Subgroups — #28608389

Order 15104.

710 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14273747	C₂	1	1	yes	maximal, characteristic
2	#21432764	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432762	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424986	C₂	1	2	yes	maximal
5	#21424747	C₂	1	2	yes	maximal, complemented
6	#21424742	C₂	1	2	yes	maximal, complemented
7	#21424267	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424117	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423979	C₂	1	2	yes	maximal, complemented
10	#21423965	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	1	yes	characteristic
13	C₄×#11745685	C₂²	1	1	yes	characteristic
14	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
15	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
16	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
17	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
18	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
19	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
20	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
21	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
22	#16837463	—	2	2	no	—
23	#16837462	—	2	2	no	—
24	#16837459	—	2	1	no	—
25	#16837458	—	2	1	no	—
26	#16837455	—	2	1	no	—
27	#16837454	—	2	1	no	—
28	C₂×#14273662	C₂²	1	2	yes	—
29	C₂×#14273662	C₂²	1	2	yes	—
30	#16837438	C₂²	1	1	yes	characteristic
31	#16837426	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×#14273655	C₂²	1	2	yes	—
34	#16837398	C₂²	1	1	yes	characteristic
35	#16837396	C₂²	1	1	yes	characteristic
36	#16837370	C₂²	1	2	yes	—
37	#16837369	C₂²	1	2	yes	—
38	#16837360	C₂²	1	2	yes	—
39	#16837358	C₂²	1	2	yes	—
40	C₂×#14273638	C₂²	1	2	yes	—
41	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
42	#16837162	C₂²	1	2	yes	—
43	#16837157	C₂²	1	2	yes	—
44	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#423	C₂²	1	1	yes	characteristic
46	C₂×#104×C₅₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
48	C₅₉×#339	C₂²	1	2	yes	—
49	C₂×#11745685	C₂³	1	1	yes	characteristic
50	#14273747	—	2	2	no	—
51	#14273747	—	2	2	no	—
52	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
53	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
54	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
55	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
56	C₂×#11745664	C₂³	1	2	yes	—
57	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
59	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
62	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₅₉	—	2	1	no	—
65	C₄×C₂²⋊D₅₉	—	2	1	no	—
66	#14273686	C₂³	1	1	yes	characteristic
67	#14273684	—	2	1	no	—
68	C₄²×D₅₉	—	2	1	no	—
69	#14273662	—	2	4	no	—
70	#14273662	—	4	2	no	—
71	#14273660	C₂×C₄	1	1	yes	characteristic
72	#14273660	C₂×C₄	1	1	yes	characteristic
73	#14273658	C₂×C₄	1	1	yes	characteristic
74	#14273658	C₂×C₄	1	1	yes	characteristic
75	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
78	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
80	#14273655	—	4	2	no	—
