Subgroups — #28494617

Order 15104.

774 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	C₂²×#14273663	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837357	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837171	C₂	1	2	yes	maximal
4	#21423815	C₂	1	2	yes	maximal
5	C₂²×#106×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11745664	C₂²	1	2	yes	—
7	C₂²×#11745664	C₂²	1	1	yes	characteristic
8	C₂×#14273686	C₂²	1	1	yes	characteristic
9	C₂×#14273663	—	2	2	no	—
10	C₂×#14273663	—	2	2	no	—
11	C₂×#14273663	C₄	1	4	yes	complemented
12	#16837357	—	2	2	no	—
13	#16837357	C₄	1	4	yes	complemented
14	C₂×#14273637	—	2	1	no	—
15	C₂×C₈×Dic₅₉	—	2	1	no	—
16	#16837171	—	2	4	no	—
17	#16837164	—	2	4	no	—
18	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
20	C₂×#106×C₅₉	—	2	2	no	—
21	C₂×#106×C₅₉	—	2	1	no	—
22	C₂×#106×C₅₉	—	2	1	no	—
23	C₂×#106×C₅₉	C₄	1	4	yes	complemented
24	C₂×#11745664	—	2	1	no	—
25	C₂×#11745664	—	2	1	no	—
26	C₂×#11745664	—	2	1	no	—
27	C₂×#11745664	—	2	2	no	—
28	C₂×#11745664	—	2	2	no	—
29	C₂×#11745664	—	2	2	no	—
30	C₂×#11745664	—	2	2	no	—
31	C₂×#11745664	—	2	2	no	—
32	C₂×#11745664	C₂×C₄	1	4	yes	—
33	C₂×#11745664	C₂×C₄	1	2	yes	—
34	C₂×#11745664	D₄	1	2	yes	—
35	C₂×#11745664	Q₈	1	2	yes	—
36	C₂²×C₅₉⋊C₈	—	2	1	no	—
37	C₂²×C₅₉⋊C₈	—	2	2	no	—
38	#14273686	—	2	1	no	—
39	#14273686	—	2	1	no	—
40	#14273686	C₂×C₄	1	2	yes	—
41	#14273686	Q₈	1	2	yes	—
42	C₂×C₄⋊Dic₅₉	D₄	1	2	yes	—
43	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
44	C₂×C₄×Dic₅₉	—	2	1	no	—
45	#14273663	—	2	8	no	—
46	#14273637	—	2	4	no	—
47	C₈×Dic₅₉	—	2	4	no	—
48	C₂³×C₄×C₅₉	—	2	2	no	—
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
52	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₅₉	D₄	1	2	yes	—
54	C₂²×C₈×C₅₉	D₄	1	2	yes	—
55	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	Q₈	1	2	yes	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	4	yes	—
64	#106×C₅₉	—	2	4	no	—
65	#106×C₅₉	—	2	4	no	—
66	C₂⁴×C₅₉	#41	1	1	yes	characteristic
67	C₂²×C₄×C₅₉	—	2	4	no	—
68	C₂²×C₄×C₅₉	—	4	2	no	—
69	C₂²×C₄×C₅₉	—	4	2	no	—
70	C₂²×C₄×C₅₉	—	8	4	no	—
71	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
85	C₂²×Dic₅₉	—	2	2	no	—
86	C₂×C₈×C₅₉	C₄²	1	4	yes	—
87	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
88	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
89	C₂×C₈×C₅₉	C₂²⋊C₄	1	4	yes	—
90	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
91	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₅₉	C₄⋊C₄	1	4	yes	—
93	C₂×C₈×C₅₉	C₄⋊C₄	1	2	yes	—
94	C₂×C₈×C₅₉	C₄⋊C₄	1	2	yes	—
95	C₂×C₈×C₅₉	C₄⋊C₄	1	4	yes	—
96	C₄⋊C₄×C₅₉	—	2	4	no	—
97	C₄⋊C₄×C₅₉	—	2	4	no	—
98	C₄⋊C₄×C₅₉	—	4	2	no	—
99	C₄⋊C₄×C₅₉	—	4	2	no	—
100	C₂²⋊Dic₅₉	—	2	2	no	—
101	C₂²⋊Dic₅₉	—	2	2	no	—
102	C₄⋊Dic₅₉	—	2	2	no	—
103	C₄⋊Dic₅₉	C₄⋊C₄	1	4	yes	—
104	C₄×Dic₅₉	—	2	2	no	—
