Subgroups — #34271881

Order 20224.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23774742	C₂	1	1	yes	maximal, characteristic, complemented
2	#23773774	C₂	1	1	yes	maximal, characteristic
3	#23772349	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762966	C₂	1	2	yes	maximal, complemented
5	#23762938	C₂	1	2	yes	maximal, complemented
6	#23762842	C₂	1	2	yes	maximal, complemented
7	#23762814	C₂	1	2	yes	maximal, complemented
8	#23762153	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098307	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#3208	C₂	1	1	yes	maximal, characteristic
12	#19099120	C₂²	1	1	yes	characteristic
13	#19098927	—	2	2	no	—
14	#19098909	C₂²	1	2	yes	—
15	#19098909	C₂²	1	2	yes	—
16	#19098858	C₂²	1	2	yes	complemented
17	#19098855	—	2	1	no	—
18	#19098802	—	2	2	no	—
19	#19098773	C₂²	1	2	yes	complemented
20	#19098770	—	2	1	no	—
21	#19098694	—	2	2	no	—
22	#19098694	C₂²	1	2	yes	complemented
23	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	complemented
24	#19098590	—	2	1	no	—
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#19098568	—	2	1	no	—
28	#19098568	—	2	1	no	—
29	#19098519	—	2	1	no	—
30	C₄×#11929608	C₂²	1	1	yes	characteristic
31	#19098315	C₂²	1	2	yes	complemented
32	#19098313	C₂²	1	2	yes	complemented
33	#19098311	C₂²	1	1	yes	characteristic, complemented
34	#19098311	C₂²	1	1	yes	characteristic, complemented
35	#19098310	C₂²	1	1	yes	characteristic, complemented
36	#19098310	C₂²	1	1	yes	characteristic, complemented
37	#19098307	C₂²	1	2	yes	—
38	#19098307	C₂²	1	2	yes	—
39	#533×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
41	#492×C₇₉	—	2	1	no	—
42	#486×C₇₉	—	2	1	no	—
43	#460×C₇₉	C₂²	1	2	yes	—
44	#460×C₇₉	C₂²	1	2	yes	—
45	#450×C₇₉	—	2	2	no	—
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929614	—	2	2	no	—
48	C₂×#11929608	D₄	1	1	yes	characteristic
49	C₂×#11929608	D₄	1	1	yes	characteristic
50	C₂²×C₇₉⋊C₈	—	2	1	no	—
51	C₂²×C₇₉⋊C₈	—	2	1	no	—
52	#14579161	C₂³	1	1	yes	characteristic
53	#14579161	C₂³	1	1	yes	characteristic
54	#14579153	—	2	1	no	—
55	#14579140	—	2	1	no	—
56	#14579140	—	2	1	no	—
57	C₄×Dic₁₅₈	—	2	1	no	—
58	C₄×Dic₁₅₈	—	2	1	no	—
59	#14579120	—	2	1	no	—
60	#14579094	—	2	2	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
68	#14579085	—	2	2	no	—
69	#14579084	—	2	2	no	—
70	#14579082	—	2	2	no	—
71	#14579082	—	2	2	no	—
72	#14579082	—	2	2	no	—
73	#14579082	—	2	2	no	—
74	#14579072	—	2	2	no	—
75	#14579072	D₄	1	2	yes	—
76	C₄×C₇₉⋊C₈	—	2	2	no	—
77	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
78	C₂²×D₄×C₇₉	—	2	1	no	—
79	C₂²×D₄×C₇₉	—	2	1	no	—
80	C₂²×D₄×C₇₉	—	2	1	no	—
81	C₂×SD₁₆×C₇₉	—	2	2	no	—
82	C₂×SD₁₆×C₇₉	—	2	2	no	—
83	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
84	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
85	#127×C₇₉	—	2	1	no	—
86	#127×C₇₉	—	2	1	no	—
87	#127×C₇₉	—	2	1	no	—
88	#127×C₇₉	C₂³	1	2	yes	—
89	#125×C₇₉	—	2	1	no	—
90	C₂²⋊Q₈×C₇₉	—	2	1	no	—
91	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
92	C₄×Q₈×C₇₉	—	2	1	no	—
