Subgroups — C₅₉×#62930 #28475039

Order 15104.

7318 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3558	C₂	1	8	yes	maximal, complemented
2	C₅₉×#3549	C₂	1	4	yes	maximal, complemented
3	C₅₉×#3547	C₂	1	4	yes	maximal, complemented
4	C₅₉×#3542	C₂	1	8	yes	maximal, complemented
5	C₅₉×#3540	C₂	1	8	yes	maximal, complemented
6	C₅₉×#3537	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3519	C₂	1	4	yes	maximal, complemented
8	C₅₉×#3511	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3506	C₂	1	4	yes	maximal, complemented
10	C₅₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3494	C₂	1	4	yes	maximal, complemented
12	C₅₉×#3493	C₂	1	2	yes	maximal, complemented
13	C₅₉×#3488	C₂	1	4	yes	maximal, complemented
14	C₂×C₅₉×#555	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#41×C₅₉	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3449	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	2	yes	complemented
19	C₂²×#41×C₅₉	C₂²	1	4	yes	complemented
20	C₅₉×#562	C₂²	1	16	yes	complemented
21	C₅₉×H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	C₅₉×#560	C₂²	1	16	yes	complemented
23	C₅₉×#559	C₂²	1	16	yes	complemented
24	C₅₉×#556	C₂²	1	8	yes	complemented
25	C₅₉×#556	C₂²	1	4	yes	complemented
26	C₅₉×#555	C₂²	1	4	yes	complemented
27	C₅₉×#555	C₂²	1	4	yes	complemented
28	C₅₉×#555	C₂²	1	8	yes	complemented
29	C₅₉×#555	C₂²	1	8	yes	complemented
30	C₅₉×#555	C₂²	1	4	yes	complemented
31	C₅₉×#555	C₂²	1	8	yes	complemented
32	C₅₉×#554	C₂²	1	4	yes	complemented
33	C₅₉×#553	C₂²	1	8	yes	complemented
34	C₅₉×#553	C₂²	1	8	yes	complemented
35	C₅₉×#553	C₂²	1	8	yes	complemented
36	C₅₉×#553	C₂²	1	8	yes	complemented
37	C₅₉×#552	C₂²	1	8	yes	complemented
38	C₅₉×#551	C₂²	1	16	yes	complemented
39	C₅₉×#550	C₂²	1	8	yes	complemented
40	C₅₉×#550	C₂²	1	2	yes	complemented
41	D₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
42	C₅₉×#548	C₂²	1	8	yes	complemented
43	C₅₉×#548	C₂²	1	4	yes	complemented
44	C₅₉×#548	C₂²	1	8	yes	complemented
45	C₅₉×#547	C₂²	1	2	yes	complemented
46	C₅₉×#547	C₂²	1	4	yes	complemented
47	C₅₉×#547	C₂²	1	4	yes	complemented
48	C₅₉×#547	C₂²	1	4	yes	complemented
49	C₅₉×#546	C₂²	1	8	yes	complemented
50	C₅₉×#546	C₂²	1	16	yes	complemented
51	C₅₉×#546	C₂²	1	8	yes	complemented
52	C₅₉×#546	C₂²	1	4	yes	complemented
53	C₅₉×#546	C₂²	1	8	yes	complemented
54	C₅₉×#546	C₂²	1	16	yes	complemented
55	D₄²×C₅₉	C₂²	1	8	yes	complemented
56	D₄²×C₅₉	C₂²	1	4	yes	complemented
57	D₄²×C₅₉	C₂²	1	4	yes	complemented
58	D₄²×C₅₉	C₂²	1	16	yes	complemented
59	D₄²×C₅₉	C₂²	1	8	yes	complemented
60	D₄²×C₅₉	C₂²	1	2	yes	complemented
61	C₅₉×#544	C₂²	1	4	yes	complemented
62	C₅₉×#544	C₂²	1	1	yes	characteristic, complemented
63	C₅₉×#542	C₂²	1	8	yes	complemented
64	C₅₉×#542	C₂²	1	4	yes	complemented
65	C₅₉×#542	C₂²	1	8	yes	complemented
66	C₅₉×#542	C₂²	1	16	yes	complemented
67	C₅₉×#540	C₂²	1	8	yes	complemented
68	C₅₉×#540	C₂²	1	4	yes	complemented
69	C₅₉×#540	C₂²	1	8	yes	complemented
70	C₅₉×#538	C₂²	1	16	yes	complemented
71	C₅₉×#538	C₂²	1	16	yes	complemented
72	C₅₉×#538	C₂²	1	8	yes	complemented
73	C₅₉×#538	C₂²	1	8	yes	complemented
74	C₅₉×#538	C₂²	1	4	yes	complemented
75	C₅₉×#537	C₂²	1	4	yes	complemented
76	C₅₉×#537	C₂²	1	8	yes	complemented
77	C₅₉×#537	C₂²	1	1	yes	characteristic, complemented
78	C₅₉×#537	C₂²	1	2	yes	complemented
79	C₅₉×#536	C₂²	1	8	yes	complemented
80	C₅₉×#535	C₂²	1	8	yes	complemented
81	C₅₉×#535	C₂²	1	8	yes	complemented
82	C₅₉×#535	C₂²	1	16	yes	complemented
83	C₅₉×#535	C₂²	1	8	yes	complemented
84	C₅₉×#535	C₂²	1	4	yes	complemented
85	C₅₉×#535	C₂²	1	2	yes	complemented
86	C₅₉×#534	C₂²	1	8	yes	complemented
87	C₅₉×#534	C₂²	1	8	yes	complemented
88	C₅₉×#534	C₂²	1	4	yes	complemented
89	C₅₉×#533	C₂²	1	4	yes	complemented
90	C₅₉×#532	C₂²	1	4	yes	complemented
91	C₅₉×#532	C₂²	1	4	yes	complemented
92	C₅₉×#532	C₂²	1	2	yes	complemented
93	C₅₉×#532	C₂²	1	4	yes	complemented
94	C₅₉×#532	C₂²	1	8	yes	complemented
95	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
96	C₅₉×#529	C₂²	1	4	yes	complemented
97	C₅₉×#529	C₂²	1	8	yes	complemented
98	C₂×#124×C₅₉	C₂²	1	4	yes	complemented
99	C₅₉×#525	C₂²	1	8	yes	complemented
100	C₅₉×#525	C₂²	1	8	yes	complemented
101	C₅₉×#525	C₂²	1	8	yes	complemented
102	C₅₉×#525	C₂²	1	4	yes	complemented
103	C₅₉×#525	C₂²	1	8	yes	complemented
104	C₅₉×#525	C₂²	1	4	yes	complemented
105	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
106	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
107	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
108	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
109	C₅₉×#520	C₂²	1	4	yes	complemented
110	C₅₉×#520	C₂²	1	4	yes	complemented
111	C₅₉×#518	C₂²	1	4	yes	complemented
112	C₄×#41×C₅₉	C₂²	1	2	yes	complemented
113	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
114	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
116	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
117	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
118	H(5,𝔽₂)×C₅₉	—	4	8	no	—
119	C₂×#41×C₅₉	—	4	16	no	—
120	C₂×#41×C₅₉	C₂³	1	2	yes	—
121	C₂×#41×C₅₉	C₂³	1	4	yes	—
122	C₂×#41×C₅₉	C₂³	1	4	yes	—
123	C₂×#41×C₅₉	C₂³	1	4	yes	—
124	C₂×#41×C₅₉	C₂³	1	4	yes	—
125	C₂×#41×C₅₉	C₂³	1	8	yes	—
126	C₂×#41×C₅₉	C₂³	1	8	yes	—
127	C₂×#41×C₅₉	C₂³	1	8	yes	—
128	C₂×#41×C₅₉	C₂³	1	8	yes	—
129	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
130	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
134	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
135	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
