Subgroups — C₅₉×#33532 #28445641

Order 15104.

1090 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3584	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#510	C₂	1	2	yes	maximal, complemented
3	C₅₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2191	C₂	1	8	yes	maximal, complemented
5	C₅₉×#2145	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#585	—	2	1	no	—
8	C₅₉×#578	—	2	2	no	—
9	C₅₉×#577	—	2	4	no	—
10	C₅₉×#576	—	2	2	no	—
11	C₅₉×#575	—	2	1	no	—
12	C₅₉×#575	C₂²	1	4	yes	—
13	C₂×#135×C₅₉	—	2	2	no	—
14	C₂×#135×C₅₉	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#536	—	2	1	no	—
18	C₅₉×#510	—	2	4	no	—
19	C₅₉×#510	C₂²	1	8	yes	complemented
20	C₂×Q₃₂×C₅₉	—	2	2	no	—
21	C₂×SD₃₂×C₅₉	—	2	2	no	—
22	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
23	C₅₉×#470	C₂²	1	4	yes	complemented
24	C₅₉×#467	—	2	2	no	—
25	C₅₉×#427	C₂²	1	1	yes	characteristic, complemented
26	C₅₉×#419	—	2	1	no	—
27	C₅₉×#360	C₂²	1	8	yes	complemented
28	C₅₉×#349	C₂²	1	4	yes	complemented
29	2₋¹⁺⁴×C₅₉	—	2	4	no	—
30	2₋¹⁺⁴×C₅₉	—	4	1	no	—
31	H(5,𝔽₂)×C₅₉	—	2	4	no	—
32	H(5,𝔽₂)×C₅₉	—	4	2	no	—
33	H(5,𝔽₂)×C₅₉	—	4	1	no	—
34	C₂×#41×C₅₉	—	2	4	no	—
35	C₂×#41×C₅₉	—	2	2	no	—
36	C₂×#41×C₅₉	—	4	4	no	—
37	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₅₉	—	2	1	no	—
39	#137×C₅₉	—	2	4	no	—
40	#137×C₅₉	—	2	8	no	—
41	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
42	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
43	#135×C₅₉	—	2	4	no	—
44	#135×C₅₉	—	2	4	no	—
45	#135×C₅₉	—	2	2	no	—
46	#135×C₅₉	—	2	4	no	—
47	#135×C₅₉	—	2	2	no	—
48	#135×C₅₉	D₄	1	4	yes	—
49	#135×C₅₉	C₂³	1	4	yes	—
50	C₂×Q₁₆×C₅₉	—	2	2	no	—
51	C₂×Q₁₆×C₅₉	—	2	2	no	—
52	C₂×Q₁₆×C₅₉	—	2	2	no	—
53	C₂×Q₁₆×C₅₉	—	2	1	no	—
54	C₂×Q₁₆×C₅₉	D₄	1	2	yes	—
55	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
56	C₂×SD₁₆×C₅₉	—	2	4	no	—
57	C₂×SD₁₆×C₅₉	—	2	2	no	—
58	C₂×D₈×C₅₉	—	2	2	no	—
59	C₂×D₈×C₅₉	D₄	1	2	yes	—
60	#131×C₅₉	—	2	2	no	—
61	#131×C₅₉	—	2	2	no	—
62	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
63	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₅₉	D₄	1	2	yes	—
65	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₅₉	—	4	1	no	—
67	#124×C₅₉	—	4	1	no	—
68	#123×C₅₉	—	4	2	no	—
69	C₂²⋊Q₈×C₅₉	—	2	4	no	—
70	#117×C₅₉	—	2	1	no	—
71	Q₃₂×C₅₉	—	2	8	no	—
72	SD₃₂×C₅₉	—	2	8	no	—
73	M₃₂×C₅₉	—	2	2	no	—
74	M₃₂×C₅₉	C₂³	1	4	yes	—
75	C₂×C₁₆×C₅₉	—	2	2	no	—
76	#107×C₅₉	—	2	1	no	—
77	#106×C₅₉	C₂³	1	2	yes	—
78	#103×C₅₉	—	2	4	no	—
79	#41×C₅₉	—	2	2	no	—
80	#41×C₅₉	—	2	2	no	—
81	#41×C₅₉	—	2	8	no	—
82	#41×C₅₉	—	2	4	no	—
83	#41×C₅₉	—	2	4	no	—
84	#41×C₅₉	—	4	4	no	—
85	#41×C₅₉	—	4	8	no	—
86	#41×C₅₉	—	4	4	no	—
87	#41×C₅₉	—	4	4	no	—