81	#14273651	C₂×C₄	1	1	yes	characteristic
82	#14273651	C₂×C₄	1	1	yes	characteristic
83	#14273650	C₂×C₄	1	1	yes	characteristic
84	#14273650	C₂×C₄	1	1	yes	characteristic
85	#14273648	C₂×C₄	1	1	yes	characteristic
86	#14273648	C₂×C₄	1	1	yes	characteristic
87	#14273647	C₂×C₄	1	1	yes	characteristic
88	#14273647	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
91	(C₂×D₅₉)⋊C₈	—	2	2	no	—
92	(C₂×D₅₉)⋊C₈	—	2	2	no	—
93	#14273638	—	2	2	no	—
94	#14273638	—	2	4	no	—
95	#14273637	—	2	2	no	—
96	C₄×C₅₉⋊C₈	—	2	2	no	—
97	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₅₉	—	2	2	no	—
102	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
104	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₅₉	—	2	1	no	—
107	C₄×D₄×C₅₉	—	2	1	no	—
108	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
110	#117×C₅₉	—	2	1	no	—
111	#117×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₄²×C₅₉	—	2	1	no	—
114	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₅₉	—	2	1	no	—
117	C₄⋊C₈×C₅₉	—	2	1	no	—
118	#104×C₅₉	—	4	2	no	—
119	#95×C₅₉	—	2	1	no	—
120	#41×C₅₉	—	2	1	no	—
121	#41×C₅₉	—	2	1	no	—
122	#41×C₅₉	—	2	1	no	—
123	#41×C₅₉	—	2	1	no	—
124	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₅₉	—	2	1	no	—
126	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	2	no	—
131	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₉	—	2	1	no	—
135	#11745685	—	2	1	no	—
136	#11745685	—	2	1	no	—
137	#11745685	—	2	1	no	—
138	#11745685	—	2	1	no	—
139	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₅₉	—	2	1	no	—
141	C₂×C₄×D₅₉	—	2	1	no	—
142	C₂×C₄×D₅₉	—	2	1	no	—
143	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
144	M₁₆×C₅₉	—	2	2	no	—
145	M₁₆×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₄⋊C₄×C₅₉	—	2	1	no	—
148	C₄⋊C₄×C₅₉	—	2	1	no	—
149	C₄⋊C₄×C₅₉	—	4	2	no	—
150	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²⋊C₄×C₅₉	—	2	1	no	—
153	C₂²⋊C₄×C₅₉	—	2	1	no	—
154	C₂²⋊C₄×C₅₉	—	2	1	no	—
155	C₄²×C₅₉	—	2	1	no	—
156	C₄²×C₅₉	—	2	1	no	—
157	C₄²×C₅₉	—	2	1	no	—
158	C₄²×C₅₉	—	2	2	no	—
159	C₄²×C₅₉	—	2	2	no	—
160	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂²⋊Dic₅₉	—	2	1	no	—
165	#11745672	—	2	2	no	—
166	#11745671	—	2	2	no	—
167	#11745670	—	2	2	no	—
168	#11745669	—	2	2	no	—
169	(C₂×D₅₉)⋊C₄	—	2	1	no	—
170	(C₂×D₅₉)⋊C₄	—	2	1	no	—
171	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
173	Dic₅₉⋊C₄	—	2	1	no	—
174	Dic₅₉⋊C₄	—	2	1	no	—
175	C₄×Dic₅₉	—	2	1	no	—
176	C₄×Dic₅₉	—	2	1	no	—
177	C₄×Dic₅₉	—	2	1	no	—
178	#11745664	—	2	2	no	—
179	#11745664	—	2	2	no	—
180	C₂×C₅₉⋊C₈	—	2	2	no	—
181	C₂×C₅₉⋊C₈	—	2	1	no	—
182	C₂×C₅₉⋊C₈	—	2	1	no	—
183	C₂×C₅₉⋊C₈	—	2	2	no	—
184	C₂×C₅₉⋊C₈	—	2	2	no	—
185	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
190	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
191	C₂×C₅₉⋊C₈	#41	1	2	yes	—
192	C₂×C₅₉⋊C₈	#41	1	2	yes	—
193	C₂³×C₅₉	—	2	1	no	—
194	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
195	C₂²×D₅₉	—	2	1	no	—
196	Q₈×C₅₉	—	2	1	no	—
197	Q₈×C₅₉	—	2	1	no	—
198	D₄×C₅₉	—	2	1	no	—
199	D₄×C₅₉	—	2	1	no	—
200	D₄×C₅₉	—	4	1	no	—
201	D₄×C₅₉	—	4	1	no	—