136	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
137	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
138	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
139	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
140	C₂²×D₄×C₅₉	C₂³	1	16	yes	—
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₉	C₂³	1	8	yes	—
144	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
145	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
146	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₅₉	C₂³	1	8	yes	—
148	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
149	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
150	#127×C₅₉	C₂³	1	2	yes	—
151	#127×C₅₉	C₂³	1	8	yes	—
152	#127×C₅₉	C₂³	1	4	yes	—
153	#127×C₅₉	C₂³	1	4	yes	—
154	#127×C₅₉	C₂³	1	16	yes	—
155	#126×C₅₉	C₂³	1	8	yes	—
156	#126×C₅₉	C₂³	1	16	yes	—
157	#126×C₅₉	C₂³	1	16	yes	—
158	#126×C₅₉	C₂³	1	16	yes	—
159	#125×C₅₉	C₂³	1	4	yes	—
160	#125×C₅₉	C₂³	1	8	yes	—
161	#125×C₅₉	C₂³	1	8	yes	—
162	#124×C₅₉	C₂³	1	16	yes	—
163	#124×C₅₉	C₂³	1	16	yes	—
164	#124×C₅₉	C₂³	1	4	yes	—
165	#124×C₅₉	C₂³	1	8	yes	—
166	#124×C₅₉	C₂³	1	16	yes	—
167	#124×C₅₉	C₂³	1	8	yes	—
168	#124×C₅₉	C₂³	1	8	yes	—
169	#124×C₅₉	C₂³	1	4	yes	—
170	#124×C₅₉	C₂³	1	8	yes	—
171	#124×C₅₉	C₂³	1	16	yes	—
172	#124×C₅₉	C₂³	1	16	yes	—
173	#124×C₅₉	C₂³	1	16	yes	—
174	#123×C₅₉	C₂³	1	8	yes	—
175	#123×C₅₉	C₂³	1	16	yes	—
176	#123×C₅₉	C₂³	1	16	yes	—
177	#123×C₅₉	C₂³	1	8	yes	—
178	#123×C₅₉	C₂³	1	16	yes	—
179	#123×C₅₉	C₂³	1	8	yes	—
180	#123×C₅₉	C₂³	1	8	yes	—
181	#123×C₅₉	C₂³	1	8	yes	—
182	#123×C₅₉	C₂³	1	16	yes	—
183	#123×C₅₉	C₂³	1	16	yes	—
184	#123×C₅₉	C₂³	1	16	yes	—
185	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
186	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
187	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
188	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
189	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
192	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
193	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
195	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₅₉	C₂³	1	16	yes	—
197	C₂²⋊Q₈×C₅₉	C₂³	1	16	yes	—
198	#121×C₅₉	C₂³	1	4	yes	—
199	#121×C₅₉	C₂³	1	8	yes	—
200	#121×C₅₉	C₂³	1	4	yes	—
201	#121×C₅₉	C₂³	1	4	yes	—
202	#121×C₅₉	C₂³	1	8	yes	—
203	#121×C₅₉	C₂³	1	8	yes	—
204	#121×C₅₉	C₂³	1	8	yes	—
205	#121×C₅₉	C₂³	1	8	yes	—
206	#121×C₅₉	C₂³	1	8	yes	—
207	#121×C₅₉	C₂³	1	8	yes	—
208	#121×C₅₉	C₂³	1	16	yes	—
209	#121×C₅₉	C₂³	1	16	yes	—
210	#121×C₅₉	C₂³	1	8	yes	—
211	#121×C₅₉	C₂³	1	4	yes	—
212	#121×C₅₉	C₂³	1	4	yes	—
213	#121×C₅₉	C₂³	1	4	yes	—
214	#121×C₅₉	C₂³	1	4	yes	—
215	#121×C₅₉	C₂³	1	4	yes	—
216	#121×C₅₉	C₂³	1	8	yes	—
217	#121×C₅₉	C₂³	1	8	yes	—
218	#121×C₅₉	C₂³	1	8	yes	—
219	#121×C₅₉	C₂³	1	8	yes	—
220	#121×C₅₉	C₂³	1	4	yes	—
221	#121×C₅₉	C₂³	1	16	yes	—
222	#121×C₅₉	C₂³	1	8	yes	—
223	#121×C₅₉	C₂³	1	4	yes	—
224	#121×C₅₉	C₂³	1	4	yes	—
225	#121×C₅₉	C₂³	1	8	yes	—
226	#121×C₅₉	C₂³	1	8	yes	—
227	#121×C₅₉	C₂³	1	16	yes	—
228	#121×C₅₉	C₂³	1	16	yes	—
229	#121×C₅₉	C₂³	1	16	yes	—
230	#121×C₅₉	C₂³	1	16	yes	—
231	#120×C₅₉	C₂³	1	16	yes	—
232	#120×C₅₉	C₂³	1	8	yes	—
233	#120×C₅₉	C₂³	1	16	yes	—
234	#120×C₅₉	C₂³	1	8	yes	—
235	#120×C₅₉	C₂³	1	8	yes	—
236	#120×C₅₉	C₂³	1	16	yes	—
237	#120×C₅₉	C₂³	1	8	yes	—
238	#120×C₅₉	C₂³	1	16	yes	—
239	#120×C₅₉	C₂³	1	16	yes	—
240	#120×C₅₉	C₂³	1	16	yes	—
241	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
244	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
245	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
246	C₄×D₄×C₅₉	C₂³	1	2	yes	—
247	C₄×D₄×C₅₉	C₂³	1	4	yes	—
248	C₄×D₄×C₅₉	C₂³	1	4	yes	—
249	C₄×D₄×C₅₉	C₂³	1	8	yes	—
250	C₄×D₄×C₅₉	C₂³	1	4	yes	—
251	C₄×D₄×C₅₉	C₂³	1	4	yes	—
252	C₄×D₄×C₅₉	C₂³	1	2	yes	—
253	C₄×D₄×C₅₉	C₂³	1	8	yes	—
254	C₄×D₄×C₅₉	C₂³	1	4	yes	—
255	C₄×D₄×C₅₉	C₂³	1	4	yes	—
256	C₄×D₄×C₅₉	C₂³	1	4	yes	—
257	C₄×D₄×C₅₉	C₂³	1	2	yes	—
258	C₄×D₄×C₅₉	C₂³	1	4	yes	—
259	C₄×D₄×C₅₉	C₂³	1	2	yes	—
260	C₄×D₄×C₅₉	C₂³	1	8	yes	—
261	C₄×D₄×C₅₉	C₂³	1	8	yes	—
262	C₄×D₄×C₅₉	C₂³	1	8	yes	—
263	C₄×D₄×C₅₉	C₂³	1	8	yes	—
264	C₄×D₄×C₅₉	C₂³	1	16	yes	—
265	C₄×D₄×C₅₉	C₂³	1	16	yes	—
266	C₄×D₄×C₅₉	C₂³	1	8	yes	—
267	C₄×D₄×C₅₉	C₂³	1	8	yes	—
268	C₄×D₄×C₅₉	C₂³	1	4	yes	—
269	C₄×D₄×C₅₉	C₂³	1	16	yes	—
270	C₄×D₄×C₅₉	C₂³	1	8	yes	—
271	C₄×D₄×C₅₉	C₂³	1	16	yes	—
272	#117×C₅₉	C₂³	1	4	yes	—
273	#117×C₅₉	C₂³	1	8	yes	—
274	#117×C₅₉	C₂³	1	8	yes	—
275	#117×C₅₉	C₂³	1	4	yes	—
276	#117×C₅₉	C₂³	1	8	yes	—
277	#117×C₅₉	C₂³	1	2	yes	—
278	#117×C₅₉	C₂³	1	4	yes	—
279	#117×C₅₉	C₂³	1	4	yes	—
280	#117×C₅₉	C₂³	1	8	yes	—
281	#117×C₅₉	C₂³	1	8	yes	—
282	#117×C₅₉	C₂³	1	16	yes	—
283	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
288	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
289	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
290	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
291	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
292	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
295	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
296	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
297	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
298	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
300	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
301	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
302	C₂⁴×C₅₉	C₂⁴	1	8	yes	—
303	C₂⁴×C₅₉	C₂⁴	1	8	yes	—
304	#41×C₅₉	—	2	8	no	—
305	#41×C₅₉	—	2	16	no	—
306	#41×C₅₉	—	4	16	no	—
307	#41×C₅₉	—	4	8	no	—
308	#41×C₅₉	—	4	16	no	—
