Subgroups — C₄×#16838239 #29495303

Order 15104.

11346 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838239	C₂	1	1	yes	maximal, characteristic
2	2₋¹⁺⁴×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14273775	C₂	1	5	yes	maximal, complemented
4	#21437305	C₂	1	5	yes	maximal, complemented
5	C₄×#14273773	C₂	1	10	yes	maximal, complemented
6	#21437302	C₂	1	10	yes	maximal, complemented
7	#21437298	C₂	1	5	yes	maximal, complemented
8	#21437296	C₂	1	10	yes	maximal, complemented
9	C₂×C₄×#11745689	C₂	1	5	yes	maximal, complemented
10	C₄×#41×D₅₉	C₂	1	10	yes	maximal, complemented
11	C₄×2₋¹⁺⁴×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838239	C₄	1	32	yes	direct product factor
13	C₂×#14273775	C₂²	1	5	yes	—
14	C₂×#14273773	C₂²	1	10	yes	—
15	C₂²×#11745689	C₂²	1	5	yes	—
16	C₂×#41×D₅₉	C₂²	1	10	yes	—
17	#16837885	C₂²	1	10	yes	complemented
18	#16837884	C₂²	1	20	yes	complemented
19	#16837884	C₂²	1	20	yes	complemented
20	#16837883	C₂²	1	30	yes	complemented
21	#16837882	C₂²	1	30	yes	complemented
22	#16837880	C₂²	1	5	yes	complemented
23	#16837878	C₂²	1	20	yes	complemented
24	#16837876	C₂²	1	30	yes	complemented
25	#16837874	C₂²	1	60	yes	complemented
26	#41×Dic₅₉	C₂²	1	10	yes	complemented
27	C₄×#11745689	C₂²	1	10	yes	complemented
28	C₄×#11745689	C₂²	1	10	yes	complemented
29	C₄×#11745689	C₂²	1	20	yes	complemented
30	C₄×#11745689	C₂²	1	20	yes	complemented
31	C₄×#11745689	C₂²	1	20	yes	complemented
32	C₄×#11745685	C₂²	1	30	yes	complemented
33	#16837870	C₂²	1	30	yes	complemented
34	C₄×#11745687	C₂²	1	10	yes	complemented
35	C₄×#11745687	C₂²	1	30	yes	complemented
36	C₂×Q₈×Dic₅₉	C₂²	1	5	yes	complemented
37	C₄×Q₈×D₅₉	C₂²	1	10	yes	complemented
38	C₄×Q₈×D₅₉	C₂²	1	10	yes	complemented
39	C₂×C₄×D₂₃₆	C₂²	1	15	yes	complemented
40	C₂×#14273689	C₂²	1	15	yes	complemented
41	C₄×D₄×D₅₉	C₂²	1	30	yes	complemented
42	C₄×D₄×D₅₉	C₂²	1	30	yes	complemented
43	C₂×#14273685	C₂²	1	15	yes	complemented
44	#117×D₅₉	C₂²	1	30	yes	complemented