105	C₄×Dic₅₉	—	2	2	no	—
106	#11745664	—	2	2	no	—
107	#11745664	—	2	2	no	—
108	#11745664	—	2	2	no	—
109	#11745664	—	2	4	no	—
110	#11745664	—	2	4	no	—
111	#11745664	—	4	2	no	—
112	#11745664	—	4	2	no	—
113	#11745664	C₄⋊C₄	1	4	yes	—
114	C₂×C₅₉⋊C₈	—	2	2	no	—
115	C₂×C₅₉⋊C₈	—	2	2	no	—
116	C₂×C₅₉⋊C₈	—	2	2	no	—
117	C₂×C₅₉⋊C₈	—	2	4	no	—
118	C₂×C₅₉⋊C₈	—	4	2	no	—
119	C₂×C₅₉⋊C₈	—	4	2	no	—
120	C₂³×C₅₉	—	2	4	no	—
121	C₂³×C₅₉	#117	1	1	yes	characteristic
122	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
123	C₂³×C₅₉	C₄×Q₈	1	1	yes	characteristic
124	C₂³×C₅₉	#121	1	1	yes	characteristic
125	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₅₉	#124	1	1	yes	characteristic
127	C₂³×C₅₉	#125	1	1	yes	characteristic
128	C₂×C₄×C₅₉	—	4	4	no	—
129	C₂×C₄×C₅₉	—	8	4	no	—
130	C₂×C₄×C₅₉	—	8	4	no	—
131	C₂×C₄×C₅₉	—	8	4	no	—
132	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
155	C₂×C₄×C₅₉	#125	1	1	yes	characteristic
156	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×Dic₅₉	—	2	4	no	—
161	C₂×Dic₅₉	—	4	4	no	—
162	C₈×C₅₉	#95	1	4	yes	—
163	C₈×C₅₉	#95	1	4	yes	—
164	C₅₉⋊C₈	—	2	4	no	—
165	C₅₉⋊C₈	—	4	4	no	—
166	#10869	—	59	1	no	maximal, Sylow
167	C₂²×C₅₉	—	2	2	no	—
168	C₂²×C₅₉	—	2	2	no	—
169	C₂²×C₅₉	—	2	2	no	—
170	C₂²×C₅₉	—	2	2	no	—
171	C₂²×C₅₉	—	2	2	no	—
172	C₂²×C₅₉	—	2	2	no	—
173	C₂²×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₅₉	#380	1	1	yes	characteristic
175	C₂²×C₅₉	#382	1	1	yes	characteristic
176	C₂²×C₅₉	#389	1	1	yes	characteristic
177	C₂²×C₅₉	#389	1	1	yes	characteristic
178	C₂²×C₅₉	#390	1	1	yes	characteristic
179	C₂²×C₅₉	#391	1	1	yes	characteristic
180	C₂²×C₅₉	#471	1	4	yes	—
181	C₄×C₅₉	—	8	4	no	—
182	C₄×C₅₉	C₂×#95	1	1	yes	characteristic
183	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
184	C₄×C₅₉	#380	1	1	yes	characteristic
185	C₄×C₅₉	#384	1	1	yes	characteristic
186	C₄×C₅₉	#389	1	1	yes	characteristic
187	C₄×C₅₉	#389	1	1	yes	characteristic
188	C₄×C₅₉	#390	1	1	yes	characteristic
189	C₄×C₅₉	#391	1	1	yes	characteristic
190	Dic₅₉	—	4	4	no	—
191	C₂²×#108	—	59	1	no	—
192	C₂²×#106	D₅₉	1	1	yes	characteristic
193	C₂×#405	—	59	1	no	—
194	C₂×#343	—	59	2	no	—
195	#1736	—	59	2	no	—
196	C₂×C₅₉	—	2	1	no	—
197	C₂×C₅₉	—	2	1	no	—
198	C₂×C₅₉	—	2	1	no	—
199	C₂×C₅₉	—	2	1	no	—
200	C₂×C₅₉	C₄⋊#95	1	1	yes	characteristic
201	C₂×C₅₉	#1815	1	2	yes	—
202	C₂×C₅₉	#1951	1	2	yes	—
203	C₂×C₅₉	#1977	1	2	yes	—
204	C₂²×M₁₆	—	59	1	no	—
205	C₂²×M₁₆	—	59	2	no	—
206	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
207	C₂×#117	—	59	1	no	—
208	C₂²×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
209	C₂×#108	—	59	4	no	—
210	C₂×#108	—	118	2	no	—
211	C₂×#108	—	118	2	no	—
212	C₂×#106	—	2	1	no	—
213	C₂×#106	—	2	1	no	—
214	C₂×#106	—	2	2	no	—
215	C₂×#106	Dic₅₉	1	4	yes	complemented
216	#405	—	59	4	no	—
217	#405	—	118	2	no	—
218	C₂×#97	—	118	1	no	—