309	#41×C₅₉	—	4	8	no	—
310	#41×C₅₉	—	4	8	no	—
311	#41×C₅₉	—	4	16	no	—
312	#41×C₅₉	—	8	8	no	—
313	C₂×Q₈×C₅₉	—	4	8	no	—
314	C₂×Q₈×C₅₉	—	8	2	no	—
315	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
316	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₅₉	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₅₉	C₂⁴	1	8	yes	—
320	C₂×D₄×C₅₉	—	2	4	no	—
321	C₂×D₄×C₅₉	—	4	2	no	—
322	C₂×D₄×C₅₉	—	4	8	no	—
323	C₂×D₄×C₅₉	—	4	8	no	—
324	C₂×D₄×C₅₉	—	4	8	no	—
325	C₂×D₄×C₅₉	—	4	16	no	—
326	C₂×D₄×C₅₉	—	4	16	no	—
327	C₂×D₄×C₅₉	—	4	16	no	—
328	C₂×D₄×C₅₉	—	8	4	no	—
329	C₂×D₄×C₅₉	—	8	16	no	—
330	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
331	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
332	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
333	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
334	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
335	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
336	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
337	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
338	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
339	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
340	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
341	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
342	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
343	C₂×D₄×C₅₉	C₂⁴	1	16	yes	—
344	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
345	C₂×D₄×C₅₉	C₂⁴	1	16	yes	—
346	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
347	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
348	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
349	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
350	C₂×D₄×C₅₉	C₂⁴	1	16	yes	—
351	C₂²×C₄×C₅₉	—	2	8	no	—
352	C₂²×C₄×C₅₉	—	4	4	no	—
353	C₂²×C₄×C₅₉	—	4	16	no	—
354	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
360	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
365	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₅₉	C₂⁴	1	16	yes	—
369	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
370	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
372	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
376	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
378	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
380	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
382	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₅₉	C₂⁴	1	16	yes	—
384	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
390	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
391	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₅₉	C₂⁴	1	16	yes	—
393	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
394	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₅₉	C₂⁴	1	4	yes	—
397	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
401	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
402	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
403	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
404	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₅₉	C₂⁴	1	4	yes	—
406	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₅₉	C₂⁴	1	4	yes	—
409	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
410	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
411	C₂²⋊C₄×C₅₉	C₂⁴	1	4	yes	—
412	C₂²⋊C₄×C₅₉	C₂⁴	1	4	yes	—
413	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
416	C₄²×C₅₉	C₂⁴	1	2	yes	—
417	C₄²×C₅₉	C₂⁴	1	8	yes	—
418	C₄²×C₅₉	C₂⁴	1	8	yes	—
419	C₄²×C₅₉	C₂⁴	1	2	yes	—
420	C₄²×C₅₉	C₂⁴	1	4	yes	—
421	C₄²×C₅₉	C₂⁴	1	4	yes	—
422	C₄²×C₅₉	C₂⁴	1	4	yes	—
423	C₄²×C₅₉	C₂⁴	1	16	yes	—
424	C₂³×C₅₉	—	2	4	no	—
425	C₂³×C₅₉	—	2	4	no	—
426	C₂³×C₅₉	—	4	8	no	—
427	C₂³×C₅₉	—	4	2	no	—
428	C₂³×C₅₉	—	4	2	no	—
429	C₂³×C₅₉	—	4	8	no	—
430	C₂³×C₅₉	—	4	2	no	—
431	C₂³×C₅₉	—	4	2	no	—
432	C₂³×C₅₉	—	4	8	no	—
433	C₂³×C₅₉	—	4	8	no	—
434	C₂³×C₅₉	—	4	8	no	—
435	C₂³×C₅₉	—	4	8	no	—
436	C₂³×C₅₉	C₂⁵	1	4	yes	—
437	C₂³×C₅₉	C₂⁵	1	8	yes	—
438	C₂³×C₅₉	C₂⁵	1	4	yes	—
439	C₂³×C₅₉	C₂⁵	1	4	yes	—
440	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
441	Q₈×C₅₉	—	2	4	no	—
442	Q₈×C₅₉	—	2	8	no	—
443	Q₈×C₅₉	—	4	8	no	—
444	Q₈×C₅₉	—	4	8	no	—
445	Q₈×C₅₉	—	4	4	no	—
446	D₄×C₅₉	—	2	16	no	—
447	D₄×C₅₉	—	2	8	no	—
448	D₄×C₅₉	—	2	8	no	—
449	D₄×C₅₉	—	2	8	no	—
450	D₄×C₅₉	—	2	4	no	—
451	D₄×C₅₉	—	2	4	no	—
452	D₄×C₅₉	—	2	8	no	—
453	D₄×C₅₉	—	4	16	no	—
454	D₄×C₅₉	—	4	2	no	—
455	D₄×C₅₉	—	4	8	no	—
456	D₄×C₅₉	—	4	8	no	—
457	D₄×C₅₉	—	4	8	no	—
458	D₄×C₅₉	—	4	8	no	—
459	D₄×C₅₉	—	4	8	no	—
460	D₄×C₅₉	—	4	8	no	—
461	D₄×C₅₉	—	4	8	no	—
462	D₄×C₅₉	—	4	16	no	—
463	D₄×C₅₉	—	4	16	no	—
464	D₄×C₅₉	—	4	4	no	—
465	D₄×C₅₉	—	4	8	no	—
466	D₄×C₅₉	—	4	4	no	—
467	C₂×C₄×C₅₉	—	2	4	no	—
468	C₂×C₄×C₅₉	—	2	8	no	—
469	C₂×C₄×C₅₉	—	2	8	no	—
470	C₂×C₄×C₅₉	—	2	8	no	—
471	C₂×C₄×C₅₉	—	2	16	no	—
472	C₂×C₄×C₅₉	—	2	2	no	—
473	C₂×C₄×C₅₉	—	2	8	no	—
474	C₂×C₄×C₅₉	—	2	8	no	—
475	C₂×C₄×C₅₉	—	4	4	no	—
476	C₂×C₄×C₅₉	—	4	2	no	—
477	C₂×C₄×C₅₉	—	4	8	no	—
478	C₂×C₄×C₅₉	—	4	8	no	—
479	C₂×C₄×C₅₉	—	4	8	no	—
480	C₂×C₄×C₅₉	—	4	8	no	—
481	C₂×C₄×C₅₉	—	4	4	no	—
482	C₂×C₄×C₅₉	—	4	16	no	—
483	C₂×C₄×C₅₉	—	4	1	no	—
484	C₂×C₄×C₅₉	—	4	4	no	—
485	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
486	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
487	C₂×C₄×C₅₉	C₂⁵	1	2	yes	—
488	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
489	C₂×C₄×C₅₉	C₂⁵	1	8	yes	—
490	C₂×C₄×C₅₉	C₂⁵	1	2	yes	—
491	C₂×C₄×C₅₉	C₂⁵	1	2	yes	—
492	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
