Subgroups — C₅₉×#25615 #28437724

Order 15104.

1116 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3511	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2007	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1882	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₅₉	C₂²	1	4	yes	—
11	C₂×#137×C₅₉	C₂²	1	2	yes	—
12	C₅₉×#556	—	2	1	no	—
13	C₅₉×#555	—	2	1	no	—
14	C₅₉×#554	—	2	1	no	—
15	C₅₉×#553	—	2	2	no	—
16	C₅₉×#548	—	2	2	no	—
17	C₅₉×#547	—	2	1	no	—
18	C₅₉×#542	—	2	2	no	—
19	C₅₉×#537	C₂²	1	2	yes	—
20	C₅₉×#533	—	2	1	no	—
21	C₅₉×#532	—	2	1	no	—
22	C₅₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#520	C₂²	1	2	yes	—
26	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#497	—	2	2	no	—
28	C₅₉×#494	—	2	1	no	—
29	C₅₉×#492	—	2	1	no	—
30	C₅₉×#462	—	2	1	no	—
31	C₅₉×#462	—	2	1	no	—
32	C₅₉×#461	—	2	1	no	—
33	C₅₉×#461	—	2	1	no	—
34	C₅₉×#423	C₂²	1	1	yes	characteristic
35	C₂×#104×C₅₉	C₂²	1	2	yes	—
36	C₂×#104×C₅₉	C₂²	1	4	yes	—
37	C₅₉×#419	C₂²	1	2	yes	—
38	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#391	—	2	2	no	—
40	C₅₉×#391	C₂²	1	4	yes	—
41	C₅₉×#382	—	2	2	no	—
42	C₄³×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#343	C₂²	1	4	yes	—
44	C₅₉×#339	C₂²	1	2	yes	—
45	C₂×#41×C₅₉	—	2	2	no	—
46	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
47	C₂×#41×C₅₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₅₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
50	#137×C₅₉	—	2	8	no	—
51	#137×C₅₉	—	4	4	no	—
52	#137×C₅₉	—	4	4	no	—
53	C₂×Q₁₆×C₅₉	—	2	2	no	—
54	C₂×Q₁₆×C₅₉	—	2	4	no	—
55	C₂×SD₁₆×C₅₉	—	2	2	no	—
56	C₂×SD₁₆×C₅₉	—	2	4	no	—
57	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₅₉	—	2	1	no	—
60	C₄⋊Q₈×C₅₉	—	2	1	no	—
61	C₄⋊Q₈×C₅₉	—	2	1	no	—
62	C₄⋊Q₈×C₅₉	—	2	1	no	—
63	C₄⋊Q₈×C₅₉	—	2	1	no	—
64	C₄⋊Q₈×C₅₉	—	2	1	no	—
65	C₄⋊Q₈×C₅₉	—	2	1	no	—
66	C₄⋊Q₈×C₅₉	—	2	1	no	—
67	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
68	#127×C₅₉	D₄	1	1	yes	characteristic
69	#126×C₅₉	—	2	4	no	—
70	#125×C₅₉	—	2	2	no	—
71	#124×C₅₉	—	2	2	no	—
72	#124×C₅₉	—	2	4	no	—
73	#124×C₅₉	D₄	1	2	yes	—
74	#123×C₅₉	—	2	4	no	—
75	C₂²⋊Q₈×C₅₉	—	2	2	no	—
76	C₂²⋊Q₈×C₅₉	—	2	4	no	—
77	C₂²⋊Q₈×C₅₉	—	2	2	no	—
78	C₂²⋊Q₈×C₅₉	—	2	2	no	—
79	#121×C₅₉	—	2	2	no	—
80	#121×C₅₉	—	2	2	no	—
81	#121×C₅₉	—	2	2	no	—
82	#121×C₅₉	—	2	1	no	—
83	#121×C₅₉	—	2	1	no	—
84	#121×C₅₉	—	2	4	no	—
85	C₄×Q₈×C₅₉	—	2	2	no	—
86	C₄×Q₈×C₅₉	—	2	2	no	—
87	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
89	C₄×D₄×C₅₉	—	2	2	no	—
90	C₄×D₄×C₅₉	—	2	2	no	—
91	C₄×D₄×C₅₉	—	2	1	no	—
92	C₄×D₄×C₅₉	—	2	1	no	—
93	C₄×D₄×C₅₉	—	2	4	no	—
94	C₄×D₄×C₅₉	—	2	1	no	—
95	C₄×D₄×C₅₉	—	2	1	no	—
96	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
97	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
98	#117×C₅₉	—	2	2	no	—
99	#117×C₅₉	—	2	2	no	—
100	#117×C₅₉	—	2	1	no	—
101	#117×C₅₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	—	2	1	no	—
108	C₂×C₄²×C₅₉	—	2	1	no	—
109	C₂×C₄²×C₅₉	—	2	1	no	—
110	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₅₉	—	2	1	no	—
113	C₄⋊C₈×C₅₉	—	2	1	no	—
114	#104×C₅₉	—	2	4	no	—
115	#104×C₅₉	—	4	4	no	—
116	#103×C₅₉	—	2	2	no	—
117	#103×C₅₉	—	2	2	no	—
118	#97×C₅₉	—	2	1	no	—
119	C₄×C₈×C₅₉	—	2	1	no	—
120	#95×C₅₉	—	2	8	no	—
