Subgroups — #34273519

Order 20224.

650 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773487	C₂	1	1	yes	maximal, characteristic
2	#23773404	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772423	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762834	C₂	1	2	yes	maximal, complemented
5	#23762806	C₂	1	2	yes	maximal, complemented
6	#23762796	C₂	1	2	yes	maximal, complemented
7	#23762772	C₂	1	2	yes	maximal, complemented
8	#23762180	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762110	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762062	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
13	#19098891	—	2	1	no	—
14	#19098879	—	2	1	no	—
15	#19098850	C₂²	1	2	yes	—
16	#19098850	C₂²	1	2	yes	—
17	#19098765	C₂²	1	2	yes	—
18	#19098755	C₂²	1	2	yes	—
19	#19098713	—	2	1	no	—
20	#19098696	—	2	1	no	—
21	#19098673	—	2	2	no	—
22	C₄×#11929611	—	2	2	no	—
23	C₈×D₃₁₆	C₂²	1	2	yes	—
24	C₈×D₃₁₆	C₂²	1	2	yes	—
25	#19098628	—	2	2	no	—
26	#19098620	C₂²	1	1	yes	characteristic
27	#19098616	C₂²	1	1	yes	characteristic
28	#19098616	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₇₉	—	2	2	no	—
30	#19098316	C₂²	1	2	yes	complemented
31	#19098314	C₂²	1	2	yes	complemented
32	#19098312	C₂²	1	2	yes	complemented
33	#19098312	C₂²	1	2	yes	complemented
34	#19098309	C₂²	1	2	yes	complemented
35	#19098307	C₂²	1	2	yes	complemented
36	#533×C₇₉	C₂²	1	1	yes	characteristic
37	#532×C₇₉	C₂²	1	1	yes	characteristic
38	#500×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#498×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#482×C₇₉	—	2	2	no	—
43	#478×C₇₉	—	2	2	no	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₉	—	2	1	no	—
47	C₂×#11929611	—	2	2	no	—
48	C₂×#11929609	—	2	2	no	—
49	C₂×C₈×D₇₉	—	2	2	no	—
50	C₂×C₈×D₇₉	—	2	2	no	—
51	C₄×D₃₁₆	—	2	1	no	—
52	C₄×D₃₁₆	—	2	1	no	—
53	C₄×D₃₁₆	D₄	1	2	yes	—
54	C₄×D₃₁₆	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
57	#14579092	—	2	2	no	—
58	#14579092	—	2	2	no	—
59	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
62	#14579085	—	2	2	no	—
63	#14579082	—	2	2	no	—
64	#14579081	—	2	2	no	—
65	#14579081	—	2	2	no	—
66	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
69	(C₂×D₇₉)⋊C₈	—	2	2	no	—
70	(C₂×D₇₉)⋊C₈	—	2	2	no	—
71	#14579072	—	2	1	no	—
72	C₄×C₇₉⋊C₈	—	2	1	no	—
73	C₄×C₇₉⋊C₈	—	2	1	no	—
74	C₂×#41×C₇₉	—	2	1	no	—
75	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
78	#127×C₇₉	C₂³	1	1	yes	characteristic
79	#125×C₇₉	—	2	1	no	—
80	#124×C₇₉	—	2	1	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	—	2	1	no	—
83	#121×C₇₉	—	2	1	no	—
84	#121×C₇₉	—	2	1	no	—
85	C₄×Q₈×C₇₉	—	2	1	no	—
86	C₄×Q₈×C₇₉	—	2	1	no	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	#117×C₇₉	—	2	1	no	—
90	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
91	#107×C₇₉	—	2	2	no	—
92	#106×C₇₉	—	2	2	no	—
93	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