202	C₂×C₄×C₅₉	—	2	2	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	4	1	no	—
207	C₂×C₄×C₅₉	—	4	1	no	—
208	C₂×C₄×C₅₉	—	4	1	no	—
209	C₂×C₄×C₅₉	—	4	2	no	—
210	C₂×C₄×C₅₉	—	4	2	no	—
211	C₂×C₄×C₅₉	—	4	2	no	—
212	C₂×C₄×C₅₉	—	4	2	no	—
213	C₂×C₄×C₅₉	—	8	1	no	—
214	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
224	C₂²⋊D₅₉	—	4	1	no	—
225	C₂²⋊D₅₉	—	4	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	—	2	1	no	—
229	D₂₃₆	—	2	1	no	—
230	D₂₃₆	—	2	1	no	—
231	C₄×D₅₉	—	4	1	no	—
232	C₄×D₅₉	—	4	1	no	—
233	C₄×D₅₉	—	4	2	no	—
234	C₄×D₅₉	—	8	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	C₈×C₅₉	—	4	2	no	—
238	C₅₉⋊C₈	—	2	1	no	—
239	C₅₉⋊C₈	—	2	1	no	—
240	C₅₉⋊C₈	—	2	2	no	—
241	C₅₉⋊C₈	—	2	2	no	—
242	C₅₉⋊C₈	—	4	2	no	—
243	C₅₉⋊C₈	#117	1	2	yes	—
244	C₅₉⋊C₈	#117	1	2	yes	—
245	#22803	—	59	1	no	maximal, Sylow
246	C₂²×C₅₉	—	2	1	no	—
247	C₂²×C₅₉	—	2	1	no	—
248	C₂²×C₅₉	—	4	1	no	—
249	C₂²×C₅₉	—	4	1	no	—
250	C₂²×C₅₉	—	4	1	no	—
251	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₅₉	#555	1	1	yes	characteristic
253	C₂²×C₅₉	#556	1	1	yes	characteristic
254	C₂×D₅₉	—	4	1	no	—
255	C₂×D₅₉	—	4	1	no	—
256	C₂×D₅₉	—	4	1	no	—
257	C₄×C₅₉	—	2	1	no	—
258	C₄×C₅₉	—	2	1	no	—
259	C₄×C₅₉	—	2	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₄×C₅₉	—	8	2	no	—
264	C₄×C₅₉	#444	1	2	yes	—
265	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
266	C₄×C₅₉	#520	1	1	yes	characteristic
267	C₄×C₅₉	#547	1	1	yes	characteristic
268	C₄×C₅₉	#550	1	1	yes	characteristic
269	Dic₅₉	—	4	1	no	—
270	Dic₅₉	—	4	1	no	—
271	Dic₅₉	—	4	1	no	—
272	C₄×#135	—	59	1	no	—
273	#2925	—	59	1	no	—
274	#2925	—	59	1	no	—
275	#1975	—	59	2	no	—
276	#1929	—	59	2	no	—
277	#1929	—	59	2	no	—
278	#1848	—	59	1	no	—
279	#1806	—	59	1	no	—
280	#1806	D₅₉	1	1	yes	characteristic, complemented
281	#1773	—	59	2	no	—
282	#1770	—	59	1	no	—
283	C₂×C₅₉	—	2	1	no	—
284	C₂×C₅₉	—	2	1	no	—
285	C₂×C₅₉	—	8	1	no	—
286	C₂×C₅₉	#2354	1	1	yes	characteristic
287	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
288	C₂×C₅₉	#2957	1	1	yes	characteristic
289	D₅₉	—	8	1	no	—
290	C₂×#135	—	59	1	no	—
291	C₄×#41	—	59	1	no	—
292	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
293	C₄×Q₁₆	—	59	1	no	—
294	C₄×Q₁₆	—	59	1	no	—
295	C₄×SD₁₆	—	59	1	no	—
296	C₄×SD₁₆	—	59	1	no	—
297	C₄×SD₁₆	—	59	1	no	—
298	C₄×SD₁₆	—	59	1	no	—
299	C₄×D₈	—	59	1	no	—
300	C₄×D₈	—	59	1	no	—
301	#433	—	118	2	no	—
302	#433	—	118	2	no	—
303	#432	—	118	1	no	—
304	#432	—	118	1	no	—
305	#431	—	118	1	no	—
306	#431	—	118	1	no	—
307	C₂×#108	—	59	2	no	—
308	C₂×#108	—	59	2	no	—
309	#427	—	59	1	no	—
310	#423	—	59	1	no	—
311	#423	C₂×D₅₉	1	1	yes	characteristic
312	C₂×C₄⋊C₈	—	59	1	no	—
313	C₂×#104	—	59	2	no	—
314	C₂×#104	C₂×D₅₉	1	2	yes	—
315	#416	—	59	1	no	—
316	#416	—	59	1	no	—
317	#408	—	59	2	no	—
318	#408	—	59	2	no	—
319	#405	—	59	2	no	—
320	#405	—	59	2	no	—
321	C₂×#97	—	59	2	no	—
322	C₂×C₄×C₈	—	59	1	no	—
323	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
324	#339	—	59	2	no	—
325	#339	C₂×D₅₉	1	2	yes	—
326	#336	—	59	2	no	—
327	C₅₉	#22803	1	1	yes	characteristic, complemented, Sylow
