Subgroups — C₂×C₅₉×#2888 #28472183

Order 15104.

5114 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#568	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2888	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₉×#413	C₂	1	6	yes	maximal, complemented
5	C₂²×#100×C₅₉	C₂	1	6	yes	maximal, complemented
6	C₂×H(5,𝔽₂)×C₅₉	—	2	8	no	—
7	C₂×H(5,𝔽₂)×C₅₉	—	2	8	no	—
8	C₂×H(5,𝔽₂)×C₅₉	C₄	1	8	yes	—
9	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	8	yes	—
10	C₂²×#41×C₅₉	C₄	1	2	yes	—
11	C₂²×#41×C₅₉	C₂²	1	3	yes	—
12	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₅₉	C₄	1	6	yes	—
14	C₂³×D₄×C₅₉	C₂²	1	3	yes	—
15	C₅₉×#568	—	2	8	no	—
16	C₅₉×#568	C₂²	1	16	yes	complemented
17	C₂×#131×C₅₉	—	2	8	no	—
18	C₂²×M₁₆×C₅₉	C₂²	1	12	yes	complemented
19	C₅₉×#413	C₂²	1	48	yes	complemented
20	C₂×#101×C₅₉	C₂²	1	4	yes	complemented
21	C₂×#100×C₅₉	C₂²	1	12	yes	complemented
22	C₂×#100×C₅₉	C₂²	1	48	yes	complemented
23	C₂⁵×C₅₉	C₂×C₄	1	6	yes	—
24	H(5,𝔽₂)×C₅₉	—	2	64	no	—
25	H(5,𝔽₂)×C₅₉	—	2	64	no	—
26	C₂×#41×C₅₉	—	2	8	no	—
27	C₂×#41×C₅₉	—	2	8	no	—
28	C₂×#41×C₅₉	—	2	12	no	—
29	C₂×#41×C₅₉	—	2	12	no	—
30	C₂×#41×C₅₉	C₂×C₄	1	16	yes	—
31	C₂×#41×C₅₉	C₂×C₄	1	12	yes	—
32	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
33	C₂×#41×C₅₉	D₄	1	8	yes	—
34	C₂×#41×C₅₉	D₄	1	8	yes	—
35	C₂×#41×C₅₉	C₂³	1	12	yes	—
36	C₂×#41×C₅₉	C₂³	1	4	yes	—
37	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₅₉	—	2	24	no	—
40	C₂²×D₄×C₅₉	—	2	24	no	—
41	C₂²×D₄×C₅₉	—	2	12	no	—
42	C₂²×D₄×C₅₉	—	2	12	no	—
43	C₂²×D₄×C₅₉	C₂×C₄	1	6	yes	—
44	C₂²×D₄×C₅₉	C₂×C₄	1	6	yes	—
45	C₂²×D₄×C₅₉	C₂×C₄	1	48	yes	—
46	C₂²×D₄×C₅₉	C₂×C₄	1	12	yes	—
47	C₂²×D₄×C₅₉	C₂×C₄	1	3	yes	—
48	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
49	C₂²×D₄×C₅₉	C₂³	1	12	yes	—
50	C₂³×C₄×C₅₉	C₂×C₄	1	6	yes	—
51	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
52	#131×C₅₉	—	2	64	no	—
53	C₂×M₁₆×C₅₉	—	2	12	no	—
54	C₂×M₁₆×C₅₉	—	2	24	no	—
55	C₂×M₁₆×C₅₉	C₂³	1	8	yes	—
56	C₂×M₁₆×C₅₉	C₂³	1	48	yes	complemented
57	C₂²×C₈×C₅₉	—	2	12	no	—
58	#101×C₅₉	C₂³	1	16	yes	complemented
59	#100×C₅₉	C₂³	1	48	yes	complemented
60	C₂⁴×C₅₉	—	2	12	no	—
61	C₂⁴×C₅₉	—	2	12	no	—
62	C₂⁴×C₅₉	—	8	12	no	—
63	C₂⁴×C₅₉	C₂²×C₄	1	6	yes	—
64	C₂⁴×C₅₉	C₂²×C₄	1	24	yes	—
65	C₂⁴×C₅₉	C₂²×C₄	1	3	yes	—
66	#41×C₅₉	—	2	64	no	—
67	#41×C₅₉	—	2	48	no	—
68	#41×C₅₉	—	2	48	no	—
69	#41×C₅₉	C₂²⋊C₄	1	32	yes	—
70	#41×C₅₉	C₂×D₄	1	32	yes	—
71	C₂×Q₈×C₅₉	—	2	2	no	—
