Subgroups — #34306751

Order 20224.

846 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098679	C₂	1	1	yes	maximal, characteristic
2	#23772277	C₂	1	1	yes	maximal, characteristic
3	#23772274	C₂	1	1	yes	maximal, characteristic
4	#23771994	C₂	1	2	yes	maximal, complemented
5	#23764186	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763636	C₂	1	2	yes	maximal, complemented
7	#23763630	C₂	1	2	yes	maximal, complemented
8	#23763563	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763458	C₂	1	2	yes	maximal, complemented
10	#23763280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579183	C₂²	1	1	yes	characteristic
13	C₂×#14579169	C₂²	1	2	yes	—
14	#19099044	C₂²	1	2	yes	—
15	#19099043	C₂²	1	2	yes	—
16	#19098679	C₄	1	8	yes	complemented
17	#19098665	—	2	2	no	—
18	#19098662	—	2	2	no	—
19	C₄×Dic₃₁₆	—	2	1	no	—
20	#19098657	—	2	1	no	—
21	C₄×D₆₃₂	—	2	1	no	—
22	#19098645	—	2	1	no	—
23	C₂×#14579096	C₂²	1	1	yes	characteristic
24	#19098605	C₂²	1	2	yes	—
25	#19098604	—	2	2	no	—
26	#19098602	—	2	2	no	—
27	#19098600	—	2	2	no	—
28	#19098599	C₂²	1	1	yes	characteristic
29	C₂×#14579095	C₂²	1	1	yes	characteristic
30	C₂×#14579092	C₂²	1	2	yes	—
31	#106×D₇₉	—	2	2	no	—
32	C₂×#14579087	C₂²	1	2	yes	—
33	#19098565	C₂²	1	2	yes	—
34	#19098562	C₂²	1	2	yes	—
35	#19098518	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
37	#19098428	C₂²	1	2	yes	—
38	#19098331	C₂²	1	2	yes	—
39	#19098324	C₂²	1	1	yes	characteristic
40	#19098322	C₂²	1	1	yes	characteristic
41	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
42	#428×C₇₉	C₂²	1	2	yes	—
43	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
44	#405×C₇₉	C₂²	1	1	yes	characteristic
45	#343×C₇₉	C₂²	1	2	yes	—
46	C₂×#11929624	C₂³	1	2	yes	—
47	#14579183	C₂×C₄	1	4	yes	—
48	#14579183	Q₈	1	4	yes	—
49	C₂×Dic₃₁₆	D₄	1	1	yes	characteristic
50	C₂×#11929613	D₄	1	2	yes	—
51	C₂×D₆₃₂	D₄	1	1	yes	characteristic
52	#14579169	—	2	4	no	—
53	#14579169	C₂×C₄	1	8	yes	complemented
54	C₂×#11929608	C₂³	1	1	yes	characteristic
55	C₂×#11929607	—	2	2	no	—
56	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₇₉	—	2	2	no	—
58	C₄×Dic₁₅₈	—	2	2	no	—
59	#14579126	—	2	2	no	—
60	C₄×D₃₁₆	—	2	2	no	—
61	#14579123	—	2	2	no	—
62	C₄×C₂²⋊D₇₉	—	4	2	no	—
63	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
64	#14579120	C₂³	1	1	yes	characteristic
65	#14579119	—	2	2	no	—
66	#14579119	—	2	2	no	—
67	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
68	C₄⋊C₄×D₇₉	—	2	2	no	—
69	C₄⋊C₄×D₇₉	—	2	2	no	—
70	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
71	#14579096	—	2	2	no	—
72	#14579095	—	2	1	no	—
73	#14579095	—	2	1	no	—
74	#14579095	—	2	2	no	—
75	#14579094	D₄	1	1	yes	characteristic
76	#14579094	D₄	1	1	yes	characteristic
77	#14579093	—	2	2	no	—
78	#14579092	—	2	2	no	—
79	#14579092	—	2	2	no	—
80	#14579092	D₄	1	1	yes	characteristic
81	#14579092	D₄	1	1	yes	characteristic
82	#14579087	C₂×C₄	1	8	yes	complemented
83	#14579086	—	2	2	no	—
84	#14579084	—	2	2	no	—
85	#14579083	—	2	2	no	—
86	#14579081	—	2	2	no	—
87	#14579071	—	2	1	no	—
88	C₈×Dic₇₉	—	2	1	no	—
89	C₈×Dic₇₉	C₂×C₄	1	4	yes	complemented
90	C₇₉⋊#95	—	4	2	no	—
91	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
93	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
94	#117×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
96	#108×C₇₉	C₂×C₄	1	4	yes	complemented