94	#102×C₇₉	—	2	2	no	—
95	#102×C₇₉	—	2	2	no	—
96	C₂²⋊C₈×C₇₉	D₄	1	2	yes	—
97	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂³×D₇₉	—	2	1	no	—
100	C₂×D₃₁₆	—	2	4	no	—
101	C₂×D₃₁₆	—	2	1	no	—
102	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
103	C₂²×Dic₇₉	—	2	1	no	—
104	C₂×C₄×D₇₉	—	2	2	no	—
105	C₂×C₄×D₇₉	—	2	2	no	—
106	C₂×C₄×D₇₉	—	8	2	no	—
107	#11929611	—	4	4	no	—
108	#11929609	—	4	4	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₈×D₇₉	—	8	2	no	—
113	C₈×D₇₉	—	8	2	no	—
114	C₄⋊Dic₇₉	—	2	1	no	—
115	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
116	(C₂×D₇₉)⋊C₄	—	2	2	no	—
117	(C₂×D₇₉)⋊C₄	—	2	2	no	—
118	#41×C₇₉	—	8	2	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	—	2	1	no	—
121	C₂×Q₈×C₇₉	—	2	1	no	—
122	C₂×D₄×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	2	1	no	—
124	C₂×D₄×C₇₉	—	2	1	no	—
125	C₂×D₄×C₇₉	—	4	1	no	—
126	C₂²×C₄×C₇₉	—	4	1	no	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
130	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₇₉	—	2	1	no	—
133	C₄⋊C₄×C₇₉	—	2	1	no	—
134	C₄⋊C₄×C₇₉	—	2	1	no	—
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	—	4	1	no	—
139	C₄⋊C₄×C₇₉	—	4	1	no	—
140	C₂²⋊C₄×C₇₉	—	4	1	no	—
141	C₂²⋊C₄×C₇₉	—	4	1	no	—
142	C₂²⋊C₄×C₇₉	—	4	1	no	—
143	C₄²×C₇₉	—	4	1	no	—
144	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₉	#41	1	1	yes	characteristic
147	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₇₉	—	4	1	no	—
149	C₂³×C₇₉	#121	1	1	yes	characteristic
150	C₂²×D₇₉	—	2	2	no	—
151	C₂²×D₇₉	—	2	4	no	—
152	C₂²×D₇₉	—	8	1	no	—
153	C₂²×D₇₉	—	8	1	no	—
154	Q₈×C₇₉	—	4	2	no	—
155	Q₈×C₇₉	—	8	1	no	—
156	Q₈×C₇₉	—	8	1	no	—
157	D₄×C₇₉	—	4	2	no	—
158	D₄×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	8	1	no	—
160	D₄×C₇₉	—	8	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	—	8	2	no	—
168	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	8	1	no	—
176	D₃₁₆	—	2	4	no	—
177	D₃₁₆	—	2	2	no	—
178	D₃₁₆	#135	1	4	yes	—
179	C₄×D₇₉	—	4	2	no	—
180	C₄×D₇₉	—	4	2	no	—
181	C₄×D₇₉	—	8	2	no	—
182	C₈×C₇₉	—	2	2	no	—
183	C₈×C₇₉	—	2	2	no	—
184	C₇₉⋊C₈	—	4	2	no	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₂²×C₇₉	—	2	1	no	—
188	C₂²×C₇₉	—	2	1	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	8	1	no	—
191	C₂²×C₇₉	—	8	1	no	—
192	C₂²×C₇₉	—	8	1	no	—
193	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
194	C₂×D₇₉	—	2	4	no	—
195	C₂×D₇₉	—	4	2	no	—
196	C₂×D₇₉	—	4	2	no	—
197	C₂×D₇₉	—	8	4	no	—
198	C₄×C₇₉	—	2	1	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	8	1	no	—
203	C₄×C₇₉	—	8	1	no	—
204	C₄×C₇₉	—	8	1	no	—
205	C₄×C₇₉	C₂×#135	1	2	yes	—
206	C₄×C₇₉	#577	1	2	yes	—
207	Dic₇₉	—	4	2	no	—
208	#19394	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	—	4	1	no	—
210	C₂×C₇₉	—	16	1	no	—
211	C₂×C₇₉	#3042	1	1	yes	characteristic
212	C₂×C₇₉	#3050	1	1	yes	characteristic