493	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
494	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
495	C₂×C₄×C₅₉	C₂⁵	1	8	yes	—
496	C₂×C₄×C₅₉	C₂⁵	1	2	yes	—
497	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
498	#62930	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
499	C₂²×C₅₉	—	2	1	no	—
500	C₂²×C₅₉	—	2	1	no	—
501	C₂²×C₅₉	—	2	4	no	—
502	C₂²×C₅₉	—	2	4	no	—
503	C₂²×C₅₉	—	2	8	no	—
504	C₂²×C₅₉	—	2	4	no	—
505	C₂²×C₅₉	—	2	4	no	—
506	C₂²×C₅₉	—	2	4	no	—
507	C₂²×C₅₉	—	2	4	no	—
508	C₂²×C₅₉	—	2	8	no	—
509	C₂²×C₅₉	—	2	8	no	—
510	C₂²×C₅₉	—	2	4	no	—
511	C₂²×C₅₉	—	2	4	no	—
512	C₂²×C₅₉	—	2	4	no	—
513	C₂²×C₅₉	—	8	4	no	—
514	C₂²×C₅₉	—	8	4	no	—
515	C₂²×C₅₉	—	8	16	no	—
516	C₂²×C₅₉	—	16	8	no	—
517	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
518	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
519	C₄×C₅₉	—	2	2	no	—
520	C₄×C₅₉	—	2	2	no	—
521	C₄×C₅₉	—	2	8	no	—
522	C₄×C₅₉	—	2	4	no	—
523	C₄×C₅₉	—	2	1	no	—
524	C₄×C₅₉	—	2	4	no	—
525	C₄×C₅₉	—	2	4	no	—
526	C₄×C₅₉	—	2	4	no	—
527	C₄×C₅₉	—	2	8	no	—
528	C₄×C₅₉	—	2	2	no	—
529	C₄×C₅₉	C₂×H(5,𝔽₂)	1	4	yes	—
530	C₄×C₅₉	#585	1	2	yes	—
531	#3558	C₂×C₅₉	1	8	yes	complemented
532	#3549	C₂×C₅₉	1	4	yes	complemented
533	#3547	C₂×C₅₉	1	4	yes	complemented
534	#3542	C₂×C₅₉	1	8	yes	complemented
535	#3540	C₂×C₅₉	1	8	yes	complemented
536	#3537	C₂×C₅₉	1	4	yes	complemented
537	#3519	C₂×C₅₉	1	4	yes	complemented
538	#3511	C₂×C₅₉	1	2	yes	complemented
539	#3506	C₂×C₅₉	1	4	yes	complemented
540	#3496	C₂×C₅₉	1	1	yes	characteristic, complemented
541	#3494	C₂×C₅₉	1	4	yes	complemented
542	#3493	C₂×C₅₉	1	2	yes	complemented
543	#3488	C₂×C₅₉	1	4	yes	complemented
544	C₂×#555	C₂×C₅₉	1	1	yes	characteristic, complemented
545	D₄×#41	C₂×C₅₉	1	2	yes	complemented
546	#3460	C₂×C₅₉	1	1	yes	characteristic, complemented
547	#3449	C₂×C₅₉	1	2	yes	complemented
548	C₂×C₅₉	—	2	2	no	—
549	C₂×C₅₉	—	4	4	no	—
550	C₂×C₅₉	—	4	4	no	—
551	C₂×C₅₉	—	4	8	no	—
552	C₂×C₅₉	—	4	4	no	—
553	C₂×C₅₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×C₅₉	C₂×#585	1	1	yes	characteristic
555	C₂×C₅₉	H(7,𝔽₂)	1	1	yes	characteristic
556	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	2	yes	complemented
557	C₂²×#41	C₂²×C₅₉	1	4	yes	complemented
558	#562	C₂²×C₅₉	1	16	yes	complemented
559	H(3,𝔽₄)	C₂²×C₅₉	1	16	yes	complemented
560	#560	C₂²×C₅₉	1	16	yes	complemented
561	#559	C₂²×C₅₉	1	16	yes	complemented
562	#556	C₂²×C₅₉	1	8	yes	complemented
563	#556	C₂²×C₅₉	1	4	yes	complemented
564	#555	C₂²×C₅₉	1	4	yes	complemented
565	#555	C₂²×C₅₉	1	8	yes	complemented
566	#555	C₂²×C₅₉	1	4	yes	complemented
567	#555	C₂²×C₅₉	1	8	yes	complemented
568	#555	C₂²×C₅₉	1	8	yes	complemented
569	#555	C₂²×C₅₉	1	4	yes	complemented
570	#554	C₂²×C₅₉	1	4	yes	complemented
571	#553	C₂²×C₅₉	1	8	yes	complemented
572	#553	C₂²×C₅₉	1	8	yes	complemented
573	#553	C₂²×C₅₉	1	8	yes	complemented
574	#553	C₂²×C₅₉	1	8	yes	complemented
575	#552	C₂²×C₅₉	1	8	yes	complemented
576	#551	C₂²×C₅₉	1	16	yes	complemented
577	#550	C₂²×C₅₉	1	2	yes	complemented
578	#550	C₂²×C₅₉	1	8	yes	complemented
579	D₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
580	#548	C₂²×C₅₉	1	4	yes	complemented
581	#548	C₂²×C₅₉	1	8	yes	complemented
582	#548	C₂²×C₅₉	1	8	yes	complemented
583	#547	C₂²×C₅₉	1	4	yes	complemented
584	#547	C₂²×C₅₉	1	2	yes	complemented
585	#547	C₂²×C₅₉	1	4	yes	complemented
586	#547	C₂²×C₅₉	1	4	yes	complemented
587	#546	C₂²×C₅₉	1	4	yes	complemented
588	#546	C₂²×C₅₉	1	8	yes	complemented
589	#546	C₂²×C₅₉	1	16	yes	complemented
590	#546	C₂²×C₅₉	1	8	yes	complemented
591	#546	C₂²×C₅₉	1	8	yes	complemented
592	#546	C₂²×C₅₉	1	16	yes	complemented
593	D₄²	C₂²×C₅₉	1	4	yes	complemented
594	D₄²	C₂²×C₅₉	1	2	yes	complemented
595	D₄²	C₂²×C₅₉	1	16	yes	complemented
596	D₄²	C₂²×C₅₉	1	8	yes	complemented
597	D₄²	C₂²×C₅₉	1	4	yes	complemented
598	D₄²	C₂²×C₅₉	1	8	yes	complemented
599	#544	C₂²×C₅₉	1	1	yes	characteristic, complemented
600	#544	C₂²×C₅₉	1	4	yes	complemented
601	#542	C₂²×C₅₉	1	4	yes	complemented
602	#542	C₂²×C₅₉	1	8	yes	complemented
603	#542	C₂²×C₅₉	1	8	yes	complemented
604	#542	C₂²×C₅₉	1	16	yes	complemented
605	#540	C₂²×C₅₉	1	4	yes	complemented
606	#540	C₂²×C₅₉	1	8	yes	complemented
607	#540	C₂²×C₅₉	1	8	yes	complemented
608	#538	C₂²×C₅₉	1	4	yes	complemented
609	#538	C₂²×C₅₉	1	8	yes	complemented
610	#538	C₂²×C₅₉	1	16	yes	complemented
611	#538	C₂²×C₅₉	1	16	yes	complemented
612	#538	C₂²×C₅₉	1	8	yes	complemented
613	#537	C₂²×C₅₉	1	1	yes	characteristic, complemented
614	#537	C₂²×C₅₉	1	4	yes	complemented
615	#537	C₂²×C₅₉	1	2	yes	complemented
616	#537	C₂²×C₅₉	1	8	yes	complemented
617	#536	C₂²×C₅₉	1	8	yes	complemented
618	#535	C₂²×C₅₉	1	8	yes	complemented
619	#535	C₂²×C₅₉	1	2	yes	complemented
620	#535	C₂²×C₅₉	1	8	yes	complemented
621	#535	C₂²×C₅₉	1	4	yes	complemented
622	#535	C₂²×C₅₉	1	8	yes	complemented
623	#535	C₂²×C₅₉	1	16	yes	complemented
624	#534	C₂²×C₅₉	1	8	yes	complemented
625	#534	C₂²×C₅₉	1	4	yes	complemented
626	#534	C₂²×C₅₉	1	8	yes	complemented
627	#533	C₂²×C₅₉	1	4	yes	complemented
628	#532	C₂²×C₅₉	1	8	yes	complemented
629	#532	C₂²×C₅₉	1	4	yes	complemented
630	#532	C₂²×C₅₉	1	2	yes	complemented
631	#532	C₂²×C₅₉	1	4	yes	complemented
632	#532	C₂²×C₅₉	1	4	yes	complemented
633	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
634	#529	C₂²×C₅₉	1	4	yes	complemented
635	#529	C₂²×C₅₉	1	8	yes	complemented
636	C₂×#124	C₂²×C₅₉	1	4	yes	complemented
637	#525	C₂²×C₅₉	1	8	yes	complemented
638	#525	C₂²×C₅₉	1	8	yes	complemented
639	#525	C₂²×C₅₉	1	4	yes	complemented