45	C₂×C₄²×D₅₉	C₂²	1	15	yes	complemented
46	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#520	C₂²	1	10	yes	complemented
48	C₅₉×#519	C₂²	1	5	yes	complemented
49	C₄×#41×C₅₉	C₂²	1	10	yes	complemented
50	C₂×C₄×Q₈×C₅₉	C₂²	1	5	yes	complemented
51	#14273775	C₂×C₄	1	80	yes	complemented
52	#14273773	C₂×C₄	1	160	yes	complemented
53	C₂×#11745689	C₂×C₄	1	80	yes	complemented
54	C₂×#11745689	C₂³	1	10	yes	—
55	C₂×#11745689	C₂³	1	20	yes	—
56	C₂×#11745685	C₂³	1	30	yes	—
57	C₂×#11745687	C₂³	1	10	yes	—
58	#41×D₅₉	C₂×C₄	1	160	yes	complemented
59	C₂×Q₈×D₅₉	C₂³	1	10	yes	—
60	C₂²×D₂₃₆	C₂³	1	15	yes	—
61	C₂×D₄×D₅₉	C₂³	1	30	yes	—
62	C₂²×C₄×D₅₉	C₂³	1	15	yes	—
63	C₂²×C₄×D₅₉	C₂³	1	15	yes	—
64	C₂²×C₄×D₅₉	C₂³	1	15	yes	—
65	Q₈×Dic₅₉	C₂³	1	10	yes	—
66	Q₈×Dic₅₉	C₂³	1	10	yes	—
67	Q₈×Dic₅₉	C₂³	1	20	yes	—
68	C₄×Dic₁₁₈	C₂³	1	10	yes	—
69	C₄×Dic₁₁₈	C₂³	1	30	yes	—
70	#14273692	C₂³	1	10	yes	—
71	#14273692	C₂³	1	30	yes	—
72	C₄×D₂₃₆	C₂³	1	30	yes	—
73	C₄×D₂₃₆	C₂³	1	30	yes	—
74	C₄×D₂₃₆	C₂³	1	60	yes	—
75	D₄×Dic₅₉	C₂³	1	10	yes	—
76	D₄×Dic₅₉	C₂³	1	30	yes	—
77	#14273689	C₂³	1	30	yes	—
78	#14273689	C₂³	1	30	yes	—
79	#14273689	C₂³	1	60	yes	—
80	C₄×C₂²⋊D₅₉	C₂³	1	20	yes	—
81	C₄×C₂²⋊D₅₉	C₂³	1	60	yes	—
82	(C₂²⋊D₅₉)⋊C₄	C₂³	1	20	yes	—
83	(C₂²⋊D₅₉)⋊C₄	C₂³	1	60	yes	—
84	#14273686	C₂³	1	30	yes	—
85	#14273685	C₂³	1	10	yes	—
86	#14273685	C₂³	1	30	yes	—
87	#14273685	C₂³	1	60	yes	—
88	#14273684	C₂³	1	60	yes	—
89	#14273683	C₂³	1	20	yes	—
90	C₂×C₄⋊Dic₅₉	C₂³	1	15	yes	—
91	C₄⋊C₄×D₅₉	C₂³	1	30	yes	—
92	C₄⋊C₄×D₅₉	C₂³	1	30	yes	—
93	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	30	yes	—
94	C₂²⋊C₄×D₅₉	C₂³	1	60	yes	—
95	C₂×C₄×Dic₅₉	C₂³	1	5	yes	—
96	C₂×C₄×Dic₅₉	C₂³	1	15	yes	—
97	C₂×C₄×Dic₅₉	C₂³	1	15	yes	—
98	C₄²×D₅₉	C₂³	1	10	yes	—
99	C₄²×D₅₉	C₂³	1	30	yes	—
100	C₄²×D₅₉	C₂³	1	30	yes	—
101	C₄²×D₅₉	C₂³	1	30	yes	—
102	2₋¹⁺⁴×C₅₉	C₂×C₄	1	16	yes	complemented
103	C₂×#41×C₅₉	C₂³	1	10	yes	—
104	C₂²×Q₈×C₅₉	C₂³	1	5	yes	—
105	C₄×Q₈×C₅₉	C₂³	1	10	yes	—
106	C₄×Q₈×C₅₉	C₂³	1	20	yes	—
