Subgroups — #28742956

Order 15104.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837832	C₂	1	2	yes	maximal, complemented
2	#21434524	C₂	1	1	yes	maximal, characteristic, complemented
3	#21426158	C₂	1	2	yes	maximal, complemented
4	#21426151	C₂	1	2	yes	maximal, complemented
5	#21426146	C₂	1	1	yes	maximal, characteristic, complemented
6	#21426141	C₂	1	1	yes	maximal, characteristic, complemented
7	#21426136	C₂	1	1	yes	maximal, characteristic, complemented
8	#21426131	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#21425801	C₂	1	2	yes	maximal, complemented
11	C₄×#135×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273749	—	2	1	no	—
13	C₂×#14273749	C₂²	1	2	yes	—
14	#16837952	—	2	1	no	—
15	#16837832	—	2	8	no	—
16	C₂×#14273673	C₂²	1	2	yes	—
17	C₂×#14273671	C₂²	1	2	yes	—
18	C₂×#14273670	C₂²	1	2	yes	—
19	C₂×#14273668	C₂²	1	2	yes	—
20	C₂²×C₅₉⋊C₁₆	C₂²	1	2	yes	—
21	#16837786	—	2	1	no	—
22	#16837786	C₂²	1	2	yes	—
23	#16837782	C₂²	1	1	yes	characteristic
24	#16837779	C₂²	1	1	yes	characteristic
25	#16837775	—	2	1	no	—
26	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
27	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
28	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	—
29	#16837205	C₂²	1	2	yes	—
30	#16837205	C₂²	1	2	yes	—
31	#16837202	C₂²	1	2	yes	—
32	#16837202	C₂²	1	2	yes	—
33	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
34	C₄×#41×C₅₉	—	2	1	no	—
35	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
36	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₅₉	—	2	1	no	—
38	C₄×SD₁₆×C₅₉	—	2	1	no	—
39	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#427	C₂²	1	1	yes	characteristic
42	C₅₉×#416	—	2	1	no	—
43	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#11745685	—	2	2	no	—
45	#14273749	—	2	4	no	—
46	#14273749	—	2	4	no	—
47	#14273749	—	4	4	no	—
48	C₂×Dic₂₃₆	—	2	1	no	—
49	C₂×Dic₂₃₆	C₂³	1	2	yes	—
50	C₂×#11745660	—	2	2	no	—
51	C₂×#11745660	—	2	2	no	—
52	C₂×D₄₇₂	—	2	1	no	—
53	C₂×D₄₇₂	C₂³	1	2	yes	—
54	#14273727	—	2	1	no	—
55	#14273724	—	2	1	no	—
56	#14273715	—	2	2	no	—
57	#14273701	—	4	1	no	—
58	#14273701	—	4	1	no	—
59	C₄×D₂₃₆	—	4	1	no	—
60	C₄×D₂₃₆	—	4	1	no	—
61	#14273673	—	2	4	no	—
62	#14273671	—	2	4	no	—
63	#14273670	—	2	4	no	—
64	#14273668	—	2	4	no	—
65	C₂×C₅₉⋊C₁₆	—	2	4	no	—
66	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
68	C₂×#41×C₅₉	—	2	1	no	—
69	#135×C₅₉	—	2	2	no	—
70	#135×C₅₉	D₄	1	4	yes	complemented
71	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₅₉	—	2	1	no	—
73	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₅₉	—	2	1	no	—
77	C₄×Q₈×C₅₉	—	2	1	no	—
78	C₄×D₄×C₅₉	—	2	1	no	—
79	C₄×D₄×C₅₉	—	2	1	no	—
80	C₄×D₄×C₅₉	—	4	1	no	—
81	C₄×D₄×C₅₉	—	4	1	no	—
82	#117×C₅₉	—	2	1	no	—
83	#117×C₅₉	—	4	1	no	—
84	C₂×C₄²×C₅₉	—	4	1	no	—
85	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
86	#107×C₅₉	C₂³	1	1	yes	characteristic
87	#107×C₅₉	C₂³	1	1	yes	characteristic
88	#106×C₅₉	—	2	1	no	—
89	#103×C₅₉	—	2	1	no	—
90	#103×C₅₉	—	2	1	no	—
91	#102×C₅₉	—	2	1	no	—
92	#102×C₅₉	—	2	1	no	—
93	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
