Subgroups — C₅₉×#35514 #28447623

Order 15104.

3614 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#121×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2537	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2535	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2428	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2427	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2412	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2410	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#535	—	2	8	no	—
19	C₂×#127×C₅₉	C₂²	1	2	yes	complemented
20	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
21	C₅₉×#525	—	2	8	no	—
22	C₂×#123×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#121×C₅₉	—	2	8	no	—
25	C₂×#121×C₅₉	C₂²	1	4	yes	—
26	C₂×#121×C₅₉	C₂²	1	4	yes	—
27	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
28	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
29	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
31	C₂×#120×C₅₉	C₂²	1	2	yes	—
32	C₂×#120×C₅₉	C₂²	1	4	yes	—
33	C₅₉×#518	—	2	8	no	—
34	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
35	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
37	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
42	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
43	C₅₉×#397	C₂²	1	8	yes	complemented
44	C₅₉×#394	C₂²	1	8	yes	complemented
45	C₅₉×#394	C₂²	1	8	yes	complemented
46	C₅₉×#392	C₂²	1	8	yes	complemented
47	C₅₉×#391	C₂²	1	2	yes	complemented
48	C₅₉×#390	C₂²	1	2	yes	complemented
49	C₅₉×#389	C₂²	1	4	yes	complemented
50	C₅₉×#386	C₂²	1	4	yes	—
51	C₅₉×#386	C₂²	1	8	yes	complemented
52	C₅₉×#386	C₂²	1	8	yes	complemented
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#384	C₂²	1	2	yes	complemented
55	C₅₉×#382	C₂²	1	2	yes	complemented
56	C₅₉×#381	C₂²	1	2	yes	—
57	C₅₉×#380	C₂²	1	2	yes	complemented
58	C₅₉×#380	C₂²	1	4	yes	complemented
59	C₅₉×#380	C₂²	1	2	yes	complemented
60	C₅₉×#380	C₂²	1	8	yes	complemented
61	C₅₉×#379	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
63	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
64	C₂⁵×C₅₉	C₂³	1	2	yes	—
65	C₂×#41×C₅₉	—	2	4	no	—
66	C₂×#41×C₅₉	—	2	4	no	—
67	C₂×#41×C₅₉	—	2	4	no	—
68	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₅₉	—	2	8	no	—
70	C₂²×D₄×C₅₉	—	2	4	no	—
71	C₂²×D₄×C₅₉	—	2	4	no	—
72	C₂²×D₄×C₅₉	—	4	8	no	—
73	C₂²×D₄×C₅₉	D₄	1	8	yes	complemented
74	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
77	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₅₉	—	2	4	no	—
83	C₂³×C₄×C₅₉	—	2	4	no	—
84	C₂³×C₄×C₅₉	—	2	4	no	—
85	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅₉	C₂³	1	8	yes	—
90	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
92	#127×C₅₉	—	2	8	no	—
93	#124×C₅₉	—	2	8	no	—
94	#123×C₅₉	—	2	8	no	—
95	C₂²⋊Q₈×C₅₉	—	2	8	no	—
96	#121×C₅₉	—	2	16	no	—
97	#121×C₅₉	—	2	16	no	—
98	#121×C₅₉	—	2	8	no	—
99	#121×C₅₉	—	2	8	no	—
100	#121×C₅₉	—	2	8	no	—
101	#121×C₅₉	—	4	16	no	—
102	#120×C₅₉	—	2	16	no	—