72	C₂×Q₈×C₅₉	—	2	2	no	—
73	C₂×Q₈×C₅₉	C₂²⋊C₄	1	4	yes	—
74	C₂×Q₈×C₅₉	C₂²⋊C₄	1	4	yes	—
75	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
76	C₂×Q₈×C₅₉	C₂²×C₄	1	4	yes	—
77	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
78	C₂×D₄×C₅₉	—	2	12	no	—
79	C₂×D₄×C₅₉	—	2	12	no	—
80	C₂×D₄×C₅₉	—	2	192	no	—
81	C₂×D₄×C₅₉	—	2	12	no	—
82	C₂×D₄×C₅₉	—	2	12	no	—
83	C₂×D₄×C₅₉	—	2	48	no	—
84	C₂×D₄×C₅₉	—	2	6	no	—
85	C₂×D₄×C₅₉	—	2	6	no	—
86	C₂×D₄×C₅₉	—	2	48	no	—
87	C₂×D₄×C₅₉	C₂²⋊C₄	1	12	yes	—
88	C₂×D₄×C₅₉	C₂²⋊C₄	1	12	yes	—
89	C₂×D₄×C₅₉	C₂²×C₄	1	24	yes	—
90	C₂×D₄×C₅₉	C₂²×C₄	1	24	yes	—
91	C₂×D₄×C₅₉	C₂²×C₄	1	6	yes	—
92	C₂×D₄×C₅₉	C₂²×C₄	1	12	yes	—
93	C₂×D₄×C₅₉	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₅₉	—	2	12	no	—
95	C₂²×C₄×C₅₉	—	2	12	no	—
96	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₅₉	C₂²×C₄	1	24	yes	—
98	C₂²×C₄×C₅₉	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₅₉	C₂²×C₄	1	6	yes	—
100	C₂²×C₄×C₅₉	C₂×D₄	1	12	yes	—
101	C₂²×C₄×C₅₉	C₂×D₄	1	12	yes	—
102	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
104	M₁₆×C₅₉	—	2	8	no	—
105	M₁₆×C₅₉	—	2	48	no	—
106	M₁₆×C₅₉	C₂⁴	1	16	yes	—
107	C₂×C₈×C₅₉	—	2	8	no	—
108	C₂×C₈×C₅₉	—	2	48	no	—
109	C₂³×C₅₉	—	2	6	no	—
110	C₂³×C₅₉	—	2	6	no	—
111	C₂³×C₅₉	—	2	48	no	—
112	C₂³×C₅₉	—	4	6	no	—
113	C₂³×C₅₉	—	4	12	no	—
114	C₂³×C₅₉	—	8	24	no	—
115	C₂³×C₅₉	—	8	24	no	—
116	C₂³×C₅₉	—	8	24	no	—
117	C₂³×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
118	C₂³×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
119	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
120	C₂³×C₅₉	C₂³×C₄	1	12	yes	—
121	C₂³×C₅₉	C₂³×C₄	1	6	yes	—
122	Q₈×C₅₉	—	2	4	no	—
123	Q₈×C₅₉	—	2	4	no	—
124	Q₈×C₅₉	C₂×C₂²⋊C₄	1	16	yes	—
125	D₄×C₅₉	—	2	48	no	—
126	D₄×C₅₉	—	2	48	no	—
127	D₄×C₅₉	—	2	12	no	—
128	D₄×C₅₉	—	2	12	no	—
129	D₄×C₅₉	C₂×C₂²⋊C₄	1	48	yes	—
130	C₂×C₄×C₅₉	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	2	no	—
132	C₂×C₄×C₅₉	—	2	48	no	—
133	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
134	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	24	yes	—
135	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	6	yes	—
136	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
137	C₂×C₄×C₅₉	C₂³×C₄	1	6	yes	—
138	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₅₉	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
143	C₈×C₅₉	—	2	16	no	—
