Subgroups — #15752648

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117219	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718872	C₂	1	1	yes	maximal, characteristic
3	#13112690	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#407	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×M₁₆	—	2	1	no	—
7	C₂²×C₂²⋊Dic₁₃	—	2	1	no	—
8	C₂×#88180	C₄	1	2	yes	complemented
9	C₁₃×#407	—	2	1	no	—
10	C₁₃×#407	—	2	1	no	—
11	C₁₃×#407	C₄	1	2	yes	complemented
12	C₁₃×#407	C₂²	1	2	yes	—
13	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	complemented
15	#11718908	—	2	1	no	—
16	#11718873	—	2	1	no	—
17	#11718873	—	2	1	no	—
18	#11718872	—	2	1	no	—
19	#11718872	—	2	1	no	—
20	#11718872	—	2	1	no	—
21	#11718872	C₄	1	2	yes	complemented
22	#11718872	C₂²	1	2	yes	—
23	C₄×C₂²⋊Dic₁₃	C₄	1	2	yes	complemented
24	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
25	C₂×#88071	—	2	1	no	—
26	C₂×#88071	C₄	1	2	yes	complemented
27	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	—	4	4	no	—
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×Dic₁₃	—	2	2	no	—
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂×C₁₃×M₁₆	—	2	2	no	—
46	C₂×C₁₃×M₁₆	—	4	4	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
49	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
50	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
51	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
52	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
53	C₂×C₂²⋊Dic₁₃	—	4	4	no	—
54	#88180	—	4	4	no	—
55	C₂×C₄⋊Dic₁₃	—	2	2	no	—
56	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	complemented
57	C₁₃×C₂²⋊C₈	—	2	2	no	—
58	C₁₃×C₂²⋊C₈	—	2	2	no	—
59	C₁₃×C₂²⋊C₈	—	2	2	no	—
60	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
61	#88071	—	2	2	no	—
62	#88071	—	2	2	no	—
63	#88071	—	2	2	no	—
64	#88071	—	2	2	no	—
65	#88071	—	2	2	no	—
66	#88071	C₂×C₄	1	4	yes	—
67	#7943	—	13	1	no	maximal, Sylow
68	C₂⁴×C₁₃	—	2	4	no	—
69	C₂⁴×C₁₃	—	4	2	no	—
70	C₂⁴×C₁₃	—	4	2	no	—
71	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	4	no	—
80	C₂²×C₄×C₁₃	—	4	2	no	—
81	C₂²×C₄×C₁₃	—	4	2	no	—
82	C₂²×C₄×C₁₃	—	4	2	no	—
83	C₂²×C₄×C₁₃	—	4	2	no	—
84	C₂²×C₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×Dic₁₃	—	2	4	no	—
121	C₂²×Dic₁₃	—	2	4	no	—
122	C₂²×Dic₁₃	—	4	4	no	—
123	C₂²×Dic₁₃	—	4	4	no	—
124	C₂²×Dic₁₃	—	4	4	no	—
125	C₁₃×M₁₆	—	4	4	no	—
126	C₁₃×M₁₆	—	4	4	no	—
127	C₂×C₈×C₁₃	—	2	4	no	—
128	C₂×C₈×C₁₃	—	4	4	no	—
129	C₂²⋊Dic₁₃	—	4	4	no	—
130	C₂²⋊Dic₁₃	—	4	4	no	—
131	C₂²⋊Dic₁₃	—	4	4	no	—
132	C₂²⋊Dic₁₃	—	4	4	no	—
133	C₂²⋊Dic₁₃	—	4	4	no	—
134	C₄⋊Dic₁₃	—	4	4	no	—
135	C₄×Dic₁₃	—	4	4	no	—
136	C₂×#407	D₁₃	1	1	yes	characteristic
137	#2280	—	13	1	no	—
138	C₂×#381	—	13	1	no	—
139	#1284	—	13	4	no	—
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	2	no	—
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	16	no	—
161	C₂³×C₁₃	#95	1	1	yes	characteristic
162	C₂³×C₁₃	#95	1	1	yes	characteristic
163	C₂³×C₁₃	#95	1	1	yes	characteristic
164	C₂³×C₁₃	#95	1	1	yes	characteristic
165	C₂³×C₁₃	#99	1	4	yes	—
166	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
198	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
199	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×Dic₁₃	—	4	4	no	—
