Subgroups — #28607157

Order 15104.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837520	C₂	1	2	yes	maximal
2	C₄×#14273749	C₂	1	1	yes	maximal, characteristic
3	#21432661	C₂	1	2	yes	maximal, complemented
4	#21424844	C₂	1	2	yes	maximal, complemented
5	#21424374	C₂	1	4	yes	maximal, complemented
6	#21424268	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424117	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14273749	C₂²	1	1	yes	characteristic
10	C₂×#14273733	C₂²	1	4	yes	—
11	C₄×#11745685	C₂²	1	2	yes	—
12	#16837520	—	2	8	no	—
13	C₄×Dic₂₃₆	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₂₃₆	C₄	1	1	yes	characteristic, complemented
15	C₄×#11745660	C₄	1	2	yes	complemented
16	C₄×#11745660	C₄	1	2	yes	complemented
17	C₄×D₄₇₂	C₄	1	1	yes	characteristic, complemented
18	C₄×D₄₇₂	C₄	1	1	yes	characteristic, complemented
19	C₂×#14273663	C₂²	1	2	yes	—
20	C₂×#14273663	C₂²	1	2	yes	—
21	#16837440	C₂²	1	1	yes	characteristic
22	#16837428	C₂²	1	4	yes	—
23	#16837427	—	2	4	no	—
24	#16837426	C₂²	1	2	yes	—
25	#16837424	—	2	2	no	—
26	C₄⋊C₈×D₅₉	—	2	2	no	—
27	C₂×#14273655	C₂²	1	4	yes	—
28	#16837399	C₂²	1	2	yes	—
29	#16837162	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#336	C₂²	1	2	yes	—
35	C₂×#11745685	C₂³	1	2	yes	—
36	#14273749	D₄	1	4	yes	—
37	#14273749	Q₈	1	4	yes	—
38	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
39	C₂×#11745660	C₂×C₄	1	2	yes	—
40	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
41	#14273733	—	2	8	no	—
42	#14273733	—	4	4	no	—
43	C₂×#11745664	C₂³	1	4	yes	—
44	C₂×#11745659	—	2	4	no	—
45	C₂×C₈×D₅₉	—	2	4	no	—
46	C₄×Dic₁₁₈	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₁₈	C₂×C₄	1	2	yes	—
48	C₄×D₂₃₆	C₂×C₄	1	2	yes	—
49	C₄×D₂₃₆	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₅₉	—	2	2	no	—
51	C₄×C₂²⋊D₅₉	—	2	2	no	—
52	#14273686	C₂³	1	2	yes	—
53	#14273684	—	2	2	no	—
54	C₄²×D₅₉	—	2	2	no	—
55	#14273663	—	2	4	no	—
56	#14273663	—	4	2	no	—
57	#14273661	C₂×C₄	1	1	yes	characteristic
58	#14273661	C₂×C₄	1	1	yes	characteristic
59	#14273659	C₂×C₄	1	2	yes	—
60	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
62	Dic₅₉⋊C₈	—	2	4	no	—
63	Dic₅₉⋊C₈	—	2	4	no	—
64	#14273655	—	2	8	no	—
65	#14273652	C₂×C₄	1	2	yes	—
66	#14273652	C₂×C₄	1	2	yes	—
67	#14273649	C₂×C₄	1	2	yes	—
68	#14273649	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
78	C₄×C₈×C₅₉	—	2	4	no	—
79	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
83	#95×C₅₉	—	2	1	no	—
84	C₂²×C₄×C₅₉	—	2	2	no	—
85	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
88	C₂×C₂²⋊D₅₉	—	2	2	no	—
89	#11745685	—	2	2	no	—
90	#11745685	—	2	2	no	—
91	#11745685	C₂×D₄	1	4	yes	—
92	#11745685	C₂×Q₈	1	4	yes	—
93	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₅₉	—	2	2	no	—
95	C₂×C₄×D₅₉	—	2	2	no	—
96	C₂×C₄×D₅₉	—	2	2	no	—
97	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₅₉	—	2	2	no	—