640	#525	C₂²×C₅₉	1	4	yes	complemented
641	#525	C₂²×C₅₉	1	8	yes	complemented
642	#525	C₂²×C₅₉	1	8	yes	complemented
643	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
644	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
645	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
646	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
647	#520	C₂²×C₅₉	1	4	yes	complemented
648	#520	C₂²×C₅₉	1	4	yes	complemented
649	#518	C₂²×C₅₉	1	4	yes	complemented
650	C₄×#41	C₂²×C₅₉	1	2	yes	complemented
651	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
652	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
653	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
654	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
655	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
656	C₅₉	#62930	1	1	yes	characteristic, direct product factor, Sylow
657	H(5,𝔽₂)	—	4	8	no	—
658	C₂×#41	—	4	16	no	—
659	C₂×#41	C₂³×C₅₉	1	2	yes	—
660	C₂×#41	C₂³×C₅₉	1	4	yes	—
661	C₂×#41	C₂³×C₅₉	1	4	yes	—
662	C₂×#41	C₂³×C₅₉	1	4	yes	—
663	C₂×#41	C₂³×C₅₉	1	4	yes	—
664	C₂×#41	C₂³×C₅₉	1	8	yes	—
665	C₂×#41	C₂³×C₅₉	1	8	yes	—
666	C₂×#41	C₂³×C₅₉	1	8	yes	—
667	C₂×#41	C₂³×C₅₉	1	8	yes	—
668	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
669	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
670	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
671	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
672	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
673	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
674	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
675	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
676	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
677	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
678	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
679	C₂²×D₄	C₂³×C₅₉	1	16	yes	—
680	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
681	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
682	C₂³×C₄	C₂³×C₅₉	1	8	yes	—
683	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
684	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
685	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₅₉	1	8	yes	—
687	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
688	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
689	#127	C₂³×C₅₉	1	2	yes	—
690	#127	C₂³×C₅₉	1	8	yes	—
691	#127	C₂³×C₅₉	1	4	yes	—
692	#127	C₂³×C₅₉	1	4	yes	—
693	#127	C₂³×C₅₉	1	16	yes	—
694	#126	C₂³×C₅₉	1	8	yes	—
695	#126	C₂³×C₅₉	1	16	yes	—
696	#126	C₂³×C₅₉	1	16	yes	—
697	#126	C₂³×C₅₉	1	16	yes	—
698	#125	C₂³×C₅₉	1	4	yes	—
699	#125	C₂³×C₅₉	1	8	yes	—
700	#125	C₂³×C₅₉	1	8	yes	—
701	#124	C₂³×C₅₉	1	16	yes	—
702	#124	C₂³×C₅₉	1	16	yes	—
703	#124	C₂³×C₅₉	1	4	yes	—
704	#124	C₂³×C₅₉	1	8	yes	—
705	#124	C₂³×C₅₉	1	16	yes	—
706	#124	C₂³×C₅₉	1	8	yes	—
707	#124	C₂³×C₅₉	1	8	yes	—
708	#124	C₂³×C₅₉	1	4	yes	—
709	#124	C₂³×C₅₉	1	8	yes	—
710	#124	C₂³×C₅₉	1	16	yes	—
711	#124	C₂³×C₅₉	1	16	yes	—
712	#124	C₂³×C₅₉	1	16	yes	—
713	#123	C₂³×C₅₉	1	8	yes	—
714	#123	C₂³×C₅₉	1	16	yes	—
715	#123	C₂³×C₅₉	1	16	yes	—
716	#123	C₂³×C₅₉	1	8	yes	—
717	#123	C₂³×C₅₉	1	16	yes	—
718	#123	C₂³×C₅₉	1	8	yes	—
719	#123	C₂³×C₅₉	1	8	yes	—
720	#123	C₂³×C₅₉	1	8	yes	—
721	#123	C₂³×C₅₉	1	16	yes	—
722	#123	C₂³×C₅₉	1	16	yes	—
723	#123	C₂³×C₅₉	1	16	yes	—
724	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
725	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
726	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
727	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
728	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
729	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
730	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
731	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
732	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
734	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
735	C₂²⋊Q₈	C₂³×C₅₉	1	16	yes	—
736	C₂²⋊Q₈	C₂³×C₅₉	1	16	yes	—
737	#121	C₂³×C₅₉	1	4	yes	—
738	#121	C₂³×C₅₉	1	8	yes	—
739	#121	C₂³×C₅₉	1	4	yes	—
740	#121	C₂³×C₅₉	1	4	yes	—
741	#121	C₂³×C₅₉	1	8	yes	—
742	#121	C₂³×C₅₉	1	8	yes	—
743	#121	C₂³×C₅₉	1	8	yes	—
744	#121	C₂³×C₅₉	1	8	yes	—
745	#121	C₂³×C₅₉	1	8	yes	—
746	#121	C₂³×C₅₉	1	8	yes	—
747	#121	C₂³×C₅₉	1	16	yes	—
748	#121	C₂³×C₅₉	1	16	yes	—
749	#121	C₂³×C₅₉	1	8	yes	—
750	#121	C₂³×C₅₉	1	4	yes	—
751	#121	C₂³×C₅₉	1	4	yes	—
752	#121	C₂³×C₅₉	1	4	yes	—
753	#121	C₂³×C₅₉	1	4	yes	—
754	#121	C₂³×C₅₉	1	4	yes	—
755	#121	C₂³×C₅₉	1	8	yes	—
756	#121	C₂³×C₅₉	1	8	yes	—
757	#121	C₂³×C₅₉	1	8	yes	—
758	#121	C₂³×C₅₉	1	8	yes	—
759	#121	C₂³×C₅₉	1	4	yes	—
760	#121	C₂³×C₅₉	1	16	yes	—
761	#121	C₂³×C₅₉	1	8	yes	—
762	#121	C₂³×C₅₉	1	4	yes	—
763	#121	C₂³×C₅₉	1	4	yes	—
764	#121	C₂³×C₅₉	1	8	yes	—
765	#121	C₂³×C₅₉	1	8	yes	—
766	#121	C₂³×C₅₉	1	16	yes	—
767	#121	C₂³×C₅₉	1	16	yes	—
768	#121	C₂³×C₅₉	1	16	yes	—
769	#121	C₂³×C₅₉	1	16	yes	—
770	#120	C₂³×C₅₉	1	16	yes	—
771	#120	C₂³×C₅₉	1	8	yes	—
772	#120	C₂³×C₅₉	1	16	yes	—
773	#120	C₂³×C₅₉	1	8	yes	—
774	#120	C₂³×C₅₉	1	8	yes	—
775	#120	C₂³×C₅₉	1	16	yes	—
776	#120	C₂³×C₅₉	1	8	yes	—
777	#120	C₂³×C₅₉	1	16	yes	—
778	#120	C₂³×C₅₉	1	16	yes	—
779	#120	C₂³×C₅₉	1	16	yes	—
780	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
781	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
782	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
783	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
784	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
785	C₄×D₄	C₂³×C₅₉	1	2	yes	—