97	#107×C₇₉	—	2	1	no	—
98	#107×C₇₉	—	2	1	no	—
99	#107×C₇₉	—	2	2	no	—
100	#106×C₇₉	—	2	2	no	—
101	#97×C₇₉	—	2	1	no	—
102	C₄×C₈×C₇₉	—	2	1	no	—
103	#11929624	—	2	2	no	—
104	#11929624	—	2	2	no	—
105	#11929624	C₂²×C₄	1	4	yes	—
106	#11929624	C₂×Q₈	1	4	yes	—
107	C₂×Dic₁₅₈	C₂×D₄	1	2	yes	—
108	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
109	C₂×C₂²⋊D₇₉	—	2	2	no	—
110	C₂²×Dic₇₉	—	2	1	no	—
111	C₂²×Dic₇₉	—	2	2	no	—
112	C₂×C₄×D₇₉	—	2	2	no	—
113	C₂×C₄×D₇₉	—	4	2	no	—
114	C₂×C₄×D₇₉	—	4	2	no	—
115	Dic₃₁₆	C₄⋊C₄	1	4	yes	—
116	#11929613	C₄⋊C₄	1	8	yes	—
117	D₆₃₂	C₄⋊C₄	1	4	yes	—
118	#11929608	—	2	1	no	—
119	#11929608	—	2	1	no	—
120	#11929607	—	2	8	no	—
121	C₂×C₇₉⋊C₈	—	2	1	no	—
122	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₇₉⋊C₈	#41	1	2	yes	—
126	C₈×D₇₉	—	2	8	no	—
127	C₄⋊Dic₇₉	—	2	2	no	—
128	C₄⋊Dic₇₉	—	2	2	no	—
129	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
130	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
131	Dic₇₉⋊C₄	—	4	2	no	—
132	Dic₇₉⋊C₄	—	4	2	no	—
133	C₂²⋊Dic₇₉	—	2	1	no	—
134	(C₂×D₇₉)⋊C₄	—	4	2	no	—
135	(C₂×D₇₉)⋊C₄	—	4	2	no	—
136	C₄×Dic₇₉	—	2	1	no	—
137	C₄×Dic₇₉	—	2	1	no	—
138	C₄×Dic₇₉	—	4	2	no	—
139	C₄×Dic₇₉	—	4	2	no	—
140	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
143	M₁₆×C₇₉	—	2	2	no	—
144	M₁₆×C₇₉	—	2	1	no	—
145	M₁₆×C₇₉	—	2	1	no	—
146	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	1	no	—
149	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂²⋊C₄×C₇₉	—	2	1	no	—
158	C₄²×C₇₉	—	2	1	no	—
159	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂²×D₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	8	2	no	—
165	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂²⋊D₇₉	—	2	4	no	—
172	C₂²⋊D₇₉	—	2	4	no	—
173	C₂×Dic₇₉	—	2	2	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	1	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	C₂×Dic₇₉	—	4	1	no	—
178	C₂×Dic₇₉	—	4	1	no	—
179	C₂×Dic₇₉	—	4	2	no	—
180	C₂×Dic₇₉	—	8	2	no	—
181	D₃₁₆	—	2	2	no	—
182	D₃₁₆	C₂×C₄⋊C₄	1	4	yes	—
183	C₄×D₇₉	—	2	4	no	—
184	C₄×D₇₉	—	2	4	no	—
185	C₄×D₇₉	—	16	2	no	—
186	C₄×D₇₉	—	16	2	no	—
187	Dic₁₅₈	—	2	2	no	—
188	Dic₁₅₈	C₂×C₄⋊C₄	1	4	yes	—
189	C₈×C₇₉	—	2	4	no	—
190	C₈×C₇₉	—	4	1	no	—
191	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
192	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
193	C₇₉⋊C₈	—	4	1	no	—
194	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
195	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
196	C₂²×C₇₉	—	2	1	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	#520	1	1	yes	characteristic
199	C₂²×C₇₉	D₄²	1	1	yes	characteristic
200	C₂²×C₇₉	#554	1	1	yes	characteristic
201	C₂×D₇₉	—	2	4	no	—
202	C₂×D₇₉	—	4	2	no	—
203	C₂×D₇₉	—	4	2	no	—
204	C₄×C₇₉	—	4	1	no	—
205	C₄×C₇₉	—	4	1	no	—
206	C₄×C₇₉	—	8	2	no	—
207	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
208	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₇₉	#547	1	1	yes	characteristic
210	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
211	Dic₇₉	—	2	4	no	—
212	Dic₇₉	—	4	2	no	—
213	Dic₇₉	—	4	1	no	—
214	Dic₇₉	—	4	1	no	—
215	Dic₇₉	—	8	2	no	—
216	#22690	—	79	1	no	maximal, Sylow
217	C₂×C₇₉	—	2	1	no	—
218	C₂×C₇₉	—	2	1	no	—
219	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₇₉	#3290	1	1	yes	characteristic
221	C₂×C₇₉	#3290	1	1	yes	characteristic
222	D₇₉	—	4	4	no	—