93	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
94	#117×C₇₉	—	2	1	no	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
98	#102×C₇₉	—	2	2	no	—
99	#102×C₇₉	—	2	2	no	—
100	C₂²⋊C₈×C₇₉	—	2	1	no	—
101	C₄×C₈×C₇₉	—	2	1	no	—
102	C₂×Dic₁₅₈	—	2	1	no	—
103	C₂×Dic₁₅₈	—	2	1	no	—
104	#11929614	—	8	2	no	—
105	#11929608	—	2	2	no	—
106	#11929608	—	2	2	no	—
107	C₂×C₇₉⋊C₈	—	2	1	no	—
108	C₂×C₇₉⋊C₈	—	2	1	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	4	2	no	—
111	C₂×C₇₉⋊C₈	—	8	1	no	—
112	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
113	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
114	C₄⋊Dic₇₉	—	2	1	no	—
115	C₄⋊Dic₇₉	—	2	1	no	—
116	C₄⋊Dic₇₉	—	2	1	no	—
117	C₄⋊Dic₇₉	—	2	1	no	—
118	Dic₇₉⋊C₄	—	4	1	no	—
119	Dic₇₉⋊C₄	—	4	1	no	—
120	C₂²⋊Dic₇₉	—	4	1	no	—
121	C₄×Dic₇₉	—	4	1	no	—
122	C₂⁴×C₇₉	—	4	1	no	—
123	C₂×Q₈×C₇₉	—	2	1	no	—
124	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	4	1	no	—
129	C₂×D₄×C₇₉	—	4	1	no	—
130	C₂×D₄×C₇₉	—	4	1	no	—
131	C₂×D₄×C₇₉	—	4	2	no	—
132	C₂×D₄×C₇₉	—	4	2	no	—
133	C₂×D₄×C₇₉	—	8	1	no	—
134	C₂×D₄×C₇₉	—	8	1	no	—
135	C₂×D₄×C₇₉	—	8	2	no	—
136	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
139	SD₁₆×C₇₉	—	8	2	no	—
140	SD₁₆×C₇₉	—	8	2	no	—
141	C₂×C₈×C₇₉	—	2	1	no	—
142	C₂×C₈×C₇₉	—	2	1	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	2	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	—	2	2	no	—
151	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₇₉	#41	1	1	yes	characteristic
154	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₇₉	—	4	2	no	—
156	C₂³×C₇₉	—	8	2	no	—
157	C₂³×C₇₉	—	8	2	no	—
158	C₂³×C₇₉	—	8	2	no	—
159	C₂³×C₇₉	#121	1	1	yes	characteristic
160	Q₈×C₇₉	—	2	2	no	—
161	Q₈×C₇₉	—	2	2	no	—
162	Q₈×C₇₉	—	8	1	no	—
163	D₄×C₇₉	—	4	2	no	—
164	D₄×C₇₉	—	4	2	no	—
165	D₄×C₇₉	—	4	2	no	—
166	D₄×C₇₉	—	4	2	no	—
167	D₄×C₇₉	—	8	2	no	—
168	D₄×C₇₉	—	8	2	no	—
169	D₄×C₇₉	—	8	2	no	—
170	D₄×C₇₉	—	8	2	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	1	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	4	1	no	—
176	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₇₉	#135	1	2	yes	—
180	C₂×C₄×C₇₉	#137	1	2	yes	—
181	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₇₉	—	4	1	no	—
185	C₂×Dic₇₉	—	4	1	no	—
186	Dic₁₅₈	—	4	1	no	—
187	Dic₁₅₈	—	4	1	no	—
188	Dic₁₅₈	—	8	1	no	—
189	C₈×C₇₉	—	4	1	no	—
190	C₈×C₇₉	—	4	1	no	—
191	C₇₉⋊C₈	—	2	2	no	—
192	C₇₉⋊C₈	—	2	2	no	—
193	C₇₉⋊C₈	—	4	1	no	—
194	C₇₉⋊C₈	—	4	1	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₂²×C₇₉	—	2	1	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	8	2	no	—
199	C₂²×C₇₉	—	8	2	no	—
200	C₂²×C₇₉	—	8	2	no	—
201	C₂²×C₇₉	—	16	4	no	—
202	C₂²×C₇₉	#464	1	2	yes	—
203	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	4	2	no	—
208	C₄×C₇₉	—	4	2	no	—
209	C₄×C₇₉	#464	1	2	yes	—
210	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
211	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
212	C₄×C₇₉	#576	1	1	yes	characteristic
213	C₄×C₇₉	#577	1	1	yes	characteristic
214	Dic₇₉	—	8	1	no	—
