Subgroups — #23774993

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579186	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14579185	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099212	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099197	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098934	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098812	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098807	C₂	1	1	yes	maximal, characteristic, complemented
8	#19098767	C₂	1	1	yes	maximal, characteristic, complemented
9	#19098756	C₂	1	1	yes	maximal, characteristic, complemented
10	#19098716	C₂	1	1	yes	maximal, characteristic, complemented
11	#19098712	C₂	1	1	yes	maximal, characteristic, complemented
12	#19098709	C₂	1	1	yes	maximal, characteristic, complemented
13	#19098643	C₂	1	1	yes	maximal, characteristic, complemented
14	#19098638	C₂	1	1	yes	maximal, characteristic, complemented
15	#449×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11929623	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₇₉	—	2	1	no	—
19	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic
20	#14579186	—	2	4	no	—
21	#14579185	—	2	4	no	—
22	C₂×#11929613	C₂²	1	1	yes	characteristic
23	C₂×#11929613	C₂²	1	1	yes	characteristic, complemented
24	C₂×#11929612	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11929611	C₂²	1	1	yes	characteristic
26	C₂×#11929611	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11929609	C₂²	1	1	yes	characteristic
28	C₂×#11929609	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11929608	C₂²	1	1	yes	characteristic, complemented
30	C₂×#11929607	C₂²	1	1	yes	characteristic, complemented
31	#14579159	C₂²	1	1	yes	characteristic, complemented
32	#14579157	C₂²	1	1	yes	characteristic
33	#14579144	—	2	1	no	—
34	#14579142	—	2	1	no	—
35	#14579140	C₂²	1	1	yes	characteristic, complemented
36	#14579137	C₂²	1	1	yes	characteristic, complemented
37	#14579136	C₂²	1	1	yes	characteristic
38	#14579134	—	2	1	no	—
39	#14579133	—	2	1	no	—
40	#14579131	—	2	1	no	—
41	#14579129	—	2	1	no	—
42	D₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
43	#14579123	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
45	C₂×Dic₇₉⋊C₄	—	2	1	no	—
46	#14579094	C₂²	1	1	yes	characteristic, complemented
47	Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#14579084	C₂²	1	1	yes	characteristic, complemented
49	#14579083	C₂²	1	1	yes	characteristic
50	#14579083	C₂²	1	1	yes	characteristic, complemented
51	#14579082	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
57	#121×C₇₉	C₂²	1	1	yes	characteristic
58	#103×C₇₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₇₉	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₇₉	—	2	1	no	—
