Subgroups — C₂×C₅₉×#2217 #28445708

Order 15104.

754 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SD₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#466	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2217	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅₉×#367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
13	C₂×#121×C₅₉	—	2	1	no	—
14	C₂×SD₃₂×C₅₉	—	2	4	no	—
15	C₂×SD₃₂×C₅₉	C₂²	1	4	yes	complemented
16	C₂²×C₁₆×C₅₉	—	2	4	no	—
17	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₆×C₅₉	C₂²	1	4	yes	complemented
20	C₅₉×#467	—	2	2	no	—
21	C₅₉×#467	C₂²	1	4	yes	complemented
22	C₅₉×#466	—	2	2	no	—
23	C₅₉×#466	C₂²	1	4	yes	—
24	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₅₉	—	2	1	no	—
27	C₂×#102×C₅₉	—	2	1	no	—
28	C₅₉×#367	C₂²	1	4	yes	complemented
29	C₅₉×#358	C₂²	1	4	yes	complemented
30	C₅₉×#357	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₅₉	—	2	1	no	—
32	C₂²×D₄×C₅₉	—	2	1	no	—
33	C₂²×D₄×C₅₉	—	4	1	no	—
34	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
35	C₂×Q₁₆×C₅₉	—	2	2	no	—
36	C₂×Q₁₆×C₅₉	—	2	1	no	—
37	C₂×Q₁₆×C₅₉	—	2	2	no	—
38	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
39	C₂×D₈×C₅₉	—	2	2	no	—
40	C₂×D₈×C₅₉	—	2	1	no	—
41	C₂×D₈×C₅₉	—	2	2	no	—
42	C₂×D₈×C₅₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₅₉	—	2	2	no	—
44	C₂²×C₈×C₅₉	—	2	2	no	—
45	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₅₉	D₄	1	2	yes	—
47	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
49	C₂²⋊Q₈×C₅₉	—	2	4	no	—
50	C₂²⋊Q₈×C₅₉	—	4	2	no	—
51	#121×C₅₉	—	2	4	no	—
52	#121×C₅₉	—	4	2	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₅₉	—	4	1	no	—
56	C₂×C₂²⋊C₄×C₅₉	—	4	1	no	—
57	C₂×C₂²⋊C₄×C₅₉	—	4	1	no	—
58	SD₃₂×C₅₉	—	2	8	no	—
59	C₂×C₁₆×C₅₉	—	2	2	no	—
60	C₂×C₁₆×C₅₉	—	2	8	no	—
61	C₂×C₁₆×C₅₉	D₄	1	4	yes	complemented
62	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
63	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
64	#107×C₅₉	—	2	1	no	—
65	#107×C₅₉	—	2	1	no	—
66	#107×C₅₉	C₂³	1	2	yes	—
67	#107×C₅₉	C₂³	1	2	yes	—
68	#103×C₅₉	—	2	4	no	—
69	#102×C₅₉	—	2	4	no	—
70	C₂⁴×C₅₉	—	4	1	no	—
71	C₂⁴×C₅₉	D₈	1	1	yes	characteristic
72	C₂×Q₈×C₅₉	—	2	2	no	—
73	C₂×Q₈×C₅₉	—	4	1	no	—
74	C₂×Q₈×C₅₉	—	4	2	no	—
75	C₂×Q₈×C₅₉	—	4	2	no	—
76	C₂×D₄×C₅₉	—	2	2	no	—
77	C₂×D₄×C₅₉	—	4	4	no	—
78	C₂×D₄×C₅₉	—	4	2	no	—
79	C₂×D₄×C₅₉	—	4	1	no	—
80	C₂×D₄×C₅₉	—	4	2	no	—
81	C₂×D₄×C₅₉	—	8	4	no	—
82	C₂²×C₄×C₅₉	—	2	2	no	—
83	C₂²×C₄×C₅₉	—	2	2	no	—
84	C₂²×C₄×C₅₉	—	4	1	no	—
85	C₂²×C₄×C₅₉	—	4	1	no	—
86	C₂²×C₄×C₅₉	—	4	1	no	—
87	C₂²×C₄×C₅₉	D₈	1	2	yes	—
88	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	Q₁₆×C₅₉	—	2	2	no	—
92	Q₁₆×C₅₉	—	2	2	no	—
93	Q₁₆×C₅₉	—	4	2	no	—
94	D₈×C₅₉	—	2	2	no	—
95	D₈×C₅₉	—	2	2	no	—
96	D₈×C₅₉	—	4	2	no	—
97	C₂×C₈×C₅₉	—	2	2	no	—
98	C₂×C₈×C₅₉	—	2	4	no	—
99	C₂×C₈×C₅₉	—	2	2	no	—
100	C₂×C₈×C₅₉	—	2	2	no	—
