Subgroups — C₂×C₅₉×#2139 #28445488

Order 15104.

1214 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#107×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2139	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅₉×#358	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₉×#357	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₅₉	—	2	1	no	—
8	C₂×#135×C₅₉	—	2	2	no	—
9	C₂×#135×C₅₉	—	2	4	no	—
10	C₂×#135×C₅₉	C₄	1	8	yes	complemented
11	C₂×#135×C₅₉	C₂²	1	4	yes	—
12	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₅₉	—	2	1	no	—
14	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
17	C₂×M₃₂×C₅₉	—	2	4	no	—
18	C₂×M₃₂×C₅₉	C₂²	1	4	yes	complemented
19	C₂²×C₁₆×C₅₉	C₂²	1	2	yes	—
20	C₂×#107×C₅₉	—	2	2	no	—
21	C₂×#107×C₅₉	—	2	1	no	—
22	C₂×#107×C₅₉	C₂²	1	2	yes	—
23	C₂×#107×C₅₉	C₂²	1	4	yes	complemented
24	C₅₉×#358	C₂²	1	8	yes	complemented
25	C₅₉×#357	C₂²	1	8	yes	complemented
26	C₂×#41×C₅₉	—	2	8	no	—
27	C₂×#41×C₅₉	—	2	4	no	—
28	C₂×#41×C₅₉	—	4	2	no	—
29	C₂×#41×C₅₉	—	4	4	no	—
30	C₂²×Q₈×C₅₉	—	2	1	no	—
31	C₂²×D₄×C₅₉	—	2	1	no	—
32	C₂²×D₄×C₅₉	—	4	1	no	—
33	C₂³×C₄×C₅₉	—	4	1	no	—
34	C₂³×C₄×C₅₉	—	4	1	no	—
35	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
36	#135×C₅₉	—	2	16	no	—
37	#135×C₅₉	—	2	8	no	—
38	#135×C₅₉	C₂×C₄	1	16	yes	complemented
39	C₂×Q₁₆×C₅₉	—	2	1	no	—
40	C₂×Q₁₆×C₅₉	—	2	2	no	—
41	C₂×Q₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
42	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
43	C₂×SD₁₆×C₅₉	—	2	8	no	—
44	C₂×SD₁₆×C₅₉	—	2	4	no	—
45	C₂×D₈×C₅₉	—	2	1	no	—
46	C₂×D₈×C₅₉	—	2	2	no	—
47	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	complemented
48	C₂×D₈×C₅₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₅₉	D₄	1	2	yes	—
52	C₂²×C₈×C₅₉	D₄	1	4	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₅₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₅₉	—	4	1	no	—
59	M₃₂×C₅₉	—	2	8	no	—
60	C₂×C₁₆×C₅₉	—	2	4	no	—
61	C₂×C₁₆×C₅₉	C₂³	1	4	yes	—
62	#107×C₅₉	—	2	2	no	—
63	#107×C₅₉	—	2	4	no	—
64	#107×C₅₉	C₂³	1	4	yes	—
65	C₂⁴×C₅₉	—	4	1	no	—
66	C₂⁴×C₅₉	D₈	1	1	yes	characteristic
67	#41×C₅₉	—	2	16	no	—
68	#41×C₅₉	—	4	16	no	—
69	#41×C₅₉	—	4	8	no	—
70	C₂×Q₈×C₅₉	—	2	4	no	—
71	C₂×Q₈×C₅₉	—	2	2	no	—
72	C₂×Q₈×C₅₉	—	4	1	no	—
73	C₂×Q₈×C₅₉	—	4	2	no	—
74	C₂×D₄×C₅₉	—	2	4	no	—
75	C₂×D₄×C₅₉	—	2	2	no	—
76	C₂×D₄×C₅₉	—	4	8	no	—
77	C₂×D₄×C₅₉	—	4	4	no	—
78	C₂×D₄×C₅₉	—	4	1	no	—
79	C₂×D₄×C₅₉	—	4	2	no	—
80	C₂²×C₄×C₅₉	—	4	1	no	—
81	C₂²×C₄×C₅₉	—	4	8	no	—
82	C₂²×C₄×C₅₉	—	4	4	no	—
83	C₂²×C₄×C₅₉	—	4	4	no	—
84	C₂²×C₄×C₅₉	—	4	2	no	—
85	C₂²×C₄×C₅₉	—	8	4	no	—
86	C₂²×C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
87	C₂²×C₄×C₅₉	D₈	1	2	yes	—
88	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₅₉	SD₁₆	1	4	yes	—
90	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
92	Q₁₆×C₅₉	—	2	4	no	—
93	Q₁₆×C₅₉	—	2	2	no	—
94	Q₁₆×C₅₉	C₂²×C₄	1	4	yes	complemented
95	SD₁₆×C₅₉	—	2	16	no	—
96	D₈×C₅₉	—	2	4	no	—