62	C₂³×D₇₉	—	2	1	no	—
63	#11929623	—	2	2	no	—
64	#11929623	—	4	1	no	—
65	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
66	C₂×D₃₁₆	—	2	1	no	—
67	C₂×D₃₁₆	—	2	2	no	—
68	C₂×D₃₁₆	—	2	1	no	—
69	C₂×D₃₁₆	—	4	1	no	—
70	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
71	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₇₉	—	2	1	no	—
73	C₂×C₂²⋊D₇₉	—	2	1	no	—
74	C₂×C₂²⋊D₇₉	—	2	1	no	—
75	C₂×C₂²⋊D₇₉	—	2	1	no	—
76	C₂×C₂²⋊D₇₉	D₄	1	1	yes	characteristic
77	D₄×D₇₉	—	2	2	no	—
78	D₄×D₇₉	—	4	4	no	—
79	D₄×D₇₉	—	4	1	no	—
80	C₂²×Dic₇₉	—	2	1	no	—
81	C₂²×Dic₇₉	—	2	1	no	—
82	C₂×C₄×D₇₉	—	2	1	no	—
83	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
84	#11929613	—	2	2	no	—
85	#11929613	—	4	1	no	—
86	#11929612	—	2	2	no	—
87	#11929611	—	2	2	no	—
88	#11929611	—	2	2	no	—
89	#11929609	—	2	2	no	—
90	#11929609	D₄	1	4	yes	complemented
91	#11929608	—	2	2	no	—
92	#11929607	—	2	2	no	—
93	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
96	Dic₇₉⋊C₄	—	2	1	no	—
97	Dic₇₉⋊C₄	—	2	1	no	—
98	Dic₇₉⋊C₄	—	2	1	no	—
99	Dic₇₉⋊C₄	—	2	1	no	—
100	Dic₇₉⋊C₄	D₄	1	1	yes	characteristic
101	C₂²⋊Dic₇₉	—	2	1	no	—
102	C₂²⋊Dic₇₉	—	2	1	no	—
103	C₂²⋊Dic₇₉	D₄	1	1	yes	characteristic
104	(C₂×D₇₉)⋊C₄	—	2	1	no	—
105	(C₂×D₇₉)⋊C₄	—	2	1	no	—
106	(C₂×D₇₉)⋊C₄	—	2	1	no	—
107	(C₂×D₇₉)⋊C₄	D₄	1	1	yes	characteristic
108	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
109	#41×C₇₉	—	2	2	no	—
110	#41×C₇₉	—	4	1	no	—
111	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₇₉	—	2	1	no	—
113	C₂×D₄×C₇₉	—	2	1	no	—
114	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	—	2	1	no	—
117	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
118	SD₁₆×C₇₉	—	4	1	no	—
119	D₈×C₇₉	—	2	2	no	—
120	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂²⋊C₄×C₇₉	—	2	1	no	—
124	C₂³×C₇₉	—	2	1	no	—
125	C₂³×C₇₉	—	2	1	no	—
126	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₇₉	—	2	1	no	—
128	C₂²×D₇₉	—	2	1	no	—
129	C₂²×D₇₉	—	4	2	no	—
130	C₂²×D₇₉	—	4	2	no	—
131	C₂²×D₇₉	—	4	2	no	—
132	C₂²×D₇₉	—	4	2	no	—
133	C₂²×D₇₉	—	8	1	no	—
134	C₂²×D₇₉	—	8	1	no	—
135	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₇₉	—	2	1	no	—
137	Q₈×C₇₉	—	2	1	no	—
138	D₄×C₇₉	—	2	1	no	—
139	D₄×C₇₉	—	2	1	no	—
140	D₄×C₇₉	—	2	1	no	—
141	D₄×C₇₉	—	4	2	no	—
142	D₄×C₇₉	—	4	2	no	—
143	D₄×C₇₉	C₂×D₄	1	2	yes	complemented
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	C₂²⋊D₇₉	—	2	2	no	—
152	C₂²⋊D₇₉	—	4	2	no	—
153	C₂²⋊D₇₉	—	4	2	no	—
154	C₂²⋊D₇₉	—	4	2	no	—
155	C₂²⋊D₇₉	—	8	1	no	—
156	C₂×Dic₇₉	—	2	1	no	—
157	C₂×Dic₇₉	—	2	1	no	—
158	C₂×Dic₇₉	—	4	2	no	—
159	C₂×Dic₇₉	—	4	2	no	—
160	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