107	C₄×Q₈×C₅₉	C₂³	1	10	yes	—
108	C₄×D₄×C₅₉	C₂³	1	10	yes	—
109	C₄×D₄×C₅₉	C₂³	1	30	yes	—
110	#117×C₅₉	C₂³	1	30	yes	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	15	yes	—
112	C₂×C₄²×C₅₉	C₂³	1	15	yes	—
113	C₂³×D₅₉	C₂⁴	1	15	yes	—
114	#41×C₅₉	C₂²×C₄	1	80	yes	complemented
115	C₂×Q₈×C₅₉	C₂²×C₄	1	40	yes	complemented
116	C₂×Q₈×C₅₉	C₂⁴	1	10	yes	—
117	C₂×D₄×C₅₉	C₂⁴	1	10	yes	—
118	C₂²×C₄×C₅₉	C₂⁴	1	5	yes	—
119	C₂²×C₄×C₅₉	C₂⁴	1	15	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	15	yes	—
121	C₂×C₂²⋊D₅₉	C₂⁴	1	20	yes	—
122	C₂²×Dic₅₉	C₂⁴	1	5	yes	—
123	C₂²×Dic₅₉	C₂⁴	1	15	yes	—
124	C₂²×Dic₅₉	C₂⁴	1	5	yes	—
125	#11745689	C₂²×C₄	1	80	yes	complemented
126	#11745689	C₂²×C₄	1	160	yes	complemented
127	Q₈×D₅₉	C₂²×C₄	1	80	yes	complemented
128	#11745687	C₂²×C₄	1	80	yes	complemented
129	D₄×D₅₉	C₂²×C₄	1	240	yes	complemented
130	#11745685	C₂²×C₄	1	240	yes	complemented
131	C₂×D₂₃₆	C₂²×C₄	1	120	yes	complemented
132	C₂×D₂₃₆	C₂⁴	1	30	yes	—
133	C₂×C₄×D₅₉	—	4	30	no	—
134	C₂×C₄×D₅₉	—	4	30	no	—
135	C₂×C₄×D₅₉	C₂²×C₄	1	120	yes	complemented
136	C₂×C₄×D₅₉	C₂⁴	1	10	yes	—
137	C₂×C₄×D₅₉	C₂⁴	1	10	yes	—
138	C₂×C₄×D₅₉	C₂⁴	1	30	yes	—
139	C₂×C₄×D₅₉	C₂⁴	1	30	yes	—
140	C₂×C₄×D₅₉	C₂⁴	1	10	yes	—
141	C₂×C₄×D₅₉	C₂⁴	1	30	yes	—
142	C₂×Dic₁₁₈	C₂⁴	1	10	yes	—
143	C₄⋊C₄×C₅₉	C₂⁴	1	30	yes	—
144	C₄⋊C₄×C₅₉	C₂⁴	1	10	yes	—
145	C₂²⋊C₄×C₅₉	C₂⁴	1	20	yes	—
146	C₄²×C₅₉	C₂⁴	1	10	yes	—
147	C₄²×C₅₉	C₂⁴	1	30	yes	—
148	C₂²⋊Dic₅₉	C₂⁴	1	20	yes	—
149	(C₂×D₅₉)⋊C₄	C₂⁴	1	20	yes	—
150	(C₂×D₅₉)⋊C₄	C₂⁴	1	60	yes	—
151	C₄⋊Dic₅₉	C₂⁴	1	10	yes	—
152	C₄⋊Dic₅₉	C₂⁴	1	30	yes	—
153	Dic₅₉⋊C₄	C₂⁴	1	20	yes	—
154	Dic₅₉⋊C₄	C₂⁴	1	20	yes	—
155	C₄×Dic₅₉	C₂⁴	1	1	yes	characteristic
156	C₄×Dic₅₉	C₂⁴	1	5	yes	—
157	C₄×Dic₅₉	C₂⁴	1	5	yes	—
158	C₄×Dic₅₉	C₂⁴	1	5	yes	—
159	C₄×Dic₅₉	C₂⁴	1	10	yes	—
160	C₄×Dic₅₉	C₂⁴	1	10	yes	—
161	C₄×Dic₅₉	C₂⁴	1	30	yes	—
162	C₄×Dic₅₉	C₂⁴	1	30	yes	—
163	C₂³×C₅₉	C₂⁵	1	5	yes	—
164	C₂²×D₅₉	—	4	15	no	—
165	C₂²×D₅₉	—	4	15	no	—
166	C₂²×D₅₉	C₂³×C₄	1	60	yes	—
167	C₂²×D₅₉	C₂⁵	1	10	yes	—