206	C₂×Dic₁₃	—	4	4	no	—
207	C₂×Dic₁₃	—	4	4	no	—
208	C₂×Dic₁₃	—	4	4	no	—
209	C₂×Dic₁₃	—	4	4	no	—
210	C₂×Dic₁₃	—	4	4	no	—
211	C₂×Dic₁₃	—	8	8	no	—
212	C₈×C₁₃	—	4	4	no	—
213	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
214	C₂²×M₁₆	—	2	1	no	—
215	C₂×#117	—	13	2	no	—
216	C₂²×C₂²⋊C₄	—	26	1	no	—
217	#407	—	2	1	no	—
218	#407	—	2	1	no	—
219	#407	Dic₁₃	1	2	yes	complemented
220	#407	C₂×D₁₃	1	2	yes	—
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	complemented
223	#381	—	13	2	no	—
224	#381	—	13	2	no	—
225	#381	—	26	1	no	—
226	#381	—	26	1	no	—
227	#381	—	26	1	no	—
228	#380	—	26	1	no	—
229	#380	—	26	1	no	—
230	#379	—	26	1	no	—
231	C₄×C₂²⋊C₄	—	13	2	no	—
232	C₄×C₂²⋊C₄	—	13	2	no	—
233	C₂×#95	—	13	2	no	—
234	C₂×#95	—	26	1	no	—
235	C₂²×C₁₃	—	2	8	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	H(3,ℤ/4)	1	2	yes	—
259	C₂²×C₁₃	#342	1	2	yes	—
260	C₂²×C₁₃	#342	1	2	yes	—
261	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×#99	1	2	yes	—
263	C₂²×C₁₃	#421	1	2	yes	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	—	2	1	no	—
269	C₄×C₁₃	—	2	1	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	1	no	—
272	Dic₁₃	—	8	4	no	—
273	Dic₁₃	—	8	4	no	—
274	C₂⁵	D₅₂	1	1	yes	characteristic
275	C₂³×C₄	—	4	4	no	—
276	C₂³×C₄	—	26	2	no	—
277	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
278	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
279	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
280	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
281	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
283	C₂³×C₄	D₅₂	1	1	yes	characteristic
284	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
287	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
288	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
289	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	4	4	no	—
294	C₂²×C₈	—	2	2	no	—
295	#117	—	52	4	no	—
296	C₂×C₄⋊C₄	—	26	2	no	—
297	C₂×C₂²⋊C₄	—	26	2	no	—
298	C₂×C₂²⋊C₄	—	26	2	no	—
299	C₂×C₂²⋊C₄	—	26	2	no	—
300	C₂×C₂²⋊C₄	—	26	2	no	—
301	C₂×C₂²⋊C₄	—	26	2	no	—
302	C₂×C₂²⋊C₄	—	52	4	no	—
303	C₂×C₄²	—	13	4	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	complemented
308	#95	—	13	4	no	—
309	#95	—	26	2	no	—
310	#95	—	26	2	no	—
311	#95	—	26	2	no	—
312	#95	—	26	2	no	—
313	#95	—	26	2	no	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	2	2	no	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	2	2	no	—
318	C₂×C₁₃	—	2	2	no	—
319	C₂×C₁₃	—	4	1	no	—
320	C₂×C₁₃	—	4	1	no	—
321	C₂×C₁₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
322	C₂×C₁₃	#1733	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#342	1	1	yes	characteristic
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
328	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
329	C₂⁴	#6103	1	1	yes	characteristic
330	C₂⁴	#6103	1	1	yes	characteristic
331	C₂⁴	#6103	1	1	yes	characteristic
332	C₂⁴	#6103	1	1	yes	characteristic
333	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	26	4	no	—
349	C₂²×C₄	—	26	4	no	—
350	C₂²×C₄	—	52	4	no	—
351	C₂²×C₄	—	52	4	no	—
352	C₂²×C₄	—	52	4	no	—
353	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
357	C₂²×C₄	#6101	1	1	yes	characteristic
