Subgroups — #34260287

Order 20224.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773959	C₂	1	1	yes	maximal, characteristic
2	#23772501	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772466	C₂	1	1	yes	maximal, characteristic
4	#23762301	C₂	1	2	yes	maximal, complemented
5	#23762242	C₂	1	2	yes	maximal, complemented
6	#23762235	C₂	1	2	yes	maximal, complemented
7	#23762211	C₂	1	2	yes	maximal, complemented
8	#23761820	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761816	C₂	1	1	yes	maximal, characteristic
10	#23761689	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099120	C₂²	1	1	yes	characteristic
13	#19099113	C₂²	1	1	yes	characteristic
14	#19098961	C₄	1	1	yes	characteristic
15	#19098936	C₄	1	1	yes	characteristic
16	#19098914	C₄	1	1	yes	characteristic
17	#19098910	C₄	1	1	yes	characteristic
18	#19098792	C₄	1	2	yes	—
19	#19098792	C₄	1	2	yes	—
20	#19098693	—	2	1	no	—
21	#19098690	C₂²	1	2	yes	—
22	C₈×Dic₁₅₈	—	2	1	no	—
23	#19098687	C₂²	1	2	yes	—
24	C₄×#11929613	C₂²	1	2	yes	—
25	C₄×#11929613	C₂²	1	2	yes	—
26	#19098642	—	2	1	no	—
27	#19098640	C₂²	1	2	yes	—
28	C₈×D₃₁₆	—	2	1	no	—
29	#19098628	C₂²	1	2	yes	—
30	#19098621	—	2	2	no	—
31	#19098616	C₂²	1	1	yes	characteristic
32	#19098528	—	2	2	no	—
33	C₄×#11929608	C₂²	1	1	yes	characteristic
34	#19098293	C₂²	1	2	yes	—
35	#19098293	C₂²	1	2	yes	—
36	#19098290	C₂²	1	2	yes	—
37	#19098290	C₂²	1	2	yes	—
38	#19098285	C₂²	1	2	yes	—
39	#19098284	C₂²	1	2	yes	—
40	#431×C₇₉	C₂²	1	1	yes	characteristic
41	#431×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	#335×C₇₉	C₂²	1	1	yes	characteristic
44	#335×C₇₉	C₂²	1	1	yes	characteristic
45	#334×C₇₉	C₂²	1	1	yes	characteristic
46	#334×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	—	2	1	no	—
48	C₂×#11929613	C₂×C₄	1	2	yes	—
49	C₂×#11929613	C₂×C₄	1	2	yes	—
50	C₂×#11929608	—	2	1	no	—
51	C₂×#11929607	—	2	2	no	—
52	C₂×C₈×D₇₉	—	2	2	no	—
53	#14579161	C₂×C₄	1	1	yes	characteristic
54	#14579161	C₂×C₄	1	1	yes	characteristic
55	#14579161	C₂×C₄	1	1	yes	characteristic
56	#14579158	C₂×C₄	1	1	yes	characteristic
57	#14579153	—	2	1	no	—
58	#14579149	—	2	1	no	—
59	#14579140	—	2	1	no	—
60	#14579140	C₂×C₄	1	2	yes	—
61	#14579135	—	2	1	no	—
62	#14579135	C₂×C₄	1	2	yes	—
63	C₄×Dic₁₅₈	—	2	1	no	—
64	C₄×Dic₁₅₈	C₂³	1	2	yes	—
65	C₄×D₃₁₆	—	2	1	no	—
66	C₄×D₃₁₆	C₂³	1	2	yes	—
67	#14579120	—	2	1	no	—
68	#14579093	C₂×C₄	1	2	yes	—
69	#14579093	C₂×C₄	1	2	yes	—
70	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
71	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
72	Dic₇₉⋊C₈	—	2	2	no	—
73	Dic₇₉⋊C₈	—	2	2	no	—
74	#14579086	C₂×C₄	1	2	yes	—
75	#14579086	C₂×C₄	1	2	yes	—
76	#14579083	C₂×C₄	1	2	yes	—
77	#14579083	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
79	(C₂×D₇₉)⋊C₈	—	2	2	no	—
80	(C₂×D₇₉)⋊C₈	—	2	2	no	—
81	#14579072	—	2	1	no	—
82	#14579071	—	2	2	no	—