168	Q₈×C₅₉	C₂³×C₄	1	40	yes	—
169	D₄×C₅₉	C₂³×C₄	1	40	yes	—
170	C₂×C₄×C₅₉	—	2	10	no	—
171	C₂×C₄×C₅₉	—	4	15	no	—
172	C₂×C₄×C₅₉	C₂³×C₄	1	60	yes	—
173	C₂×C₄×C₅₉	C₂⁵	1	10	yes	—
174	C₂×C₄×C₅₉	C₂⁵	1	5	yes	—
175	C₂×C₄×C₅₉	C₂⁵	1	10	yes	—
176	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
177	C₂²⋊D₅₉	C₂³×C₄	1	80	yes	—
178	C₂×Dic₅₉	—	2	10	no	—
179	C₂×Dic₅₉	—	4	15	no	—
180	C₂×Dic₅₉	C₂³×C₄	1	20	yes	—
181	C₂×Dic₅₉	C₂⁵	1	5	yes	—
182	C₂×Dic₅₉	C₂⁵	1	10	yes	—
183	C₂×Dic₅₉	C₂⁵	1	1	yes	characteristic
184	C₂×Dic₅₉	C₂⁵	1	5	yes	—
185	C₂×Dic₅₉	C₂⁵	1	1	yes	characteristic
186	D₂₃₆	C₂³×C₄	1	120	yes	—
187	C₄×D₅₉	—	2	20	no	—
188	C₄×D₅₉	—	2	20	no	—
189	C₄×D₅₉	—	4	30	no	—
190	C₄×D₅₉	—	4	30	no	—
191	C₄×D₅₉	C₂³×C₄	1	40	yes	—
192	C₄×D₅₉	C₂³×C₄	1	120	yes	—
193	Dic₁₁₈	C₂³×C₄	1	40	yes	—
194	C₄×#585	—	59	1	no	maximal, Sylow
195	C₂²×C₅₉	—	2	5	no	—
196	C₂²×C₅₉	—	2	5	no	—
197	C₂²×C₅₉	C₂⁴×C₄	1	10	yes	—
198	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
199	C₂×D₅₉	—	2	10	no	—
200	C₂×D₅₉	—	2	10	no	—
201	C₂×D₅₉	—	4	60	no	—
202	C₂×D₅₉	C₂⁴×C₄	1	20	yes	—
203	C₄×C₅₉	—	2	10	no	—
204	C₄×C₅₉	—	2	5	no	—
205	C₄×C₅₉	C₂⁴×C₄	1	20	yes	—
206	C₄×C₅₉	#585	1	2	yes	complemented
207	Dic₅₉	—	2	10	no	—
208	Dic₅₉	—	2	5	no	—
209	Dic₅₉	C₂⁴×C₄	1	10	yes	—
210	Dic₅₉	C₂⁴×C₄	1	2	yes	—
211	Dic₅₉	#585	1	2	yes	complemented
212	C₂×#585	—	59	1	no	—
213	C₄×2₋¹⁺⁴	—	59	1	no	—
214	C₄×2₋¹⁺⁴	—	59	5	no	—
215	C₄×2₋¹⁺⁴	—	59	5	no	—
216	C₄×2₋¹⁺⁴	D₅₉	1	1	yes	characteristic, complemented
217	C₄×H(5,𝔽₂)	—	59	10	no	—
218	C₄×H(5,𝔽₂)	—	59	10	no	—
219	#3428	—	59	10	no	—
220	#3428	—	59	5	no	—
221	C₂×C₄×#41	—	59	10	no	—
222	C₂×C₄×#41	—	59	5	no	—
223	C₂×C₅₉	—	2	10	no	—
224	C₂×C₅₉	C₂⁵×C₄	1	1	yes	characteristic
225	C₂×C₅₉	C₂×#585	1	1	yes	characteristic
226	C₂×C₅₉	C₂×#585	1	1	yes	characteristic
227	D₅₉	—	2	20	no	—
228	#585	—	59	32	no	—
229	C₂×2₋¹⁺⁴	—	59	5	no	—
230	C₂×2₋¹⁺⁴	C₂×D₅₉	1	1	yes	characteristic
231	C₂×H(5,𝔽₂)	—	59	10	no	—
232	C₂²×#41	—	59	10	no	—
233	C₂²×#41	—	59	5	no	—
234	#520	—	59	10	no	—