101	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₅₉	#41	1	2	yes	—
105	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₅₉	—	2	2	no	—
107	C₄⋊C₄×C₅₉	—	2	2	no	—
108	C₄⋊C₄×C₅₉	—	4	1	no	—
109	C₄⋊C₄×C₅₉	—	4	1	no	—
110	C₄⋊C₄×C₅₉	—	4	4	no	—
111	C₂²⋊C₄×C₅₉	—	4	4	no	—
112	C₂²⋊C₄×C₅₉	—	4	4	no	—
113	C₁₆×C₅₉	—	2	2	no	—
114	C₁₆×C₅₉	C₂×D₄	1	4	yes	complemented
115	C₂³×C₅₉	—	2	2	no	—
116	C₂³×C₅₉	—	2	2	no	—
117	C₂³×C₅₉	—	4	2	no	—
118	C₂³×C₅₉	—	8	2	no	—
119	C₂³×C₅₉	—	8	2	no	—
120	C₂³×C₅₉	—	8	2	no	—
121	C₂³×C₅₉	SD₃₂	1	4	yes	complemented
122	C₂³×C₅₉	C₂×D₈	1	2	yes	—
123	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
124	Q₈×C₅₉	—	4	2	no	—
125	Q₈×C₅₉	—	4	2	no	—
126	Q₈×C₅₉	—	8	2	no	—
127	D₄×C₅₉	—	4	2	no	—
128	D₄×C₅₉	—	4	2	no	—
129	D₄×C₅₉	—	8	8	no	—
130	D₄×C₅₉	—	8	2	no	—
131	C₂×C₄×C₅₉	—	2	2	no	—
132	C₂×C₄×C₅₉	—	2	2	no	—
133	C₂×C₄×C₅₉	—	2	2	no	—
134	C₂×C₄×C₅₉	—	2	4	no	—
135	C₂×C₄×C₅₉	—	4	2	no	—
136	C₂×C₄×C₅₉	—	4	2	no	—
137	C₂×C₄×C₅₉	—	4	2	no	—
138	C₂×C₄×C₅₉	—	8	2	no	—
139	C₂×C₄×C₅₉	—	8	2	no	—
140	C₂×C₄×C₅₉	—	8	2	no	—
141	C₂×C₄×C₅₉	#121	1	2	yes	—
142	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
143	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₅₉	#135	1	2	yes	—
145	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
146	C₈×C₅₉	—	2	2	no	—
147	C₈×C₅₉	#121	1	2	yes	—
148	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
149	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
150	C₂×#2217	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂²×C₅₉	—	2	2	no	—
152	C₂²×C₅₉	—	2	8	no	—
153	C₂²×C₅₉	—	2	2	no	—
154	C₂²×C₅₉	—	8	2	no	—
155	C₂²×C₅₉	—	8	2	no	—
156	C₂²×C₅₉	—	8	2	no	—
157	C₂²×C₅₉	—	16	4	no	—
158	C₂²×C₅₉	#466	1	2	yes	—
159	C₂²×C₅₉	C₂×SD₃₂	1	2	yes	—
160	C₂²×C₅₉	C₂×SD₃₂	1	4	yes	complemented
161	C₂²×C₅₉	#508	1	2	yes	—
162	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
163	C₄×C₅₉	—	2	2	no	—
164	C₄×C₅₉	—	8	2	no	—
165	C₄×C₅₉	—	8	2	no	—
166	C₄×C₅₉	—	8	2	no	—
167	C₄×C₅₉	#466	1	2	yes	—
168	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
169	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
170	C₂²×SD₃₂	C₂×C₅₉	1	1	yes	characteristic, complemented
171	C₂³×C₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
172	C₂×#467	C₂×C₅₉	1	1	yes	characteristic, complemented
173	C₂×#466	C₂×C₅₉	1	1	yes	characteristic
174	#2217	C₂×C₅₉	1	8	yes	direct product factor
175	C₂×#367	C₂×C₅₉	1	1	yes	characteristic, complemented
176	C₂×#358	C₂×C₅₉	1	1	yes	characteristic, complemented
177	C₂×#357	C₂×C₅₉	1	1	yes	characteristic, complemented
178	C₂×C₅₉	—	2	4	no	—
179	C₂×C₅₉	—	16	2	no	—
180	C₂×C₅₉	#2217	1	4	yes	direct product factor
181	C₂×C₅₉	C₂×#466	1	1	yes	characteristic
182	C₂×C₅₉	C₂²×SD₃₂	1	1	yes	characteristic
183	C₂×C₅₉	C₂×#508	1	1	yes	characteristic
184	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