121	#41×C₅₉	—	2	2	no	—
122	#41×C₅₉	—	2	4	no	—
123	#41×C₅₉	—	2	4	no	—
124	#41×C₅₉	—	2	2	no	—
125	#41×C₅₉	—	8	4	no	—
126	C₂×Q₈×C₅₉	—	2	2	no	—
127	C₂×Q₈×C₅₉	—	2	2	no	—
128	C₂×Q₈×C₅₉	—	2	2	no	—
129	C₂×Q₈×C₅₉	—	2	2	no	—
130	C₂×Q₈×C₅₉	—	2	4	no	—
131	C₂×Q₈×C₅₉	—	2	4	no	—
132	C₂×Q₈×C₅₉	—	4	4	no	—
133	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₅₉	—	2	1	no	—
136	C₂×D₄×C₅₉	—	2	2	no	—
137	C₂×D₄×C₅₉	—	2	4	no	—
138	C₂×D₄×C₅₉	—	2	1	no	—
139	C₂×D₄×C₅₉	—	2	1	no	—
140	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	—	2	2	no	—
143	C₂²×C₄×C₅₉	—	2	4	no	—
144	C₂²×C₄×C₅₉	—	2	1	no	—
145	C₂²×C₄×C₅₉	—	2	1	no	—
146	C₂²×C₄×C₅₉	—	2	1	no	—
147	C₂²×C₄×C₅₉	—	2	2	no	—
148	C₂²×C₄×C₅₉	—	2	2	no	—
149	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₅₉	—	4	8	no	—
154	Q₁₆×C₅₉	—	4	4	no	—
155	SD₁₆×C₅₉	—	4	8	no	—
156	SD₁₆×C₅₉	—	4	4	no	—
157	M₁₆×C₅₉	—	2	2	no	—
158	M₁₆×C₅₉	—	2	4	no	—
159	M₁₆×C₅₉	#41	1	4	yes	complemented
160	C₂×C₈×C₅₉	—	2	2	no	—
161	C₂×C₈×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	4	no	—
163	C₄⋊C₄×C₅₉	—	2	4	no	—
164	C₄⋊C₄×C₅₉	—	2	2	no	—
165	C₄⋊C₄×C₅₉	—	2	2	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	1	no	—
168	C₄⋊C₄×C₅₉	—	2	1	no	—
169	C₄⋊C₄×C₅₉	—	2	1	no	—
170	C₄⋊C₄×C₅₉	—	2	2	no	—
171	C₄⋊C₄×C₅₉	—	2	2	no	—
172	C₄⋊C₄×C₅₉	—	4	1	no	—
173	C₄⋊C₄×C₅₉	—	4	1	no	—
174	C₄⋊C₄×C₅₉	—	4	1	no	—
175	C₄⋊C₄×C₅₉	—	4	1	no	—
176	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
178	C₂²⋊C₄×C₅₉	—	2	4	no	—
179	C₂²⋊C₄×C₅₉	—	2	4	no	—
180	C₂²⋊C₄×C₅₉	—	2	4	no	—
181	C₂²⋊C₄×C₅₉	—	2	1	no	—
182	C₂²⋊C₄×C₅₉	—	2	1	no	—
183	C₂²⋊C₄×C₅₉	—	2	1	no	—
184	C₂²⋊C₄×C₅₉	—	2	2	no	—
185	C₂²⋊C₄×C₅₉	—	2	2	no	—
186	C₄²×C₅₉	—	2	4	no	—
187	C₄²×C₅₉	—	2	4	no	—
188	C₄²×C₅₉	—	2	1	no	—
189	C₄²×C₅₉	—	2	1	no	—
190	C₄²×C₅₉	—	2	1	no	—
191	C₄²×C₅₉	—	2	2	no	—
192	C₄²×C₅₉	—	2	2	no	—
193	C₄²×C₅₉	—	4	2	no	—
194	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₅₉	—	2	1	no	—
199	C₂³×C₅₉	—	2	2	no	—
200	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₅₉	—	2	1	no	—
202	Q₈×C₅₉	—	2	1	no	—
203	Q₈×C₅₉	—	2	4	no	—
204	Q₈×C₅₉	—	4	4	no	—
205	Q₈×C₅₉	—	4	2	no	—
206	Q₈×C₅₉	—	4	2	no	—
207	Q₈×C₅₉	—	4	4	no	—
208	Q₈×C₅₉	—	8	2	no	—
209	D₄×C₅₉	—	2	1	no	—
210	D₄×C₅₉	—	2	1	no	—
211	D₄×C₅₉	—	2	4	no	—
212	D₄×C₅₉	—	4	2	no	—
213	D₄×C₅₉	—	4	4	no	—
214	D₄×C₅₉	—	4	2	no	—
215	D₄×C₅₉	—	4	2	no	—
216	D₄×C₅₉	—	8	4	no	—
217	C₂×C₄×C₅₉	—	2	2	no	—
218	C₂×C₄×C₅₉	—	2	2	no	—
219	C₂×C₄×C₅₉	—	2	4	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	2	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	2	4	no	—
225	C₂×C₄×C₅₉	—	4	2	no	—
226	C₂×C₄×C₅₉	—	4	2	no	—
227	C₂×C₄×C₅₉	—	4	2	no	—
228	C₂×C₄×C₅₉	—	4	2	no	—
229	C₂×C₄×C₅₉	—	4	2	no	—
230	C₂×C₄×C₅₉	—	4	2	no	—
231	C₂×C₄×C₅₉	—	4	2	no	—
232	C₂×C₄×C₅₉	—	4	4	no	—
233	C₂×C₄×C₅₉	—	4	2	no	—
234	C₂×C₄×C₅₉	—	4	4	no	—
235	C₂×C₄×C₅₉	—	8	4	no	—
236	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
237	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
238	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
239	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
240	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
243	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
244	C₈×C₅₉	—	2	4	no	—
