Subgroups — #15828547

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
3	#13113129	C₂	1	2	yes	maximal, complemented
4	#13113126	C₂	1	2	yes	maximal, complemented
5	#13113123	C₂	1	2	yes	maximal, complemented
6	#13113120	C₂	1	2	yes	maximal, complemented
7	#13113117	C₂	1	2	yes	maximal, complemented
8	M₁₆×#1055	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×#1055	C₄	1	2	yes	—
12	C₁₃×#432	C₄	1	2	yes	—
13	C₁₃×#432	C₄	1	2	yes	—
14	C₁₃×#431	C₂²	1	2	yes	—
15	C₁₃×#431	C₂²	1	2	yes	—
16	C₁₃×#423	C₄	1	2	yes	—
17	C₁₃×#407	C₄	1	2	yes	—
18	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
19	#11718868	C₄	1	2	yes	—
20	#11718587	C₄	1	2	yes	—
21	#11718587	C₄	1	2	yes	—
22	#11718586	C₂²	1	2	yes	—
23	#11718586	C₂²	1	2	yes	—
24	#11718585	C₄	1	2	yes	—
25	C₄×#6099	C₂²	1	2	yes	—
26	C₂×C₄×#1055	C₄	1	2	yes	—
27	C₂×C₄×#1055	C₄	1	2	yes	—
28	C₂×C₄×#1055	C₄	1	2	yes	—
29	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
30	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
35	#11718047	C₂²	1	4	yes	complemented
36	#11718046	C₂²	1	4	yes	complemented
37	#11718046	C₂²	1	4	yes	complemented
38	C₈×#1055	C₂²	1	4	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂×C₄	1	4	yes	—
56	C₂²×#1055	—	2	8	no	—
57	C₂²×#1055	C₂×C₄	1	2	yes	—
58	C₂²×#1055	C₂×C₄	1	2	yes	—
59	C₂²×#1055	C₂×C₄	1	2	yes	—
60	C₂²×#1055	C₂×C₄	1	2	yes	—
61	C₂²×#1055	C₂×C₄	1	2	yes	—
62	C₂²×#1055	C₂×C₄	1	2	yes	—
63	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
65	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₁₃×#97	C₂×C₄	1	4	yes	—
68	C₄×C₈×C₁₃	C₂³	1	4	yes	—
69	C₂²⋊#1055	C₂×C₄	1	4	yes	—
70	C₂²⋊#1055	C₂×C₄	1	4	yes	—
71	C₄⋊#1055	C₂×C₄	1	4	yes	—
72	C₄⋊#1055	C₂×C₄	1	4	yes	—
73	#88043	C₂×C₄	1	4	yes	—
74	C₄×#1055	C₂×C₄	1	2	yes	—
75	C₄×#1055	C₂×C₄	1	2	yes	—
76	C₄×#1055	C₂×C₄	1	2	yes	—
77	C₄×#1055	C₂×C₄	1	2	yes	—
78	C₄×#1055	C₂×C₄	1	2	yes	—
79	C₄×#1055	C₂×C₄	1	2	yes	—
80	C₄×#1055	C₂³	1	1	yes	characteristic
81	C₄×#1055	C₂³	1	4	yes	—
82	C₄×#1055	C₂³	1	1	yes	characteristic
83	C₄×#1055	C₂³	1	1	yes	characteristic
84	C₄×#1055	C₂³	1	1	yes	characteristic
85	#17323	—	13	1	no	maximal, Sylow
86	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₁₃×M₁₆	—	2	8	no	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
110	C₄²×C₁₃	C₄²	1	1	yes	characteristic
111	C₄²×C₁₃	C₄²	1	1	yes	characteristic
112	C₄²×C₁₃	C₄²	1	1	yes	characteristic
113	C₄²×C₁₃	C₄²	1	1	yes	characteristic
114	C₄²×C₁₃	C₄²	1	1	yes	characteristic
115	C₄²×C₁₃	C₄²	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
126	#6099	—	2	8	no	—
127	C₂×#1055	—	2	4	no	—
128	C₂×#1055	—	2	4	no	—
129	C₂×#1055	—	2	4	no	—
130	C₂×#1055	—	2	4	no	—
131	C₂×#1055	—	2	4	no	—
132	C₂×#1055	M₁₆	1	8	yes	complemented
133	C₂×#1055	C₂²×C₄	1	8	yes	—
134	C₂×#1055	C₂²×C₄	1	2	yes	—
135	C₂×#1055	C₂²×C₄	1	2	yes	—
136	C₂×#1055	C₂²×C₄	1	2	yes	—
137	C₂×#1055	C₂²×C₄	1	2	yes	—
138	#2920	—	13	1	no	—
139	#2920	D₁₃	1	1	yes	characteristic
140	C₂²×C₄×C₈	—	13	1	no	—
141	#1452	—	13	2	no	—
142	#1451	—	13	2	no	—
143	#1451	—	13	2	no	—
144	#1450	—	13	2	no	—
145	C₈×M₁₆	—	13	2	no	—
146	C₈×M₁₆	—	13	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
152	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
178	C₂×C₄×C₁₃	#131	1	4	yes	—
179	C₂×C₄×C₁₃	#131	1	4	yes	—
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₁₃	—	2	8	no	—
184	#1055	—	2	2	no	—
185	#1055	—	2	2	no	—
186	#1055	—	2	8	no	—
187	#1055	C₂×M₁₆	1	4	yes	—
188	#1055	C₂×M₁₆	1	4	yes	—
189	C₂³×C₈	—	13	2	no	—
190	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
191	#432	—	13	2	no	—
192	#432	—	13	2	no	—
193	#432	Dic₁₃	1	2	yes	—
194	#432	Dic₁₃	1	2	yes	—
195	#431	—	13	2	no	—
196	#431	—	13	2	no	—
197	#431	C₂×D₁₃	1	2	yes	—
198	#431	C₂×D₁₃	1	2	yes	—
199	#423	—	13	2	no	—
200	#423	Dic₁₃	1	2	yes	—
201	#407	—	13	2	no	—
202	#407	Dic₁₃	1	2	yes	—
203	C₄×M₁₆	—	13	2	no	—
204	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
205	C₂×C₄×C₈	—	13	2	no	—
206	C₂×C₄×C₈	—	13	2	no	—
207	C₂×C₄×C₈	—	13	2	no	—
208	C₂×C₄×C₈	—	13	1	no	—
209	C₂×C₄×C₈	—	13	1	no	—
210	C₂×C₄×C₈	—	13	1	no	—
211	C₂×C₄×C₈	—	13	1	no	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	—	13	1	no	—
214	#322	—	13	4	no	—
215	#322	—	13	4	no	—
216	#322	—	13	4	no	—
217	C₈²	—	13	4	no	—
218	C₂²×C₁₃	—	2	8	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
226	C₂²×C₁₃	#405	1	2	yes	—
227	C₂²×C₁₃	#405	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