328	C₂×#41	—	59	1	no	—
329	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
330	#135	—	118	2	no	—
331	#135	—	118	2	no	—
332	C₂×Q₁₆	—	59	1	no	—
333	C₂×SD₁₆	—	59	1	no	—
334	C₂×SD₁₆	—	59	1	no	—
335	C₂×D₈	—	59	1	no	—
336	C₂×M₁₆	—	59	2	no	—
337	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
338	C₂²×C₈	—	59	1	no	—
339	C₂²×C₈	—	59	1	no	—
340	C₂²×C₈	—	59	2	no	—
341	C₄×Q₈	—	59	1	no	—
342	C₄×Q₈	—	59	1	no	—
343	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
344	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	59	1	no	—
348	C₄×D₄	—	59	1	no	—
349	C₄×D₄	—	118	1	no	—
350	C₄×D₄	—	118	1	no	—
351	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
352	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
353	#117	—	2	1	no	—
354	#117	—	59	1	no	—
355	#117	—	118	1	no	—
356	#117	C₂²×D₅₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	118	1	no	—
360	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
361	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
362	#108	—	118	4	no	—
363	#108	—	236	2	no	—
364	#107	—	59	1	no	—
365	#107	—	59	1	no	—
366	#106	—	59	1	no	—
367	#106	—	59	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	59	1	no	—
371	C₄⋊C₈	—	59	1	no	—
372	C₄⋊C₈	—	59	2	no	—
373	C₄⋊C₈	—	118	1	no	—
374	C₄⋊C₈	—	118	1	no	—
375	#104	—	4	2	no	—
376	#104	—	236	2	no	—
377	#103	—	59	1	no	—
378	#103	—	59	1	no	—
379	#103	—	59	1	no	—
380	#103	—	59	1	no	—
381	#102	—	59	1	no	—
382	#102	—	59	1	no	—
383	#102	—	59	1	no	—
384	#102	—	59	1	no	—
385	C₂²⋊C₈	—	118	2	no	—
386	C₂²⋊C₈	—	118	2	no	—
387	C₂²⋊C₈	—	118	2	no	—
388	C₂²⋊C₈	—	118	2	no	—
389	#97	—	118	4	no	—
390	#97	—	118	2	no	—
391	#97	—	118	2	no	—
392	C₄×C₈	—	59	1	no	—
393	C₄×C₈	—	59	1	no	—
394	C₄×C₈	—	59	1	no	—
395	C₄×C₈	—	59	1	no	—
396	C₄×C₈	—	118	2	no	—
397	C₄×C₈	—	118	2	no	—
398	#95	—	2	1	no	—
399	#41	—	2	1	no	—
400	#41	—	2	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	118	1	no	—
404	#41	—	118	1	no	—
405	#41	—	118	1	no	—
406	#41	—	118	1	no	—
407	C₂×Q₈	—	59	1	no	—
408	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	59	1	no	—
411	C₂×D₄	—	118	1	no	—
412	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	118	1	no	—
418	C₂²×C₄	—	118	1	no	—
419	C₂²×C₄	—	118	1	no	—
420	C₂²×C₄	#11745687	1	1	yes	characteristic
421	C₂²×C₄	#11745687	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
423	Q₁₆	—	118	2	no	—
424	SD₁₆	—	118	2	no	—
425	SD₁₆	—	118	2	no	—
426	D₈	—	118	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	118	2	no	—
430	M₁₆	—	118	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	59	1	no	—
433	C₂×C₈	—	59	1	no	—
434	C₂×C₈	—	59	2	no	—
435	C₂×C₈	—	59	2	no	—
436	C₂×C₈	—	59	1	no	—
437	C₂×C₈	—	59	1	no	—
438	C₂×C₈	—	59	2	no	—
439	C₂×C₈	—	59	2	no	—
440	C₂×C₈	—	118	2	no	—
441	C₂×C₈	—	118	1	no	—
442	C₂×C₈	—	118	2	no	—
443	C₂×C₈	—	118	1	no	—
444	C₂×C₈	—	118	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	59	1	no	—
449	C₄⋊C₄	—	59	1	no	—
450	C₄⋊C₄	—	118	1	no	—
451	C₄⋊C₄	—	118	1	no	—
452	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