95	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
97	#41×C₅₉	—	2	4	no	—
98	#41×C₅₉	—	4	2	no	—
99	C₂×Q₈×C₅₉	—	2	1	no	—
100	C₂×D₄×C₅₉	—	2	1	no	—
101	C₂×D₄×C₅₉	—	4	1	no	—
102	C₂²×C₄×C₅₉	—	4	1	no	—
103	C₂²×C₄×C₅₉	—	4	1	no	—
104	C₂²×C₄×C₅₉	—	4	1	no	—
105	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₅₉	—	4	2	no	—
109	#11745685	—	4	4	no	—
110	#11745685	—	4	4	no	—
111	C₂×D₂₃₆	—	2	2	no	—
112	C₂×D₂₃₆	—	4	1	no	—
113	C₂×D₂₃₆	—	4	1	no	—
114	C₂×C₄×D₅₉	—	4	2	no	—
115	C₂×Dic₁₁₈	—	2	2	no	—
116	Q₁₆×C₅₉	—	2	1	no	—
117	Q₁₆×C₅₉	C₂×D₄	1	2	yes	—
118	SD₁₆×C₅₉	—	2	4	no	—
119	D₈×C₅₉	—	2	1	no	—
120	D₈×C₅₉	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₅₉	#41	1	2	yes	—
127	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	—	4	1	no	—
131	C₄⋊C₄×C₅₉	—	4	1	no	—
132	C₂²⋊C₄×C₅₉	—	4	1	no	—
133	C₂²⋊C₄×C₅₉	—	4	1	no	—
134	C₂²⋊C₄×C₅₉	—	4	1	no	—
135	C₄²×C₅₉	—	4	1	no	—
136	C₄²×C₅₉	—	4	1	no	—
137	C₄²×C₅₉	—	4	1	no	—
138	C₄²×C₅₉	D₈	1	1	yes	characteristic
139	C₄²×C₅₉	D₈	1	1	yes	characteristic
140	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
142	(C₂×D₅₉)⋊C₄	—	4	2	no	—
143	(C₂×D₅₉)⋊C₄	—	4	2	no	—
144	C₄⋊Dic₅₉	—	4	1	no	—
145	C₄⋊Dic₅₉	—	4	1	no	—
146	Dic₂₃₆	—	2	2	no	—
147	Dic₂₃₆	—	2	2	no	—
148	Dic₂₃₆	—	4	2	no	—
149	D₄₇₂	—	2	2	no	—
150	D₄₇₂	—	2	2	no	—
151	D₄₇₂	—	4	2	no	—
152	#11745660	—	4	4	no	—
153	#11745660	—	4	4	no	—
154	C₅₉⋊C₁₆	—	2	2	no	—
155	C₅₉⋊C₁₆	—	2	2	no	—
156	C₂³×C₅₉	—	4	1	no	—
157	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
158	C₂²×D₅₉	—	4	2	no	—
159	Q₈×C₅₉	—	2	2	no	—
160	Q₈×C₅₉	—	4	1	no	—
161	D₄×C₅₉	—	2	2	no	—
162	D₄×C₅₉	—	4	4	no	—
163	D₄×C₅₉	—	4	1	no	—
164	C₂×C₄×C₅₉	—	2	2	no	—
165	C₂×C₄×C₅₉	—	4	1	no	—
166	C₂×C₄×C₅₉	—	4	1	no	—
167	C₂×C₄×C₅₉	—	4	4	no	—
168	C₂×C₄×C₅₉	—	4	1	no	—
169	C₂×C₄×C₅₉	—	4	1	no	—
170	C₂×C₄×C₅₉	—	8	2	no	—
171	C₂×C₄×C₅₉	—	8	2	no	—
172	C₂×C₄×C₅₉	#121	1	2	yes	—
173	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
180	C₂²⋊D₅₉	—	8	4	no	—
181	C₂×Dic₅₉	—	4	2	no	—
182	D₂₃₆	—	4	2	no	—
183	D₂₃₆	—	4	2	no	—
184	D₂₃₆	—	8	2	no	—
185	D₂₃₆	—	8	2	no	—
186	C₄×D₅₉	—	8	4	no	—
187	Dic₁₁₈	—	4	2	no	—
188	Dic₁₁₈	—	4	2	no	—
189	C₈×C₅₉	—	2	1	no	—
190	C₈×C₅₉	—	2	1	no	—
191	C₈×C₅₉	#121	1	2	yes	—
192	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
194	#33579	—	59	1	no	maximal, Sylow
195	C₂²×C₅₉	—	2	1	no	—
196	C₂²×C₅₉	—	2	1	no	—
197	C₂²×C₅₉	—	4	2	no	—
198	C₂²×C₅₉	—	8	1	no	—
199	C₂²×C₅₉	—	8	1	no	—
200	C₂²×C₅₉	#459	1	2	yes	—
201	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
202	C₂×D₅₉	—	8	2	no	—
203	C₂×D₅₉	—	8	2	no	—
204	C₂×D₅₉	—	8	2	no	—
205	C₄×C₅₉	—	2	1	no	—
206	C₄×C₅₉	—	2	1	no	—
207	C₄×C₅₉	—	2	1	no	—
208	C₄×C₅₉	—	4	2	no	—
209	C₄×C₅₉	—	8	1	no	—
210	C₄×C₅₉	—	8	1	no	—
211	C₄×C₅₉	#459	1	2	yes	—
212	C₄×C₅₉	#508	1	2	yes	complemented
213	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
214	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	Dic₅₉	—	8	2	no	—
216	C₂×#508	—	59	2	no	—
217	#3147	—	59	1	no	—
218	C₄×#135	D₅₉	1	1	yes	characteristic, complemented
219	#2211	—	59	2	no	—
220	#2210	—	59	2	no	—
221	#2209	—	59	1	no	—