245	C₈×C₅₉	—	4	2	no	—
246	#25615	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₅₉	—	2	1	no	—
248	C₂²×C₅₉	—	2	1	no	—
249	C₂²×C₅₉	—	4	2	no	—
250	C₂²×C₅₉	—	4	1	no	—
251	C₂²×C₅₉	—	4	1	no	—
252	C₂²×C₅₉	—	4	2	no	—
253	C₂²×C₅₉	—	4	1	no	—
254	C₂²×C₅₉	—	4	2	no	—
255	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
256	C₂²×C₅₉	#550	1	2	yes	—
257	C₄×C₅₉	—	2	1	no	—
258	C₄×C₅₉	—	2	1	no	—
259	C₄×C₅₉	—	4	4	no	—
260	C₄×C₅₉	—	4	2	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₄×C₅₉	—	4	4	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	—	8	2	no	—
266	C₄×C₅₉	#455	1	2	yes	—
267	C₄×C₅₉	#456	1	2	yes	—
268	C₄×C₅₉	#532	1	1	yes	characteristic
269	C₄×C₅₉	#535	1	1	yes	characteristic
270	C₄×C₅₉	#546	1	2	yes	—
271	#3511	C₂×C₅₉	1	1	yes	characteristic
272	#3152	C₂×C₅₉	1	1	yes	characteristic, complemented
273	#3039	C₂×C₅₉	1	1	yes	characteristic, complemented
274	#2862	C₂×C₅₉	1	1	yes	characteristic, complemented
275	#2007	C₂×C₅₉	1	4	yes	complemented
276	#1997	C₂×C₅₉	1	1	yes	characteristic, complemented
277	#1962	C₂×C₅₉	1	1	yes	characteristic, complemented
278	#1882	C₂×C₅₉	1	4	yes	complemented
279	C₄×#104	C₂×C₅₉	1	1	yes	characteristic, complemented
280	C₂×C₅₉	—	2	2	no	—
281	C₂×C₅₉	—	8	1	no	—
282	C₂×C₅₉	—	8	2	no	—
283	C₂×C₅₉	#2431	1	1	yes	characteristic
284	C₂×C₅₉	C₂×#455	1	1	yes	characteristic
285	C₂×C₅₉	C₂×#456	1	1	yes	characteristic
286	C₂×#137	C₂²×C₅₉	1	4	yes	—
287	C₂×#137	C₂²×C₅₉	1	2	yes	—
288	#556	—	2	1	no	—
289	#555	—	2	1	no	—
290	#554	—	2	1	no	—
291	#553	—	2	2	no	—
292	#548	—	2	2	no	—
293	#547	—	2	1	no	—
294	#542	—	2	2	no	—
295	#537	C₂²×C₅₉	1	2	yes	—
296	#533	—	2	1	no	—
297	#532	—	2	1	no	—
298	#532	C₂²×C₅₉	1	1	yes	characteristic
299	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
301	#520	C₂²×C₅₉	1	2	yes	—
302	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
303	#497	—	2	2	no	—
304	#494	—	2	1	no	—
305	#492	—	2	1	no	—
306	#462	—	2	1	no	—
307	#462	—	2	1	no	—
308	#461	—	2	1	no	—
309	#461	—	2	1	no	—
310	#423	C₂²×C₅₉	1	1	yes	characteristic
311	C₂×#104	C₂²×C₅₉	1	2	yes	—
312	C₂×#104	C₂²×C₅₉	1	4	yes	—
313	#419	C₂²×C₅₉	1	2	yes	—
314	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
315	#391	—	2	2	no	—
316	#391	C₂²×C₅₉	1	4	yes	—
317	#382	—	2	2	no	—
318	C₄³	C₂²×C₅₉	1	1	yes	characteristic
319	#343	C₂²×C₅₉	1	4	yes	—
320	#339	C₂²×C₅₉	1	2	yes	—
321	C₅₉	#25615	1	1	yes	characteristic, direct product factor, Sylow
322	C₂×#41	—	2	2	no	—
323	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
324	C₂×#41	C₂³×C₅₉	1	2	yes	—
325	C₂²×Q₈	D₄×C₅₉	1	2	yes	—
326	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
327	#137	—	2	8	no	—
328	#137	—	4	4	no	—
329	#137	—	4	4	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	2	4	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	4	no	—
334	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
335	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
345	#127	D₄×C₅₉	1	1	yes	characteristic
346	#126	—	2	4	no	—
347	#125	—	2	2	no	—
348	#124	—	2	2	no	—
349	#124	—	2	4	no	—
350	#124	D₄×C₅₉	1	2	yes	—
351	#123	—	2	4	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	2	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	4	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