163	D₃₁₆	—	2	1	no	—
164	D₃₁₆	—	2	1	no	—
165	D₃₁₆	—	2	1	no	—
166	D₃₁₆	—	4	2	no	—
167	D₃₁₆	—	4	2	no	—
168	D₃₁₆	C₂×D₄	1	2	yes	—
169	C₄×D₇₉	—	2	1	no	—
170	C₄×D₇₉	—	2	1	no	—
171	C₄×D₇₉	—	4	2	no	—
172	Dic₁₅₈	—	2	1	no	—
173	Dic₁₅₈	—	2	1	no	—
174	C₈×C₇₉	—	2	1	no	—
175	C₈×C₇₉	—	2	1	no	—
176	C₇₉⋊C₈	—	2	1	no	—
177	C₇₉⋊C₈	C₂×D₄	1	2	yes	complemented
178	C₂²×C₇₉	—	2	2	no	—
179	C₂²×C₇₉	—	2	1	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	1	no	—
182	C₂²×C₇₉	—	4	1	no	—
183	C₂²×C₇₉	—	4	1	no	—
184	C₂²×C₇₉	—	4	1	no	—
185	C₂²×C₇₉	—	4	1	no	—
186	C₂²×C₇₉	—	4	1	no	—
187	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×D₇₉	—	2	1	no	—
189	C₂×D₇₉	—	2	2	no	—
190	C₂×D₇₉	—	2	1	no	—
191	C₂×D₇₉	—	2	1	no	—
192	C₂×D₇₉	—	4	1	no	—
193	C₂×D₇₉	—	4	1	no	—
194	C₂×D₇₉	—	4	1	no	—
195	C₂×D₇₉	—	4	1	no	—
196	C₂×D₇₉	—	4	1	no	—
197	C₂×D₇₉	—	8	4	no	—
198	C₂×D₇₉	—	8	4	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	4	1	no	—
201	C₄×C₇₉	—	4	1	no	—
202	C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
204	Dic₇₉	—	2	1	no	—
205	Dic₇₉	—	2	1	no	—
206	Dic₇₉	—	4	1	no	—
207	Dic₇₉	—	4	1	no	—
208	Dic₇₉	AGL(1,ℤ/8)	1	2	yes	complemented
209	C₂×C₇₉	—	4	1	no	—
210	C₂×C₇₉	—	4	2	no	—
211	C₂×C₇₉	—	8	1	no	—
212	C₂×C₇₉	D₄²	1	1	yes	characteristic
213	C₂×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₇₉	#577	1	1	yes	characteristic
215	D₇₉	—	4	1	no	—
216	D₇₉	—	4	2	no	—
217	D₇₉	—	8	1	no	—
218	#3272	—	79	1	no	maximal, Sylow
219	C₇₉	#3272	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	79	1	no	—
221	C₂×AGL(1,ℤ/8)	—	79	1	no	—
222	#547	—	79	1	no	—
223	D₄²	—	79	1	no	—
224	#492	—	79	1	no	—
225	#468	—	79	1	no	—
226	#468	—	79	1	no	—
227	#461	—	79	1	no	—
228	#459	—	79	1	no	—
229	#450	—	79	1	no	—
230	#450	—	79	1	no	—
231	#449	—	79	1	no	—
232	#449	D₇₉	1	1	yes	characteristic, complemented
233	C₄×D₈	—	79	1	no	—
234	#436	—	79	1	no	—
235	C₂×#41	—	79	1	no	—
236	C₂×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	79	1	no	—
238	C₂²×D₄	—	79	1	no	—
239	C₂²×D₄	—	158	1	no	—
240	AGL(1,ℤ/8)	—	158	4	no	—
241	AGL(1,ℤ/8)	—	158	4	no	—
242	C₂×SD₁₆	—	79	1	no	—
243	C₂×SD₁₆	—	79	1	no	—
244	C₂×SD₁₆	—	79	1	no	—
245	C₂×SD₁₆	—	79	1	no	—
246	C₂×SD₁₆	—	79	1	no	—
247	C₂×SD₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
248	C₂×D₈	—	79	1	no	—
249	C₂×D₈	—	79	1	no	—
250	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic, complemented
251	C₂×M₁₆	—	79	1	no	—
252	C₂×M₁₆	—	79	1	no	—
253	C₄⋊Q₈	—	79	1	no	—
254	#127	—	79	1	no	—
255	#123	—	158	1	no	—
256	#123	—	158	1	no	—
257	C₂²⋊Q₈	—	79	1	no	—
258	C₂²⋊Q₈	—	79	1	no	—
259	#121	—	79	1	no	—
260	#121	—	158	1	no	—
261	#121	—	158	1	no	—
262	#121	C₂×D₇₉	1	1	yes	characteristic
263	#120	—	158	1	no	—