222	#2208	—	59	1	no	—
223	#2207	—	59	1	no	—
224	#2206	—	59	1	no	—
225	C₂×C₄⋊C₁₆	—	59	1	no	—
226	#2138	—	59	2	no	—
227	C₂×C₅₉	—	2	2	no	—
228	C₂×C₅₉	—	8	2	no	—
229	C₂×C₅₉	C₂×#459	1	1	yes	characteristic
230	C₂×C₅₉	C₂×#508	1	1	yes	characteristic
231	C₂×C₅₉	#3414	1	1	yes	characteristic
232	D₅₉	—	16	2	no	—
233	C₂×#135	—	59	2	no	—
234	C₂×#135	—	118	1	no	—
235	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
236	#532	—	118	1	no	—
237	C₄×#41	—	2	1	no	—
238	#508	—	118	8	no	—
239	C₂×Q₃₂	—	59	2	no	—
240	C₂×SD₃₂	—	59	2	no	—
241	C₂×SD₃₂	—	59	2	no	—
242	C₂×D₁₆	—	59	2	no	—
243	C₂²×C₁₆	—	59	2	no	—
244	#495	—	59	2	no	—
245	#495	—	118	1	no	—
246	#494	—	59	1	no	—
247	#493	—	59	1	no	—
248	#492	—	118	1	no	—
249	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
250	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
251	C₄×SD₁₆	—	2	1	no	—
252	C₄×SD₁₆	—	2	1	no	—
253	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
254	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
255	#427	C₂×D₅₉	1	1	yes	characteristic
256	#416	—	2	1	no	—
257	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
258	C₄⋊C₁₆	—	59	1	no	—
259	C₄⋊C₁₆	—	59	1	no	—
260	C₄⋊C₁₆	—	59	2	no	—
261	#358	—	59	2	no	—
262	#358	—	59	2	no	—
263	#357	—	59	2	no	—
264	#357	—	59	2	no	—
265	C₅₉	#33579	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	2	1	no	—
267	C₂×#41	—	118	2	no	—
268	#135	—	2	2	no	—
269	#135	—	118	4	no	—
270	#135	—	118	4	no	—
271	#135	—	236	4	no	—
272	#135	D₂₃₆	1	4	yes	complemented
273	C₂×Q₁₆	—	59	2	no	—
274	C₂×Q₁₆	—	118	1	no	—
275	C₂×Q₁₆	C₂²×D₅₉	1	1	yes	characteristic
276	C₂×SD₁₆	—	2	1	no	—
277	C₂×SD₁₆	—	118	2	no	—
278	C₂×SD₁₆	—	118	2	no	—
279	C₂×D₈	—	59	2	no	—
280	C₂×D₈	—	118	1	no	—
281	C₂×D₈	C₂²×D₅₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	118	1	no	—
285	#127	—	118	1	no	—
286	#124	—	118	2	no	—
287	#121	—	236	1	no	—
288	#121	—	236	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	4	1	no	—
294	C₄×D₄	—	4	1	no	—
295	C₄×D₄	—	236	1	no	—
296	C₄×D₄	—	236	1	no	—
297	#117	—	2	1	no	—
298	#117	—	4	1	no	—
299	C₂×C₄²	—	4	1	no	—
300	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
301	Q₃₂	—	118	4	no	—
302	SD₃₂	—	118	4	no	—
303	SD₃₂	—	118	4	no	—
304	D₁₆	—	118	4	no	—
305	C₂×C₁₆	—	59	2	no	—
306	C₂×C₁₆	—	59	2	no	—
307	C₂×C₁₆	—	118	4	no	—
308	#107	C₂²×D₅₉	1	1	yes	characteristic
309	#107	C₂²×D₅₉	1	1	yes	characteristic
310	#106	—	2	1	no	—
311	#103	—	2	1	no	—
312	#103	—	2	1	no	—
313	#102	—	2	1	no	—
314	#102	—	2	1	no	—
315	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
316	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	236	4	no	—
322	#41	—	236	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	118	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	118	2	no	—
328	C₂×D₄	—	236	2	no	—
329	C₂×D₄	—	236	1	no	—
330	C₂×D₄	—	236	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	236	2	no	—
335	C₂²×C₄	#11745669	1	1	yes	characteristic
336	C₂²×C₄	#11745669	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	118	2	no	—
340	Q₁₆	—	118	2	no	—
341	Q₁₆	—	236	2	no	—
342	Q₁₆	C₂×D₂₃₆	1	2	yes	—