213	C₂×C₇₉	#3068	1	1	yes	characteristic
214	D₇₉	—	4	4	no	—
215	#3228	D₇₉	1	1	yes	characteristic, complemented
216	#3109	—	79	1	no	—
217	#3101	—	79	1	no	—
218	#2972	—	79	1	no	—
219	#1681	—	79	2	no	—
220	#1677	—	79	2	no	—
221	#1675	—	79	2	no	—
222	#1671	—	79	2	no	—
223	#1572	—	79	1	no	—
224	#1554	—	79	1	no	—
225	#1543	—	79	1	no	—
226	C₇₉	#19394	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₇₉	1	1	yes	characteristic
228	#532	C₂×D₇₉	1	1	yes	characteristic
229	C₂×C₄×D₄	—	79	1	no	—
230	#500	C₂×D₇₉	1	1	yes	characteristic, complemented
231	#498	C₂×D₇₉	1	1	yes	characteristic, complemented
232	#486	C₂×D₇₉	1	1	yes	characteristic, complemented
233	#486	C₂×D₇₉	1	1	yes	characteristic, complemented
234	#483	—	158	1	no	—
235	#482	—	2	2	no	—
236	#481	—	158	1	no	—
237	#478	—	2	2	no	—
238	#476	—	79	2	no	—
239	#476	—	79	2	no	—
240	#461	—	79	2	no	—
241	#459	—	79	2	no	—
242	#450	—	158	1	no	—
243	#447	—	158	1	no	—
244	#442	—	158	2	no	—
245	C₄×SD₁₆	—	158	2	no	—
246	C₈×D₄	—	79	2	no	—
247	C₈×D₄	—	79	2	no	—
248	C₈×D₄	—	158	2	no	—
249	#432	—	79	1	no	—
250	#431	—	79	1	no	—
251	#431	—	79	1	no	—
252	#431	C₂×D₇₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	—	158	2	no	—
254	#335	—	79	2	no	—
255	#334	—	79	2	no	—
256	#333	—	79	2	no	—
257	#333	—	79	2	no	—
258	#332	—	79	2	no	—
259	#331	—	79	2	no	—
260	C₂×#41	—	2	1	no	—
261	C₂²×D₄	—	79	1	no	—
262	C₂³×C₄	—	158	1	no	—
263	C₂×SD₁₆	—	158	2	no	—
264	C₂×D₈	—	158	2	no	—
265	C₂²×C₈	—	158	2	no	—
266	C₂²×C₈	—	158	2	no	—
267	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
268	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
270	#127	C₂²×D₇₉	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	#124	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	79	2	no	—
282	C₄×D₄	—	79	2	no	—
283	C₄×D₄	—	158	1	no	—
284	C₄×D₄	—	158	1	no	—
285	#117	—	2	1	no	—
286	C₂×C₄⋊C₄	—	79	1	no	—
287	C₂×C₂²⋊C₄	—	158	1	no	—
288	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	158	2	no	—
292	#106	—	158	2	no	—
293	C₄⋊C₈	—	79	2	no	—
294	C₄⋊C₈	—	79	2	no	—
295	C₄⋊C₈	—	79	2	no	—
296	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
297	#103	—	158	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	158	2	no	—
301	#102	—	158	2	no	—
302	#102	—	158	2	no	—
303	C₂²⋊C₈	—	158	1	no	—
304	C₂²⋊C₈	—	158	1	no	—
305	C₂²⋊C₈	—	158	1	no	—
306	C₂²⋊C₈	—	158	2	no	—
307	C₂²⋊C₈	—	158	2	no	—
308	C₂²⋊C₈	C₂²⋊D₇₉	1	2	yes	—
309	#97	—	158	1	no	—
310	C₄×C₈	—	158	1	no	—
311	C₄×C₈	—	158	1	no	—
312	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
314	C₂⁴	—	158	1	no	—
315	#41	—	8	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	79	2	no	—
324	C₂×D₄	—	158	4	no	—
325	C₂×D₄	—	158	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	632	2	no	—
328	C₂²×C₄	—	158	2	no	—
329	C₂²×C₄	—	158	1	no	—
330	C₂²×C₄	—	158	2	no	—
331	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