264	#120	—	158	1	no	—
265	C₄×D₄	—	79	1	no	—
266	C₄×D₄	—	79	1	no	—
267	C₄×D₄	—	79	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	#107	—	79	1	no	—
270	C₄⋊C₈	—	79	1	no	—
271	#103	—	79	1	no	—
272	#103	C₂×D₇₉	1	1	yes	characteristic, complemented
273	#102	—	79	1	no	—
274	#102	—	79	1	no	—
275	#102	—	79	1	no	—
276	#102	C₂×D₇₉	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	79	1	no	—
278	C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic, complemented
279	C₄×C₈	—	79	1	no	—
280	C₂⁴	—	158	1	no	—
281	C₂⁴	—	158	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	#41	—	316	1	no	—
285	#41	—	158	2	no	—
286	C₂×Q₈	—	79	1	no	—
287	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	316	1	no	—
291	C₂×D₄	—	316	4	no	—
292	C₂×D₄	—	316	1	no	—
293	C₂×D₄	—	79	1	no	—
294	C₂×D₄	—	79	1	no	—
295	C₂×D₄	—	79	1	no	—
296	C₂×D₄	—	158	1	no	—
297	C₂×D₄	—	158	2	no	—
298	C₂×D₄	—	158	1	no	—
299	C₂×D₄	—	158	1	no	—
300	C₂×D₄	—	158	1	no	—
301	C₂×D₄	—	158	2	no	—
302	C₂×D₄	—	158	1	no	—
303	C₂×D₄	—	158	1	no	—
304	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	79	1	no	—
308	C₂²×C₄	—	158	1	no	—
309	C₂²×C₄	—	158	1	no	—
310	C₂²×C₄	—	158	1	no	—
311	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
312	SD₁₆	—	4	1	no	—
313	SD₁₆	—	316	1	no	—
314	SD₁₆	—	158	2	no	—
315	SD₁₆	—	158	2	no	—
316	SD₁₆	—	158	2	no	—
317	SD₁₆	—	158	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	79	4	no	—
320	D₈	—	158	2	no	—
321	M₁₆	—	158	2	no	—
322	M₁₆	—	158	2	no	—
323	C₂×C₈	—	79	1	no	—
324	C₂×C₈	—	79	1	no	—
325	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₄⋊C₄	—	79	1	no	—
328	C₄⋊C₄	—	79	1	no	—
329	C₄⋊C₄	—	158	1	no	—
330	C₄⋊C₄	—	158	1	no	—
331	C₄⋊C₄	—	158	1	no	—
332	C₄⋊C₄	—	158	1	no	—
333	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	79	1	no	—
336	C₂²⋊C₄	—	79	1	no	—
337	C₂²⋊C₄	—	158	1	no	—
338	C₂²⋊C₄	—	158	1	no	—
339	C₂²⋊C₄	—	158	1	no	—
340	C₂²⋊C₄	—	158	1	no	—
341	C₂²⋊C₄	—	158	1	no	—
342	C₄²	—	79	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	316	2	no	—
346	C₂³	—	316	2	no	—
347	C₂³	—	316	2	no	—
348	C₂³	—	316	2	no	—
349	C₂³	—	79	1	no	—
350	C₂³	—	632	1	no	—
351	C₂³	—	632	1	no	—
352	C₂³	—	158	1	no	—
353	C₂³	—	158	1	no	—
354	C₂³	D₄×D₇₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	158	1	no	—
358	Q₈	—	158	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	316	2	no	—
365	D₄	—	316	2	no	—
366	D₄	—	316	2	no	—
367	D₄	—	316	2	no	—
368	D₄	—	316	2	no	—
369	D₄	—	79	2	no	—
370	D₄	—	632	1	no	—
371	D₄	—	158	2	no	—
372	D₄	—	158	1	no	—
373	D₄	—	158	1	no	—
374	D₄	—	158	1	no	—
375	D₄	D₄×D₇₉	1	2	yes	complemented
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	316	2	no	—
383	C₂×C₄	—	316	2	no	—
384	C₂×C₄	—	79	1	no	—