786	C₄×D₄	C₂³×C₅₉	1	4	yes	—
787	C₄×D₄	C₂³×C₅₉	1	4	yes	—
788	C₄×D₄	C₂³×C₅₉	1	8	yes	—
789	C₄×D₄	C₂³×C₅₉	1	4	yes	—
790	C₄×D₄	C₂³×C₅₉	1	4	yes	—
791	C₄×D₄	C₂³×C₅₉	1	2	yes	—
792	C₄×D₄	C₂³×C₅₉	1	8	yes	—
793	C₄×D₄	C₂³×C₅₉	1	4	yes	—
794	C₄×D₄	C₂³×C₅₉	1	4	yes	—
795	C₄×D₄	C₂³×C₅₉	1	4	yes	—
796	C₄×D₄	C₂³×C₅₉	1	2	yes	—
797	C₄×D₄	C₂³×C₅₉	1	4	yes	—
798	C₄×D₄	C₂³×C₅₉	1	2	yes	—
799	C₄×D₄	C₂³×C₅₉	1	8	yes	—
800	C₄×D₄	C₂³×C₅₉	1	8	yes	—
801	C₄×D₄	C₂³×C₅₉	1	8	yes	—
802	C₄×D₄	C₂³×C₅₉	1	8	yes	—
803	C₄×D₄	C₂³×C₅₉	1	16	yes	—
804	C₄×D₄	C₂³×C₅₉	1	16	yes	—
805	C₄×D₄	C₂³×C₅₉	1	8	yes	—
806	C₄×D₄	C₂³×C₅₉	1	8	yes	—
807	C₄×D₄	C₂³×C₅₉	1	4	yes	—
808	C₄×D₄	C₂³×C₅₉	1	16	yes	—
809	C₄×D₄	C₂³×C₅₉	1	8	yes	—
810	C₄×D₄	C₂³×C₅₉	1	16	yes	—
811	#117	C₂³×C₅₉	1	4	yes	—
812	#117	C₂³×C₅₉	1	8	yes	—
813	#117	C₂³×C₅₉	1	8	yes	—
814	#117	C₂³×C₅₉	1	4	yes	—
815	#117	C₂³×C₅₉	1	8	yes	—
816	#117	C₂³×C₅₉	1	2	yes	—
817	#117	C₂³×C₅₉	1	4	yes	—
818	#117	C₂³×C₅₉	1	4	yes	—
819	#117	C₂³×C₅₉	1	8	yes	—
820	#117	C₂³×C₅₉	1	8	yes	—
821	#117	C₂³×C₅₉	1	16	yes	—
822	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
825	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
827	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
828	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
835	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
836	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
837	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
839	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
840	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
841	C₂⁴	C₂⁴×C₅₉	1	8	yes	—
842	C₂⁴	C₂⁴×C₅₉	1	8	yes	—
843	#41	—	2	8	no	—
844	#41	—	2	16	no	—
845	#41	—	4	16	no	—
846	#41	—	4	8	no	—
847	#41	—	4	16	no	—
848	#41	—	4	8	no	—
849	#41	—	4	8	no	—
850	#41	—	4	16	no	—
851	#41	—	8	8	no	—
852	C₂×Q₈	—	4	8	no	—
853	C₂×Q₈	—	8	2	no	—
854	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
855	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
856	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
857	C₂×Q₈	C₂⁴×C₅₉	1	8	yes	—
858	C₂×Q₈	C₂⁴×C₅₉	1	8	yes	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	4	8	no	—
861	C₂×D₄	—	4	16	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	8	no	—
865	C₂×D₄	—	4	16	no	—
866	C₂×D₄	—	4	16	no	—
867	C₂×D₄	—	8	4	no	—
868	C₂×D₄	—	8	16	no	—
869	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
870	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
871	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
872	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
873	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
874	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
875	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
876	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
877	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
878	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
879	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
880	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
881	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
882	C₂×D₄	C₂⁴×C₅₉	1	16	yes	—
883	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
884	C₂×D₄	C₂⁴×C₅₉	1	16	yes	—
885	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
886	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
887	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
888	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
889	C₂×D₄	C₂⁴×C₅₉	1	16	yes	—
890	C₂²×C₄	—	2	8	no	—
891	C₂²×C₄	—	4	16	no	—
892	C₂²×C₄	—	4	4	no	—
893	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
896	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
897	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
898	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
899	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
900	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
901	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
904	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
905	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
906	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
907	C₂²×C₄	C₂⁴×C₅₉	1	16	yes	—
908	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
909	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
910	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
911	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
912	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
913	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
914	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
915	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
917	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
918	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
919	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
921	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₅₉	1	16	yes	—
923	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
924	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
926	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
928	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
929	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
930	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
931	C₄⋊C₄	C₂⁴×C₅₉	1	16	yes	—
932	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
933	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
934	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
935	C₂²⋊C₄	C₂⁴×C₅₉	1	4	yes	—