185	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
187	C₂×C₂²⋊Q₈	—	2	1	no	—
188	C₂×#121	—	2	1	no	—
189	C₂×SD₃₂	—	2	4	no	—
190	C₂×SD₃₂	C₂²×C₅₉	1	4	yes	complemented
191	C₂²×C₁₆	—	2	4	no	—
192	C₂²×C₁₆	C₂²×C₅₉	1	1	yes	characteristic
193	C₂²×C₁₆	C₂²×C₅₉	1	1	yes	characteristic
194	C₂²×C₁₆	C₂²×C₅₉	1	4	yes	complemented
195	#467	—	2	2	no	—
196	#467	C₂²×C₅₉	1	4	yes	complemented
197	#466	—	2	2	no	—
198	#466	C₂²×C₅₉	1	4	yes	—
199	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
200	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
201	C₂×#103	—	2	1	no	—
202	C₂×#102	—	2	1	no	—
203	#367	C₂²×C₅₉	1	4	yes	complemented
204	#358	C₂²×C₅₉	1	4	yes	complemented
205	#357	C₂²×C₅₉	1	4	yes	complemented
206	C₅₉	C₂×#2217	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×Q₈	—	2	1	no	—
208	C₂²×D₄	—	2	1	no	—
209	C₂²×D₄	—	4	1	no	—
210	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
211	C₂×Q₁₆	—	2	2	no	—
212	C₂×Q₁₆	—	2	1	no	—
213	C₂×Q₁₆	—	2	2	no	—
214	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
215	C₂×D₈	—	2	2	no	—
216	C₂×D₈	—	2	1	no	—
217	C₂×D₈	—	2	2	no	—
218	C₂×D₈	C₂³×C₅₉	1	2	yes	—
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
222	C₂²×C₈	D₄×C₅₉	1	2	yes	—
223	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
224	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
225	C₂²⋊Q₈	—	2	4	no	—
226	C₂²⋊Q₈	—	4	2	no	—
227	#121	—	2	4	no	—
228	#121	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	4	1	no	—
232	C₂×C₂²⋊C₄	—	4	1	no	—
233	C₂×C₂²⋊C₄	—	4	1	no	—
234	SD₃₂	—	2	8	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	—	2	8	no	—
237	C₂×C₁₆	D₄×C₅₉	1	4	yes	complemented
238	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
239	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
240	#107	—	2	1	no	—
241	#107	—	2	1	no	—
242	#107	C₂³×C₅₉	1	2	yes	—
243	#107	C₂³×C₅₉	1	2	yes	—
244	#103	—	2	4	no	—
245	#102	—	2	4	no	—
246	C₂⁴	—	4	1	no	—
247	C₂⁴	D₈×C₅₉	1	1	yes	characteristic
248	C₂×Q₈	—	2	2	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	—	4	2	no	—
251	C₂×Q₈	—	4	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	—	8	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	D₈×C₅₉	1	1	yes	characteristic
264	C₂²×C₄	D₈×C₅₉	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
267	Q₁₆	—	2	2	no	—
268	Q₁₆	—	2	2	no	—
269	Q₁₆	—	4	2	no	—
270	D₈	—	2	2	no	—
271	D₈	—	2	2	no	—
272	D₈	—	4	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
278	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
280	C₂×C₈	#41×C₅₉	1	2	yes	—
281	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₁₆	—	2	2	no	—
290	C₁₆	C₂×D₄×C₅₉	1	4	yes	complemented
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	8	2	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	SD₃₂×C₅₉	1	4	yes	complemented
298	C₂³	C₂×D₈×C₅₉	1	2	yes	—