235	#520	—	59	20	no	—
236	#520	—	59	20	no	—
237	#520	—	59	30	no	—
238	#520	—	59	30	no	—
239	#520	C₂×D₅₉	1	10	yes	complemented
240	#519	—	59	5	no	—
241	#519	—	59	20	no	—
242	#519	C₂×D₅₉	1	5	yes	complemented
243	#518	—	59	60	no	—
244	#518	—	59	30	no	—
245	C₄×#41	—	59	10	no	—
246	C₄×#41	—	59	10	no	—
247	C₄×#41	—	59	10	no	—
248	C₄×#41	—	59	20	no	—
249	C₄×#41	—	59	20	no	—
250	C₄×#41	—	59	20	no	—
251	C₄×#41	—	59	10	no	—
252	C₄×#41	—	59	30	no	—
253	C₄×#41	—	59	30	no	—
254	C₄×#41	—	59	30	no	—
255	C₄×#41	C₂×D₅₉	1	10	yes	complemented
256	C₂×C₄×Q₈	—	59	5	no	—
257	C₂×C₄×Q₈	—	59	10	no	—
258	C₂×C₄×Q₈	—	59	10	no	—
259	C₂×C₄×Q₈	C₂×D₅₉	1	5	yes	complemented
260	C₂×C₄×D₄	—	59	30	no	—
261	C₂×C₄×D₄	—	59	30	no	—
262	C₂×C₄×D₄	—	59	15	no	—
263	C₂×C₄×D₄	—	59	15	no	—
264	C₂×#117	—	59	30	no	—
265	C₂×#117	—	59	15	no	—
266	C₂²×C₄²	—	59	15	no	—
267	C₅₉	C₄×#585	1	1	yes	characteristic, complemented, Sylow
268	2₋¹⁺⁴	—	59	80	no	—
269	2₋¹⁺⁴	C₄×D₅₉	1	16	yes	complemented
270	H(5,𝔽₂)	—	59	160	no	—
271	C₂×#41	—	59	160	no	—
272	C₂×#41	—	59	80	no	—
273	C₂×#41	—	59	10	no	—
274	C₂×#41	—	59	20	no	—
275	C₂×#41	—	59	10	no	—
276	C₂×#41	—	59	30	no	—
277	C₂×#41	C₂²×D₅₉	1	10	yes	—
278	C₂²×Q₈	—	59	10	no	—
279	C₂²×Q₈	C₂²×D₅₉	1	5	yes	—
280	C₂²×D₄	—	59	30	no	—
281	C₂²×D₄	—	59	15	no	—
282	C₂³×C₄	—	59	15	no	—
283	C₂³×C₄	—	59	15	no	—
284	C₂³×C₄	—	59	15	no	—
285	C₄×Q₈	—	59	10	no	—
286	C₄×Q₈	—	59	20	no	—
287	C₄×Q₈	—	59	10	no	—
288	C₄×Q₈	—	59	10	no	—
289	C₄×Q₈	—	59	30	no	—
290	C₄×Q₈	—	59	10	no	—
291	C₄×Q₈	—	59	30	no	—
292	C₄×Q₈	C₂²×D₅₉	1	10	yes	—
293	C₄×Q₈	C₂²×D₅₉	1	10	yes	—
294	C₄×Q₈	C₂²×D₅₉	1	20	yes	—
295	C₄×D₄	—	59	10	no	—
296	C₄×D₄	—	59	30	no	—
297	C₄×D₄	—	59	20	no	—
298	C₄×D₄	—	59	60	no	—
299	C₄×D₄	—	59	30	no	—
300	C₄×D₄	—	59	30	no	—
301	C₄×D₄	—	59	60	no	—
302	C₄×D₄	—	59	20	no	—
303	C₄×D₄	—	59	60	no	—
304	C₄×D₄	—	59	30	no	—
305	C₄×D₄	—	59	30	no	—
306	C₄×D₄	—	59	60	no	—
307	C₄×D₄	C₂²×D₅₉	1	10	yes	—
308	C₄×D₄	C₂²×D₅₉	1	30	yes	—
309	#117	—	59	30	no	—