223	C₂×#443	—	79	1	no	—
224	#2951	—	79	1	no	—
225	#2951	—	79	1	no	—
226	#2912	—	79	2	no	—
227	#1952	—	79	1	no	—
228	#1952	D₇₉	1	1	yes	characteristic, complemented
229	#1860	—	79	2	no	—
230	#1860	—	79	2	no	—
231	#1846	—	79	1	no	—
232	#1815	—	79	2	no	—
233	#1772	—	79	1	no	—
234	C₇₉	#22690	1	1	yes	characteristic, complemented, Sylow
235	C₂×#135	—	79	1	no	—
236	C₂×#131	—	79	2	no	—
237	#520	—	79	2	no	—
238	#520	—	79	2	no	—
239	#443	—	79	8	no	—
240	#440	—	158	2	no	—
241	#440	—	158	2	no	—
242	C₄×Q₁₆	—	158	1	no	—
243	C₄×Q₁₆	—	158	1	no	—
244	C₄×D₈	—	158	1	no	—
245	C₄×D₈	—	158	1	no	—
246	C₂×#108	—	79	1	no	—
247	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
248	#428	—	79	2	no	—
249	#428	—	158	2	no	—
250	#428	—	158	2	no	—
251	#428	C₂×D₇₉	1	2	yes	—
252	#427	—	79	1	no	—
253	#427	—	158	2	no	—
254	C₂×#107	—	79	1	no	—
255	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
256	C₂×#106	—	79	2	no	—
257	C₂×#106	—	158	2	no	—
258	C₂×#104	—	79	2	no	—
259	#417	—	79	2	no	—
260	#417	—	79	2	no	—
261	#405	—	79	1	no	—
262	#405	C₂×D₇₉	1	1	yes	characteristic
263	C₂×C₄×C₈	—	79	1	no	—
264	#382	—	79	2	no	—
265	#343	—	79	2	no	—
266	#343	C₂×D₇₉	1	2	yes	—
267	#339	—	79	1	no	—
268	#339	—	79	1	no	—
269	C₂×#41	—	79	2	no	—
270	#135	—	79	4	no	—
271	#135	—	79	4	no	—
272	C₂×Q₁₆	—	79	1	no	—
273	C₂×SD₁₆	—	79	2	no	—
274	C₂×D₈	—	79	1	no	—
275	#131	—	79	8	no	—
276	#131	—	158	4	no	—
277	C₂×M₁₆	—	79	1	no	—
278	C₂×M₁₆	—	158	2	no	—
279	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
280	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
281	C₂²×C₈	—	79	1	no	—
282	C₂²×C₈	—	158	2	no	—
283	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₄×Q₈	—	158	2	no	—
285	C₄×Q₈	—	158	2	no	—
286	C₄×D₄	—	316	2	no	—
287	C₄×D₄	—	316	2	no	—
288	C₄×D₄	—	158	2	no	—
289	C₄×D₄	—	158	2	no	—
290	#117	—	79	1	no	—
291	#117	—	158	2	no	—
292	#117	—	158	2	no	—
293	#117	C₂²×D₇₉	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	79	2	no	—
295	C₂×C₄⋊C₄	—	158	2	no	—
296	C₂×C₄⋊C₄	—	158	2	no	—
297	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
298	C₂×C₄²	—	79	1	no	—
299	#108	—	158	2	no	—
300	#108	C₄×D₇₉	1	4	yes	complemented
301	#107	—	2	1	no	—
302	#107	—	2	1	no	—
303	#107	—	2	2	no	—
304	#107	—	79	1	no	—
305	#107	—	79	1	no	—
306	#107	—	158	2	no	—
307	#107	—	158	1	no	—
308	#107	—	158	1	no	—
309	#106	—	2	2	no	—
310	#106	—	79	1	no	—
311	#106	—	79	1	no	—
312	#106	—	158	2	no	—
313	#106	—	158	2	no	—
314	#106	—	158	2	no	—
315	#104	—	79	8	no	—
316	#103	—	158	2	no	—
317	#103	—	158	2	no	—
318	#102	—	158	2	no	—
319	#102	—	158	2	no	—
320	#97	—	2	1	no	—
321	#97	—	158	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	79	4	no	—
324	C₄×C₈	—	158	1	no	—
325	#95	—	316	2	no	—
326	#41	—	79	4	no	—
327	#41	—	79	4	no	—
328	#41	—	158	2	no	—
329	#41	—	158	2	no	—
330	C₂×Q₈	—	79	2	no	—
331	C₂×D₄	—	79	2	no	—
332	C₂×D₄	—	158	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	316	2	no	—
335	C₂²×C₄	—	316	2	no	—
336	C₂²×C₄	—	158	1	no	—
337	C₂²×C₄	—	158	2	no	—
338	C₂²×C₄	—	158	2	no	—
339	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
340	Q₁₆	—	79	4	no	—
341	SD₁₆	—	79	8	no	—
342	D₈	—	79	4	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	158	8	no	—
347	M₁₆	—	158	1	no	—
348	M₁₆	—	158	1	no	—
349	M₁₆	C₂×C₄×D₇₉	1	4	yes	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	79	2	no	—