936	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
937	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
938	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
939	C₂²⋊C₄	C₂⁴×C₅₉	1	16	yes	—
940	C₂²⋊C₄	C₂⁴×C₅₉	1	16	yes	—
941	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₅₉	1	16	yes	—
943	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
944	C₂²⋊C₄	C₂⁴×C₅₉	1	4	yes	—
945	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₅₉	1	4	yes	—
948	C₂²⋊C₄	C₂⁴×C₅₉	1	16	yes	—
949	C₂²⋊C₄	C₂⁴×C₅₉	1	16	yes	—
950	C₂²⋊C₄	C₂⁴×C₅₉	1	4	yes	—
951	C₂²⋊C₄	C₂⁴×C₅₉	1	4	yes	—
952	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
954	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
955	C₄²	C₂⁴×C₅₉	1	2	yes	—
956	C₄²	C₂⁴×C₅₉	1	8	yes	—
957	C₄²	C₂⁴×C₅₉	1	8	yes	—
958	C₄²	C₂⁴×C₅₉	1	2	yes	—
959	C₄²	C₂⁴×C₅₉	1	4	yes	—
960	C₄²	C₂⁴×C₅₉	1	4	yes	—
961	C₄²	C₂⁴×C₅₉	1	4	yes	—
962	C₄²	C₂⁴×C₅₉	1	16	yes	—
963	C₂³	—	2	4	no	—
964	C₂³	—	2	4	no	—
965	C₂³	—	4	8	no	—
966	C₂³	—	4	2	no	—
967	C₂³	—	4	2	no	—
968	C₂³	—	4	8	no	—
969	C₂³	—	4	2	no	—
970	C₂³	—	4	2	no	—
971	C₂³	—	4	8	no	—
972	C₂³	—	4	8	no	—
973	C₂³	—	4	8	no	—
974	C₂³	—	4	8	no	—
975	C₂³	C₂⁵×C₅₉	1	4	yes	—
976	C₂³	C₂⁵×C₅₉	1	8	yes	—
977	C₂³	C₂⁵×C₅₉	1	4	yes	—
978	C₂³	C₂⁵×C₅₉	1	4	yes	—
979	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
980	Q₈	—	2	4	no	—
981	Q₈	—	2	8	no	—
982	Q₈	—	4	8	no	—
983	Q₈	—	4	8	no	—
984	Q₈	—	4	4	no	—
985	D₄	—	2	16	no	—
986	D₄	—	2	8	no	—
987	D₄	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	2	4	no	—
990	D₄	—	2	4	no	—
991	D₄	—	2	8	no	—
992	D₄	—	4	16	no	—
993	D₄	—	4	2	no	—
994	D₄	—	4	8	no	—
995	D₄	—	4	8	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	8	no	—
999	D₄	—	4	8	no	—
1000	D₄	—	4	8	no	—
1001	D₄	—	4	16	no	—
1002	D₄	—	4	16	no	—
1003	D₄	—	4	4	no	—
1004	D₄	—	4	8	no	—
1005	D₄	—	4	4	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	8	no	—
1010	C₂×C₄	—	2	16	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	8	no	—
1013	C₂×C₄	—	2	8	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	4	8	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	8	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	16	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
1025	C₂×C₄	C₂⁵×C₅₉	1	4	yes	—
1026	C₂×C₄	C₂⁵×C₅₉	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₅₉	1	4	yes	—
1028	C₂×C₄	C₂⁵×C₅₉	1	8	yes	—
1029	C₂×C₄	C₂⁵×C₅₉	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₅₉	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1032	C₂×C₄	C₂⁵×C₅₉	1	4	yes	—
1033	C₂×C₄	C₂⁵×C₅₉	1	4	yes	—
1034	C₂×C₄	C₂⁵×C₅₉	1	8	yes	—
1035	C₂×C₄	C₂⁵×C₅₉	1	2	yes	—
1036	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	4	no	—
1040	C₂²	—	2	4	no	—
1041	C₂²	—	2	8	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	2	4	no	—
1046	C₂²	—	2	8	no	—
1047	C₂²	—	2	8	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	8	4	no	—
1052	C₂²	—	8	4	no	—
1053	C₂²	—	8	16	no	—
1054	C₂²	—	16	8	no	—
1055	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
1056	C₂²	C₂⁶×C₅₉	1	1	yes	characteristic
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	8	no	—
1060	C₄	—	2	4	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	4	no	—
1065	C₄	—	2	8	no	—
1066	C₄	—	2	2	no	—
1067	C₄	C₂×H(5,𝔽₂)×C₅₉	1	4	yes	—
1068	C₄	C₅₉×#585	1	2	yes	—
1069	C₂	—	2	2	no	—
1070	C₂	—	4	4	no	—
1071	C₂	—	4	4	no	—
1072	C₂	—	4	8	no	—
1073	C₂	—	4	4	no	—
1074	C₂	C₂²×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1075	C₂	C₂×C₅₉×#585	1	1	yes	characteristic
1076	C₂	C₅₉×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3558	C₂	semidirect
2. C₅₉×#3549	C₂	semidirect
3. C₅₉×#3547	C₂	semidirect
4. C₅₉×#3542	C₂	semidirect
5. C₅₉×#3540	C₂	semidirect
6. C₅₉×#3537	C₂	semidirect
7. C₅₉×#3519	C₂	semidirect
8. C₅₉×#3511	C₂	semidirect
9. C₅₉×#3506	C₂	semidirect
10. C₅₉×#3496	C₂	semidirect
11. C₅₉×#3494	C₂	semidirect
12. C₅₉×#3493	C₂	semidirect
13. C₅₉×#3488	C₂	semidirect
14. C₂×C₅₉×#555	C₂	semidirect
15. D₄×#41×C₅₉	C₂	semidirect
16. C₅₉×#3460	C₂	semidirect
17. C₅₉×#3449	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
19. C₂²×#41×C₅₉	C₂²	semidirect
20. C₅₉×#562	C₂²	semidirect
21. C₅₉×H(3,𝔽₄)	C₂²	semidirect
22. C₅₉×#560	C₂²	semidirect
23. C₅₉×#559	C₂²	semidirect
24. C₅₉×#556	C₂²	semidirect
25. C₅₉×#556	C₂²	semidirect
26. C₅₉×#555	C₂²	semidirect
27. C₅₉×#555	C₂²	semidirect
28. C₅₉×#555	C₂²	semidirect
29. C₅₉×#555	C₂²	semidirect
30. C₅₉×#555	C₂²	semidirect
31. C₅₉×#555	C₂²	semidirect
32. C₅₉×#554	C₂²	semidirect
33. C₅₉×#553	C₂²	semidirect
34. C₅₉×#553	C₂²	semidirect
35. C₅₉×#553	C₂²	semidirect
36. C₅₉×#553	C₂²	semidirect
37. C₅₉×#552	C₂²	semidirect
38. C₅₉×#551	C₂²	semidirect
39. C₅₉×#550	C₂²	semidirect
40. C₅₉×#550	C₂²	semidirect
41. D₄×Q₈×C₅₉	C₂²	semidirect
42. C₅₉×#548	C₂²	semidirect
43. C₅₉×#548	C₂²	semidirect
44. C₅₉×#548	C₂²	semidirect
45. C₅₉×#547	C₂²	semidirect
46. C₅₉×#547	C₂²	semidirect
47. C₅₉×#547	C₂²	semidirect
48. C₅₉×#547	C₂²	semidirect
49. C₅₉×#546	C₂²	semidirect
50. C₅₉×#546	C₂²	semidirect
51. C₅₉×#546	C₂²	semidirect
52. C₅₉×#546	C₂²	semidirect
53. C₅₉×#546	C₂²	semidirect
54. C₅₉×#546	C₂²	semidirect
55. D₄²×C₅₉	C₂²	semidirect
56. D₄²×C₅₉	C₂²	semidirect
57. D₄²×C₅₉	C₂²	semidirect
58. D₄²×C₅₉	C₂²	semidirect
59. D₄²×C₅₉	C₂²	semidirect
60. D₄²×C₅₉	C₂²	semidirect
61. C₅₉×#544	C₂²	semidirect
62. C₅₉×#544	C₂²	semidirect
63. C₅₉×#542	C₂²	semidirect
64. C₅₉×#542	C₂²	semidirect
65. C₅₉×#542	C₂²	semidirect
66. C₅₉×#542	C₂²	semidirect
67. C₅₉×#540	C₂²	semidirect
68. C₅₉×#540	C₂²	semidirect