83	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
84	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₇₉	—	2	2	no	—
86	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₇₉	—	2	1	no	—
94	C₂²⋊C₈×C₇₉	—	2	1	no	—
95	C₄×C₈×C₇₉	—	2	1	no	—
96	C₄×C₈×C₇₉	—	2	1	no	—
97	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	#11929624	—	8	1	no	—
102	#11929624	—	8	1	no	—
103	C₂×Dic₁₅₈	—	2	1	no	—
104	C₂×Dic₁₅₈	—	2	1	no	—
105	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
106	C₂×D₃₁₆	—	2	1	no	—
107	C₂×D₃₁₆	—	2	1	no	—
108	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
109	C₂×C₂²⋊D₇₉	—	2	2	no	—
110	C₂×C₄×D₇₉	—	2	2	no	—
111	#11929613	—	2	4	no	—
112	#11929613	—	4	2	no	—
113	#11929608	—	4	2	no	—
114	#11929607	—	8	2	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
117	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
118	C₈×D₇₉	—	8	2	no	—
119	C₄⋊Dic₇₉	—	2	1	no	—
120	C₄⋊Dic₇₉	—	2	1	no	—
121	C₄⋊Dic₇₉	—	2	1	no	—
122	C₄⋊Dic₇₉	—	2	1	no	—
123	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
124	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
125	Dic₇₉⋊C₄	—	2	2	no	—
126	Dic₇₉⋊C₄	—	2	2	no	—
127	C₂²⋊Dic₇₉	—	2	2	no	—
128	(C₂×D₇₉)⋊C₄	—	2	2	no	—
129	(C₂×D₇₉)⋊C₄	—	2	2	no	—
130	C₄×Dic₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	1	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	4	1	no	—
140	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₇₉	C₂²×C₄	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	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	1	no	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₇₉	—	8	2	no	—
162	C₂×Dic₇₉	—	2	2	no	—
163	C₂×Dic₇₉	—	2	2	no	—
164	C₂×Dic₇₉	—	2	2	no	—
165	D₃₁₆	—	2	2	no	—
166	D₃₁₆	—	2	2	no	—
167	D₃₁₆	—	4	2	no	—
168	D₃₁₆	—	8	1	no	—
169	C₄×D₇₉	—	4	2	no	—
170	C₄×D₇₉	—	4	2	no	—
171	Dic₁₅₈	—	2	2	no	—
172	Dic₁₅₈	—	2	2	no	—
173	Dic₁₅₈	—	4	2	no	—
174	Dic₁₅₈	—	8	1	no	—
175	C₈×C₇₉	—	2	1	no	—
176	C₈×C₇₉	—	2	1	no	—
177	C₈×C₇₉	—	2	1	no	—
178	C₈×C₇₉	—	4	1	no	—
179	C₈×C₇₉	—	4	1	no	—
180	C₈×C₇₉	—	4	1	no	—
181	C₈×C₇₉	—	4	1	no	—
182	C₈×C₇₉	#131	1	2	yes	—
183	C₇₉⋊C₈	—	2	2	no	—
184	C₇₉⋊C₈	—	2	2	no	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	2	1	no	—
188	C₂²×C₇₉	—	2	1	no	—
189	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂×D₇₉	—	4	2	no	—
191	C₂×D₇₉	—	4	2	no	—
192	C₂×D₇₉	—	4	2	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	#444	1	2	yes	—
197	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
198	C₄×C₇₉	#568	1	1	yes	characteristic
199	C₄×C₇₉	#577	1	1	yes	characteristic
200	C₄×C₇₉	#577	1	1	yes	characteristic
201	Dic₇₉	—	4	2	no	—
202	Dic₇₉	—	4	2	no	—
203	Dic₇₉	—	4	2	no	—
204	#18089	—	79	1	no	maximal, Sylow
205	C₂×C₇₉	—	4	1	no	—
206	C₂×C₇₉	#2935	1	1	yes	characteristic
207	C₂×C₇₉	#2949	1	1	yes	characteristic
