Subgroups — #28608394

Order 15104.

710 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432762	C₂	1	2	yes	maximal, complemented
2	#21424990	C₂	1	2	yes	maximal
3	#21424746	C₂	1	4	yes	maximal, complemented
4	#21424268	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424116	C₂	1	2	yes	maximal, complemented
6	#21423982	C₂	1	2	yes	maximal, complemented
7	#21423963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₅₉	C₂	1	1	yes	maximal, characteristic
9	#16837463	—	2	4	no	—
10	#16837459	—	2	2	no	—
11	#16837455	—	2	2	no	—
12	C₂×#14273663	C₂²	1	2	yes	—
13	C₂×#14273663	C₂²	1	2	yes	—
14	#16837426	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14273654	C₂²	1	4	yes	—
17	#16837369	C₂²	1	4	yes	—
18	#16837358	C₂²	1	4	yes	—
19	C₂×#14273637	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
21	#16837161	C₂²	1	4	yes	—
22	#16837156	C₂²	1	2	yes	—
23	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₅₉	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₅₉	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₅₉	C₄	1	2	yes	complemented
29	C₄×D₈×C₅₉	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₅₉	C₄	1	1	yes	characteristic, complemented
31	C₅₉×#427	C₂²	1	1	yes	characteristic
32	C₅₉×#416	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#11745664	C₂³	1	4	yes	—
35	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₅₉	—	2	1	no	—
37	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
38	#14273663	—	2	4	no	—
39	#14273663	—	4	2	no	—
40	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
43	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
44	#14273654	—	4	4	no	—
45	C₂²⋊(C₅₉⋊C₈)	—	2	4	no	—
46	C₂²⋊(C₅₉⋊C₈)	—	2	4	no	—
47	#14273638	—	2	4	no	—
48	#14273637	—	2	4	no	—
49	C₄×C₅₉⋊C₈	—	2	4	no	—
50	C₅₉⋊#95	—	2	1	no	—
51	C₂×#41×C₅₉	C₂³	1	2	yes	—
52	#135×C₅₉	—	2	2	no	—
53	#135×C₅₉	—	2	2	no	—
54	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
55	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
56	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₅₉	—	2	2	no	—
62	C₄×D₄×C₅₉	—	2	2	no	—
63	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
65	#117×C₅₉	—	2	2	no	—
66	#117×C₅₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₅₉	—	2	2	no	—
68	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
69	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
70	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
71	#106×C₅₉	C₂×C₄	1	2	yes	—
72	#103×C₅₉	C₂×C₄	1	2	yes	—
73	#103×C₅₉	C₂×C₄	1	2	yes	—
74	#102×C₅₉	C₂×C₄	1	2	yes	—
75	#102×C₅₉	C₂×C₄	1	2	yes	—
76	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	#41×C₅₉	—	2	2	no	—
81	#41×C₅₉	—	2	2	no	—
82	#41×C₅₉	—	2	2	no	—
83	#41×C₅₉	—	2	2	no	—
84	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₅₉	—	2	2	no	—
86	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₉	—	2	2	no	—
88	C₂²×C₄×C₅₉	—	2	2	no	—
89	C₂²×C₄×C₅₉	—	2	2	no	—
90	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₅₉	—	2	2	no	—
94	Q₁₆×C₅₉	—	2	2	no	—
95	SD₁₆×C₅₉	—	2	4	no	—
96	D₈×C₅₉	—	2	2	no	—
97	C₂×C₈×C₅₉	—	2	1	no	—
98	C₂×C₈×C₅₉	—	2	1	no	—
99	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₉	#41	1	2	yes	—
104	C₂×C₈×C₅₉	#41	1	2	yes	—
105	C₄⋊C₄×C₅₉	—	2	2	no	—
106	C₄⋊C₄×C₅₉	—	2	2	no	—
107	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
108	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
109	C₂²⋊C₄×C₅₉	—	2	2	no	—
110	C₂²⋊C₄×C₅₉	—	2	2	no	—
111	C₂²⋊C₄×C₅₉	—	2	2	no	—
112	C₄²×C₅₉	—	2	2	no	—
113	C₄²×C₅₉	—	2	2	no	—
114	C₄²×C₅₉	—	2	2	no	—
115	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₅₉	—	4	2	no	—
120	C₄×Dic₅₉	—	2	2	no	—
121	C₄×Dic₅₉	—	2	2	no	—
122	#11745664	—	2	4	no	—
123	#11745664	—	2	4	no	—