97	D₈×C₅₉	—	2	2	no	—
98	D₈×C₅₉	C₂²×C₄	1	4	yes	complemented
99	C₂×C₈×C₅₉	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₅₉	C₂²⋊C₄	1	8	yes	—
101	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
107	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₅₉	—	2	4	no	—
109	C₄⋊C₄×C₅₉	—	4	4	no	—
110	C₄⋊C₄×C₅₉	—	4	2	no	—
111	C₁₆×C₅₉	—	2	4	no	—
112	C₂³×C₅₉	—	2	2	no	—
113	C₂³×C₅₉	—	2	2	no	—
114	C₂³×C₅₉	—	4	2	no	—
115	C₂³×C₅₉	—	4	4	no	—
116	C₂³×C₅₉	—	8	2	no	—
117	C₂³×C₅₉	—	8	2	no	—
118	C₂³×C₅₉	#102	1	4	yes	—
119	C₂³×C₅₉	C₂×D₈	1	2	yes	—
120	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
121	Q₈×C₅₉	—	2	4	no	—
122	Q₈×C₅₉	—	4	2	no	—
123	Q₈×C₅₉	—	4	4	no	—
124	D₄×C₅₉	—	2	4	no	—
125	D₄×C₅₉	—	4	16	no	—
126	D₄×C₅₉	—	4	2	no	—
127	D₄×C₅₉	—	4	4	no	—
128	C₂×C₄×C₅₉	—	4	2	no	—
129	C₂×C₄×C₅₉	—	4	4	no	—
130	C₂×C₄×C₅₉	—	4	16	no	—
131	C₂×C₄×C₅₉	—	4	4	no	—
132	C₂×C₄×C₅₉	—	8	8	no	—
133	C₂×C₄×C₅₉	—	8	4	no	—
134	C₂×C₄×C₅₉	#102	1	4	yes	—
135	C₂×C₄×C₅₉	#102	1	8	yes	—
136	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
139	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
141	C₂×C₄×C₅₉	C₂×SD₁₆	1	4	yes	—
142	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
143	C₈×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
144	C₈×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
145	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
146	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×#2139	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂²×C₅₉	—	2	2	no	—
149	C₂²×C₅₉	—	2	2	no	—
150	C₂²×C₅₉	—	2	8	no	—
151	C₂²×C₅₉	—	4	4	no	—
152	C₂²×C₅₉	—	8	2	no	—
153	C₂²×C₅₉	—	8	2	no	—
154	C₂²×C₅₉	—	8	8	no	—
155	C₂²×C₅₉	C₂×#102	1	4	yes	—
156	C₂²×C₅₉	C₂×#102	1	2	yes	—
157	C₂²×C₅₉	#509	1	2	yes	—
158	C₂²×C₅₉	#510	1	2	yes	—
159	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
160	C₄×C₅₉	—	4	4	no	—
161	C₄×C₅₉	—	8	4	no	—
162	C₄×C₅₉	C₂×#102	1	4	yes	—
163	C₄×C₅₉	C₂×#102	1	2	yes	—
164	C₄×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
166	C₂²×#135	C₂×C₅₉	1	1	yes	characteristic
167	C₂²×M₃₂	C₂×C₅₉	1	1	yes	characteristic, complemented
168	C₂²×#107	C₂×C₅₉	1	1	yes	characteristic, complemented
169	#2139	C₂×C₅₉	1	8	yes	direct product factor
170	C₂×#358	C₂×C₅₉	1	2	yes	complemented
171	C₂×#357	C₂×C₅₉	1	2	yes	complemented
172	C₂×C₅₉	—	2	4	no	—
173	C₂×C₅₉	—	8	4	no	—
174	C₂×C₅₉	#2139	1	4	yes	direct product factor
175	C₂×C₅₉	C₂²×#102	1	1	yes	characteristic
176	C₂×C₅₉	C₂×#509	1	1	yes	characteristic
177	C₂×C₅₉	C₂×#510	1	1	yes	characteristic
178	C₂²×#41	—	2	1	no	—
179	C₂×#135	—	2	2	no	—
180	C₂×#135	—	2	4	no	—
181	C₂×#135	C₄×C₅₉	1	8	yes	complemented
182	C₂×#135	C₂²×C₅₉	1	4	yes	—
183	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
184	C₂²×SD₁₆	—	2	1	no	—
185	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂×M₃₂	—	2	4	no	—
189	C₂×M₃₂	C₂²×C₅₉	1	4	yes	complemented
190	C₂²×C₁₆	C₂²×C₅₉	1	2	yes	—
191	C₂×#107	—	2	2	no	—