219	C₂×C₄×C₈	—	118	1	no	—
220	#343	—	118	4	no	—
221	#340	—	118	4	no	—
222	C₅₉	#10869	1	1	yes	characteristic, complemented, Sylow
223	C₂³×C₄	—	2	2	no	—
224	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
225	C₂×M₁₆	—	59	2	no	—
226	C₂×M₁₆	—	59	2	no	—
227	C₂×M₁₆	—	59	2	no	—
228	C₂×M₁₆	—	59	4	no	—
229	C₂×M₁₆	—	118	1	no	—
230	C₂×M₁₆	—	118	1	no	—
231	C₂×M₁₆	—	118	1	no	—
232	C₂×M₁₆	—	118	2	no	—
233	C₂×M₁₆	—	118	2	no	—
234	C₂×M₁₆	—	118	2	no	—
235	C₂×M₁₆	—	118	2	no	—
236	C₂×M₁₆	—	118	2	no	—
237	C₂²×C₈	—	118	1	no	—
238	C₂²×C₈	—	118	2	no	—
239	C₂²×C₈	Dic₁₁₈	1	2	yes	—
240	C₂²×C₈	C₄×D₅₉	1	2	yes	—
241	C₂²×C₈	C₄×D₅₉	1	2	yes	—
242	C₂²×C₈	D₂₃₆	1	2	yes	—
243	C₂²×C₈	C₂×Dic₅₉	1	2	yes	—
244	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
245	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
246	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
247	#117	—	59	2	no	—
248	#117	—	59	2	no	—
249	#117	—	118	1	no	—
250	#117	—	118	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	59	2	no	—
257	C₂×C₄⋊C₄	C₂×Dic₅₉	1	4	yes	—
258	C₂×C₂²⋊C₄	—	118	1	no	—
259	C₂×C₄²	—	118	1	no	—
260	#108	—	118	8	no	—
261	#106	—	2	4	no	—
262	#106	—	2	4	no	—
263	#97	—	118	4	no	—
264	C₄×C₈	—	118	4	no	—
265	C₂⁴	#11745687	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	8	4	no	—
270	C₂²×C₄	—	118	2	no	—
271	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
277	C₂²×C₄	#11745687	1	1	yes	characteristic
278	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
280	C₂²×C₄	#11745689	1	1	yes	characteristic
281	C₂²×C₄	#11745689	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
285	M₁₆	—	59	4	no	—
286	M₁₆	—	118	2	no	—
287	M₁₆	—	118	2	no	—
288	M₁₆	—	118	2	no	—
289	M₁₆	—	118	4	no	—
290	M₁₆	—	118	4	no	—
291	M₁₆	—	236	2	no	—
292	M₁₆	—	236	2	no	—
293	C₂×C₈	—	118	2	no	—
294	C₂×C₈	—	118	2	no	—
295	C₂×C₈	—	118	2	no	—
296	C₂×C₈	—	118	4	no	—
297	C₂×C₈	—	236	2	no	—
298	C₂×C₈	—	236	2	no	—
299	C₂×C₈	C₄×Dic₅₉	1	4	yes	—
300	C₂×C₈	Dic₅₉⋊C₄	1	4	yes	—
301	C₂×C₈	Dic₅₉⋊C₄	1	2	yes	—
302	C₂×C₈	Dic₅₉⋊C₄	1	2	yes	—
303	C₂×C₈	C₄⋊Dic₅₉	1	4	yes	—
304	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
305	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
306	C₂×C₈	(C₂×D₅₉)⋊C₄	1	4	yes	—
307	C₂×C₈	C₂²⋊Dic₅₉	1	2	yes	—
308	C₂×C₈	C₂²⋊Dic₅₉	1	2	yes	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	59	4	no	—
314	C₄⋊C₄	—	118	2	no	—
315	C₂²⋊C₄	—	118	2	no	—
316	C₂²⋊C₄	—	118	2	no	—
317	C₄²	—	118	2	no	—
318	C₄²	—	118	2	no	—
319	C₂³	—	2	4	no	—
320	C₂³	#14273685	1	1	yes	characteristic
321	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
322	C₂³	#14273692	1	1	yes	characteristic
323	C₂³	#14273698	1	1	yes	characteristic
324	C₂³	#14273707	1	1	yes	characteristic
325	C₂³	#14273714	1	1	yes	characteristic
326	C₂³	#14273718	1	1	yes	characteristic