103	#120×C₅₉	—	2	8	no	—
104	C₄×D₄×C₅₉	—	2	16	no	—
105	C₄×D₄×C₅₉	—	2	16	no	—
106	C₄×D₄×C₅₉	—	2	16	no	—
107	#117×C₅₉	—	2	4	no	—
108	#117×C₅₉	—	2	4	no	—
109	#117×C₅₉	D₄	1	8	yes	complemented
110	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
130	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
136	#95×C₅₉	C₂³	1	4	yes	—
137	#95×C₅₉	C₂³	1	4	yes	—
138	#95×C₅₉	C₂³	1	8	yes	—
139	#95×C₅₉	C₂³	1	8	yes	—
140	C₂⁴×C₅₉	—	2	2	no	—
141	C₂⁴×C₅₉	—	2	4	no	—
142	C₂⁴×C₅₉	—	2	4	no	—
143	C₂⁴×C₅₉	—	2	4	no	—
144	C₂⁴×C₅₉	—	2	2	no	—
145	C₂⁴×C₅₉	—	2	2	no	—
146	C₂⁴×C₅₉	—	4	2	no	—
147	C₂⁴×C₅₉	—	4	4	no	—
148	C₂⁴×C₅₉	—	4	4	no	—
149	C₂⁴×C₅₉	C₂×D₄	1	8	yes	—
150	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
151	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
152	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
153	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
154	#41×C₅₉	—	4	16	no	—
155	C₂×Q₈×C₅₉	—	2	2	no	—
156	C₂×Q₈×C₅₉	—	2	2	no	—
157	C₂×Q₈×C₅₉	—	2	2	no	—
158	C₂×D₄×C₅₉	—	2	4	no	—
159	C₂×D₄×C₅₉	—	2	4	no	—
160	C₂×D₄×C₅₉	—	2	16	no	—
161	C₂×D₄×C₅₉	—	2	4	no	—
162	C₂×D₄×C₅₉	—	2	8	no	—
163	C₂×D₄×C₅₉	—	2	16	no	—
164	C₂×D₄×C₅₉	—	2	8	no	—
165	C₂×D₄×C₅₉	—	2	8	no	—
166	C₂×D₄×C₅₉	—	2	32	no	—
167	C₂×D₄×C₅₉	—	2	4	no	—
168	C₂×D₄×C₅₉	—	2	4	no	—
169	C₂×D₄×C₅₉	—	2	8	no	—
170	C₂×D₄×C₅₉	—	2	2	no	—
171	C₂×D₄×C₅₉	—	2	2	no	—
172	C₂×D₄×C₅₉	—	2	4	no	—
173	C₂×D₄×C₅₉	—	2	4	no	—
174	C₂×D₄×C₅₉	—	2	2	no	—
175	C₂×D₄×C₅₉	—	4	8	no	—
176	C₂×D₄×C₅₉	—	4	4	no	—
177	C₂×D₄×C₅₉	—	4	8	no	—
178	C₂×D₄×C₅₉	—	4	8	no	—
179	C₂×D₄×C₅₉	—	4	32	no	—
180	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
181	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
182	C₂²×C₄×C₅₉	—	2	2	no	—
183	C₂²×C₄×C₅₉	—	2	4	no	—
184	C₂²×C₄×C₅₉	—	2	2	no	—
185	C₂²×C₄×C₅₉	—	2	2	no	—
186	C₂²×C₄×C₅₉	—	2	4	no	—
187	C₂²×C₄×C₅₉	—	2	4	no	—
188	C₂²×C₄×C₅₉	—	2	4	no	—
189	C₂²×C₄×C₅₉	—	2	4	no	—
190	C₂²×C₄×C₅₉	—	2	4	no	—
191	C₂²×C₄×C₅₉	—	2	4	no	—
192	C₂²×C₄×C₅₉	—	2	4	no	—
193	C₂²×C₄×C₅₉	—	2	4	no	—
194	C₂²×C₄×C₅₉	—	2	4	no	—
195	C₂²×C₄×C₅₉	—	2	16	no	—
196	C₂²×C₄×C₅₉	—	4	4	no	—
197	C₂²×C₄×C₅₉	—	4	8	no	—
198	C₂²×C₄×C₅₉	—	4	8	no	—
199	C₂²×C₄×C₅₉	—	4	16	no	—
200	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₅₉	#41	1	4	yes	—
203	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₅₉	—	2	4	no	—
213	C₄⋊C₄×C₅₉	—	2	4	no	—
214	C₄⋊C₄×C₅₉	—	2	4	no	—
215	C₄⋊C₄×C₅₉	—	2	2	no	—
216	C₄⋊C₄×C₅₉	—	2	2	no	—
217	C₄⋊C₄×C₅₉	—	2	8	no	—
218	C₄⋊C₄×C₅₉	—	4	8	no	—
219	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	complemented
220	C₂²⋊C₄×C₅₉	—	2	4	no	—
221	C₂²⋊C₄×C₅₉	—	2	16	no	—
222	C₂²⋊C₄×C₅₉	—	2	4	no	—
223	C₂²⋊C₄×C₅₉	—	2	8	no	—
224	C₂²⋊C₄×C₅₉	—	2	8	no	—
225	C₂²⋊C₄×C₅₉	—	2	8	no	—
226	C₂²⋊C₄×C₅₉	—	2	16	no	—
227	C₂²⋊C₄×C₅₉	—	2	8	no	—
228	C₂²⋊C₄×C₅₉	—	2	8	no	—
229	C₂²⋊C₄×C₅₉	—	4	4	no	—
230	C₂²⋊C₄×C₅₉	—	4	8	no	—
231	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
232	C₄²×C₅₉	—	2	4	no	—
233	C₄²×C₅₉	—	2	4	no	—
234	C₄²×C₅₉	C₂×D₄	1	8	yes	complemented