88	#41×C₅₉	—	4	4	no	—
89	#41×C₅₉	—	4	2	no	—
90	#41×C₅₉	—	4	2	no	—
91	C₂×Q₈×C₅₉	—	2	4	no	—
92	C₂×Q₈×C₅₉	—	2	2	no	—
93	C₂×Q₈×C₅₉	—	2	2	no	—
94	C₂×Q₈×C₅₉	—	4	4	no	—
95	C₂×Q₈×C₅₉	—	4	1	no	—
96	C₂×Q₈×C₅₉	—	4	2	no	—
97	C₂×Q₈×C₅₉	—	4	2	no	—
98	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
99	C₂×D₄×C₅₉	—	2	4	no	—
100	C₂×D₄×C₅₉	—	2	2	no	—
101	C₂×D₄×C₅₉	—	4	8	no	—
102	C₂×D₄×C₅₉	—	4	4	no	—
103	C₂×D₄×C₅₉	—	4	4	no	—
104	C₂×D₄×C₅₉	—	4	2	no	—
105	C₂×D₄×C₅₉	D₈	1	2	yes	—
106	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	—	4	4	no	—
108	C₂²×C₄×C₅₉	—	4	2	no	—
109	C₂²×C₄×C₅₉	—	4	1	no	—
110	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
112	Q₁₆×C₅₉	—	2	4	no	—
113	Q₁₆×C₅₉	—	2	2	no	—
114	Q₁₆×C₅₉	—	2	4	no	—
115	Q₁₆×C₅₉	—	4	1	no	—
116	Q₁₆×C₅₉	—	4	1	no	—
117	Q₁₆×C₅₉	C₂×D₄	1	4	yes	—
118	SD₁₆×C₅₉	—	2	8	no	—
119	SD₁₆×C₅₉	—	2	4	no	—
120	SD₁₆×C₅₉	—	2	4	no	—
121	D₈×C₅₉	—	2	4	no	—
122	D₈×C₅₉	—	2	2	no	—
123	D₈×C₅₉	C₂×D₄	1	4	yes	—
124	M₁₆×C₅₉	—	2	2	no	—
125	M₁₆×C₅₉	—	2	4	no	—
126	C₂×C₈×C₅₉	—	2	2	no	—
127	C₂×C₈×C₅₉	—	2	2	no	—
128	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	4	4	no	—
135	C₂²⋊C₄×C₅₉	—	4	1	no	—
136	C₂²⋊C₄×C₅₉	—	4	4	no	—
137	C₄²×C₅₉	—	4	1	no	—
138	C₁₆×C₅₉	—	2	4	no	—
139	C₂³×C₅₉	—	4	4	no	—
140	C₂³×C₅₉	—	4	2	no	—
141	C₂³×C₅₉	C₂×D₈	1	2	yes	—
142	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
143	Q₈×C₅₉	—	2	2	no	—
144	Q₈×C₅₉	—	2	4	no	—
145	Q₈×C₅₉	—	4	4	no	—
146	Q₈×C₅₉	—	4	2	no	—
147	Q₈×C₅₉	—	4	2	no	—
148	Q₈×C₅₉	—	4	2	no	—
149	Q₈×C₅₉	—	8	2	no	—
150	D₄×C₅₉	—	2	4	no	—
151	D₄×C₅₉	—	2	4	no	—
152	D₄×C₅₉	—	2	2	no	—
153	D₄×C₅₉	—	4	4	no	—
154	D₄×C₅₉	—	4	8	no	—
155	D₄×C₅₉	—	4	4	no	—
156	D₄×C₅₉	—	4	4	no	—
157	D₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	—	2	2	no	—
159	C₂×C₄×C₅₉	—	2	2	no	—
160	C₂×C₄×C₅₉	—	4	8	no	—
161	C₂×C₄×C₅₉	—	4	4	no	—
162	C₂×C₄×C₅₉	—	4	2	no	—
163	C₂×C₄×C₅₉	—	4	4	no	—
164	C₂×C₄×C₅₉	—	4	4	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	8	2	no	—
168	C₂×C₄×C₅₉	#120	1	2	yes	—
169	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₅₉	—	2	2	no	—
174	C₈×C₅₉	#120	1	1	yes	characteristic
175	C₈×C₅₉	#120	1	1	yes	characteristic
176	C₈×C₅₉	C₂²×D₄	1	2	yes	—
177	#33532	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₅₉	—	2	2	no	—
179	C₂²×C₅₉	—	4	1	no	—
180	C₂²×C₅₉	—	4	2	no	—
181	C₂²×C₅₉	—	4	4	no	—
182	C₂²×C₅₉	—	16	2	no	—
183	C₂²×C₅₉	—	16	4	no	—
184	C₂²×C₅₉	#447	1	2	yes	—
185	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₅₉	—	2	2	no	—
187	C₄×C₅₉	—	4	4	no	—
188	C₄×C₅₉	—	8	2	no	—
189	C₄×C₅₉	—	8	2	no	—
190	C₄×C₅₉	#447	1	2	yes	—
191	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