385	C₂×C₄	—	79	1	no	—
386	C₂×C₄	—	79	1	no	—
387	C₂×C₄	—	158	1	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	79	2	no	—
396	C₈	—	158	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	316	1	no	—
407	C₂²	—	316	1	no	—
408	C₂²	—	316	1	no	—
409	C₂²	—	316	1	no	—
410	C₂²	—	316	1	no	—
411	C₂²	—	632	4	no	—
412	C₂²	—	632	4	no	—
413	C₂²	—	158	1	no	—
414	C₂²	—	158	2	no	—
415	C₂²	—	158	1	no	—
416	C₂²	—	158	1	no	—
417	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	316	1	no	—
422	C₄	—	316	1	no	—
423	C₄	—	79	2	no	—
424	C₄	—	158	1	no	—
425	C₄	—	158	1	no	—
426	C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
427	C₄	#14579206	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	316	2	no	—
432	C₂	—	316	1	no	—
433	C₂	—	632	1	no	—
434	C₂	#19099195	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
436	C₂	#19099370	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#449×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
hypercenter	#449	D₇₉
hypocenter	C₇₉	#3272
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

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

N	H ≅ G/N	type
1. C₂×#14579186	C₂	semidirect
2. C₂×#14579185	C₂	semidirect
3. #19099212	C₂	semidirect
4. #19099197	C₂	semidirect
5. #19098934	C₂	semidirect
6. #19098812	C₂	semidirect
7. #19098807	C₂	semidirect
8. #19098767	C₂	semidirect
9. #19098756	C₂	semidirect
10. #19098716	C₂	semidirect
11. #19098712	C₂	semidirect
12. #19098709	C₂	semidirect
13. #19098643	C₂	semidirect
14. #19098638	C₂	semidirect
15. #449×C₇₉	C₂	semidirect
16. C₂×#11929623	C₂²	semidirect
23. C₂×#11929613	C₂²	semidirect
24. C₂×#11929612	C₂²	semidirect
26. C₂×#11929611	C₂²	semidirect
28. C₂×#11929609	C₂²	semidirect
29. C₂×#11929608	C₂²	semidirect
30. C₂×#11929607	C₂²	semidirect
31. #14579159	C₂²	semidirect
35. #14579140	C₂²	semidirect
36. #14579137	C₂²	semidirect
42. D₄×Dic₇₉	C₂²	semidirect
46. #14579094	C₂²	semidirect
47. Dic₇₉⋊C₈	C₂²	semidirect
48. #14579084	C₂²	semidirect
50. #14579083	C₂²	semidirect
51. #14579082	C₂²	semidirect
52. (C₂×D₇₉)⋊C₈	C₂²	semidirect
53. C₈×Dic₇₉	C₂²	semidirect
54. C₂×#41×C₇₉	C₂²	semidirect
55. C₂×SD₁₆×C₇₉	C₂²	semidirect
56. C₂×D₈×C₇₉	C₂²	semidirect
58. #103×C₇₉	C₂²	semidirect
59. #102×C₇₉	C₂²	semidirect
60. C₂²⋊C₈×C₇₉	C₂²	semidirect
90. #11929609	D₄	semidirect
143. D₄×C₇₉	C₂×D₄	semidirect
177. C₇₉⋊C₈	C₂×D₄	semidirect
208. Dic₇₉	AGL(1,ℤ/8)	semidirect
219. C₇₉	#3272	semidirect
232. #449	D₇₉	semidirect
236. C₂×#41	C₂×D₇₉	semidirect
247. C₂×SD₁₆	C₂×D₇₉	semidirect
250. C₂×D₈	C₂×D₇₉	semidirect
272. #103	C₂×D₇₉	semidirect
276. #102	C₂×D₇₉	semidirect
278. C₂²⋊C₈	C₂×D₇₉	semidirect
375. D₄	D₄×D₇₉	semidirect