235	C₂³×C₅₉	—	2	2	no	—
236	C₂³×C₅₉	—	2	2	no	—
237	C₂³×C₅₉	—	2	8	no	—
238	C₂³×C₅₉	—	2	4	no	—
239	C₂³×C₅₉	—	2	2	no	—
240	C₂³×C₅₉	—	2	2	no	—
241	C₂³×C₅₉	—	2	2	no	—
242	C₂³×C₅₉	—	2	4	no	—
243	C₂³×C₅₉	—	2	8	no	—
244	C₂³×C₅₉	—	2	2	no	—
245	C₂³×C₅₉	—	2	2	no	—
246	C₂³×C₅₉	—	2	8	no	—
247	C₂³×C₅₉	—	2	2	no	—
248	C₂³×C₅₉	—	2	16	no	—
249	C₂³×C₅₉	—	2	2	no	—
250	C₂³×C₅₉	—	2	2	no	—
251	C₂³×C₅₉	—	2	2	no	—
252	C₂³×C₅₉	—	2	4	no	—
253	C₂³×C₅₉	—	2	4	no	—
254	C₂³×C₅₉	—	4	8	no	—
255	C₂³×C₅₉	—	4	8	no	—
256	C₂³×C₅₉	—	4	8	no	—
257	C₂³×C₅₉	—	4	8	no	—
258	C₂³×C₅₉	—	4	4	no	—
259	C₂³×C₅₉	—	4	4	no	—
260	C₂³×C₅₉	—	8	8	no	—
261	C₂³×C₅₉	—	8	8	no	—
262	C₂³×C₅₉	C₂²×D₄	1	8	yes	—
263	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
264	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
265	C₂³×C₅₉	C₂×#41	1	2	yes	—
266	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
267	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
268	Q₈×C₅₉	—	4	4	no	—
269	D₄×C₅₉	—	2	16	no	—
270	D₄×C₅₉	—	2	16	no	—
271	D₄×C₅₉	—	4	16	no	—
272	D₄×C₅₉	—	4	32	no	—
273	D₄×C₅₉	—	4	8	no	—
274	D₄×C₅₉	—	4	4	no	—
275	D₄×C₅₉	—	8	8	no	—
276	D₄×C₅₉	—	8	8	no	—
277	C₂×C₄×C₅₉	—	2	4	no	—
278	C₂×C₄×C₅₉	—	2	4	no	—
279	C₂×C₄×C₅₉	—	2	4	no	—
280	C₂×C₄×C₅₉	—	2	2	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	2	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	4	no	—
286	C₂×C₄×C₅₉	—	2	2	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	2	no	—
289	C₂×C₄×C₅₉	—	2	4	no	—
290	C₂×C₄×C₅₉	—	2	4	no	—
291	C₂×C₄×C₅₉	—	2	8	no	—
292	C₂×C₄×C₅₉	—	2	4	no	—
293	C₂×C₄×C₅₉	—	2	4	no	—
294	C₂×C₄×C₅₉	—	4	8	no	—
295	C₂×C₄×C₅₉	—	4	4	no	—
296	C₂×C₄×C₅₉	—	4	8	no	—
297	C₂×C₄×C₅₉	—	4	8	no	—
298	C₂×C₄×C₅₉	—	4	8	no	—
299	C₂×C₄×C₅₉	—	8	16	no	—
300	C₂×C₄×C₅₉	#121	1	16	yes	complemented
301	C₂×C₄×C₅₉	C₂²×D₄	1	8	yes	—
302	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
307	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
308	#35514	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂²×C₅₉	—	2	2	no	—
310	C₂²×C₅₉	—	2	2	no	—
311	C₂²×C₅₉	—	2	4	no	—
312	C₂²×C₅₉	—	2	4	no	—
313	C₂²×C₅₉	—	2	8	no	—
314	C₂²×C₅₉	—	2	4	no	—
315	C₂²×C₅₉	—	2	8	no	—
316	C₂²×C₅₉	—	2	8	no	—
317	C₂²×C₅₉	—	2	4	no	—
318	C₂²×C₅₉	—	2	4	no	—
319	C₂²×C₅₉	—	4	16	no	—
320	C₂²×C₅₉	—	4	2	no	—
321	C₂²×C₅₉	—	4	2	no	—
322	C₂²×C₅₉	—	4	8	no	—
323	C₂²×C₅₉	—	4	2	no	—
324	C₂²×C₅₉	—	4	2	no	—
325	C₂²×C₅₉	—	4	8	no	—
326	C₂²×C₅₉	—	4	2	no	—
327	C₂²×C₅₉	—	4	2	no	—
328	C₂²×C₅₉	—	4	2	no	—
329	C₂²×C₅₉	—	4	4	no	—
330	C₂²×C₅₉	—	4	4	no	—
331	C₂²×C₅₉	—	8	16	no	—
332	C₂²×C₅₉	C₂×#121	1	4	yes	—
333	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
334	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₅₉	#585	1	2	yes	—
338	C₄×C₅₉	—	2	8	no	—
339	C₄×C₅₉	—	4	2	no	—
340	C₄×C₅₉	—	4	2	no	—
341	C₄×C₅₉	—	4	4	no	—
342	C₄×C₅₉	—	4	2	no	—
343	C₄×C₅₉	—	4	2	no	—
344	C₄×C₅₉	—	4	4	no	—
345	C₄×C₅₉	C₂×#121	1	4	yes	—
346	C₄×C₅₉	C₂×#121	1	4	yes	—
347	C₂×#535	C₂×C₅₉	1	1	yes	characteristic, complemented
