Subgroups — #28607156

Order 15104.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837519	C₂	1	2	yes	maximal
2	#21432664	C₂	1	2	yes	maximal, complemented
3	#21424845	C₂	1	2	yes	maximal, complemented
4	#21424373	C₂	1	4	yes	maximal, complemented
5	#21424268	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424116	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₅₉	C₂	1	1	yes	maximal, characteristic
9	C₂×#14273734	C₂²	1	4	yes	—
10	#16837519	—	2	8	no	—
11	C₂×#14273663	C₂²	1	2	yes	—
12	C₂×#14273663	C₂²	1	2	yes	—
13	#16837429	—	2	4	no	—
14	#16837429	C₂²	1	4	yes	—
15	#16837426	—	2	2	no	—
16	#16837426	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
18	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#14273654	C₂²	1	4	yes	—
20	C₂×C₈×Dic₅₉	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
22	#16837161	C₂²	1	4	yes	—
23	#16837156	C₂²	1	2	yes	—
24	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
25	C₄×#41×C₅₉	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
27	C₄×Q₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₅₉	C₄	1	2	yes	complemented
29	C₄×SD₁₆×C₅₉	C₄	1	2	yes	complemented
30	C₄×D₈×C₅₉	C₄	1	1	yes	characteristic, complemented
31	C₄×D₈×C₅₉	C₄	1	1	yes	characteristic, complemented
32	C₅₉×#427	C₂²	1	1	yes	characteristic
33	C₅₉×#416	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
35	#14273734	—	2	8	no	—
36	#14273734	—	4	4	no	—
37	C₂×#11745664	—	2	4	no	—
38	C₂×#11745664	C₂³	1	4	yes	—
39	C₂²×C₅₉⋊C₈	—	2	4	no	—
40	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₅₉	—	2	1	no	—
42	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
43	#14273663	—	2	4	no	—
44	#14273663	—	4	2	no	—
45	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
48	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
49	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
50	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
51	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
52	#14273654	—	2	8	no	—
53	C₈×Dic₅₉	—	2	4	no	—
54	C₅₉⋊#95	—	2	1	no	—
55	C₂×#41×C₅₉	C₂³	1	2	yes	—
56	#135×C₅₉	D₄	1	4	yes	—
57	#135×C₅₉	Q₈	1	4	yes	—
58	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
60	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₅₉	—	2	2	no	—
66	C₄×D₄×C₅₉	—	2	2	no	—
67	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
69	#117×C₅₉	—	2	2	no	—
70	#117×C₅₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₅₉	—	2	2	no	—
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
74	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
75	#106×C₅₉	C₂×C₄	1	2	yes	—
76	#103×C₅₉	C₂×C₄	1	2	yes	—
77	#103×C₅₉	C₂×C₄	1	2	yes	—
78	#102×C₅₉	C₂×C₄	1	2	yes	—
79	#102×C₅₉	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
84	#41×C₅₉	—	2	2	no	—
85	#41×C₅₉	—	2	2	no	—
86	#41×C₅₉	C₂×D₄	1	4	yes	—
87	#41×C₅₉	C₂×Q₈	1	4	yes	—
88	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₅₉	—	2	2	no	—
90	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅₉	—	2	2	no	—
92	C₂²×C₄×C₅₉	—	2	2	no	—
93	C₂²×C₄×C₅₉	—	2	2	no	—
94	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₅₉	—	2	2	no	—
98	Q₁₆×C₅₉	C₄⋊C₄	1	4	yes	complemented
99	SD₁₆×C₅₉	C₄⋊C₄	1	8	yes	complemented
100	D₈×C₅₉	C₄⋊C₄	1	4	yes	complemented
101	C₂×C₈×C₅₉	—	2	1	no	—
102	C₂×C₈×C₅₉	—	2	1	no	—
103	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₅₉	—	2	2	no	—
110	C₄⋊C₄×C₅₉	—	2	2	no	—
111	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
112	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
113	C₂²⋊C₄×C₅₉	—	2	2	no	—
114	C₂²⋊C₄×C₅₉	—	2	2	no	—
115	C₂²⋊C₄×C₅₉	—	2	2	no	—
116	C₄²×C₅₉	—	2	2	no	—
117	C₄²×C₅₉	—	2	2	no	—
118	C₄²×C₅₉	—	2	2	no	—
119	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₄⋊Dic₅₉	—	2	4	no	—
124	C₄×Dic₅₉	—	2	2	no	—
125	C₄×Dic₅₉	—	2	2	no	—
126	#11745664	—	2	4	no	—
127	#11745664	—	2	4	no	—
128	#11745664	—	4	8	no	—
129	C₂×C₅₉⋊C₈	—	2	2	no	—
130	C₂×C₅₉⋊C₈	—	2	2	no	—
131	C₂×C₅₉⋊C₈	—	2	4	no	—
132	C₂×C₅₉⋊C₈	—	4	8	no	—