99	C₂×C₈×C₅₉	—	2	1	no	—
100	C₂×C₈×C₅₉	—	2	2	no	—
101	C₂×C₈×C₅₉	—	2	1	no	—
102	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
110	C₄⋊C₄×C₅₉	—	2	4	no	—
111	C₄²×C₅₉	—	2	2	no	—
112	C₄²×C₅₉	—	2	2	no	—
113	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²⋊Dic₅₉	—	2	2	no	—
118	(C₂×D₅₉)⋊C₄	—	2	2	no	—
119	(C₂×D₅₉)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
121	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
122	Dic₅₉⋊C₄	—	2	2	no	—
123	Dic₅₉⋊C₄	—	2	2	no	—
124	C₄×Dic₅₉	—	2	2	no	—
125	C₄×Dic₅₉	—	2	2	no	—
126	C₄×Dic₅₉	—	2	2	no	—
127	#11745664	—	2	4	no	—
128	#11745664	—	2	4	no	—
129	C₂×C₅₉⋊C₈	—	2	4	no	—
130	Dic₂₃₆	C₄⋊C₄	1	4	yes	complemented
131	D₄₇₂	C₄⋊C₄	1	4	yes	complemented
132	#11745660	C₄⋊C₄	1	8	yes	complemented
133	#11745659	—	4	8	no	—
134	C₈×D₅₉	—	4	8	no	—
135	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
136	C₂²×D₅₉	—	2	2	no	—
137	C₂×C₄×C₅₉	—	2	2	no	—
138	C₂×C₄×C₅₉	—	2	4	no	—
139	C₂×C₄×C₅₉	—	4	1	no	—
140	C₂×C₄×C₅₉	—	4	2	no	—
141	C₂×C₄×C₅₉	—	4	2	no	—
142	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂²⋊D₅₉	—	2	4	no	—
153	C₂²⋊D₅₉	—	2	4	no	—
154	C₂×Dic₅₉	—	2	2	no	—
155	C₂×Dic₅₉	—	2	2	no	—
156	C₂×Dic₅₉	—	2	2	no	—
157	D₂₃₆	—	2	2	no	—
158	D₂₃₆	C₂×C₄⋊C₄	1	4	yes	—
159	C₄×D₅₉	—	2	4	no	—
160	C₄×D₅₉	—	2	4	no	—
161	C₄×D₅₉	—	4	4	no	—
162	C₄×D₅₉	—	8	2	no	—
163	Dic₁₁₈	—	2	2	no	—
164	Dic₁₁₈	C₂×C₄⋊C₄	1	4	yes	—
165	C₈×C₅₉	—	2	1	no	—
166	C₈×C₅₉	—	2	1	no	—
167	C₈×C₅₉	—	2	2	no	—
168	C₈×C₅₉	—	2	2	no	—
169	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
170	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
171	C₅₉⋊C₈	—	4	4	no	—
172	#22688	—	59	1	no	maximal, Sylow
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂²×C₅₉	#547	1	1	yes	characteristic
177	C₂²×C₅₉	#554	1	1	yes	characteristic
178	C₂×D₅₉	—	2	4	no	—
179	C₂×D₅₉	—	4	2	no	—
180	C₂×D₅₉	—	4	2	no	—
181	C₄×C₅₉	—	2	1	no	—
182	C₄×C₅₉	—	2	1	no	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	4	4	no	—
185	C₄×C₅₉	#443	1	2	yes	complemented
186	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₅₉	#520	1	1	yes	characteristic
188	C₄×C₅₉	D₄²	1	1	yes	characteristic
189	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
190	Dic₅₉	—	2	4	no	—
191	Dic₅₉	—	4	2	no	—
192	Dic₅₉	—	4	2	no	—
193	C₂×#443	—	59	2	no	—
194	C₄×#135	—	59	1	no	—
195	#2906	—	59	2	no	—
196	#1945	—	59	2	no	—
197	#1866	—	59	4	no	—
198	#1848	—	59	1	no	—
199	#1806	—	59	2	no	—
200	C₈×C₄⋊C₄	D₅₉	1	1	yes	characteristic, complemented
201	C₂×C₅₉	—	2	1	no	—
202	C₂×C₅₉	—	2	1	no	—
203	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
205	C₂×C₅₉	#2957	1	1	yes	characteristic
206	D₅₉	—	4	4	no	—
207	C₂×#135	—	59	1	no	—
208	C₂×#131	—	59	4	no	—
209	C₄×#41	—	59	2	no	—
210	#443	—	118	8	no	—
211	C₄×Q₁₆	—	59	1	no	—
212	C₄×Q₁₆	—	59	1	no	—
213	C₄×SD₁₆	—	59	2	no	—
214	C₄×SD₁₆	—	59	2	no	—
215	C₄×D₈	—	59	1	no	—