299	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
300	Q₈	—	4	2	no	—
301	Q₈	—	4	2	no	—
302	Q₈	—	8	2	no	—
303	D₄	—	4	2	no	—
304	D₄	—	4	2	no	—
305	D₄	—	8	8	no	—
306	D₄	—	8	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	—	8	2	no	—
317	C₂×C₄	#121×C₅₉	1	2	yes	—
318	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
319	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
320	C₂×C₄	#135×C₅₉	1	2	yes	—
321	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	#121×C₅₉	1	2	yes	—
324	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
325	C₈	C₂×#41×C₅₉	1	1	yes	characteristic
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	8	2	no	—
330	C₂²	—	8	2	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	16	4	no	—
333	C₂²	C₅₉×#466	1	2	yes	—
334	C₂²	C₂×SD₃₂×C₅₉	1	2	yes	—
335	C₂²	C₂×SD₃₂×C₅₉	1	4	yes	complemented
336	C₂²	C₅₉×#508	1	2	yes	—
337	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	C₅₉×#466	1	2	yes	—
343	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
344	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
345	C₂	—	2	4	no	—
346	C₂	—	16	2	no	—
347	C₂	C₅₉×#2217	1	4	yes	direct product factor
348	C₂	C₂×C₅₉×#466	1	1	yes	characteristic
349	C₂	C₂²×SD₃₂×C₅₉	1	1	yes	characteristic
350	C₂	C₂×C₅₉×#508	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ C₂³×C₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×SD₃₂×C₅₉	C₂	semidirect
2. C₂³×C₁₆×C₅₉	C₂	semidirect
3. C₂×C₅₉×#467	C₂	semidirect
5. C₅₉×#2217	C₂	direct (N × H)
6. C₂×C₅₉×#367	C₂	semidirect
7. C₂×C₅₉×#358	C₂	semidirect
8. C₂×C₅₉×#357	C₂	semidirect
15. C₂×SD₃₂×C₅₉	C₂²	semidirect
19. C₂²×C₁₆×C₅₉	C₂²	semidirect
21. C₅₉×#467	C₂²	semidirect
28. C₅₉×#367	C₂²	semidirect
29. C₅₉×#358	C₂²	semidirect
30. C₅₉×#357	C₂²	semidirect
61. C₂×C₁₆×C₅₉	D₄	semidirect
114. C₁₆×C₅₉	C₂×D₄	semidirect
121. C₂³×C₅₉	SD₃₂	semidirect
150. C₂×#2217	C₅₉	direct (N × H)
160. C₂²×C₅₉	C₂×SD₃₂	semidirect
170. C₂²×SD₃₂	C₂×C₅₉	semidirect
171. C₂³×C₁₆	C₂×C₅₉	semidirect
172. C₂×#467	C₂×C₅₉	semidirect
174. #2217	C₂×C₅₉	direct (N × H)
175. C₂×#367	C₂×C₅₉	semidirect
176. C₂×#358	C₂×C₅₉	semidirect
177. C₂×#357	C₂×C₅₉	semidirect
180. C₂×C₅₉	#2217	direct (N × H)
190. C₂×SD₃₂	C₂²×C₅₉	semidirect
194. C₂²×C₁₆	C₂²×C₅₉	semidirect
196. #467	C₂²×C₅₉	semidirect
203. #367	C₂²×C₅₉	semidirect
204. #358	C₂²×C₅₉	semidirect
205. #357	C₂²×C₅₉	semidirect
206. C₅₉	C₂×#2217	direct (N × H)
237. C₂×C₁₆	D₄×C₅₉	semidirect
290. C₁₆	C₂×D₄×C₅₉	semidirect
297. C₂³	SD₃₂×C₅₉	semidirect
335. C₂²	C₂×SD₃₂×C₅₉	semidirect
347. C₂	C₅₉×#2217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×SD₃₂×C₅₉	2
C₂³×C₁₆×C₅₉	2
C₂×C₅₉×#467	2
C₂×C₅₉×#466	2
C₅₉×#2217	2
C₂×C₅₉×#367	2
C₂×C₅₉×#358	2
C₂×C₅₉×#357	2
C₂×#2217	59

Subgroups — C2×C59×#2217 #28445708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2217 #28445708