208	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
209	D₇₉	—	8	2	no	—
210	#3167	—	79	1	no	—
211	#2986	—	79	1	no	—
212	#2979	—	79	1	no	—
213	#1592	—	79	2	no	—
214	#1583	—	79	2	no	—
215	#1582	—	79	2	no	—
216	SD₁₆⋊C₈	—	79	2	no	—
217	#1564	D₇₉	1	1	yes	characteristic, complemented
218	#1485	—	79	1	no	—
219	#1484	—	79	1	no	—
220	#1451	—	79	1	no	—
221	C₇₉	#18089	1	1	yes	characteristic, complemented, Sylow
222	#533	—	79	1	no	—
223	#532	—	79	1	no	—
224	#498	—	79	1	no	—
225	#492	—	79	1	no	—
226	#487	—	79	1	no	—
227	#486	—	79	1	no	—
228	#465	—	79	2	no	—
229	#465	—	79	2	no	—
230	#446	—	79	2	no	—
231	#446	—	158	1	no	—
232	C₈×Q₈	—	79	2	no	—
233	C₈×Q₈	—	158	1	no	—
234	C₄×SD₁₆	—	79	2	no	—
235	C₄×SD₁₆	—	79	2	no	—
236	#436	—	79	2	no	—
237	#436	—	158	1	no	—
238	C₈×D₄	—	79	2	no	—
239	C₈×D₄	—	158	1	no	—
240	#433	—	158	2	no	—
241	#431	—	79	1	no	—
242	#431	C₂×D₇₉	1	1	yes	characteristic
243	#431	C₂×D₇₉	1	1	yes	characteristic
244	#408	—	158	2	no	—
245	C₄×M₁₆	—	79	1	no	—
246	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
247	#335	C₂×D₇₉	1	1	yes	characteristic
248	#335	C₂×D₇₉	1	1	yes	characteristic
249	#334	C₂×D₇₉	1	1	yes	characteristic
250	#334	C₂×D₇₉	1	1	yes	characteristic
251	Q₈⋊C₈	—	79	2	no	—
252	Q₈⋊C₈	—	79	2	no	—
253	D₄⋊C₈	—	79	2	no	—
254	D₄⋊C₈	—	79	2	no	—
255	#322	—	79	2	no	—
256	#322	—	79	2	no	—
257	C₂×#41	—	158	1	no	—
258	C₂×SD₁₆	—	79	2	no	—
259	C₂×SD₁₆	—	79	2	no	—
260	C₂×M₁₆	—	158	2	no	—
261	C₂×M₁₆	—	158	1	no	—
262	C₂²×C₈	—	158	2	no	—
263	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
265	C₄⋊Q₈	—	79	1	no	—
266	C₄⋊Q₈	—	79	1	no	—
267	C₄⋊Q₈	—	79	1	no	—
268	#127	—	79	1	no	—
269	#125	—	158	1	no	—
270	#124	—	158	1	no	—
271	C₂²⋊Q₈	—	79	2	no	—
272	C₂²⋊Q₈	—	158	1	no	—
273	#121	—	79	2	no	—
274	#121	—	158	1	no	—
275	C₄×Q₈	—	79	2	no	—
276	C₄×Q₈	—	158	1	no	—
277	C₄×D₄	—	79	2	no	—
278	C₄×D₄	—	158	1	no	—
279	#117	—	158	1	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	#106	—	79	2	no	—
282	#106	—	79	2	no	—
283	C₄⋊C₈	—	79	1	no	—
284	C₄⋊C₈	—	79	1	no	—
285	C₄⋊C₈	—	158	2	no	—
286	C₄⋊C₈	—	158	2	no	—
287	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
291	#103	—	79	2	no	—
292	#103	—	79	2	no	—
293	#102	—	79	2	no	—
294	#102	—	79	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	79	2	no	—
298	C₂²⋊C₈	—	158	2	no	—
299	C₂²⋊C₈	—	158	2	no	—
300	#97	—	158	2	no	—
301	#97	—	158	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	79	2	no	—
305	C₄×C₈	—	79	2	no	—
306	C₄×C₈	—	158	2	no	—
307	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
308	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
311	#41	—	632	1	no	—
312	#41	—	632	1	no	—
313	C₂×Q₈	—	79	2	no	—
314	C₂×Q₈	—	158	1	no	—
315	C₂×Q₈	—	158	1	no	—
316	C₂×D₄	—	79	2	no	—
317	C₂×D₄	—	158	2	no	—
318	C₂×D₄	—	158	1	no	—
319	C₂×D₄	—	158	1	no	—
320	C₂²×C₄	—	158	2	no	—
321	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