124	C₂×C₅₉⋊C₈	—	2	2	no	—
125	C₂×C₅₉⋊C₈	—	2	2	no	—
126	C₂×C₅₉⋊C₈	—	2	4	no	—
127	C₂×C₅₉⋊C₈	C₂×D₄	1	4	yes	—
128	C₂³×C₅₉	—	2	2	no	—
129	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
130	Q₈×C₅₉	—	2	2	no	—
131	Q₈×C₅₉	—	2	2	no	—
132	D₄×C₅₉	—	2	2	no	—
133	D₄×C₅₉	—	2	2	no	—
134	D₄×C₅₉	—	4	2	no	—
135	D₄×C₅₉	—	4	2	no	—
136	C₂×C₄×C₅₉	—	2	2	no	—
137	C₂×C₄×C₅₉	—	2	2	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	—	2	2	no	—
140	C₂×C₄×C₅₉	—	4	1	no	—
141	C₂×C₄×C₅₉	—	4	2	no	—
142	C₂×C₄×C₅₉	—	4	2	no	—
143	C₂×C₄×C₅₉	—	4	4	no	—
144	C₂×C₄×C₅₉	—	8	2	no	—
145	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₅₉	—	4	2	no	—
156	C₂×Dic₅₉	—	4	2	no	—
157	C₂×Dic₅₉	—	4	2	no	—
158	C₈×C₅₉	—	2	1	no	—
159	C₈×C₅₉	—	2	1	no	—
160	C₈×C₅₉	#117	1	2	yes	—
161	C₈×C₅₉	#117	1	2	yes	—
162	C₅₉⋊C₈	—	2	4	no	—
163	C₅₉⋊C₈	—	4	4	no	—
164	#22803	—	59	1	no	maximal, Sylow
165	C₂²×C₅₉	—	2	1	no	—
166	C₂²×C₅₉	—	2	1	no	—
167	C₂²×C₅₉	—	4	2	no	—
168	C₂²×C₅₉	—	4	2	no	—
169	C₂²×C₅₉	—	4	2	no	—
170	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₅₉	#555	1	1	yes	characteristic
172	C₂²×C₅₉	#556	1	1	yes	characteristic
173	C₄×C₅₉	—	2	1	no	—
174	C₄×C₅₉	—	2	1	no	—
175	C₄×C₅₉	—	2	1	no	—
176	C₄×C₅₉	—	4	2	no	—
177	C₄×C₅₉	—	4	2	no	—
178	C₄×C₅₉	—	4	2	no	—
179	C₄×C₅₉	#444	1	2	yes	—
180	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
181	C₄×C₅₉	#520	1	1	yes	characteristic
182	C₄×C₅₉	#547	1	1	yes	characteristic
183	C₄×C₅₉	#550	1	1	yes	characteristic
184	Dic₅₉	—	8	2	no	—
185	C₄×#135	D₅₉	1	1	yes	characteristic
186	#2925	—	59	2	no	—
187	#1975	—	59	2	no	—
188	#1929	—	59	4	no	—
189	#1848	—	59	1	no	—
190	#1806	—	59	2	no	—
191	#1773	—	59	2	no	—
192	#1770	—	59	1	no	—
193	C₂×C₅₉	—	2	1	no	—
194	C₂×C₅₉	—	2	1	no	—
195	C₂×C₅₉	—	8	2	no	—
196	C₂×C₅₉	#2354	1	1	yes	characteristic
197	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
198	C₂×C₅₉	#2957	1	1	yes	characteristic
199	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
200	C₄×#41	C₂×D₅₉	1	2	yes	—
201	C₄×Q₁₆	Dic₅₉	1	1	yes	characteristic, complemented
202	C₄×Q₁₆	Dic₅₉	1	1	yes	characteristic, complemented
203	C₄×SD₁₆	Dic₅₉	1	2	yes	complemented
204	C₄×SD₁₆	Dic₅₉	1	2	yes	complemented
205	C₄×D₈	Dic₅₉	1	1	yes	characteristic, complemented
206	C₄×D₈	Dic₅₉	1	1	yes	characteristic, complemented
207	#433	—	118	4	no	—
208	#432	—	118	2	no	—
209	#431	—	118	2	no	—
210	C₂×#108	—	59	2	no	—
211	C₂×#108	—	59	2	no	—
212	#427	C₂×D₅₉	1	1	yes	characteristic
213	#423	—	59	2	no	—
214	C₂×C₄⋊C₈	—	59	1	no	—
215	C₂×#104	—	59	4	no	—
216	#416	C₂×D₅₉	1	2	yes	—
217	#408	—	59	4	no	—
218	#405	—	59	4	no	—
219	C₂×#97	—	59	2	no	—
220	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	59	1	no	—
222	#339	—	59	4	no	—
223	#336	—	59	2	no	—
224	C₅₉	#22803	1	1	yes	characteristic, complemented, Sylow
225	C₂×#41	C₂²×D₅₉	1	2	yes	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
230	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
231	C₂×M₁₆	—	59	4	no	—
232	C₂²×C₈	—	59	2	no	—
233	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
234	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
236	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
240	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
241	#117	—	2	2	no	—
242	#117	C₂²×D₅₉	1	2	yes	—
243	C₂×C₄⋊C₄	—	118	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	59	2	no	—
246	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
247	#108	—	118	4	no	—
248	#108	—	236	2	no	—
249	#107	C₂×Dic₅₉	1	1	yes	characteristic
250	#107	C₂×Dic₅₉	1	1	yes	characteristic
251	#106	C₂×Dic₅₉	1	2	yes	—
252	C₄⋊C₈	—	59	2	no	—
253	C₄⋊C₈	—	59	2	no	—
254	C₄⋊C₈	—	118	2	no	—
255	C₄⋊C₈	—	118	2	no	—
256	#104	—	236	4	no	—
257	#103	C₂×Dic₅₉	1	2	yes	—
