1	1	yes	characteristic
64	C₂²⋊C₄×D₇₉	—	4	2	no	—
65	#14579095	—	2	1	no	—
66	#14579093	—	2	1	no	—
67	#14579088	—	4	2	no	—
68	#14579083	—	2	4	no	—
69	#14579083	—	4	2	no	—
70	#14579077	—	4	2	no	—
71	#14579076	—	4	2	no	—
72	#14579071	—	2	1	no	—
73	#14579071	C₂×C₄	1	2	yes	complemented
74	C₈×Dic₇₉	—	2	1	no	—
75	C₈×Dic₇₉	C₂×C₄	1	2	yes	complemented
76	C₂×#41×C₇₉	C₂³	1	2	yes	—
77	#135×C₇₉	—	2	1	no	—
78	#135×C₇₉	—	2	1	no	—
79	#135×C₇₉	—	2	1	no	—
80	#135×C₇₉	—	2	1	no	—
81	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	complemented
83	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
84	#131×C₇₉	—	2	4	no	—
85	#131×C₇₉	—	4	2	no	—
86	C₂×M₁₆×C₇₉	—	4	2	no	—
87	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
88	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
90	#117×C₇₉	C₂³	1	1	yes	characteristic
91	#108×C₇₉	—	2	1	no	—
92	#108×C₇₉	—	2	1	no	—
93	#104×C₇₉	—	2	4	no	—
94	#97×C₇₉	D₄	1	2	yes	complemented
95	C₄×C₈×C₇₉	D₄	1	2	yes	complemented
96	C₂³×D₇₉	—	2	2	no	—
97	C₂×D₃₁₆	—	2	2	no	—
98	C₂×D₃₁₆	—	2	2	no	—
99	C₂×D₃₁₆	—	2	2	no	—
100	C₂×D₃₁₆	—	2	2	no	—
101	C₂×D₃₁₆	—	2	2	no	—
102	C₂×D₃₁₆	C₂²×C₄	1	4	yes	—
103	C₂×C₂²⋊D₇₉	—	4	4	no	—
104	C₂×C₄×D₇₉	—	4	4	no	—
105	#11929611	—	4	4	no	—
106	D₆₃₂	—	2	2	no	—
107	D₆₃₂	—	2	2	no	—
108	D₆₃₂	—	2	2	no	—
109	D₆₃₂	—	2	2	no	—
110	#11929609	—	4	4	no	—
111	#11929608	—	2	1	no	—
112	#11929608	—	2	1	no	—
113	#11929608	—	2	1	no	—
114	#11929608	—	2	1	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
117	C₄⋊Dic₇₉	—	2	2	no	—
118	C₄⋊Dic₇₉	—	2	1	no	—
119	C₄⋊Dic₇₉	—	2	1	no	—
120	C₂²⋊Dic₇₉	—	2	1	no	—
121	C₂²⋊Dic₇₉	—	2	1	no	—
122	C₂²⋊Dic₇₉	—	2	2	no	—
123	(C₂×D₇₉)⋊C₄	—	4	4	no	—
124	(C₂×D₇₉)⋊C₄	—	4	4	no	—
125	C₄×Dic₇₉	—	2	1	no	—
126	C₄×Dic₇₉	—	2	2	no	—
127	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
128	#41×C₇₉	—	2	2	no	—
129	#41×C₇₉	—	2	2	no	—
130	#41×C₇₉	—	2	2	no	—
131	#41×C₇₉	—	2	2	no	—
132	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₇₉	—	2	2	no	—
134	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₇₉	—	2	2	no	—
136	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₇₉	—	2	1	no	—
138	Q₁₆×C₇₉	—	2	1	no	—
139	SD₁₆×C₇₉	—	2	2	no	—
140	SD₁₆×C₇₉	—	2	2	no	—
141	D₈×C₇₉	—	2	1	no	—
142	D₈×C₇₉	—	2	1	no	—
143	M₁₆×C₇₉	—	2	2	no	—
144	M₁₆×C₇₉	—	2	1	no	—
145	M₁₆×C₇₉	—	2	1	no	—
146	M₁₆×C₇₉	—	2	2	no	—
147	M₁₆×C₇₉	—	4	4	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	4	4	no	—
150	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
156	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
157	C₄⋊C₄×C₇₉	—	2	1	no	—
158	C₂²⋊C₄×C₇₉	—	2	1	no	—
159	C₄²×C₇₉	C₂×D₄	1	2	yes	—
160	C₂³×C₇₉	—	2	2	no	—
161	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×D₇₉	—	2	4	no	—
163	C₂²×D₇₉	—	4	2	no	—
164	C₂²×D₇₉	—	4	2	no	—
165	C₂²×D₇₉	—	16	2	no	—
166	Q₈×C₇₉	—	2	2	no	—
167	Q₈×C₇₉	—	2	2	no	—
168	D₄×C₇₉	—	2	2	no	—
169	D₄×C₇₉	—	2	2	no	—
170	D₄×C₇₉	—	4	2	no	—
171	D₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	—	4	2	no	—
176	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²⋊D₇₉	—	16	4	no	—
183	C₂×Dic₇₉	—	2	2	no	—
184	C₂×Dic₇₉	—	4	2	no	—
185	C₂×Dic₇₉	—	4	1	no	—