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	—	118	4	no	—
332	C₂×C₄	—	236	4	no	—
333	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
334	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
337	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
338	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
339	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
342	C₂×C₄	#14273685	1	1	yes	characteristic
343	C₂×C₄	#14273689	1	1	yes	characteristic
344	C₂×C₄	#14273689	1	1	yes	characteristic
345	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
346	C₂×C₄	#14273692	1	1	yes	characteristic
347	C₂×C₄	Q₈×Dic₅₉	1	1	yes	characteristic
348	C₂×C₄	Q₈×Dic₅₉	1	1	yes	characteristic
349	C₂×C₄	#14273698	1	1	yes	characteristic
350	C₂×C₄	#14273702	1	1	yes	characteristic
351	C₂×C₄	#14273702	1	1	yes	characteristic
352	C₂×C₄	#14273703	1	1	yes	characteristic
353	C₂×C₄	#14273703	1	1	yes	characteristic
354	C₂×C₄	#14273707	1	1	yes	characteristic
355	C₂×C₄	#14273716	1	1	yes	characteristic
356	C₂×C₄	#14273718	1	1	yes	characteristic
357	C₂×C₄	#14273723	1	1	yes	characteristic
358	C₂×C₄	#14273725	1	1	yes	characteristic
359	C₂×C₄	#14273726	1	1	yes	characteristic
360	C₂×C₄	#14273726	1	1	yes	characteristic
361	C₈	—	118	4	no	—
362	C₈	—	236	4	no	—
363	C₈	C₅₉⋊#95	1	4	yes	—
364	C₈	C₅₉⋊#95	1	4	yes	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	C₄⋊C₄×Dic₅₉	1	1	yes	characteristic
372	C₂²	#16837259	1	1	yes	characteristic
373	C₂²	#16837267	1	1	yes	characteristic
374	C₂²	#16837298	1	1	yes	characteristic
375	C₂²	#16837301	1	1	yes	characteristic
376	C₂²	#16837305	1	1	yes	characteristic
377	C₂²	#16837307	1	1	yes	characteristic
378	C₂²	#16837662	1	4	yes	—
379	C₄	—	8	4	no	—
380	C₄	—	236	4	no	—
381	C₄	C₂×C₅₉⋊#95	1	1	yes	characteristic
382	C₄	C₄⋊C₄×Dic₅₉	1	1	yes	characteristic
383	C₄	#16837259	1	1	yes	characteristic
384	C₄	#16837271	1	1	yes	characteristic
385	C₄	#16837298	1	1	yes	characteristic
386	C₄	#16837301	1	1	yes	characteristic
387	C₄	#16837303	1	1	yes	characteristic
388	C₄	#16837309	1	1	yes	characteristic
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#21422325	1	1	yes	characteristic
394	C₂	#21424156	1	2	yes	—
395	C₂	#21424874	1	2	yes	—
396	C₂	#21425001	1	2	yes	—

	subgroup	G/H
center	C₂³	#14273698
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₂²×#106×C₅₉	C₂
socle	C₂³×C₅₉	#121
prime radical	C₂⁴×C₅₉	#41
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	C₂²×#106	D₅₉
hypocenter	C₅₉	#10869
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
11. C₂×#14273663	C₄	semidirect
13. #16837357	C₄	semidirect
23. C₂×#106×C₅₉	C₄	semidirect
215. C₂×#106	Dic₅₉	semidirect
222. C₅₉	#10869	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14273663	2
C₂×#16837357	2
C₂×#16837171	2
#21423815	2
C₂²×#106×C₅₉	2
#10869	59