310	#117	—	59	10	no	—
311	#117	—	59	30	no	—
312	#117	—	59	60	no	—
313	#117	—	59	20	no	—
314	#117	—	59	60	no	—
315	#117	C₂²×D₅₉	1	30	yes	—
316	C₂×C₄⋊C₄	—	59	15	no	—
317	C₂×C₄⋊C₄	—	59	30	no	—
318	C₂×C₄⋊C₄	—	59	30	no	—
319	C₂×C₄⋊C₄	C₂²×D₅₉	1	15	yes	—
320	C₂×C₂²⋊C₄	—	59	30	no	—
321	C₂×C₂²⋊C₄	—	59	60	no	—
322	C₂×C₄²	—	59	15	no	—
323	C₂×C₄²	—	59	15	no	—
324	C₂×C₄²	—	59	5	no	—
325	C₂×C₄²	—	59	30	no	—
326	C₂×C₄²	—	59	30	no	—
327	C₂×C₄²	—	59	30	no	—
328	C₂×C₄²	—	59	10	no	—
329	C₂×C₄²	C₂²×D₅₉	1	15	yes	—
330	C₂⁴	—	59	15	no	—
331	#41	—	59	80	no	—
332	#41	—	59	160	no	—
333	#41	—	59	80	no	—
334	#41	—	59	240	no	—
335	#41	C₂×C₄×D₅₉	1	80	yes	complemented
336	C₂×Q₈	—	59	80	no	—
337	C₂×Q₈	—	59	10	no	—
338	C₂×Q₈	C₂×C₄×D₅₉	1	40	yes	complemented
339	C₂×Q₈	C₂³×D₅₉	1	10	yes	—
340	C₂×D₄	—	59	20	no	—
341	C₂×D₄	—	59	240	no	—
342	C₂×D₄	—	59	120	no	—
343	C₂×D₄	—	59	30	no	—
344	C₂×D₄	C₂³×D₅₉	1	10	yes	—
345	C₂²×C₄	—	59	5	no	—
346	C₂²×C₄	—	59	120	no	—
347	C₂²×C₄	—	59	10	no	—
348	C₂²×C₄	—	59	30	no	—
349	C₂²×C₄	—	59	5	no	—
350	C₂²×C₄	—	59	15	no	—
351	C₂²×C₄	—	59	10	no	—
352	C₂²×C₄	—	59	10	no	—
353	C₂²×C₄	—	59	30	no	—
354	C₂²×C₄	—	59	30	no	—
355	C₂²×C₄	—	236	30	no	—
356	C₂²×C₄	—	236	30	no	—
357	C₂²×C₄	C₂³×D₅₉	1	5	yes	—
358	C₂²×C₄	C₂³×D₅₉	1	15	yes	—
359	C₂²×C₄	C₂³×D₅₉	1	15	yes	—
360	C₄⋊C₄	—	59	20	no	—
361	C₄⋊C₄	—	59	20	no	—
362	C₄⋊C₄	—	59	30	no	—
363	C₄⋊C₄	—	59	10	no	—
364	C₄⋊C₄	C₂³×D₅₉	1	10	yes	—
365	C₄⋊C₄	C₂³×D₅₉	1	30	yes	—
366	C₂²⋊C₄	—	59	20	no	—
367	C₂²⋊C₄	—	59	60	no	—
368	C₂²⋊C₄	—	59	20	no	—
369	C₂²⋊C₄	C₂³×D₅₉	1	20	yes	—
370	C₄²	—	59	10	no	—
371	C₄²	—	59	5	no	—
372	C₄²	—	59	5	no	—
373	C₄²	—	59	10	no	—
374	C₄²	—	59	30	no	—
375	C₄²	—	59	30	no	—
376	C₄²	—	59	1	no	—
377	C₄²	—	59	5	no	—
378	C₄²	C₂³×D₅₉	1	30	yes	—
379	C₄²	C₂³×D₅₉	1	10	yes	—
380	C₂³	—	59	10	no	—
381	C₂³	—	59	60	no	—
382	C₂³	—	236	15	no	—
383	C₂³	—	236	15	no	—
384	C₂³	C₂⁴×D₅₉	1	5	yes	—
385	Q₈	—	59	40	no	—
386	Q₈	C₂²×C₄×D₅₉	1	40	yes	—
387	D₄	—	59	80	no	—
388	D₄	—	59	120	no	—