192	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	#3584	C₂×C₅₉	1	1	yes	characteristic
194	C₂×#510	C₂×C₅₉	1	2	yes	complemented
195	#3059	C₂×C₅₉	1	1	yes	characteristic, complemented
196	#2191	C₂×C₅₉	1	8	yes	complemented
197	#2145	C₂×C₅₉	1	2	yes	complemented
198	#2115	C₂×C₅₉	1	1	yes	characteristic, complemented
199	C₂×C₅₉	—	2	1	no	—
200	C₂×C₅₉	—	2	2	no	—
201	C₂×C₅₉	—	4	2	no	—
202	C₂×C₅₉	—	8	4	no	—
203	C₂×C₅₉	C₂×#447	1	1	yes	characteristic
204	#585	—	2	1	no	—
205	#578	—	2	2	no	—
206	#577	—	2	4	no	—
207	#576	—	2	2	no	—
208	#575	—	2	1	no	—
209	#575	C₂²×C₅₉	1	4	yes	—
210	C₂×#135	—	2	2	no	—
211	C₂×#135	C₂²×C₅₉	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
213	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
214	#536	—	2	1	no	—
215	#510	—	2	4	no	—
216	#510	C₂²×C₅₉	1	8	yes	complemented
217	C₂×Q₃₂	—	2	2	no	—
218	C₂×SD₃₂	—	2	2	no	—
219	C₂×M₃₂	C₂²×C₅₉	1	2	yes	complemented
220	#470	C₂²×C₅₉	1	4	yes	complemented
221	#467	—	2	2	no	—
222	#427	C₂²×C₅₉	1	1	yes	characteristic, complemented
223	#419	—	2	1	no	—
224	#360	C₂²×C₅₉	1	8	yes	complemented
225	#349	C₂²×C₅₉	1	4	yes	complemented
226	C₅₉	#33532	1	1	yes	characteristic, direct product factor, Sylow
227	2₋¹⁺⁴	—	2	4	no	—
228	2₋¹⁺⁴	—	4	1	no	—
229	H(5,𝔽₂)	—	2	4	no	—
230	H(5,𝔽₂)	—	4	2	no	—
231	H(5,𝔽₂)	—	4	1	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	4	4	no	—
235	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
236	C₂²×Q₈	—	2	1	no	—
237	#137	—	2	4	no	—
238	#137	—	2	8	no	—
239	AGL(1,ℤ/8)	—	2	4	no	—
240	AGL(1,ℤ/8)	—	2	8	no	—
241	#135	—	2	4	no	—
242	#135	—	2	4	no	—
243	#135	—	2	2	no	—
244	#135	—	2	4	no	—
245	#135	—	2	2	no	—
246	#135	D₄×C₅₉	1	4	yes	—
247	#135	C₂³×C₅₉	1	4	yes	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	D₄×C₅₉	1	2	yes	—
253	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	D₄×C₅₉	1	2	yes	—
258	#131	—	2	2	no	—
259	#131	—	2	2	no	—
260	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
262	C₂²×C₈	D₄×C₅₉	1	2	yes	—
263	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
264	C₄⋊Q₈	—	4	1	no	—
265	#124	—	4	1	no	—
266	#123	—	4	2	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	#117	—	2	1	no	—
269	Q₃₂	—	2	8	no	—
270	SD₃₂	—	2	8	no	—
271	M₃₂	—	2	2	no	—
272	M₃₂	C₂³×C₅₉	1	4	yes	—
273	C₂×C₁₆	—	2	2	no	—
274	#107	—	2	1	no	—
275	#106	C₂³×C₅₉	1	2	yes	—
276	#103	—	2	4	no	—
277	#41	—	2	2	no	—
278	#41	—	2	2	no	—
279	#41	—	2	8	no	—
280	#41	—	2	4	no	—
281	#41	—	2	4	no	—
282	#41	—	4	4	no	—
283	#41	—	4	8	no	—
284	#41	—	4	4	no	—
285	#41	—	4	4	no	—
286	#41	—	4	4	no	—
287	#41	—	4	2	no	—
288	#41	—	4	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	D₈×C₅₉	1	1	yes	characteristic