236	C₄×C₁₃	#405	1	2	yes	—
237	C₄×C₁₃	#405	1	2	yes	—
238	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
239	C₄×C₁₃	C₂×#131	1	2	yes	—
240	C₄×C₁₃	C₂×#131	1	2	yes	—
241	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
242	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
243	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
244	C₂×M₁₆	—	13	4	no	—
245	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
246	C₂²×C₈	—	13	2	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	—	13	2	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	2	no	—
251	C₂²×C₈	—	13	2	no	—
252	C₂²×C₈	—	26	8	no	—
253	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
265	C₄⋊C₈	—	13	4	no	—
266	C₄⋊C₈	—	13	4	no	—
267	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
268	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
269	C₂²⋊C₈	—	13	4	no	—
270	C₂²⋊C₈	—	13	4	no	—
271	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
272	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
273	#97	—	13	4	no	—
274	#97	C₂×Dic₁₃	1	4	yes	—
275	C₄×C₈	—	13	2	no	—
276	C₄×C₈	—	13	2	no	—
277	C₄×C₈	—	13	2	no	—
278	C₄×C₈	—	13	2	no	—
279	C₄×C₈	—	13	2	no	—
280	C₄×C₈	—	13	2	no	—
281	C₄×C₈	—	13	1	no	—
282	C₄×C₈	—	13	4	no	—
283	C₄×C₈	—	13	1	no	—
284	C₄×C₈	—	13	1	no	—
285	C₄×C₈	—	13	1	no	—
286	C₄×C₈	C₂²×D₁₃	1	4	yes	—
287	C₂×C₁₃	—	2	2	no	—
288	C₂×C₁₃	—	2	2	no	—
289	C₂×C₁₃	—	2	2	no	—
290	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
291	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
292	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
293	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
315	M₁₆	—	2	8	no	—
316	M₁₆	—	26	8	no	—
317	C₂×C₈	—	13	8	no	—
318	C₂×C₈	—	13	2	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	8	no	—
323	C₂×C₈	—	26	4	no	—
324	C₂×C₈	—	26	4	no	—
325	C₂×C₈	—	26	4	no	—
326	C₂×C₈	—	26	4	no	—
327	C₂×C₈	—	26	4	no	—
328	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
329	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
330	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
331	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
332	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
333	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
334	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
335	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
336	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
337	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
341	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
342	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
343	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
344	C₄²	C₂³×D₁₃	1	1	yes	characteristic
345	C₁₃	#17323	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
350	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
351	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
368	C₂×C₄	#88161	1	4	yes	—
369	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
378	C₂×C₄	#88202	1	4	yes	—
379	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
382	C₈	—	2	8	no	—
383	C₈	—	13	4	no	—
384	C₈	—	13	4	no	—
385	C₈	—	26	2	no	—
386	C₈	—	26	2	no	—
387	C₈	—	26	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	#11718658	1	2	yes	—
396	C₂²	M₁₆×Dic₁₃	1	2	yes	—
397	C₂²	#11718783	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	#11718658	1	2	yes	—
406	C₄	M₁₆×Dic₁₃	1	2	yes	—
407	C₄	#11718783	1	2	yes	—
408	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
409	C₄	C₂×#88161	1	2	yes	—
410	C₄	C₂×#88202	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	C₂×M₁₆×Dic₁₃	1	1	yes	characteristic
415	C₂	C₂×#11718658	1	1	yes	characteristic
416	C₂	C₂×#11718783	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#2920	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17323
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13113129	C₂	semidirect
4. #13113126	C₂	semidirect
5. #13113123	C₂	semidirect
6. #13113120	C₂	semidirect
7. #13113117	C₂	semidirect
8. M₁₆×#1055	C₂	semidirect
35. #11718047	C₂²	semidirect
36. #11718046	C₂²	semidirect
37. #11718046	C₂²	semidirect
38. C₈×#1055	C₂²	semidirect
132. C₂×#1055	M₁₆	semidirect
345. C₁₃	#17323	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
C₂²×C₄×#1055	2
#13113129	2
#13113126	2
#13113123	2
#13113120	2
#13113117	2
M₁₆×#1055	2
C₁₃×#2920	2
#17323	13