215	Dic₇₉	—	8	1	no	—
216	#19242	—	79	1	no	maximal, Sylow
217	C₂×C₇₉	—	2	2	no	—
218	C₂×C₇₉	—	16	2	no	—
219	C₂×C₇₉	C₂×#464	1	1	yes	characteristic
220	C₂×C₇₉	#3062	1	1	yes	characteristic
221	C₂×C₇₉	#3068	1	1	yes	characteristic
222	#3249	—	79	1	no	—
223	#3208	D₇₉	1	1	yes	characteristic
224	#3138	—	79	1	no	—
225	#2962	—	79	1	no	—
226	#1702	—	79	2	no	—
227	#1698	—	79	2	no	—
228	#1682	—	79	2	no	—
229	#1678	—	79	2	no	—
230	#1565	—	79	1	no	—
231	#1542	—	79	1	no	—
232	C₂×#331	—	79	1	no	—
233	C₇₉	#19242	1	1	yes	characteristic, complemented, Sylow
234	#533	—	79	1	no	—
235	#533	C₂×D₇₉	1	1	yes	characteristic
236	C₂×#127	C₂×D₇₉	1	1	yes	characteristic
237	#492	—	2	1	no	—
238	#490	—	158	2	no	—
239	#486	—	2	1	no	—
240	#486	—	79	2	no	—
241	#486	—	79	2	no	—
242	#477	—	79	2	no	—
243	#477	—	158	1	no	—
244	#467	—	158	2	no	—
245	#462	—	79	2	no	—
246	#462	—	158	1	no	—
247	#460	C₂×D₇₉	1	2	yes	—
248	#460	C₂×D₇₉	1	2	yes	—
249	#450	—	2	2	no	—
250	#446	—	79	2	no	—
251	#446	—	158	2	no	—
252	C₈×Q₈	—	79	2	no	—
253	#431	C₂×D₇₉	1	1	yes	characteristic
254	#424	—	158	1	no	—
255	C₂×C₄⋊C₈	—	79	1	no	—
256	C₂×C₄⋊C₈	—	79	1	no	—
257	#418	—	158	1	no	—
258	#418	—	158	1	no	—
259	#405	—	158	1	no	—
260	C₄×M₁₆	—	79	1	no	—
261	#335	—	79	2	no	—
262	#334	—	79	2	no	—
263	#333	—	79	1	no	—
264	#333	—	79	1	no	—
265	#332	—	79	1	no	—
266	#332	—	79	1	no	—
267	#331	—	79	2	no	—
268	#331	—	79	2	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂×Q₁₆	—	158	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×M₁₆	—	79	1	no	—
276	C₂×M₁₆	—	79	1	no	—
277	C₂²×C₈	—	158	1	no	—
278	C₂²×C₈	—	158	1	no	—
279	C₄⋊Q₈	—	79	1	no	—
280	C₄⋊Q₈	—	79	1	no	—
281	C₄⋊Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
282	C₄⋊Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	C₂²×D₇₉	1	2	yes	—
287	#125	—	2	1	no	—
288	#125	—	158	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	158	1	no	—
291	C₂²⋊Q₈	—	158	1	no	—
292	C₂²⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	158	1	no	—
295	C₄×Q₈	—	158	1	no	—
296	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
297	#117	—	2	1	no	—
298	#117	—	158	1	no	—
299	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
300	#107	—	158	2	no	—
301	C₄⋊C₈	—	79	1	no	—
302	C₄⋊C₈	—	79	1	no	—
303	C₄⋊C₈	—	79	2	no	—
304	C₄⋊C₈	—	158	2	no	—
305	C₄⋊C₈	—	158	2	no	—
306	C₄⋊C₈	—	158	1	no	—
307	C₄⋊C₈	—	158	1	no	—
308	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
310	#103	—	158	2	no	—
311	#103	—	158	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	158	2	no	—
315	#102	—	158	2	no	—
316	#102	—	158	2	no	—
317	#102	—	158	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	#97	—	79	2	no	—
320	#97	—	158	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	79	2	no	—
323	C₄×C₈	—	158	2	no	—
324	C₂⁴	—	4	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	158	1	no	—
327	C₂×Q₈	—	158	1	no	—
328	C₂×Q₈	C₂×C₂²⋊D₇₉	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	8	1	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
342	C₂²×C₄	#11929623	1	1	yes	characteristic