343	SD₁₆	—	2	4	no	—
344	SD₁₆	—	236	4	no	—
345	SD₁₆	—	236	4	no	—
346	D₈	—	2	1	no	—
347	D₈	—	118	2	no	—
348	D₈	—	118	2	no	—
349	D₈	—	236	2	no	—
350	D₈	C₂×D₂₃₆	1	2	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
353	C₂×C₈	#11745685	1	2	yes	—
354	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
357	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	236	1	no	—
363	C₄⋊C₄	—	236	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	236	2	no	—
368	C₂²⋊C₄	—	236	2	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	#11745669	1	1	yes	characteristic
373	C₄²	#11745669	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
376	C₁₆	—	118	2	no	—
377	C₁₆	—	118	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	236	2	no	—
380	C₂³	C₂×#11745669	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	236	2	no	—
384	Q₈	—	236	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	1	no	—
388	D₄	—	472	2	no	—
389	D₄	—	472	4	no	—
390	D₄	—	472	2	no	—
391	D₄	—	236	2	no	—
392	D₄	—	236	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	472	4	no	—
402	C₂×C₄	—	236	2	no	—
403	C₂×C₄	#14273701	1	2	yes	—
404	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
405	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
406	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
407	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
408	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
409	C₂×C₄	#14273752	1	2	yes	—
410	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#14273701	1	2	yes	—
414	C₈	C₂²×D₂₃₆	1	1	yes	characteristic
415	C₈	C₂×#11745685	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	472	2	no	—
422	C₂²	—	472	2	no	—
423	C₂²	—	472	2	no	—
424	C₂²	#16837597	1	2	yes	—
425	C₂²	C₂²×#11745669	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	472	2	no	—
433	C₄	#16837597	1	2	yes	—
434	C₄	#16837832	1	2	yes	complemented
435	C₄	C₂×#14273701	1	1	yes	characteristic
436	C₄	C₂×#14273752	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	944	2	no	—
440	C₂	C₂×#16837597	1	1	yes	characteristic
441	C₂	C₂×#16837832	1	1	yes	characteristic
442	C₂	#21437230	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11745669
commutator, cosocle	C₂×C₈×C₅₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₄×#135×C₅₉	C₂
socle	C₂²×C₅₉	C₂²×D₈
hypercenter	C₄×#135	D₅₉
hypocenter	C₅₉	#33579
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#16837832	C₂	semidirect
2. #21434524	C₂	semidirect
3. #21426158	C₂	semidirect
4. #21426151	C₂	semidirect
5. #21426146	C₂	semidirect
6. #21426141	C₂	semidirect
7. #21426136	C₂	semidirect
8. #21426131	C₂	semidirect
9. C₂×C₄⋊(C₅₉⋊C₁₆)	C₂	semidirect
10. #21425801	C₂	semidirect
11. C₄×#135×C₅₉	C₂	semidirect
70. #135×C₅₉	D₄	semidirect
212. C₄×C₅₉	#508	semidirect
218. C₄×#135	D₅₉	semidirect
265. C₅₉	#33579	semidirect
272. #135	D₂₃₆	semidirect
434. C₄	#16837832	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837832	2
#21434524	2
#21426158	2
#21426151	2
#21426146	2
#21426141	2
#21426136	2
#21426131	2
C₂×C₄⋊(C₅₉⋊C₁₆)	2
#21425801	2
C₄×#135×C₅₉	2
#33579	59