192	C₂×#107	—	2	1	no	—
193	C₂×#107	C₂²×C₅₉	1	2	yes	—
194	C₂×#107	C₂²×C₅₉	1	4	yes	complemented
195	#358	C₂²×C₅₉	1	8	yes	complemented
196	#357	C₂²×C₅₉	1	8	yes	complemented
197	C₅₉	C₂×#2139	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#41	—	2	8	no	—
199	C₂×#41	—	2	4	no	—
200	C₂×#41	—	4	2	no	—
201	C₂×#41	—	4	4	no	—
202	C₂²×Q₈	—	2	1	no	—
203	C₂²×D₄	—	2	1	no	—
204	C₂²×D₄	—	4	1	no	—
205	C₂³×C₄	—	4	1	no	—
206	C₂³×C₄	—	4	1	no	—
207	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
208	#135	—	2	16	no	—
209	#135	—	2	8	no	—
210	#135	C₂×C₄×C₅₉	1	16	yes	complemented
211	C₂×Q₁₆	—	2	1	no	—
212	C₂×Q₁₆	—	2	2	no	—
213	C₂×Q₁₆	C₂×C₄×C₅₉	1	4	yes	complemented
214	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
215	C₂×SD₁₆	—	2	8	no	—
216	C₂×SD₁₆	—	2	4	no	—
217	C₂×D₈	—	2	1	no	—
218	C₂×D₈	—	2	2	no	—
219	C₂×D₈	C₂×C₄×C₅₉	1	4	yes	complemented
220	C₂×D₈	C₂³×C₅₉	1	2	yes	—
221	C₂²×C₈	C₂×C₄×C₅₉	1	4	yes	—
222	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
223	C₂²×C₈	D₄×C₅₉	1	2	yes	—
224	C₂²×C₈	D₄×C₅₉	1	4	yes	—
225	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	4	1	no	—
230	C₂×C₄⋊C₄	—	4	2	no	—
231	M₃₂	—	2	8	no	—
232	C₂×C₁₆	—	2	4	no	—
233	C₂×C₁₆	C₂³×C₅₉	1	4	yes	—
234	#107	—	2	2	no	—
235	#107	—	2	4	no	—
236	#107	C₂³×C₅₉	1	4	yes	—
237	C₂⁴	—	4	1	no	—
238	C₂⁴	D₈×C₅₉	1	1	yes	characteristic
239	#41	—	2	16	no	—
240	#41	—	4	16	no	—
241	#41	—	4	8	no	—
242	C₂×Q₈	—	2	4	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	4	1	no	—
245	C₂×Q₈	—	4	2	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	4	8	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	1	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	—	4	8	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	8	4	no	—
258	C₂²×C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
259	C₂²×C₄	D₈×C₅₉	1	1	yes	characteristic
260	C₂²×C₄	D₈×C₅₉	1	2	yes	—
261	C₂²×C₄	SD₁₆×C₅₉	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
264	Q₁₆	—	2	4	no	—
265	Q₁₆	—	2	2	no	—
266	Q₁₆	C₂²×C₄×C₅₉	1	4	yes	complemented
267	SD₁₆	—	2	16	no	—
268	D₈	—	2	4	no	—
269	D₈	—	2	2	no	—
270	D₈	C₂²×C₄×C₅₉	1	4	yes	complemented
271	C₂×C₈	C₂²⋊C₄×C₅₉	1	4	yes	—
272	C₂×C₈	C₂²⋊C₄×C₅₉	1	8	yes	—
273	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
275	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
276	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
277	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
278	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
279	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₁₆	—	2	4	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	4	4	no	—
287	C₂³	—	4	2	no	—
288	C₂³	—	8	2	no	—
289	C₂³	—	8	2	no	—
290	C₂³	#102×C₅₉	1	4	yes	—
291	C₂³	C₂×D₈×C₅₉	1	2	yes	—
292	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
293	Q₈	—	2	4	no	—
294	Q₈	—	4	4	no	—
295	Q₈	—	4	2	no	—
296	D₄	—	2	4	no	—
297	D₄	—	4	16	no	—
298	D₄	—	4	4	no	—