186	D₃₁₆	—	2	4	no	—
187	D₃₁₆	—	2	4	no	—
188	D₃₁₆	—	4	2	no	—
189	D₃₁₆	—	4	2	no	—
190	C₄×D₇₉	—	16	4	no	—
191	C₈×C₇₉	—	2	2	no	—
192	C₈×C₇₉	—	4	2	no	—
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	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
197	C₇₉⋊C₈	—	2	2	no	—
198	C₇₉⋊C₈	—	4	1	no	—
199	C₂²×C₇₉	—	4	1	no	—
200	C₂²×C₇₉	—	4	2	no	—
201	C₂²×C₇₉	—	8	2	no	—
202	C₂²×C₇₉	#518	1	1	yes	characteristic
203	C₂²×C₇₉	#535	1	1	yes	characteristic
204	C₂²×C₇₉	#540	1	1	yes	characteristic
205	C₂×D₇₉	—	4	4	no	—
206	C₂×D₇₉	—	8	4	no	—
207	C₂×D₇₉	—	8	4	no	—
208	C₂×D₇₉	—	16	2	no	—
209	C₄×C₇₉	—	4	2	no	—
210	C₄×C₇₉	—	4	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	—	8	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	2	no	—
223	C₂×C₇₉	#2328	1	1	yes	characteristic
224	D₇₉	—	8	4	no	—
225	#3155	—	79	1	no	—
226	#2957	D₇₉	1	1	yes	characteristic, complemented
227	#2948	—	79	1	no	—
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	C₂×D₇₉	1	1	yes	characteristic
239	C₂²×D₈	—	79	1	no	—
240	#568	C₂×D₇₉	1	2	yes	—
241	#535	—	79	2	no	—
242	#518	—	79	2	no	—
243	#496	—	79	4	no	—
244	#495	—	79	2	no	—
245	#493	—	79	2	no	—
246	#444	—	2	2	no	—
247	#443	—	2	2	no	—
248	#442	—	158	2	no	—
249	C₄×D₈	—	158	2	no	—
250	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
251	#427	—	79	1	no	—
252	#421	—	79	2	no	—
253	#421	C₂×D₇₉	1	2	yes	—
254	#418	—	79	2	no	—
255	#418	—	79	2	no	—
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	2	no	—
264	H(3,ℤ/4)	—	79	1	no	—
265	H(3,ℤ/4)	—	79	1	no	—
266	H(3,ℤ/4)	—	79	1	no	—
267	C₂×#41	C₂²×D₇₉	1	2	yes	—
268	C₂²×D₄	—	79	2	no	—
269	AGL(1,ℤ/8)	—	316	2	no	—
270	AGL(1,ℤ/8)	—	316	2	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	#135	—	2	1	no	—
275	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	—	79	4	no	—
277	C₂×SD₁₆	C₄×D₇₉	1	2	yes	complemented
278	C₂×D₈	—	79	4	no	—
279	C₂×D₈	—	79	2	no	—
280	C₂×D₈	—	79	2	no	—
281	C₂×D₈	—	158	1	no	—
282	C₂×D₈	—	158	1	no	—
283	C₂×D₈	—	158	1	no	—
284	C₂×D₈	—	158	1	no	—
285	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic, complemented
286	#131	—	2	4	no	—
287	#131	—	4	2	no	—
288	C₂×M₁₆	—	4	2	no	—
289	C₂×M₁₆	—	79	1	no	—
290	C₂×M₁₆	—	79	1	no	—
291	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
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	—	316	2	no	—
299	C₄×D₄	—	158	4	no	—
300	#117	—	79	1	no	—
301	#117	—	79	2	no	—
302	#117	—	79	1	no	—
303	#117	C₂²×D₇₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	316	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	158	1	no	—
308	#106	—	158	1	no	—
309	#104	—	2	4	no	—
310	#104	—	316	2	no	—
311	#102	—	316	2	no	—
312	#102	—	158	4	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	—	158	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	316	4	no	—
329	C₂×D₄	—	79	4	no	—
330	C₂×D₄	—	158	2	no	—
331	C₂×D₄	—	158	2	no	—
332	C₂×D₄	—	158	2	no	—
333	C₂×D₄	—	158	2	no	—
334	C₂×D₄	—	158	2	no	—
335	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	316	4	no	—
338	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	316	4	no	—
344	D₈	—	2	1	no	—
345	D₈	—	2	1	no	—