348	C₂×#525	C₂×C₅₉	1	1	yes	characteristic, complemented
349	C₂²×#121	C₂×C₅₉	1	1	yes	characteristic, complemented
350	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
351	#2537	C₂×C₅₉	1	4	yes	complemented
352	#2535	C₂×C₅₉	1	4	yes	complemented
353	#2428	C₂×C₅₉	1	4	yes	complemented
354	#2427	C₂×C₅₉	1	4	yes	complemented
355	#2412	C₂×C₅₉	1	4	yes	complemented
356	#2410	C₂×C₅₉	1	4	yes	complemented
357	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
358	#2311	C₂×C₅₉	1	1	yes	characteristic, complemented
359	#2280	C₂×C₅₉	1	1	yes	characteristic, complemented
360	C₂×C₅₉	—	2	4	no	—
361	C₂×C₅₉	—	4	4	no	—
362	C₂×C₅₉	—	4	8	no	—
363	C₂×C₅₉	—	8	2	no	—
364	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
365	C₂×C₅₉	#3484	1	1	yes	characteristic
366	C₂×C₅₉	#3485	1	1	yes	characteristic
367	C₂×C₅₉	#3488	1	2	yes	—
368	C₂×C₅₉	#3494	1	2	yes	—
369	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
370	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
371	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
372	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
373	#535	—	2	8	no	—
374	C₂×#127	C₂²×C₅₉	1	2	yes	complemented
375	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
376	#525	—	2	8	no	—
377	C₂×#123	C₂²×C₅₉	1	2	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
379	C₂×#121	—	2	8	no	—
380	C₂×#121	C₂²×C₅₉	1	4	yes	—
381	C₂×#121	C₂²×C₅₉	1	4	yes	—
382	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
383	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
384	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
385	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
386	C₂×#120	C₂²×C₅₉	1	2	yes	—
387	C₂×#120	C₂²×C₅₉	1	4	yes	—
388	#518	—	2	8	no	—
389	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
390	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
391	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
392	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
393	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
397	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
398	#397	C₂²×C₅₉	1	8	yes	complemented
399	#394	C₂²×C₅₉	1	8	yes	complemented
400	#394	C₂²×C₅₉	1	8	yes	complemented
401	#392	C₂²×C₅₉	1	8	yes	complemented
402	#391	C₂²×C₅₉	1	2	yes	complemented
403	#390	C₂²×C₅₉	1	2	yes	complemented
404	#389	C₂²×C₅₉	1	4	yes	complemented
405	#386	C₂²×C₅₉	1	4	yes	—
406	#386	C₂²×C₅₉	1	8	yes	complemented
407	#386	C₂²×C₅₉	1	8	yes	complemented
408	#385	C₂²×C₅₉	1	4	yes	—
409	#384	C₂²×C₅₉	1	2	yes	complemented
410	#382	C₂²×C₅₉	1	2	yes	complemented
411	#381	C₂²×C₅₉	1	2	yes	—
412	#380	C₂²×C₅₉	1	4	yes	complemented
413	#380	C₂²×C₅₉	1	8	yes	complemented
414	#380	C₂²×C₅₉	1	2	yes	complemented
415	#380	C₂²×C₅₉	1	2	yes	complemented
416	#379	C₂²×C₅₉	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
418	C₅₉	#35514	1	1	yes	characteristic, direct product factor, Sylow
419	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