389	D₄	C₂²×C₄×D₅₉	1	40	yes	—
390	C₂×C₄	—	2	10	no	—
391	C₂×C₄	—	4	15	no	—
392	C₂×C₄	—	59	20	no	—
393	C₂×C₄	—	59	1	no	—
394	C₂×C₄	—	59	1	no	—
395	C₂×C₄	—	59	5	no	—
396	C₂×C₄	—	59	40	no	—
397	C₂×C₄	—	59	120	no	—
398	C₂×C₄	—	59	5	no	—
399	C₂×C₄	—	59	10	no	—
400	C₂×C₄	—	118	20	no	—
401	C₂×C₄	—	118	10	no	—
402	C₂×C₄	—	118	20	no	—
403	C₂×C₄	—	236	30	no	—
404	C₂×C₄	—	236	30	no	—
405	C₂×C₄	—	236	15	no	—
406	C₂×C₄	C₂²×C₄×D₅₉	1	60	yes	—
407	C₂×C₄	C₂⁴×D₅₉	1	10	yes	—
408	C₂×C₄	C₂⁴×D₅₉	1	5	yes	—
409	C₂×C₄	C₂⁴×D₅₉	1	10	yes	—
410	C₂×C₄	C₂⁴×D₅₉	1	1	yes	characteristic
411	C₂²	—	2	5	no	—
412	C₂²	—	2	5	no	—
413	C₂²	—	59	20	no	—
414	C₂²	—	118	10	no	—
415	C₂²	—	118	10	no	—
416	C₂²	—	236	60	no	—
417	C₂²	C₂³×C₄×D₅₉	1	10	yes	—
418	C₂²	C₂⁵×D₅₉	1	1	yes	characteristic
419	C₄	—	2	10	no	—
420	C₄	—	2	5	no	—
421	C₄	—	59	2	no	—
422	C₄	—	59	10	no	—
423	C₄	—	59	2	no	—
424	C₄	—	118	5	no	—
425	C₄	—	118	10	no	—
426	C₄	C₂³×C₄×D₅₉	1	20	yes	—
427	C₄	#16838239	1	2	yes	direct product factor
428	C₂	—	2	10	no	—
429	C₂	—	118	20	no	—
430	C₂	C₂⁴×C₄×D₅₉	1	1	yes	characteristic
431	C₂	#585×D₅₉	1	1	yes	characteristic
432	C₂	C₂×#16838239	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₉
commutator	C₂×C₅₉	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₅₉
Fitting	C₄×2₋¹⁺⁴×C₅₉	C₂
socle, cosocle	C₂²×C₅₉	C₂⁶
prime radical	C₂×#16838239	C₂
hypercenter	C₄×2₋¹⁺⁴	D₅₉
hypocenter	C₅₉	C₄×#585
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
2. 2₋¹⁺⁴×Dic₅₉	C₂	semidirect
3. C₄×#14273775	C₂	semidirect
4. #21437305	C₂	semidirect
5. C₄×#14273773	C₂	semidirect
6. #21437302	C₂	semidirect
7. #21437298	C₂	semidirect
8. #21437296	C₂	semidirect
9. C₂×C₄×#11745689	C₂	semidirect
10. C₄×#41×D₅₉	C₂	semidirect
11. C₄×2₋¹⁺⁴×C₅₉	C₂	semidirect
12. #16838239	C₄	direct (N × H)
17. #16837885	C₂²	semidirect
18. #16837884	C₂²	semidirect
19. #16837884	C₂²	semidirect
20. #16837883	C₂²	semidirect
21. #16837882	C₂²	semidirect
22. #16837880	C₂²	semidirect
23. #16837878	C₂²	semidirect