69. C₅₉×#540	C₂²	semidirect
70. C₅₉×#538	C₂²	semidirect
71. C₅₉×#538	C₂²	semidirect
72. C₅₉×#538	C₂²	semidirect
73. C₅₉×#538	C₂²	semidirect
74. C₅₉×#538	C₂²	semidirect
75. C₅₉×#537	C₂²	semidirect
76. C₅₉×#537	C₂²	semidirect
77. C₅₉×#537	C₂²	semidirect
78. C₅₉×#537	C₂²	semidirect
79. C₅₉×#536	C₂²	semidirect
80. C₅₉×#535	C₂²	semidirect
81. C₅₉×#535	C₂²	semidirect
82. C₅₉×#535	C₂²	semidirect
83. C₅₉×#535	C₂²	semidirect
84. C₅₉×#535	C₂²	semidirect
85. C₅₉×#535	C₂²	semidirect
86. C₅₉×#534	C₂²	semidirect
87. C₅₉×#534	C₂²	semidirect
88. C₅₉×#534	C₂²	semidirect
89. C₅₉×#533	C₂²	semidirect
90. C₅₉×#532	C₂²	semidirect
91. C₅₉×#532	C₂²	semidirect
92. C₅₉×#532	C₂²	semidirect
93. C₅₉×#532	C₂²	semidirect
94. C₅₉×#532	C₂²	semidirect
95. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
96. C₅₉×#529	C₂²	semidirect
97. C₅₉×#529	C₂²	semidirect
98. C₂×#124×C₅₉	C₂²	semidirect
99. C₅₉×#525	C₂²	semidirect
100. C₅₉×#525	C₂²	semidirect
101. C₅₉×#525	C₂²	semidirect
102. C₅₉×#525	C₂²	semidirect
103. C₅₉×#525	C₂²	semidirect
104. C₅₉×#525	C₂²	semidirect
105. C₂×#121×C₅₉	C₂²	semidirect
106. C₂×#121×C₅₉	C₂²	semidirect
107. C₂×#121×C₅₉	C₂²	semidirect
108. C₂×#121×C₅₉	C₂²	semidirect
109. C₅₉×#520	C₂²	semidirect
110. C₅₉×#520	C₂²	semidirect
111. C₅₉×#518	C₂²	semidirect
112. C₄×#41×C₅₉	C₂²	semidirect
113. C₂×C₄×D₄×C₅₉	C₂²	semidirect
114. C₂×C₄×D₄×C₅₉	C₂²	semidirect
115. C₂×C₄×D₄×C₅₉	C₂²	semidirect
116. C₂×#117×C₅₉	C₂²	semidirect
117. C₂×#117×C₅₉	C₂²	semidirect
498. #62930	C₅₉	direct (N × H)
531. #3558	C₂×C₅₉	semidirect
532. #3549	C₂×C₅₉	semidirect
533. #3547	C₂×C₅₉	semidirect
534. #3542	C₂×C₅₉	semidirect
535. #3540	C₂×C₅₉	semidirect
536. #3537	C₂×C₅₉	semidirect
537. #3519	C₂×C₅₉	semidirect
538. #3511	C₂×C₅₉	semidirect
539. #3506	C₂×C₅₉	semidirect
540. #3496	C₂×C₅₉	semidirect
541. #3494	C₂×C₅₉	semidirect
542. #3493	C₂×C₅₉	semidirect
543. #3488	C₂×C₅₉	semidirect
544. C₂×#555	C₂×C₅₉	semidirect
545. D₄×#41	C₂×C₅₉	semidirect
546. #3460	C₂×C₅₉	semidirect
547. #3449	C₂×C₅₉	semidirect
556. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
557. C₂²×#41	C₂²×C₅₉	semidirect
558. #562	C₂²×C₅₉	semidirect
559. H(3,𝔽₄)	C₂²×C₅₉	semidirect
560. #560	C₂²×C₅₉	semidirect
561. #559	C₂²×C₅₉	semidirect
562. #556	C₂²×C₅₉	semidirect
563. #556	C₂²×C₅₉	semidirect
564. #555	C₂²×C₅₉	semidirect
565. #555	C₂²×C₅₉	semidirect
566. #555	C₂²×C₅₉	semidirect
567. #555	C₂²×C₅₉	semidirect
568. #555	C₂²×C₅₉	semidirect
569. #555	C₂²×C₅₉	semidirect
570. #554	C₂²×C₅₉	semidirect
571. #553	C₂²×C₅₉	semidirect
572. #553	C₂²×C₅₉	semidirect
573. #553	C₂²×C₅₉	semidirect
574. #553	C₂²×C₅₉	semidirect
575. #552	C₂²×C₅₉	semidirect
576. #551	C₂²×C₅₉	semidirect
577. #550	C₂²×C₅₉	semidirect
578. #550	C₂²×C₅₉	semidirect
579. D₄×Q₈	C₂²×C₅₉	semidirect
580. #548	C₂²×C₅₉	semidirect
581. #548	C₂²×C₅₉	semidirect
582. #548	C₂²×C₅₉	semidirect
583. #547	C₂²×C₅₉	semidirect
584. #547	C₂²×C₅₉	semidirect
585. #547	C₂²×C₅₉	semidirect
586. #547	C₂²×C₅₉	semidirect
587. #546	C₂²×C₅₉	semidirect
588. #546	C₂²×C₅₉	semidirect
589. #546	C₂²×C₅₉	semidirect
590. #546	C₂²×C₅₉	semidirect
591. #546	C₂²×C₅₉	semidirect
592. #546	C₂²×C₅₉	semidirect
593. D₄²	C₂²×C₅₉	semidirect
594. D₄²	C₂²×C₅₉	semidirect
595. D₄²	C₂²×C₅₉	semidirect
596. D₄²	C₂²×C₅₉	semidirect
597. D₄²	C₂²×C₅₉	semidirect
598. D₄²	C₂²×C₅₉	semidirect
599. #544	C₂²×C₅₉	semidirect
600. #544	C₂²×C₅₉	semidirect
601. #542	C₂²×C₅₉	semidirect
602. #542	C₂²×C₅₉	semidirect
603. #542	C₂²×C₅₉	semidirect
604. #542	C₂²×C₅₉	semidirect
605. #540	C₂²×C₅₉	semidirect
606. #540	C₂²×C₅₉	semidirect
607. #540	C₂²×C₅₉	semidirect
608. #538	C₂²×C₅₉	semidirect
609. #538	C₂²×C₅₉	semidirect
610. #538	C₂²×C₅₉	semidirect
611. #538	C₂²×C₅₉	semidirect
612. #538	C₂²×C₅₉	semidirect
613. #537	C₂²×C₅₉	semidirect
614. #537	C₂²×C₅₉	semidirect
615. #537	C₂²×C₅₉	semidirect
616. #537	C₂²×C₅₉	semidirect
617. #536	C₂²×C₅₉	semidirect
618. #535	C₂²×C₅₉	semidirect
619. #535	C₂²×C₅₉	semidirect
620. #535	C₂²×C₅₉	semidirect
621. #535	C₂²×C₅₉	semidirect
622. #535	C₂²×C₅₉	semidirect
623. #535	C₂²×C₅₉	semidirect
624. #534	C₂²×C₅₉	semidirect
625. #534	C₂²×C₅₉	semidirect
626. #534	C₂²×C₅₉	semidirect
627. #533	C₂²×C₅₉	semidirect
628. #532	C₂²×C₅₉	semidirect
629. #532	C₂²×C₅₉	semidirect
630. #532	C₂²×C₅₉	semidirect
631. #532	C₂²×C₅₉	semidirect
632. #532	C₂²×C₅₉	semidirect
633. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
634. #529	C₂²×C₅₉	semidirect
635. #529	C₂²×C₅₉	semidirect
636. C₂×#124	C₂²×C₅₉	semidirect
637. #525	C₂²×C₅₉	semidirect
638. #525	C₂²×C₅₉	semidirect
639. #525	C₂²×C₅₉	semidirect
640. #525	C₂²×C₅₉	semidirect
641. #525	C₂²×C₅₉	semidirect
642. #525	C₂²×C₅₉	semidirect
643. C₂×#121	C₂²×C₅₉	semidirect
644. C₂×#121	C₂²×C₅₉	semidirect
645. C₂×#121	C₂²×C₅₉	semidirect
646. C₂×#121	C₂²×C₅₉	semidirect
647. #520	C₂²×C₅₉	semidirect
648. #520	C₂²×C₅₉	semidirect
649. #518	C₂²×C₅₉	semidirect
650. C₄×#41	C₂²×C₅₉	semidirect
651. C₂×C₄×D₄	C₂²×C₅₉	semidirect
652. C₂×C₄×D₄	C₂²×C₅₉	semidirect
653. C₂×C₄×D₄	C₂²×C₅₉	semidirect
654. C₂×#117	C₂²×C₅₉	semidirect
655. C₂×#117	C₂²×C₅₉	semidirect
656. C₅₉	#62930	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×#3558	2
C₅₉×#3549	2
C₅₉×#3547	2
C₅₉×#3542	2
C₅₉×#3540	2
C₅₉×#3537	2
C₅₉×#3519	2
C₅₉×#3511	2
C₅₉×#3506	2
C₅₉×#3496	2
C₅₉×#3494	2
C₅₉×#3493	2
C₅₉×#3488	2
C₂×C₅₉×#555	2
D₄×#41×C₅₉	2
C₅₉×#3460	2
C₅₉×#3449	2
#62930	59

Subgroups — C59×#62930 #28475039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62930 #28475039