343	Q₁₆	—	632	2	no	—
344	SD₁₆	—	8	2	no	—
345	SD₁₆	—	8	2	no	—
346	M₁₆	—	158	2	no	—
347	M₁₆	—	158	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	316	2	no	—
351	C₂×C₈	—	79	2	no	—
352	C₂×C₈	—	79	2	no	—
353	C₂×C₈	—	632	1	no	—
354	C₂×C₈	—	158	1	no	—
355	C₂×C₈	—	158	1	no	—
356	C₂×C₈	—	158	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	316	1	no	—
363	C₄⋊C₄	—	316	1	no	—
364	C₄⋊C₄	—	158	1	no	—
365	C₄⋊C₄	—	158	1	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	1	no	—
368	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	316	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	316	1	no	—
373	C₄²	D₄×D₇₉	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
375	C₄²	#11929623	1	1	yes	characteristic
376	C₄²	C₂³×D₇₉	1	1	yes	characteristic
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#14579133	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	316	1	no	—
386	Q₈	—	316	1	no	—
387	Q₈	—	632	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	316	1	no	—
402	C₂×C₄	—	316	1	no	—
403	C₂×C₄	#14579133	1	1	yes	characteristic
404	C₂×C₄	#14579133	1	1	yes	characteristic
405	C₂×C₄	#14579133	1	1	yes	characteristic
406	C₂×C₄	#14579182	1	2	yes	—
407	C₂×C₄	#14579190	1	2	yes	—
408	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	316	1	no	—
414	C₈	—	316	1	no	—
415	C₈	—	316	2	no	—
416	C₈	—	158	2	no	—
417	C₈	—	158	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	16	4	no	—
424	C₂²	#19098783	1	2	yes	—
425	C₂²	C₂×#14579133	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	632	1	no	—
432	C₄	—	632	1	no	—
433	C₄	#19098783	1	2	yes	—
434	C₄	C₂×#14579182	1	1	yes	characteristic
435	C₄	C₂×#14579190	1	1	yes	characteristic
436	C₄	#19099366	1	1	yes	characteristic
437	C₄	#19099374	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×#19098783	1	1	yes	characteristic
441	C₂	#23773076	1	1	yes	characteristic
442	C₂	#23773125	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3208	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂×#127×C₇₉	C₂²
hypercenter	#3208	D₇₉
hypocenter	C₇₉	#19242
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3208

Complements

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

N	H ≅ G/N	type
1. #23774742	C₂	semidirect
3. #23772349	C₂	semidirect
4. #23762966	C₂	semidirect
5. #23762938	C₂	semidirect
6. #23762842	C₂	semidirect
7. #23762814	C₂	semidirect
8. #23762153	C₂	semidirect
9. #23762055	C₂	semidirect
16. #19098858	C₂²	semidirect
19. #19098773	C₂²	semidirect
22. #19098694	C₂²	semidirect
23. Q₈×C₇₉⋊C₈	C₂²	semidirect
31. #19098315	C₂²	semidirect
32. #19098313	C₂²	semidirect
33. #19098311	C₂²	semidirect
34. #19098311	C₂²	semidirect
35. #19098310	C₂²	semidirect
36. #19098310	C₂²	semidirect
233. C₇₉	#19242	semidirect

Maximal subgroups

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

subgroup	index
#23774742	2
#23773774	2
#23772349	2
#23762966	2
#23762938	2
#23762842	2
#23762814	2
#23762153	2
#23762055	2
C₂×#19098307	2
C₇₉×#3208	2
#19242	79