420	C₂⁵	C₂³×C₅₉	1	2	yes	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	—	2	4	no	—
424	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
425	C₂²×D₄	—	2	8	no	—
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	—	2	4	no	—
428	C₂²×D₄	—	4	8	no	—
429	C₂²×D₄	D₄×C₅₉	1	8	yes	complemented
430	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
431	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
433	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
434	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
435	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
436	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
437	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
438	C₂³×C₄	—	2	4	no	—
439	C₂³×C₄	—	2	4	no	—
440	C₂³×C₄	—	2	4	no	—
441	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
443	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
444	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
445	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₅₉	1	8	yes	—
447	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
448	#127	—	2	8	no	—
449	#124	—	2	8	no	—
450	#123	—	2	8	no	—
451	C₂²⋊Q₈	—	2	8	no	—
452	#121	—	2	16	no	—
453	#121	—	2	16	no	—
454	#121	—	2	8	no	—
455	#121	—	2	8	no	—
456	#121	—	2	8	no	—
457	#121	—	4	16	no	—
458	#120	—	2	16	no	—
459	#120	—	2	8	no	—
460	C₄×D₄	—	2	16	no	—
461	C₄×D₄	—	2	16	no	—
462	C₄×D₄	—	2	16	no	—
463	#117	—	2	4	no	—
464	#117	—	2	4	no	—
465	#117	D₄×C₅₉	1	8	yes	complemented
466	C₂×C₄⋊C₄	—	2	4	no	—
467	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
475	C₂×C₂²⋊C₄	—	2	8	no	—
476	C₂×C₂²⋊C₄	—	2	16	no	—
477	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
489	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
490	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
492	#95	C₂³×C₅₉	1	4	yes	—
493	#95	C₂³×C₅₉	1	4	yes	—
494	#95	C₂³×C₅₉	1	8	yes	—
495	#95	C₂³×C₅₉	1	8	yes	—
496	C₂⁴	—	2	2	no	—
497	C₂⁴	—	2	4	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	2	2	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	—	4	4	no	—
504	C₂⁴	—	4	4	no	—
505	C₂⁴	C₂×D₄×C₅₉	1	8	yes	—
506	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
507	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
508	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
509	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
510	#41	—	4	16	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	16	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	2	16	no	—
520	C₂×D₄	—	2	8	no	—
521	C₂×D₄	—	2	8	no	—
522	C₂×D₄	—	2	32	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	4	8	no	—
532	C₂×D₄	—	4	4	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂×D₄	—	4	8	no	—
535	C₂×D₄	—	4	32	no	—
536	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
537	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	16	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	8	no	—
554	C₂²×C₄	—	4	8	no	—
555	C₂²×C₄	—	4	16	no	—