258	#103	C₂×Dic₅₉	1	2	yes	—
259	#102	C₂×Dic₅₉	1	2	yes	—
260	#102	C₂×Dic₅₉	1	2	yes	—
261	C₂²⋊C₈	—	118	4	no	—
262	C₂²⋊C₈	—	118	4	no	—
263	#97	—	118	4	no	—
264	#97	—	118	4	no	—
265	C₄×C₈	—	118	4	no	—
266	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
267	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
268	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
269	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
270	#95	—	118	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	118	2	no	—
282	C₂²×C₄	#11745687	1	1	yes	characteristic
283	C₂²×C₄	#11745687	1	1	yes	characteristic
284	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	2	4	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	118	4	no	—
289	M₁₆	—	118	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	59	4	no	—
293	C₂×C₈	—	118	2	no	—
294	C₂×C₈	—	118	2	no	—
295	C₂×C₈	—	118	4	no	—
296	C₂×C₈	#11745685	1	2	yes	—
297	C₂×C₈	#11745685	1	2	yes	—
298	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
299	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
301	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	236	2	no	—
305	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
306	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	118	2	no	—
314	C₄²	—	118	2	no	—
315	C₄²	D₄×D₅₉	1	1	yes	characteristic
316	C₄²	D₄×D₅₉	1	1	yes	characteristic
317	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
318	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#11745687	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	—	236	2	no	—
337	C₂×C₄	—	236	2	no	—
338	C₂×C₄	—	236	2	no	—
339	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
341	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
343	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
344	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
345	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
346	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
347	C₂×C₄	#14273773	1	1	yes	characteristic
348	C₂×C₄	#14273774	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	118	4	no	—
352	C₈	—	236	4	no	—
353	C₈	#14273686	1	2	yes	—
354	C₈	#14273686	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
361	C₂²	#16838117	1	1	yes	characteristic
362	C₂²	#16838122	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	472	2	no	—
370	C₄	#16837524	1	2	yes	—
371	C₄	C₂×#14273686	1	1	yes	characteristic
372	C₄	#16837885	1	1	yes	characteristic
373	C₄	#16838057	1	1	yes	characteristic
374	C₄	#16838073	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	#21427045	1	1	yes	characteristic
379	C₂	C₂×#16837524	1	1	yes	characteristic
380	C₂	#21433013	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₄×#135×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#135×C₅₉	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₄×#135	D₅₉
hypocenter	C₅₉	#22803
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #21432762	C₂	semidirect
3. #21424746	C₂	semidirect
4. #21424268	C₂	semidirect
5. #21424116	C₂	semidirect
6. #21423982	C₂	semidirect
7. #21423963	C₂	semidirect
25. C₄×Q₁₆×C₅₉	C₄	semidirect
26. C₄×Q₁₆×C₅₉	C₄	semidirect
27. C₄×SD₁₆×C₅₉	C₄	semidirect
28. C₄×SD₁₆×C₅₉	C₄	semidirect
29. C₄×D₈×C₅₉	C₄	semidirect
30. C₄×D₈×C₅₉	C₄	semidirect
201. C₄×Q₁₆	Dic₅₉	semidirect
202. C₄×Q₁₆	Dic₅₉	semidirect
203. C₄×SD₁₆	Dic₅₉	semidirect
204. C₄×SD₁₆	Dic₅₉	semidirect
205. C₄×D₈	Dic₅₉	semidirect
206. C₄×D₈	Dic₅₉	semidirect
224. C₅₉	#22803	semidirect

Maximal subgroups

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

subgroup	index
#21432762	2
#21424990	2
#21424746	2
#21424268	2
#21424116	2
#21423982	2
#21423963	2
C₄×#135×C₅₉	2
#22803	59