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	D₈×C₅₉	1	2	yes	—
304	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
310	Q₁₆	—	2	4	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	2	4	no	—
313	Q₁₆	—	4	1	no	—
314	Q₁₆	—	4	1	no	—
315	Q₁₆	C₂×D₄×C₅₉	1	4	yes	—
316	SD₁₆	—	2	8	no	—
317	SD₁₆	—	2	4	no	—
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	4	no	—
320	D₈	—	2	2	no	—
321	D₈	C₂×D₄×C₅₉	1	4	yes	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
330	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₄²	—	4	1	no	—
336	C₁₆	—	2	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	C₂×D₈×C₅₉	1	2	yes	—
340	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	8	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	4	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	#120×C₅₉	1	2	yes	—
367	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
368	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
369	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	#120×C₅₉	1	1	yes	characteristic
373	C₈	#120×C₅₉	1	1	yes	characteristic
374	C₈	C₂²×D₄×C₅₉	1	2	yes	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	16	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₅₉×#447	1	2	yes	—
382	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₅₉×#447	1	2	yes	—
388	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
389	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	2	2	no	—
392	C₂	—	4	2	no	—
393	C₂	—	8	4	no	—
394	C₂	C₂×C₅₉×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
prime radical	C₅₉×#3584	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#131×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#510	C₂	semidirect
3. C₅₉×#3059	C₂	semidirect
4. C₅₉×#2191	C₂	semidirect
5. C₅₉×#2145	C₂	semidirect
6. C₅₉×#2115	C₂	semidirect
15. C₂²×Q₁₆×C₅₉	C₂²	semidirect
19. C₅₉×#510	C₂²	semidirect
22. C₂×M₃₂×C₅₉	C₂²	semidirect
23. C₅₉×#470	C₂²	semidirect
25. C₅₉×#427	C₂²	semidirect
27. C₅₉×#360	C₂²	semidirect
28. C₅₉×#349	C₂²	semidirect
177. #33532	C₅₉	direct (N × H)
194. C₂×#510	C₂×C₅₉	semidirect
195. #3059	C₂×C₅₉	semidirect
196. #2191	C₂×C₅₉	semidirect
197. #2145	C₂×C₅₉	semidirect
198. #2115	C₂×C₅₉	semidirect
212. C₂²×Q₁₆	C₂²×C₅₉	semidirect
216. #510	C₂²×C₅₉	semidirect
219. C₂×M₃₂	C₂²×C₅₉	semidirect
220. #470	C₂²×C₅₉	semidirect
222. #427	C₂²×C₅₉	semidirect
224. #360	C₂²×C₅₉	semidirect
225. #349	C₂²×C₅₉	semidirect
226. C₅₉	#33532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3584	2
C₂×C₅₉×#510	2
C₅₉×#3059	2
C₅₉×#2191	2
C₅₉×#2145	2
C₅₉×#2115	2
#33532	59

Subgroups — C59×#33532 #28445641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33532 #28445641