453	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	118	1	no	—
458	C₂²⋊C₄	—	118	1	no	—
459	C₂²⋊C₄	—	118	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	118	1	no	—
466	C₄²	—	118	1	no	—
467	C₄²	—	118	1	no	—
468	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
469	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
470	C₄²	D₄×D₅₉	1	1	yes	characteristic
471	C₄²	D₄×D₅₉	1	1	yes	characteristic
472	C₂³	—	2	1	no	—
473	C₂³	—	118	1	no	—
474	C₂³	C₂×#11745687	1	1	yes	characteristic
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	118	1	no	—
478	Q₈	—	118	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	118	1	no	—
484	D₄	—	118	1	no	—
485	D₄	—	236	1	no	—
486	D₄	—	236	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	118	1	no	—
500	C₂×C₄	—	118	1	no	—
501	C₂×C₄	—	118	1	no	—
502	C₂×C₄	—	472	1	no	—
503	C₂×C₄	—	236	2	no	—
504	C₂×C₄	—	236	1	no	—
505	C₂×C₄	—	236	1	no	—
506	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
509	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
512	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
513	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
514	C₂×C₄	#14273772	1	1	yes	characteristic
515	C₂×C₄	#14273775	1	1	yes	characteristic
516	C₈	—	4	2	no	—
517	C₈	—	59	2	no	—
518	C₈	—	59	2	no	—
519	C₈	—	118	2	no	—
520	C₈	—	118	2	no	—
521	C₈	—	118	1	no	—
522	C₈	—	118	1	no	—
523	C₈	—	236	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	236	1	no	—
530	C₂²	—	236	1	no	—
531	C₂²	—	236	1	no	—
532	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
533	C₂²	#16838116	1	1	yes	characteristic
534	C₂²	#16838123	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	8	2	no	—
542	C₄	—	236	1	no	—
543	C₄	—	236	1	no	—
544	C₄	—	236	1	no	—
545	C₄	#16837521	1	2	yes	—
546	C₄	#117×D₅₉	1	1	yes	characteristic
547	C₄	#16837883	1	1	yes	characteristic
548	C₄	#16838054	1	1	yes	characteristic
549	C₄	#16838070	1	1	yes	characteristic
550	C₂	—	2	1	no	—
551	C₂	—	2	1	no	—
552	C₂	—	8	1	no	—
553	C₂	—	472	1	no	—
554	C₂	#21427040	1	1	yes	characteristic
555	C₂	C₂×#16837521	1	1	yes	characteristic
556	C₂	#21433009	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	C₅₉×#1806	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1806	D₅₉
hypocenter	C₅₉	#22803
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
2. #21432764	C₂	semidirect
3. #21432762	C₂	semidirect
5. #21424747	C₂	semidirect
6. #21424742	C₂	semidirect
7. #21424267	C₂	semidirect
8. #21424117	C₂	semidirect
9. #21423979	C₂	semidirect
10. #21423965	C₂	semidirect
11. C₅₉×#1806	C₂	semidirect
14. C₄×#11745672	C₄	semidirect
15. C₄×#11745672	C₄	semidirect
16. C₄×#11745671	C₄	semidirect
17. C₄×#11745671	C₄	semidirect
18. C₄×#11745670	C₄	semidirect
19. C₄×#11745670	C₄	semidirect
20. C₄×#11745669	C₄	semidirect
21. C₄×#11745669	C₄	semidirect
280. #1806	D₅₉	semidirect
327. C₅₉	#22803	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14273747	2
#21432764	2
#21432762	2
#21424986	2
#21424747	2
#21424742	2
#21424267	2
#21424117	2
#21423979	2
#21423965	2
C₅₉×#1806	2
#22803	59