144	C₂×#2888	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂²×C₅₉	—	2	2	no	—
146	C₂²×C₅₉	—	2	12	no	—
147	C₂²×C₅₉	—	2	12	no	—
148	C₂²×C₅₉	—	4	6	no	—
149	C₂²×C₅₉	—	4	6	no	—
150	C₂²×C₅₉	—	4	12	no	—
151	C₂²×C₅₉	—	4	12	no	—
152	C₂²×C₅₉	—	4	12	no	—
153	C₂²×C₅₉	—	8	48	no	—
154	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	12	yes	—
156	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
158	C₄×C₅₉	—	2	4	no	—
159	C₄×C₅₉	C₂²×C₂²⋊C₄	1	12	yes	—
160	C₄×C₅₉	C₂²×C₂²⋊C₄	1	2	yes	—
161	C₄×C₅₉	C₂³×D₄	1	2	yes	—
162	C₂²×H(5,𝔽₂)	C₂×C₅₉	1	1	yes	characteristic
163	C₂×#568	C₂×C₅₉	1	2	yes	complemented
164	#2888	C₂×C₅₉	1	16	yes	direct product factor
165	C₂×#413	C₂×C₅₉	1	6	yes	complemented
166	C₂²×#100	C₂×C₅₉	1	6	yes	complemented
167	C₂×C₅₉	—	2	1	no	—
168	C₂×C₅₉	—	2	1	no	—
169	C₂×C₅₉	—	2	12	no	—
170	C₂×C₅₉	—	4	12	no	—
171	C₂×C₅₉	#2888	1	2	yes	direct product factor
172	C₂×C₅₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×H(5,𝔽₂)	—	2	8	no	—
174	C₂×H(5,𝔽₂)	—	2	8	no	—
175	C₂×H(5,𝔽₂)	C₄×C₅₉	1	8	yes	—
176	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	8	yes	—
177	C₂²×#41	C₄×C₅₉	1	2	yes	—
178	C₂²×#41	C₂²×C₅₉	1	3	yes	—
179	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
180	C₂³×D₄	C₄×C₅₉	1	6	yes	—
181	C₂³×D₄	C₂²×C₅₉	1	3	yes	—
182	#568	—	2	8	no	—
183	#568	C₂²×C₅₉	1	16	yes	complemented
184	C₂×#131	—	2	8	no	—
185	C₂²×M₁₆	C₂²×C₅₉	1	12	yes	complemented
186	#413	C₂²×C₅₉	1	48	yes	complemented
187	C₂×#101	C₂²×C₅₉	1	4	yes	complemented
188	C₂×#100	C₂²×C₅₉	1	12	yes	complemented
189	C₂×#100	C₂²×C₅₉	1	48	yes	complemented
190	C₅₉	C₂×#2888	1	1	yes	characteristic, direct product factor, Sylow
191	C₂⁵	C₂×C₄×C₅₉	1	6	yes	—
192	H(5,𝔽₂)	—	2	64	no	—
193	H(5,𝔽₂)	—	2	64	no	—
194	C₂×#41	—	2	8	no	—
195	C₂×#41	—	2	8	no	—
196	C₂×#41	—	2	12	no	—
197	C₂×#41	—	2	12	no	—
198	C₂×#41	C₂×C₄×C₅₉	1	16	yes	—
199	C₂×#41	C₂×C₄×C₅₉	1	12	yes	—
200	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
201	C₂×#41	D₄×C₅₉	1	8	yes	—
202	C₂×#41	D₄×C₅₉	1	8	yes	—
203	C₂×#41	C₂³×C₅₉	1	12	yes	—
204	C₂×#41	C₂³×C₅₉	1	4	yes	—
205	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
206	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
207	C₂²×D₄	—	2	24	no	—
208	C₂²×D₄	—	2	24	no	—
209	C₂²×D₄	—	2	12	no	—
210	C₂²×D₄	—	2	12	no	—
211	C₂²×D₄	C₂×C₄×C₅₉	1	6	yes	—
212	C₂²×D₄	C₂×C₄×C₅₉	1	6	yes	—
213	C₂²×D₄	C₂×C₄×C₅₉	1	48	yes	—
214	C₂²×D₄	C₂×C₄×C₅₉	1	12	yes	—
215	C₂²×D₄	C₂×C₄×C₅₉	1	3	yes	—