216	C₄×D₈	—	59	1	no	—
217	C₂×#108	—	59	2	no	—
218	C₂×#108	—	59	2	no	—
219	#427	—	59	1	no	—
220	#424	—	59	4	no	—
221	#424	—	118	4	no	—
222	#423	—	59	2	no	—
223	#423	—	118	2	no	—
224	C₂×C₄⋊C₈	—	118	2	no	—
225	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
226	C₂×#104	—	59	4	no	—
227	#416	—	59	2	no	—
228	C₂×C₄×C₈	C₂×D₅₉	1	2	yes	—
229	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
231	#339	—	59	4	no	—
232	#336	C₂×D₅₉	1	2	yes	—
233	C₅₉	#22688	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	59	2	no	—
235	#135	—	59	4	no	—
236	#135	—	59	4	no	—
237	C₂×Q₁₆	—	59	1	no	—
238	C₂×SD₁₆	—	59	2	no	—
239	C₂×D₈	—	59	1	no	—
240	#131	—	118	8	no	—
241	#131	—	236	4	no	—
242	C₂×M₁₆	—	59	4	no	—
243	C₂×M₁₆	—	118	4	no	—
244	C₂²×C₈	—	118	4	no	—
245	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
247	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
248	C₄×Q₈	—	59	2	no	—
249	C₄×Q₈	—	59	2	no	—
250	C₄×D₄	—	59	2	no	—
251	C₄×D₄	—	59	2	no	—
252	C₄×D₄	—	118	2	no	—
253	C₄×D₄	—	118	2	no	—
254	#117	—	59	2	no	—
255	#117	—	118	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	118	2	no	—
258	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
259	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
260	#108	—	118	4	no	—
261	#108	—	236	2	no	—
262	#107	—	59	1	no	—
263	#107	—	59	1	no	—
264	#106	—	59	2	no	—
265	C₄⋊C₈	—	118	4	no	—
266	C₄⋊C₈	—	118	4	no	—
267	C₄⋊C₈	—	118	2	no	—
268	C₄⋊C₈	—	118	2	no	—
269	C₄⋊C₈	D₂₃₆	1	1	yes	characteristic
270	C₄⋊C₈	D₂₃₆	1	1	yes	characteristic
271	C₄⋊C₈	D₂₃₆	1	2	yes	—
272	#104	—	118	8	no	—
273	#103	—	59	2	no	—
274	#103	—	59	2	no	—
275	#102	—	59	2	no	—
276	#102	—	59	2	no	—
277	C₄×C₈	—	2	4	no	—
278	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
279	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
280	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
281	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
282	#95	—	2	1	no	—
283	#41	—	59	4	no	—
284	#41	—	59	4	no	—
285	#41	—	118	2	no	—
286	#41	—	118	2	no	—
287	C₂×Q₈	—	59	2	no	—
288	C₂×D₄	—	59	2	no	—
289	C₂×D₄	—	118	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	118	2	no	—
292	C₂²×C₄	—	118	2	no	—
293	C₂²×C₄	—	118	2	no	—
294	C₂²×C₄	#11745685	1	1	yes	characteristic
295	C₂²×C₄	#11745685	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
297	Q₁₆	—	59	4	no	—
298	SD₁₆	—	59	8	no	—
299	D₈	—	59	4	no	—
300	M₁₆	—	118	4	no	—
301	M₁₆	—	118	4	no	—
302	M₁₆	—	236	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	118	4	no	—
308	C₂×C₈	—	236	8	no	—
309	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
313	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
314	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
315	C₂×C₈	D₄×D₅₉	1	2	yes	—
316	C₂×C₈	Q₈×D₅₉	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	59	2	no	—
319	C₄⋊C₄	—	59	2	no	—