323	C₂²×C₄	#11929625	1	1	yes	characteristic
324	SD₁₆	—	316	2	no	—
325	SD₁₆	—	158	4	no	—
326	M₁₆	—	316	2	no	—
327	M₁₆	—	632	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	79	2	no	—
335	C₂×C₈	—	79	2	no	—
336	C₂×C₈	—	632	2	no	—
337	C₂×C₈	—	158	2	no	—
338	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
342	C₄⋊C₄	—	79	2	no	—
343	C₄⋊C₄	—	79	2	no	—
344	C₄⋊C₄	—	158	2	no	—
345	C₄⋊C₄	—	158	2	no	—
346	C₄⋊C₄	—	158	1	no	—
347	C₄⋊C₄	—	158	1	no	—
348	C₄⋊C₄	—	158	1	no	—
349	C₄⋊C₄	—	158	1	no	—
350	C₂²⋊C₄	—	158	2	no	—
351	C₂²⋊C₄	—	158	2	no	—
352	C₂²⋊C₄	—	158	2	no	—
353	C₄²	—	158	2	no	—
354	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
355	C₄²	D₄×D₇₉	1	1	yes	characteristic
356	C₄²	#11929625	1	1	yes	characteristic
357	C₄²	C₂³×D₇₉	1	1	yes	characteristic
358	C₂³	—	158	2	no	—
359	C₂³	#14579123	1	1	yes	characteristic
360	Q₈	—	316	2	no	—
361	Q₈	—	632	1	no	—
362	Q₈	—	158	2	no	—
363	Q₈	—	158	2	no	—
364	D₄	—	316	2	no	—
365	D₄	—	632	1	no	—
366	D₄	—	632	2	no	—
367	D₄	—	158	2	no	—
368	D₄	—	158	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	316	2	no	—
375	C₂×C₄	—	316	2	no	—
376	C₂×C₄	—	158	2	no	—
377	C₂×C₄	—	158	2	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	#14579123	1	1	yes	characteristic
380	C₂×C₄	#14579123	1	1	yes	characteristic
381	C₂×C₄	#14579123	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	1	no	—
392	C₈	—	316	2	no	—
393	C₈	—	158	2	no	—
394	C₈	—	158	2	no	—
395	C₈	#14579167	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	316	2	no	—
400	C₂²	—	316	2	no	—
401	C₂²	—	316	2	no	—
402	C₂²	C₂×#14579123	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	316	2	no	—
407	C₄	—	316	2	no	—
408	C₄	—	316	2	no	—
409	C₄	#19098684	1	2	yes	—
410	C₄	C₂×#14579167	1	1	yes	characteristic
411	C₄	#19099329	1	1	yes	characteristic
412	C₄	#19099370	1	1	yes	characteristic
413	C₄	#19099370	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	632	2	no	—
416	C₂	#23772143	1	1	yes	characteristic
417	C₂	#23772258	1	1	yes	characteristic
418	C₂	C₂×#19098684	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1564	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#19099113	C₂²
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1564	D₇₉
hypocenter	C₇₉	#18089
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #23772501	C₂	semidirect
4. #23762301	C₂	semidirect
5. #23762242	C₂	semidirect
6. #23762235	C₂	semidirect
7. #23762211	C₂	semidirect
8. #23761820	C₂	semidirect
10. #23761689	C₂	semidirect
11. C₇₉×#1564	C₂	semidirect
217. #1564	D₇₉	semidirect
221. C₇₉	#18089	semidirect

Maximal subgroups

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

subgroup	index
#23773959	2
#23772501	2
#23772466	2
#23762301	2
#23762242	2
#23762235	2
#23762211	2
#23761820	2
#23761816	2
#23761689	2
C₇₉×#1564	2
#18089	79