556	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
557	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
558	C₂²×C₄	#41×C₅₉	1	4	yes	—
559	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	8	no	—
574	C₄⋊C₄	—	4	8	no	—
575	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	complemented
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	16	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	16	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	—	2	8	no	—
585	C₂²⋊C₄	—	4	8	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	C₂×D₄×C₅₉	1	8	yes	complemented
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	8	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	16	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	4	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	4	8	no	—
611	C₂³	—	4	8	no	—
612	C₂³	—	4	8	no	—
613	C₂³	—	4	8	no	—
614	C₂³	—	4	4	no	—
615	C₂³	—	4	4	no	—
616	C₂³	—	8	8	no	—
617	C₂³	—	8	8	no	—
618	C₂³	C₂²×D₄×C₅₉	1	8	yes	—
619	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
620	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
621	C₂³	C₂×#41×C₅₉	1	2	yes	—
622	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
623	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
624	Q₈	—	4	4	no	—
625	D₄	—	2	16	no	—
626	D₄	—	2	16	no	—
627	D₄	—	4	16	no	—
628	D₄	—	4	32	no	—
629	D₄	—	4	8	no	—
630	D₄	—	4	4	no	—
631	D₄	—	8	8	no	—
632	D₄	—	8	8	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	8	no	—
653	C₂×C₄	—	4	8	no	—
654	C₂×C₄	—	4	8	no	—
655	C₂×C₄	—	8	16	no	—
656	C₂×C₄	#121×C₅₉	1	16	yes	complemented
657	C₂×C₄	C₂²×D₄×C₅₉	1	8	yes	—
658	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
662	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	8	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	8	no	—
671	C₂²	—	2	8	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	4	16	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	8	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	8	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	8	16	no	—
687	C₂²	C₂×#121×C₅₉	1	4	yes	—
688	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
689	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
690	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
691	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
692	C₂²	C₅₉×#585	1	2	yes	—
693	C₄	—	2	8	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	4	no	—
700	C₄	C₂×#121×C₅₉	1	4	yes	—
701	C₄	C₂×#121×C₅₉	1	4	yes	—
702	C₂	—	2	4	no	—
703	C₂	—	4	4	no	—
704	C₂	—	4	8	no	—
705	C₂	—	8	2	no	—
706	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
707	C₂	C₅₉×#3484	1	1	yes	characteristic
708	C₂	C₅₉×#3485	1	1	yes	characteristic
709	C₂	C₅₉×#3488	1	2	yes	—
710	C₂	C₅₉×#3494	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#535	C₂	semidirect
2. C₂×C₅₉×#525	C₂	semidirect
3. C₂²×#121×C₅₉	C₂	semidirect
4. C₂×C₅₉×#518	C₂	semidirect
5. C₅₉×#2537	C₂	semidirect
6. C₅₉×#2535	C₂	semidirect