358	C₂²×C₄	#6101	1	1	yes	characteristic
359	C₂²×C₄	#6101	1	1	yes	characteristic
360	C₂²×C₄	#6101	1	1	yes	characteristic
361	C₂²×C₄	#6101	1	1	yes	characteristic
362	C₂²×C₄	#6101	1	1	yes	characteristic
363	C₂²×C₄	#6101	1	1	yes	characteristic
364	C₂²×C₄	#6101	1	1	yes	characteristic
365	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
367	C₂²×C₄	#6103	1	1	yes	characteristic
368	C₂²×C₄	#6103	1	1	yes	characteristic
369	C₂²×C₄	#6103	1	1	yes	characteristic
370	C₂²×C₄	#6103	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
381	M₁₆	—	4	4	no	—
382	M₁₆	—	4	4	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	4	4	no	—
385	C₄⋊C₄	—	52	4	no	—
386	C₂²⋊C₄	—	52	4	no	—
387	C₂²⋊C₄	—	52	4	no	—
388	C₂²⋊C₄	—	52	4	no	—
389	C₂²⋊C₄	—	52	4	no	—
390	C₂²⋊C₄	—	52	4	no	—
391	C₄²	—	52	4	no	—
392	C₁₃	#7943	1	1	yes	characteristic, complemented, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	16	no	—
414	C₂³	#88046	1	4	yes	—
415	C₂³	#88071	1	1	yes	characteristic
416	C₂³	#88071	1	1	yes	characteristic
417	C₂³	#88071	1	1	yes	characteristic
418	C₂³	#88071	1	1	yes	characteristic
419	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
420	C₂³	C₂×#6103	1	1	yes	characteristic
421	C₂³	C₂×#6103	1	1	yes	characteristic
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	52	4	no	—
451	C₂×C₄	—	52	4	no	—
452	C₂×C₄	—	52	4	no	—
453	C₂×C₄	—	52	4	no	—
454	C₂×C₄	—	52	4	no	—
455	C₂×C₄	—	52	4	no	—
456	C₂×C₄	—	104	8	no	—
457	C₂×C₄	#88071	1	1	yes	characteristic
458	C₂×C₄	#88071	1	1	yes	characteristic
459	C₂×C₄	#88071	1	1	yes	characteristic
460	C₂×C₄	#88071	1	1	yes	characteristic
461	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×#6101	1	1	yes	characteristic
463	C₂×C₄	C₂×#6101	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
465	C₈	—	4	4	no	—
466	C₂²	—	2	8	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	#11718119	1	2	yes	—
490	C₂²	#11718119	1	2	yes	—
491	C₂²	#11718149	1	2	yes	—
492	C₂²	C₂×#88046	1	2	yes	—
493	C₂²	#11718800	1	2	yes	—
494	C₂²	C₂×#88071	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	104	4	no	—
504	C₄	—	104	4	no	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	2	2	no	—
508	C₂	—	2	2	no	—
509	C₂	—	2	2	no	—
510	C₂	—	4	1	no	—
511	C₂	—	4	1	no	—
512	C₂	C₂×#11718149	1	1	yes	characteristic
513	C₂	#13114547	1	1	yes	characteristic
514	C₂	C₂×#11718119	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88071
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#407	C₂
socle	C₂²×C₁₃	C₂×#95
prime radical	C₂⁵×C₁₃	D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#407	D₁₃
hypocenter	C₁₃	#7943
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #13112690	C₂	semidirect
8. C₂×#88180	C₄	semidirect
11. C₁₃×#407	C₄	semidirect
14. C₂×C₁₃×C₂²⋊C₈	C₄	semidirect
21. #11718872	C₄	semidirect
23. C₄×C₂²⋊Dic₁₃	C₄	semidirect
26. C₂×#88071	C₄	semidirect
56. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
60. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
219. #407	Dic₁₃	semidirect
222. C₂×C₂²⋊C₈	Dic₁₃	semidirect
307. C₂²⋊C₈	C₂×Dic₁₃	semidirect
392. C₁₃	#7943	semidirect

Maximal subgroups

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

subgroup	index
#13117219	2
C₂×#11718872	2
#13112690	2
C₂×C₁₃×#407	2
#7943	13