133	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
135	C₂³×C₅₉	—	2	2	no	—
136	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
137	Q₈×C₅₉	—	2	2	no	—
138	Q₈×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
139	D₄×C₅₉	—	2	4	no	—
140	D₄×C₅₉	—	2	4	no	—
141	D₄×C₅₉	—	2	2	no	—
142	D₄×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	4	no	—
145	C₂×C₄×C₅₉	—	2	4	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	4	1	no	—
150	C₂×C₄×C₅₉	—	4	4	no	—
151	C₂×C₄×C₅₉	—	8	2	no	—
152	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×Dic₅₉	—	2	4	no	—
163	C₂×Dic₅₉	—	4	2	no	—
164	C₂×Dic₅₉	—	4	2	no	—
165	C₈×C₅₉	—	2	1	no	—
166	C₈×C₅₉	—	2	1	no	—
167	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
168	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
169	C₅₉⋊C₈	—	2	2	no	—
170	C₅₉⋊C₈	—	2	2	no	—
171	C₅₉⋊C₈	—	4	4	no	—
172	#22688	—	59	1	no	maximal, Sylow
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	—	2	4	no	—
176	C₂²×C₅₉	—	4	2	no	—
177	C₂²×C₅₉	—	4	2	no	—
178	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₅₉	#547	1	1	yes	characteristic
180	C₂²×C₅₉	#554	1	1	yes	characteristic
181	C₄×C₅₉	—	2	4	no	—
182	C₄×C₅₉	—	2	1	no	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	2	1	no	—
185	C₄×C₅₉	—	4	2	no	—
186	C₄×C₅₉	—	4	2	no	—
187	C₄×C₅₉	#443	1	2	yes	complemented
188	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₅₉	#520	1	1	yes	characteristic
190	C₄×C₅₉	D₄²	1	1	yes	characteristic
191	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
192	Dic₅₉	—	4	4	no	—
193	C₂×#443	—	59	2	no	—
194	C₄×#135	D₅₉	1	1	yes	characteristic
195	#2906	—	59	2	no	—
196	#1945	—	59	2	no	—
197	#1866	—	59	4	no	—
198	#1848	—	59	1	no	—
199	#1806	—	59	2	no	—
200	C₈×C₄⋊C₄	—	59	1	no	—
201	C₂×C₅₉	—	2	1	no	—
202	C₂×C₅₉	—	2	1	no	—
203	C₂×C₅₉	—	4	4	no	—
204	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
206	C₂×C₅₉	#2957	1	1	yes	characteristic
207	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
208	C₂×#131	—	59	4	no	—
209	C₄×#41	C₂×D₅₉	1	2	yes	—
210	#443	—	118	8	no	—
211	C₄×Q₁₆	Dic₅₉	1	1	yes	characteristic, complemented
212	C₄×Q₁₆	Dic₅₉	1	1	yes	characteristic, complemented
213	C₄×SD₁₆	Dic₅₉	1	2	yes	complemented
214	C₄×SD₁₆	Dic₅₉	1	2	yes	complemented
215	C₄×D₈	Dic₅₉	1	1	yes	characteristic, complemented
216	C₄×D₈	Dic₅₉	1	1	yes	characteristic, complemented
217	C₂×#108	—	59	2	no	—
218	C₂×#108	—	59	2	no	—
219	#427	C₂×D₅₉	1	1	yes	characteristic
220	#424	—	59	4	no	—
221	#424	—	118	4	no	—
222	#423	—	59	2	no	—
223	#423	—	118	2	no	—
224	C₂×C₄⋊C₈	—	59	1	no	—
225	C₂×C₄⋊C₈	—	118	2	no	—
226	C₂×#104	—	59	4	no	—
227	#416	C₂×D₅₉	1	2	yes	—
228	C₂×C₄×C₈	—	59	2	no	—
229	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
230	C₄×C₄⋊C₄	—	59	1	no	—
231	#339	—	59	4	no	—
232	#336	—	59	2	no	—
233	C₅₉	#22688	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	C₂²×D₅₉	1	2	yes	—
235	#135	Dic₁₁₈	1	4	yes	—
236	#135	D₂₃₆	1	4	yes	—
237	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
238	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
239	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
240	#131	—	118	8	no	—
241	#131	—	236	4	no	—
242	C₂×M₁₆	—	59	4	no	—
243	C₂×M₁₆	—	118	4	no	—
244	C₂²×C₈	—	59	2	no	—
245	C₂²×C₈	—	118	4	no	—
246	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
248	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
249	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
253	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	C₂²×D₅₉	1	2	yes	—
256	C₂×C₄⋊C₄	—	118	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	59	2	no	—
259	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
260	#108	—	118	4	no	—
261	#108	—	236	2	no	—
262	#107	C₂×Dic₅₉	1	1	yes	characteristic
263	#107	C₂×Dic₅₉	1	1	yes	characteristic
264	#106	C₂×Dic₅₉	1	2	yes	—
265	C₄⋊C₈	—	59	1	no	—
266	C₄⋊C₈	—	59	1	no	—
267	C₄⋊C₈	—	59	2	no	—
268	C₄⋊C₈	—	118	4	no	—
269	C₄⋊C₈	—	118	4	no	—
270	C₄⋊C₈	—	118	2	no	—
271	C₄⋊C₈	—	118	2	no	—
272	#104	—	118	8	no	—
273	#103	C₂×Dic₅₉	1	2	yes	—