299	D₄	—	4	2	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	16	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	8	8	no	—
305	C₂×C₄	—	8	4	no	—
306	C₂×C₄	#102×C₅₉	1	4	yes	—
307	C₂×C₄	#102×C₅₉	1	8	yes	—
308	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
310	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
311	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
312	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
313	C₂×C₄	C₂×SD₁₆×C₅₉	1	4	yes	—
314	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
315	C₈	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
316	C₈	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
317	C₈	C₂³×C₄×C₅₉	1	1	yes	characteristic
318	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	8	no	—
326	C₂²	C₂×#102×C₅₉	1	4	yes	—
327	C₂²	C₂×#102×C₅₉	1	2	yes	—
328	C₂²	C₅₉×#509	1	2	yes	—
329	C₂²	C₅₉×#510	1	2	yes	—
330	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
331	C₄	—	4	4	no	—
332	C₄	—	8	4	no	—
333	C₄	C₂×#102×C₅₉	1	4	yes	—
334	C₄	C₂×#102×C₅₉	1	2	yes	—
335	C₄	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
336	C₄	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
337	C₂	—	2	4	no	—
338	C₂	—	8	4	no	—
339	C₂	C₅₉×#2139	1	4	yes	direct product factor
340	C₂	C₂²×#102×C₅₉	1	1	yes	characteristic
341	C₂	C₂×C₅₉×#509	1	1	yes	characteristic
342	C₂	C₂×C₅₉×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂×D₈
commutator	C₈	C₂³×C₄×C₅₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
prime radical	C₂²×#135×C₅₉	C₂
LCS	G ▷ 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
2. C₂²×M₃₂×C₅₉	C₂	semidirect
3. C₂²×#107×C₅₉	C₂	semidirect
4. C₅₉×#2139	C₂	direct (N × H)
5. C₂×C₅₉×#358	C₂	semidirect
6. C₂×C₅₉×#357	C₂	semidirect
10. C₂×#135×C₅₉	C₄	semidirect
18. C₂×M₃₂×C₅₉	C₂²	semidirect
23. C₂×#107×C₅₉	C₂²	semidirect
24. C₅₉×#358	C₂²	semidirect
25. C₅₉×#357	C₂²	semidirect
38. #135×C₅₉	C₂×C₄	semidirect
41. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
47. C₂×D₈×C₅₉	C₂×C₄	semidirect
94. Q₁₆×C₅₉	C₂²×C₄	semidirect
98. D₈×C₅₉	C₂²×C₄	semidirect
147. C₂×#2139	C₅₉	direct (N × H)
167. C₂²×M₃₂	C₂×C₅₉	semidirect
168. C₂²×#107	C₂×C₅₉	semidirect
169. #2139	C₂×C₅₉	direct (N × H)
170. C₂×#358	C₂×C₅₉	semidirect
171. C₂×#357	C₂×C₅₉	semidirect
174. C₂×C₅₉	#2139	direct (N × H)
181. C₂×#135	C₄×C₅₉	semidirect
189. C₂×M₃₂	C₂²×C₅₉	semidirect
194. C₂×#107	C₂²×C₅₉	semidirect
195. #358	C₂²×C₅₉	semidirect
196. #357	C₂²×C₅₉	semidirect
197. C₅₉	C₂×#2139	direct (N × H)
210. #135	C₂×C₄×C₅₉	semidirect
213. C₂×Q₁₆	C₂×C₄×C₅₉	semidirect
219. C₂×D₈	C₂×C₄×C₅₉	semidirect
266. Q₁₆	C₂²×C₄×C₅₉	semidirect
270. D₈	C₂²×C₄×C₅₉	semidirect
339. C₂	C₅₉×#2139	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×#135×C₅₉	2
C₂²×M₃₂×C₅₉	2
C₂²×#107×C₅₉	2
C₅₉×#2139	2
C₂×C₅₉×#358	2
C₂×C₅₉×#357	2
C₂×#2139	59

Subgroups — C2×C59×#2139 #28445488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2139 #28445488