7. C₅₉×#2428	C₂	semidirect
8. C₅₉×#2427	C₂	semidirect
9. C₅₉×#2412	C₂	semidirect
10. C₅₉×#2410	C₂	semidirect
11. C₅₉×#2317	C₂	semidirect
12. C₅₉×#2311	C₂	semidirect
13. C₅₉×#2280	C₂	semidirect
19. C₂×#127×C₅₉	C₂²	semidirect
20. C₂×#124×C₅₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
27. C₂×#121×C₅₉	C₂²	semidirect
28. C₂×#121×C₅₉	C₂²	semidirect
29. C₂×#121×C₅₉	C₂²	semidirect
30. C₂×#121×C₅₉	C₂²	semidirect
34. C₂×C₄×D₄×C₅₉	C₂²	semidirect
35. C₂×C₄×D₄×C₅₉	C₂²	semidirect
36. C₂×C₄×D₄×C₅₉	C₂²	semidirect
43. C₅₉×#397	C₂²	semidirect
44. C₅₉×#394	C₂²	semidirect
45. C₅₉×#394	C₂²	semidirect
46. C₅₉×#392	C₂²	semidirect
47. C₅₉×#391	C₂²	semidirect
48. C₅₉×#390	C₂²	semidirect
49. C₅₉×#389	C₂²	semidirect
51. C₅₉×#386	C₂²	semidirect
52. C₅₉×#386	C₂²	semidirect
54. C₅₉×#384	C₂²	semidirect
55. C₅₉×#382	C₂²	semidirect
57. C₅₉×#380	C₂²	semidirect
58. C₅₉×#380	C₂²	semidirect
59. C₅₉×#380	C₂²	semidirect
60. C₅₉×#380	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
73. C₂²×D₄×C₅₉	D₄	semidirect
109. #117×C₅₉	D₄	semidirect
219. C₄⋊C₄×C₅₉	C₂×D₄	semidirect
234. C₄²×C₅₉	C₂×D₄	semidirect
300. C₂×C₄×C₅₉	#121	semidirect
308. #35514	C₅₉	direct (N × H)
347. C₂×#535	C₂×C₅₉	semidirect
348. C₂×#525	C₂×C₅₉	semidirect
349. C₂²×#121	C₂×C₅₉	semidirect
350. C₂×#518	C₂×C₅₉	semidirect
351. #2537	C₂×C₅₉	semidirect
352. #2535	C₂×C₅₉	semidirect
353. #2428	C₂×C₅₉	semidirect
354. #2427	C₂×C₅₉	semidirect
355. #2412	C₂×C₅₉	semidirect
356. #2410	C₂×C₅₉	semidirect
357. #2317	C₂×C₅₉	semidirect
358. #2311	C₂×C₅₉	semidirect
359. #2280	C₂×C₅₉	semidirect
374. C₂×#127	C₂²×C₅₉	semidirect
375. C₂×#124	C₂²×C₅₉	semidirect
378. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
382. C₂×#121	C₂²×C₅₉	semidirect
383. C₂×#121	C₂²×C₅₉	semidirect
384. C₂×#121	C₂²×C₅₉	semidirect
385. C₂×#121	C₂²×C₅₉	semidirect
389. C₂×C₄×D₄	C₂²×C₅₉	semidirect
390. C₂×C₄×D₄	C₂²×C₅₉	semidirect
391. C₂×C₄×D₄	C₂²×C₅₉	semidirect
398. #397	C₂²×C₅₉	semidirect
399. #394	C₂²×C₅₉	semidirect
400. #394	C₂²×C₅₉	semidirect
401. #392	C₂²×C₅₉	semidirect
402. #391	C₂²×C₅₉	semidirect
403. #390	C₂²×C₅₉	semidirect
404. #389	C₂²×C₅₉	semidirect
406. #386	C₂²×C₅₉	semidirect
407. #386	C₂²×C₅₉	semidirect
409. #384	C₂²×C₅₉	semidirect
410. #382	C₂²×C₅₉	semidirect
412. #380	C₂²×C₅₉	semidirect
413. #380	C₂²×C₅₉	semidirect
414. #380	C₂²×C₅₉	semidirect
415. #380	C₂²×C₅₉	semidirect
417. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
418. C₅₉	#35514	direct (N × H)
429. C₂²×D₄	D₄×C₅₉	semidirect
465. #117	D₄×C₅₉	semidirect
575. C₄⋊C₄	C₂×D₄×C₅₉	semidirect
590. C₄²	C₂×D₄×C₅₉	semidirect
656. C₂×C₄	#121×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#535	2
C₂×C₅₉×#525	2
C₂²×#121×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2537	2
C₅₉×#2535	2
C₅₉×#2428	2
C₅₉×#2427	2
C₅₉×#2412	2
C₅₉×#2410	2
C₅₉×#2317	2
C₅₉×#2311	2
C₅₉×#2280	2
#35514	59

Subgroups — C59×#35514 #28447623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35514 #28447623