274	#103	C₂×Dic₅₉	1	2	yes	—
275	#102	C₂×Dic₅₉	1	2	yes	—
276	#102	C₂×Dic₅₉	1	2	yes	—
277	C₄×C₈	—	118	4	no	—
278	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
279	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
280	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
281	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
282	#95	—	118	1	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	C₂×Dic₁₁₈	1	4	yes	—
286	#41	C₂×D₂₃₆	1	4	yes	—
287	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	118	2	no	—
294	C₂²×C₄	#11745687	1	1	yes	characteristic
295	C₂²×C₄	#11745687	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
297	Q₁₆	C₄⋊Dic₅₉	1	4	yes	complemented
298	SD₁₆	C₄⋊Dic₅₉	1	8	yes	complemented
299	D₈	C₄⋊Dic₅₉	1	4	yes	complemented
300	M₁₆	—	118	4	no	—
301	M₁₆	—	118	4	no	—
302	M₁₆	—	236	8	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	59	2	no	—
306	C₂×C₈	—	59	2	no	—
307	C₂×C₈	—	118	2	no	—
308	C₂×C₈	—	118	2	no	—
309	C₂×C₈	—	118	4	no	—
310	C₂×C₈	—	236	8	no	—
311	C₂×C₈	C₂×Dic₁₁₈	1	2	yes	—
312	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
313	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
314	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
315	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
316	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	118	4	no	—
320	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	118	2	no	—
329	C₄²	—	118	2	no	—
330	C₄²	D₄×D₅₉	1	1	yes	characteristic
331	C₄²	D₄×D₅₉	1	1	yes	characteristic
332	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
333	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	C₂×#11745687	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	C₂×C₄⋊Dic₅₉	1	4	yes	—
338	D₄	—	2	4	no	—
339	D₄	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	C₂×C₄⋊Dic₅₉	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	118	4	no	—
352	C₂×C₄	—	236	2	no	—
353	C₂×C₄	—	236	2	no	—
354	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
356	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
357	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
358	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
362	C₂×C₄	#14273773	1	1	yes	characteristic
363	C₂×C₄	#14273774	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	118	2	no	—
367	C₈	—	118	2	no	—
368	C₈	—	236	4	no	—
369	C₈	C₂×C₄⋊Dic₅₉	1	2	yes	—
370	C₈	C₂×C₄⋊Dic₅₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
377	C₂²	#16838056	1	1	yes	characteristic
378	C₂²	#16838109	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	236	4	no	—
386	C₄	#16837519	1	2	yes	complemented
387	C₄	C₂²×C₄⋊Dic₅₉	1	1	yes	characteristic
388	C₄	#16837885	1	1	yes	characteristic
389	C₄	D₄×D₂₃₆	1	1	yes	characteristic
390	C₄	D₄×Dic₁₁₈	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	D₄×C₄⋊Dic₅₉	1	1	yes	characteristic
395	C₂	C₂×#16837519	1	1	yes	characteristic
396	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	#22688
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
2. #21432664	C₂	semidirect
3. #21424845	C₂	semidirect
4. #21424373	C₂	semidirect
5. #21424268	C₂	semidirect
6. #21424116	C₂	semidirect
7. C₈×C₄⋊Dic₅₉	C₂	semidirect
26. C₄×Q₁₆×C₅₉	C₄	semidirect
27. C₄×Q₁₆×C₅₉	C₄	semidirect
28. C₄×SD₁₆×C₅₉	C₄	semidirect
29. C₄×SD₁₆×C₅₉	C₄	semidirect
30. C₄×D₈×C₅₉	C₄	semidirect
31. C₄×D₈×C₅₉	C₄	semidirect
98. Q₁₆×C₅₉	C₄⋊C₄	semidirect
99. SD₁₆×C₅₉	C₄⋊C₄	semidirect
100. D₈×C₅₉	C₄⋊C₄	semidirect
187. C₄×C₅₉	#443	semidirect
211. C₄×Q₁₆	Dic₅₉	semidirect
212. C₄×Q₁₆	Dic₅₉	semidirect
213. C₄×SD₁₆	Dic₅₉	semidirect
214. C₄×SD₁₆	Dic₅₉	semidirect
215. C₄×D₈	Dic₅₉	semidirect
216. C₄×D₈	Dic₅₉	semidirect
233. C₅₉	#22688	semidirect
297. Q₁₆	C₄⋊Dic₅₉	semidirect
298. SD₁₆	C₄⋊Dic₅₉	semidirect
299. D₈	C₄⋊Dic₅₉	semidirect
386. C₄	#16837519	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837519	2
#21432664	2
#21424845	2
#21424373	2
#21424268	2
#21424116	2
C₈×C₄⋊Dic₅₉	2
C₄×#135×C₅₉	2
#22688	59