216	C₂²×D₄	C₂³×C₅₉	1	3	yes	—
217	C₂²×D₄	C₂³×C₅₉	1	12	yes	—
218	C₂³×C₄	C₂×C₄×C₅₉	1	6	yes	—
219	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
220	#131	—	2	64	no	—
221	C₂×M₁₆	—	2	12	no	—
222	C₂×M₁₆	—	2	24	no	—
223	C₂×M₁₆	C₂³×C₅₉	1	8	yes	—
224	C₂×M₁₆	C₂³×C₅₉	1	48	yes	complemented
225	C₂²×C₈	—	2	12	no	—
226	#101	C₂³×C₅₉	1	16	yes	complemented
227	#100	C₂³×C₅₉	1	48	yes	complemented
228	C₂⁴	—	2	12	no	—
229	C₂⁴	—	2	12	no	—
230	C₂⁴	—	8	12	no	—
231	C₂⁴	C₂²×C₄×C₅₉	1	6	yes	—
232	C₂⁴	C₂²×C₄×C₅₉	1	24	yes	—
233	C₂⁴	C₂²×C₄×C₅₉	1	3	yes	—
234	#41	—	2	64	no	—
235	#41	—	2	48	no	—
236	#41	—	2	48	no	—
237	#41	C₂²⋊C₄×C₅₉	1	32	yes	—
238	#41	C₂×D₄×C₅₉	1	32	yes	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	C₂²⋊C₄×C₅₉	1	4	yes	—
242	C₂×Q₈	C₂²⋊C₄×C₅₉	1	4	yes	—
243	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
244	C₂×Q₈	C₂²×C₄×C₅₉	1	4	yes	—
245	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	—	2	12	no	—
248	C₂×D₄	—	2	192	no	—
249	C₂×D₄	—	2	12	no	—
250	C₂×D₄	—	2	12	no	—
251	C₂×D₄	—	2	48	no	—
252	C₂×D₄	—	2	6	no	—
253	C₂×D₄	—	2	6	no	—
254	C₂×D₄	—	2	48	no	—
255	C₂×D₄	C₂²⋊C₄×C₅₉	1	12	yes	—
256	C₂×D₄	C₂²⋊C₄×C₅₉	1	12	yes	—
257	C₂×D₄	C₂²×C₄×C₅₉	1	24	yes	—
258	C₂×D₄	C₂²×C₄×C₅₉	1	24	yes	—
259	C₂×D₄	C₂²×C₄×C₅₉	1	6	yes	—
260	C₂×D₄	C₂²×C₄×C₅₉	1	12	yes	—
261	C₂×D₄	C₂⁴×C₅₉	1	6	yes	—
262	C₂²×C₄	—	2	12	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₅₉	1	24	yes	—
266	C₂²×C₄	C₂²×C₄×C₅₉	1	3	yes	—
267	C₂²×C₄	C₂²×C₄×C₅₉	1	6	yes	—
268	C₂²×C₄	C₂×D₄×C₅₉	1	12	yes	—
269	C₂²×C₄	C₂×D₄×C₅₉	1	12	yes	—
270	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
272	M₁₆	—	2	8	no	—
273	M₁₆	—	2	48	no	—
274	M₁₆	C₂⁴×C₅₉	1	16	yes	—
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	48	no	—
277	C₂³	—	2	6	no	—
278	C₂³	—	2	6	no	—
279	C₂³	—	2	48	no	—
280	C₂³	—	4	6	no	—
281	C₂³	—	4	12	no	—
282	C₂³	—	8	24	no	—
283	C₂³	—	8	24	no	—
284	C₂³	—	8	24	no	—
285	C₂³	C₂×C₂²⋊C₄×C₅₉	1	6	yes	—
286	C₂³	C₂×C₂²⋊C₄×C₅₉	1	6	yes	—
287	C₂³	C₂³×C₄×C₅₉	1	1	yes	characteristic
288	C₂³	C₂³×C₄×C₅₉	1	12	yes	—
289	C₂³	C₂³×C₄×C₅₉	1	6	yes	—
290	Q₈	—	2	4	no	—
291	Q₈	—	2	4	no	—
292	Q₈	C₂×C₂²⋊C₄×C₅₉	1	16	yes	—
293	D₄	—	2	48	no	—
294	D₄	—	2	48	no	—
295	D₄	—	2	12	no	—
296	D₄	—	2	12	no	—
297	D₄	C₂×C₂²⋊C₄×C₅₉	1	48	yes	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	48	no	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	6	yes	—