353	C₂×C₈	—	79	2	no	—
354	C₂×C₈	—	79	1	no	—
355	C₂×C₈	—	79	1	no	—
356	C₂×C₈	—	158	8	no	—
357	C₂×C₈	—	158	1	no	—
358	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
359	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
360	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
361	C₂×C₈	Q₈×D₇₉	1	2	yes	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	316	2	no	—
365	C₄⋊C₄	—	316	2	no	—
366	C₄⋊C₄	—	79	1	no	—
367	C₄⋊C₄	—	79	1	no	—
368	C₄⋊C₄	—	158	2	no	—
369	C₄⋊C₄	—	158	2	no	—
370	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
371	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	316	2	no	—
374	C₂²⋊C₄	—	316	2	no	—
375	C₂²⋊C₄	—	158	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	316	2	no	—
378	C₄²	—	316	2	no	—
379	C₄²	—	79	2	no	—
380	C₄²	—	158	1	no	—
381	C₄²	—	158	1	no	—
382	C₂³	—	158	2	no	—
383	C₂³	#14579207	1	1	yes	characteristic
384	Q₈	—	79	4	no	—
385	Q₈	—	158	2	no	—
386	D₄	—	79	4	no	—
387	D₄	—	158	4	no	—
388	D₄	—	158	4	no	—
389	D₄	—	158	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	316	1	no	—
395	C₂×C₄	—	316	1	no	—
396	C₂×C₄	—	316	2	no	—
397	C₂×C₄	—	632	2	no	—
398	C₂×C₄	—	158	1	no	—
399	C₂×C₄	—	158	1	no	—
400	C₂×C₄	—	158	2	no	—
401	C₂×C₄	—	158	2	no	—
402	C₂×C₄	—	158	4	no	—
403	C₂×C₄	—	158	4	no	—
404	C₂×C₄	—	1264	2	no	—
405	C₂×C₄	—	1264	2	no	—
406	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
410	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
411	C₂×C₄	#14579209	1	1	yes	characteristic
412	C₈	—	2	4	no	—
413	C₈	—	4	1	no	—
414	C₈	—	316	1	no	—
415	C₈	—	79	2	no	—
416	C₈	—	79	2	no	—
417	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
418	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	316	2	no	—
422	C₂²	—	316	2	no	—
423	C₂²	—	158	4	no	—
424	C₂²	#19099045	1	1	yes	characteristic
425	C₂²	#19099197	1	1	yes	characteristic
426	C₂²	#19099269	1	1	yes	characteristic
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	316	2	no	—
431	C₄	—	316	1	no	—
432	C₄	—	316	1	no	—
433	C₄	—	632	2	no	—
434	C₄	—	158	4	no	—
435	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
436	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
437	C₄	#19099215	1	1	yes	characteristic
438	C₄	#19099228	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	316	4	no	—
442	C₂	#23766301	1	1	yes	characteristic
443	C₂	#23775181	1	1	yes	characteristic
444	C₂	#23775189	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19099197
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1952	C₂
socle	C₂²×C₇₉	D₄²
prime radical	C₂×#14579183	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1952	D₇₉
hypocenter	C₇₉	#22690
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
4. #23771994	C₂	semidirect
5. #23764186	C₂	semidirect
6. #23763636	C₂	semidirect
7. #23763630	C₂	semidirect
8. #23763563	C₂	semidirect
9. #23763458	C₂	semidirect
10. #23763280	C₂	semidirect
11. C₇₉×#1952	C₂	semidirect
16. #19098679	C₄	semidirect
53. #14579169	C₂×C₄	semidirect
82. #14579087	C₂×C₄	semidirect
89. C₈×Dic₇₉	C₂×C₄	semidirect
96. #108×C₇₉	C₂×C₄	semidirect
228. #1952	D₇₉	semidirect
234. C₇₉	#22690	semidirect
300. #108	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098679	2
#23772277	2
#23772274	2
#23771994	2
#23764186	2
#23763636	2
#23763630	2
#23763563	2
#23763458	2
#23763280	2
C₇₉×#1952	2
#22690	79