333	C₂²×C₄	#11929623	1	1	yes	characteristic
334	SD₁₆	—	316	4	no	—
335	D₈	—	316	4	no	—
336	C₂×C₈	—	632	2	no	—
337	C₂×C₈	—	632	2	no	—
338	C₂×C₈	—	158	2	no	—
339	C₂×C₈	—	158	2	no	—
340	C₂×C₈	—	158	2	no	—
341	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	79	2	no	—
352	C₄⋊C₄	—	158	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	158	2	no	—
357	C₂²⋊C₄	—	158	2	no	—
358	C₄²	—	4	1	no	—
359	C₄²	D₄×D₇₉	1	1	yes	characteristic
360	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
361	C₄²	#11929623	1	1	yes	characteristic
362	C₄²	C₂³×D₇₉	1	1	yes	characteristic
363	C₂³	—	4	1	no	—
364	C₂³	—	632	1	no	—
365	C₂³	—	632	1	no	—
366	C₂³	—	158	4	no	—
367	C₂³	—	158	2	no	—
368	C₂³	#14579132	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	79	4	no	—
377	D₄	—	158	4	no	—
378	D₄	—	158	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	316	2	no	—
387	C₂×C₄	—	316	2	no	—
388	C₂×C₄	—	632	2	no	—
389	C₂×C₄	—	632	1	no	—
390	C₂×C₄	—	158	2	no	—
391	C₂×C₄	#14579132	1	1	yes	characteristic
392	C₂×C₄	#14579132	1	1	yes	characteristic
393	C₂×C₄	#14579132	1	1	yes	characteristic
394	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	316	2	no	—
400	C₈	—	316	2	no	—
401	C₈	—	316	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	316	2	no	—
409	C₂²	—	316	2	no	—
410	C₂²	—	632	4	no	—
411	C₂²	—	158	4	no	—
412	C₂²	C₂×#14579132	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	316	2	no	—
421	C₄	#135×D₇₉	1	2	yes	—
422	C₄	#19099371	1	2	yes	—
423	C₂	—	4	1	no	—
424	C₂	—	16	1	no	—
425	C₂	—	316	4	no	—
426	C₂	#23772908	1	1	yes	characteristic
427	C₂	#23772977	1	1	yes	characteristic
428	C₂	#23773124	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3228	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	#23773487	C₂
hypercenter	#3228	D₇₉
hypocenter	C₇₉	#19394
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3228

Complements

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

N	H ≅ G/N	type
2. #23773404	C₂	semidirect
3. #23772423	C₂	semidirect
4. #23762834	C₂	semidirect
5. #23762806	C₂	semidirect
6. #23762796	C₂	semidirect
7. #23762772	C₂	semidirect
8. #23762180	C₂	semidirect
9. #23762110	C₂	semidirect
10. #23762062	C₂	semidirect
11. C₇₉×#3228	C₂	semidirect
30. #19098316	C₂²	semidirect
31. #19098314	C₂²	semidirect
32. #19098312	C₂²	semidirect
33. #19098312	C₂²	semidirect
34. #19098309	C₂²	semidirect
35. #19098307	C₂²	semidirect
38. #500×C₇₉	C₂²	semidirect
39. #498×C₇₉	C₂²	semidirect
40. #486×C₇₉	C₂²	semidirect
41. #486×C₇₉	C₂²	semidirect
215. #3228	D₇₉	semidirect
226. C₇₉	#19394	semidirect
230. #500	C₂×D₇₉	semidirect
231. #498	C₂×D₇₉	semidirect
232. #486	C₂×D₇₉	semidirect
233. #486	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23773487	2
#23773404	2
#23772423	2
#23762834	2
#23762806	2
#23762796	2
#23762772	2
#23762180	2
#23762110	2
#23762062	2
C₇₉×#3228	2
#19394	79