365	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
374	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
375	#117	—	2	2	no	—
376	#117	—	2	2	no	—
377	#117	—	2	1	no	—
378	#117	C₂³×C₅₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
388	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	#104	—	2	4	no	—
392	#104	—	4	4	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#97	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	#95	—	2	8	no	—
398	#41	—	2	2	no	—
399	#41	—	2	4	no	—
400	#41	—	2	4	no	—
401	#41	—	2	2	no	—
402	#41	—	8	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
411	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
418	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
430	Q₁₆	—	4	8	no	—
431	Q₁₆	—	4	4	no	—
432	SD₁₆	—	4	8	no	—
433	SD₁₆	—	4	4	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	4	no	—
436	M₁₆	#41×C₅₉	1	4	yes	complemented
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
454	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	4	2	no	—
471	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
474	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
475	C₂³	—	2	1	no	—
476	C₂³	—	2	2	no	—
477	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	4	4	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	4	no	—
485	Q₈	—	8	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	2	4	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
514	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
515	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
516	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
519	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
520	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
521	C₈	—	2	4	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
532	C₂²	C₅₉×#550	1	2	yes	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	8	2	no	—
542	C₄	C₅₉×#455	1	2	yes	—
543	C₄	C₅₉×#456	1	2	yes	—
544	C₄	C₅₉×#532	1	1	yes	characteristic
545	C₄	C₅₉×#535	1	1	yes	characteristic
546	C₄	C₅₉×#546	1	2	yes	—
547	C₂	—	2	2	no	—
548	C₂	—	8	1	no	—
549	C₂	—	8	2	no	—
550	C₂	C₅₉×#2431	1	1	yes	characteristic
551	C₂	C₂×C₅₉×#455	1	1	yes	characteristic
552	C₂	C₂×C₅₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3511	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#3152	C₂	semidirect
3. C₅₉×#3039	C₂	semidirect
4. C₅₉×#2862	C₂	semidirect
5. C₅₉×#2007	C₂	semidirect
6. C₅₉×#1997	C₂	semidirect
7. C₅₉×#1962	C₂	semidirect
8. C₅₉×#1882	C₂	semidirect
9. C₄×#104×C₅₉	C₂	semidirect
159. M₁₆×C₅₉	#41	semidirect
246. #25615	C₅₉	direct (N × H)
272. #3152	C₂×C₅₉	semidirect
273. #3039	C₂×C₅₉	semidirect
274. #2862	C₂×C₅₉	semidirect
275. #2007	C₂×C₅₉	semidirect
276. #1997	C₂×C₅₉	semidirect
277. #1962	C₂×C₅₉	semidirect
278. #1882	C₂×C₅₉	semidirect
279. C₄×#104	C₂×C₅₉	semidirect
321. C₅₉	#25615	direct (N × H)
436. M₁₆	#41×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3511	2
C₅₉×#3152	2
C₅₉×#3039	2
C₅₉×#2862	2
C₅₉×#2007	2
C₅₉×#1997	2
C₅₉×#1962	2
C₅₉×#1882	2
C₄×#104×C₅₉	2
#25615	59

Subgroups — C59×#25615 #28437724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25615 #28437724