24. #16837876	C₂²	semidirect
25. #16837874	C₂²	semidirect
26. #41×Dic₅₉	C₂²	semidirect
27. C₄×#11745689	C₂²	semidirect
28. C₄×#11745689	C₂²	semidirect
29. C₄×#11745689	C₂²	semidirect
30. C₄×#11745689	C₂²	semidirect
31. C₄×#11745689	C₂²	semidirect
32. C₄×#11745685	C₂²	semidirect
33. #16837870	C₂²	semidirect
34. C₄×#11745687	C₂²	semidirect
35. C₄×#11745687	C₂²	semidirect
36. C₂×Q₈×Dic₅₉	C₂²	semidirect
37. C₄×Q₈×D₅₉	C₂²	semidirect
38. C₄×Q₈×D₅₉	C₂²	semidirect
39. C₂×C₄×D₂₃₆	C₂²	semidirect
40. C₂×#14273689	C₂²	semidirect
41. C₄×D₄×D₅₉	C₂²	semidirect
42. C₄×D₄×D₅₉	C₂²	semidirect
43. C₂×#14273685	C₂²	semidirect
44. #117×D₅₉	C₂²	semidirect
45. C₂×C₄²×D₅₉	C₂²	semidirect
47. C₅₉×#520	C₂²	semidirect
48. C₅₉×#519	C₂²	semidirect
49. C₄×#41×C₅₉	C₂²	semidirect
50. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
51. #14273775	C₂×C₄	semidirect
52. #14273773	C₂×C₄	semidirect
53. C₂×#11745689	C₂×C₄	semidirect
58. #41×D₅₉	C₂×C₄	semidirect
102. 2₋¹⁺⁴×C₅₉	C₂×C₄	semidirect
114. #41×C₅₉	C₂²×C₄	semidirect
115. C₂×Q₈×C₅₉	C₂²×C₄	semidirect
125. #11745689	C₂²×C₄	semidirect
126. #11745689	C₂²×C₄	semidirect
127. Q₈×D₅₉	C₂²×C₄	semidirect
128. #11745687	C₂²×C₄	semidirect
129. D₄×D₅₉	C₂²×C₄	semidirect
130. #11745685	C₂²×C₄	semidirect
131. C₂×D₂₃₆	C₂²×C₄	semidirect
135. C₂×C₄×D₅₉	C₂²×C₄	semidirect
206. C₄×C₅₉	#585	semidirect
211. Dic₅₉	#585	semidirect
216. C₄×2₋¹⁺⁴	D₅₉	semidirect
239. #520	C₂×D₅₉	semidirect
242. #519	C₂×D₅₉	semidirect
255. C₄×#41	C₂×D₅₉	semidirect
259. C₂×C₄×Q₈	C₂×D₅₉	semidirect
267. C₅₉	C₄×#585	semidirect
269. 2₋¹⁺⁴	C₄×D₅₉	semidirect
335. #41	C₂×C₄×D₅₉	semidirect
338. C₂×Q₈	C₂×C₄×D₅₉	semidirect
427. C₄	#16838239	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16838239	2
2₋¹⁺⁴×Dic₅₉	2
C₄×#14273775	2
#21437305	2
C₄×#14273773	2
#21437302	2
#21437298	2
#21437296	2
C₂×C₄×#11745689	2
C₄×#41×D₅₉	2
C₄×2₋¹⁺⁴×C₅₉	2
C₄×#585	59

Subgroups — C4×#16838239 #29495303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16838239 #29495303