320	C₄⋊C₄	—	118	2	no	—
321	C₄⋊C₄	—	118	2	no	—
322	C₂²⋊C₄	—	118	2	no	—
323	C₂²⋊C₄	—	118	2	no	—
324	C₂²⋊C₄	—	118	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	118	2	no	—
328	C₄²	—	118	2	no	—
329	C₄²	—	118	2	no	—
330	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
332	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
333	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
334	C₂³	—	118	2	no	—
335	C₂³	C₂×#11745685	1	1	yes	characteristic
336	Q₈	—	59	4	no	—
337	Q₈	—	118	2	no	—
338	D₄	—	59	4	no	—
339	D₄	—	118	4	no	—
340	D₄	—	118	4	no	—
341	D₄	—	118	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	118	2	no	—
348	C₂×C₄	—	118	4	no	—
349	C₂×C₄	—	118	4	no	—
350	C₂×C₄	—	118	2	no	—
351	C₂×C₄	—	118	2	no	—
352	C₂×C₄	—	472	2	no	—
353	C₂×C₄	—	236	4	no	—
354	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
355	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
356	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
357	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
362	C₂×C₄	#14273773	1	1	yes	characteristic
363	C₂×C₄	#14273774	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	236	4	no	—
369	C₈	C₄⋊C₄×D₅₉	1	2	yes	—
370	C₈	C₄⋊C₄×D₅₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	118	4	no	—
374	C₂²	—	236	2	no	—
375	C₂²	—	236	2	no	—
376	C₂²	C₂×C₄×D₂₃₆	1	1	yes	characteristic
377	C₂²	#16838057	1	1	yes	characteristic
378	C₂²	#16838112	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	4	no	—
383	C₄	—	118	4	no	—
384	C₄	—	236	2	no	—
385	C₄	—	236	2	no	—
386	C₄	#16837520	1	2	yes	complemented
387	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
388	C₄	#16837882	1	1	yes	characteristic
389	C₄	D₄×D₂₃₆	1	1	yes	characteristic
390	C₄	Q₈×D₂₃₆	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	236	4	no	—
394	C₂	C₄⋊C₄×D₂₃₆	1	1	yes	characteristic
395	C₂	C₂×#16837520	1	1	yes	characteristic
396	C₂	#21433014	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₈×C₄⋊C₄×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273749	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₅₉
hypocenter	C₅₉	#22688
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #21432661	C₂	semidirect
4. #21424844	C₂	semidirect
5. #21424374	C₂	semidirect
6. #21424268	C₂	semidirect
7. #21424117	C₂	semidirect
8. C₈×C₄⋊C₄×C₅₉	C₂	semidirect
13. C₄×Dic₂₃₆	C₄	semidirect
14. C₄×Dic₂₃₆	C₄	semidirect
15. C₄×#11745660	C₄	semidirect
16. C₄×#11745660	C₄	semidirect
17. C₄×D₄₇₂	C₄	semidirect
18. C₄×D₄₇₂	C₄	semidirect
130. Dic₂₃₆	C₄⋊C₄	semidirect
131. D₄₇₂	C₄⋊C₄	semidirect
132. #11745660	C₄⋊C₄	semidirect
185. C₄×C₅₉	#443	semidirect
200. C₈×C₄⋊C₄	D₅₉	semidirect
233. C₅₉	#22688	semidirect
386. C₄	#16837520	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837520	2
C₄×#14273749	2
#21432661	2
#21424844	2
#21424374	2
#21424268	2
#21424117	2
C₈×C₄⋊C₄×C₅₉	2
#22688	59