302	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	6	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	24	yes	—
304	C₂×C₄	C₂³×C₄×C₅₉	1	4	yes	—
305	C₂×C₄	C₂³×C₄×C₅₉	1	6	yes	—
306	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
308	C₂×C₄	C₂²×D₄×C₅₉	1	24	yes	—
309	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
310	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
311	C₈	—	2	16	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	12	no	—
314	C₂²	—	2	12	no	—
315	C₂²	—	4	6	no	—
316	C₂²	—	4	6	no	—
317	C₂²	—	4	12	no	—
318	C₂²	—	4	12	no	—
319	C₂²	—	4	12	no	—
320	C₂²	—	8	48	no	—
321	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
322	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	12	yes	—
323	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
324	C₂²	C₂⁴×C₄×C₅₉	1	1	yes	characteristic
325	C₄	—	2	4	no	—
326	C₄	C₂²×C₂²⋊C₄×C₅₉	1	12	yes	—
327	C₄	C₂²×C₂²⋊C₄×C₅₉	1	2	yes	—
328	C₄	C₂³×D₄×C₅₉	1	2	yes	—
329	C₂	—	2	1	no	—
330	C₂	—	2	1	no	—
331	C₂	—	2	12	no	—
332	C₂	—	4	12	no	—
333	C₂	C₅₉×#2888	1	2	yes	direct product factor
334	C₂	C₂³×C₂²⋊C₄×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂⁴×C₄×C₅₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₂²×H(5,𝔽₂)×C₅₉	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#568	C₂	semidirect
3. C₅₉×#2888	C₂	direct (N × H)
4. C₂×C₅₉×#413	C₂	semidirect
5. C₂²×#100×C₅₉	C₂	semidirect
16. C₅₉×#568	C₂²	semidirect
18. C₂²×M₁₆×C₅₉	C₂²	semidirect
19. C₅₉×#413	C₂²	semidirect
20. C₂×#101×C₅₉	C₂²	semidirect
21. C₂×#100×C₅₉	C₂²	semidirect
22. C₂×#100×C₅₉	C₂²	semidirect
56. C₂×M₁₆×C₅₉	C₂³	semidirect
58. #101×C₅₉	C₂³	semidirect
59. #100×C₅₉	C₂³	semidirect
144. C₂×#2888	C₅₉	direct (N × H)
163. C₂×#568	C₂×C₅₉	semidirect
164. #2888	C₂×C₅₉	direct (N × H)
165. C₂×#413	C₂×C₅₉	semidirect
166. C₂²×#100	C₂×C₅₉	semidirect
171. C₂×C₅₉	#2888	direct (N × H)
183. #568	C₂²×C₅₉	semidirect
185. C₂²×M₁₆	C₂²×C₅₉	semidirect
186. #413	C₂²×C₅₉	semidirect
187. C₂×#101	C₂²×C₅₉	semidirect
188. C₂×#100	C₂²×C₅₉	semidirect
189. C₂×#100	C₂²×C₅₉	semidirect
190. C₅₉	C₂×#2888	direct (N × H)
224. C₂×M₁₆	C₂³×C₅₉	semidirect
226. #101	C₂³×C₅₉	semidirect
227. #100	C₂³×C₅₉	semidirect
333. C₂	C₅₉×#2888	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×H(5,𝔽₂)×C₅₉	2
C₂×C₅₉×#568	2
C₅₉×#2888	2
C₂×C₅₉×#413	2
C₂²×#100×C₅₉	2
C₂×#2888	59

Subgroups — C2×C59×#2888 #28472183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2888 #28472183