346	D₈	—	316	4	no	—
347	D₈	—	158	2	no	—
348	D₈	—	158	2	no	—
349	D₈	—	158	2	no	—
350	D₈	—	158	2	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	4	4	no	—
356	M₁₆	—	158	1	no	—
357	M₁₆	—	158	1	no	—
358	M₁₆	—	158	1	no	—
359	M₁₆	—	158	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	—	79	2	no	—
363	C₂×C₈	—	158	1	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	—	158	1	no	—
373	C₄⋊C₄	—	158	2	no	—
374	C₄⋊C₄	—	158	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	316	4	no	—
377	C₂²⋊C₄	—	316	4	no	—
378	C₂²⋊C₄	—	158	1	no	—
379	C₂²⋊C₄	—	158	2	no	—
380	C₂²⋊C₄	—	158	1	no	—
381	C₄²	—	79	2	no	—
382	C₄²	—	158	1	no	—
383	C₄²	—	158	2	no	—
384	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
385	C₂³	—	2	2	no	—
386	C₂³	—	316	2	no	—
387	C₂³	—	316	2	no	—
388	C₂³	—	158	4	no	—
389	C₂³	—	1264	2	no	—
390	C₂³	#14579207	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	316	2	no	—
398	D₄	—	316	2	no	—
399	D₄	—	158	4	no	—
400	D₄	—	158	4	no	—
401	D₄	—	1264	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	316	1	no	—
407	C₂×C₄	—	316	2	no	—
408	C₂×C₄	—	158	2	no	—
409	C₂×C₄	—	1264	4	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	#14579206	1	1	yes	characteristic
415	C₂×C₄	#14579207	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	316	1	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	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	316	4	no	—
428	C₂²	—	632	4	no	—
429	C₂²	—	632	4	no	—
430	C₂²	—	1264	2	no	—
431	C₂²	#19099035	1	1	yes	characteristic
432	C₂²	#19099127	1	1	yes	characteristic
433	C₂²	#19099164	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	316	2	no	—
437	C₄	—	632	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	#19099130	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	2	no	—
447	C₂	—	632	4	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×#2957	C₂
socle	C₂×C₇₉	#2328
prime radical	#23773887	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2957	D₇₉
hypocenter	C₇₉	#22286
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #23772253	C₂	semidirect
3. #23764308	C₂	semidirect
4. #23764299	C₂	semidirect
5. #23763929	C₂	semidirect
6. #23763927	C₂	semidirect
7. #23763884	C₂	semidirect
8. #23763880	C₂	semidirect
9. #23763525	C₂	semidirect
10. #23763155	C₂	semidirect
11. C₇₉×#2957	C₂	semidirect
16. #19098949	C₄	semidirect
17. #19098948	C₄	semidirect
18. #19098938	C₄	semidirect
45. C₂×#11929611	C₂×C₄	semidirect
52. C₂×#11929609	C₂×C₄	semidirect
55. #14579157	C₂×C₄	semidirect
56. #14579150	C₂×C₄	semidirect
73. #14579071	C₂×C₄	semidirect
75. C₈×Dic₇₉	C₂×C₄	semidirect
81. C₂×Q₁₆×C₇₉	C₂×C₄	semidirect
82. C₂×SD₁₆×C₇₉	C₂×C₄	semidirect
83. C₂×D₈×C₇₉	C₂×C₄	semidirect
94. #97×C₇₉	D₄	semidirect
95. C₄×C₈×C₇₉	D₄	semidirect
226. #2957	D₇₉	semidirect
236. C₇₉	#22286	semidirect
275. C₂×Q₁₆	C₄×D₇₉	semidirect
277. C₂×SD₁₆	C₄×D₇₉	semidirect
285. C₂×D₈	C₄×D₇₉	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
#23773887	2
#23772253	2
#23764308	2
#23764299	2
#23763929	2
#23763927	2
#23763884	2
#23763880	2
#23763525	2
#23763155	2
C₇₉×#2957	2
#22286	79