Subgroups — #15860835

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718500	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718500	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718369	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
5	#13117175	C₂	1	1	yes	maximal, characteristic
6	#13114693	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114692	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114692	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114691	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#88054	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114528	C₂	1	1	yes	maximal, characteristic
14	D₁₃×#336	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#6094	C₂²	1	1	yes	characteristic
17	C₂²×#6094	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88126	C₂²	1	1	yes	characteristic
21	C₂×#88126	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#376	C₂²	1	1	yes	characteristic
28	C₂×#88055	C₂²	1	1	yes	characteristic
29	C₂×#88055	C₂²	1	1	yes	characteristic
30	C₂×#88054	C₂²	1	1	yes	characteristic
31	C₂×#88054	C₂²	1	1	yes	characteristic
32	C₂×#88054	C₂²	1	1	yes	characteristic
33	C₂×#88054	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
36	#11718593	C₂²	1	1	yes	characteristic
37	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
38	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×#88043	C₂²	1	1	yes	characteristic
42	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
43	#11718500	C₄	1	8	yes	complemented
44	#11718500	C₄	1	8	yes	complemented
45	#11718369	—	2	4	no	—
46	#11718350	—	2	4	no	—
47	#11718327	C₄	1	2	yes	—
48	#11718327	C₄	1	2	yes	—
49	#11718310	C₄	1	2	yes	—
50	#11718310	C₄	1	2	yes	—
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	C₂²	1	1	yes	characteristic
53	#11718142	C₂²	1	1	yes	characteristic
54	#11718142	C₂²	1	1	yes	characteristic
55	#11718142	C₂²	1	1	yes	characteristic
56	#11718142	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×#6103	C₂×C₄	1	1	yes	characteristic
69	C₂×#6103	C₂×C₄	1	1	yes	characteristic
70	C₂×#6103	C₂×C₄	1	2	yes	—
71	C₂×#6101	C₂×C₄	1	1	yes	characteristic
72	C₂×#6101	C₂×C₄	1	1	yes	characteristic
73	C₂×#6101	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
77	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
78	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
79	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂²×#1055	C₂³	1	1	yes	characteristic
83	C₂²×#1055	C₂³	1	1	yes	characteristic
84	C₂²×#1055	C₂³	1	1	yes	characteristic
85	C₂²×#1055	C₂³	1	1	yes	characteristic
86	C₂×#6094	—	2	2	no	—
87	C₂×#6094	—	2	2	no	—
88	C₂×#6094	—	2	2	no	—
89	C₂×#6094	—	2	2	no	—
90	C₂×#6094	C₂×C₄	1	4	yes	—
91	C₂×#6094	C₂×C₄	1	4	yes	—
92	C₂×C₈×D₁₃	—	2	2	no	—
93	C₂×C₈×D₁₃	—	2	2	no	—
94	C₂×C₈×D₁₃	—	2	2	no	—
95	C₂×C₈×D₁₃	—	2	2	no	—
96	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
97	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
98	#88126	C₂×C₄	1	4	yes	—
99	#88126	C₂×C₄	1	4	yes	—
100	#88126	D₄	1	4	yes	—
101	#88126	Q₈	1	4	yes	—
102	C₄²×D₁₃	—	2	2	no	—
103	C₄²×D₁₃	—	2	2	no	—
104	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
105	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₁₃×#97	—	2	2	no	—
107	C₄×C₈×C₁₃	—	2	2	no	—
108	C₁₃×#95	C₂×C₄	1	2	yes	—
109	C₁₃×#95	C₂×C₄	1	2	yes	—
110	#88071	C₂×C₄	1	2	yes	—
111	#88071	C₂×C₄	1	2	yes	—
112	#88055	—	2	2	no	—
113	#88055	—	2	2	no	—
114	#88054	C₂×C₄	1	4	yes	complemented
115	#88054	C₂×C₄	1	4	yes	complemented
116	#88054	C₂×C₄	1	4	yes	complemented
117	#88054	C₂×C₄	1	4	yes	complemented
118	C₈×Dic₁₃	—	2	2	no	—
119	C₈×Dic₁₃	—	2	2	no	—
120	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
121	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
122	#88043	—	2	2	no	—
123	C₄×#1055	—	2	2	no	—
124	#20430	—	13	1	no	maximal, Sylow
125	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
134	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
135	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	—	2	4	no	—
137	C₂×C₄×D₁₃	—	2	4	no	—
138	C₂×C₄×D₁₃	—	4	2	no	—
139	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
140	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
141	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
142	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
143	C₂×C₄×D₁₃	#41	1	2	yes	—
144	C₂×C₄×D₁₃	#41	1	2	yes	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₁₃	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
163	#6103	C₄²	1	4	yes	—
164	#6103	C₄²	1	4	yes	—
165	#6103	C₄⋊C₄	1	8	yes	—
166	#6101	C₄²	1	4	yes	—
167	#6101	C₄²	1	4	yes	—
168	#6101	C₄⋊C₄	1	8	yes	—
169	C₄×Dic₁₃	—	2	1	no	—
170	C₄×Dic₁₃	—	2	1	no	—
171	C₄×Dic₁₃	—	2	4	no	—
172	C₄×Dic₁₃	—	2	4	no	—
173	C₄×Dic₁₃	—	2	4	no	—
174	C₄×Dic₁₃	—	4	2	no	—
175	C₄×Dic₁₃	—	4	2	no	—
176	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
177	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
178	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
179	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
180	C₂×#1055	—	2	1	no	—
181	C₂×#1055	—	2	1	no	—
182	C₂×#1055	—	2	1	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	1	no	—
185	C₂×#1055	—	2	1	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	C₂²×C₄	1	2	yes	—
189	C₂×#1055	C₂²×C₄	1	2	yes	—
190	C₂×#1055	C₂²×C₄	1	2	yes	—
191	C₂×#1055	C₂²×C₄	1	2	yes	—
192	#6094	—	2	8	no	—
193	#6094	—	2	8	no	—
194	C₈×D₁₃	—	2	8	no	—
195	C₈×D₁₃	—	2	8	no	—
196	C₂×#424	—	13	1	no	—
197	C₂×#424	—	13	1	no	—
198	C₂×#405	—	13	1	no	—
199	C₂×#405	—	13	1	no	—
200	C₄×#117	—	13	1	no	—
201	#1768	—	13	1	no	—
202	#1768	—	13	1	no	—
203	#1768	—	13	1	no	—
204	#1768	D₁₃	1	1	yes	characteristic, complemented
205	#1767	—	13	1	no	—
206	#1767	—	13	1	no	—
207	C₄×C₄⋊C₈	—	13	1	no	—
208	C₄×C₄⋊C₈	—	13	1	no	—
209	#1728	—	13	1	no	—
210	C₂×#336	—	13	1	no	—
211	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
212	C₂²×D₁₃	—	2	2	no	—
213	C₂²×D₁₃	—	2	2	no	—
214	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
215	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
216	C₂²×D₁₃	#117	1	2	yes	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
227	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×Dic₁₃	—	2	2	no	—
234	C₂×Dic₁₃	—	2	2	no	—
235	C₂×Dic₁₃	—	2	2	no	—
236	C₂×Dic₁₃	—	2	2	no	—
237	C₂×Dic₁₃	—	2	2	no	—
238	C₂×Dic₁₃	—	2	2	no	—
239	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
240	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
241	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
242	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
243	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
244	C₂×Dic₁₃	#117	1	2	yes	—
245	C₂×Dic₁₃	#131	1	4	yes	—
246	C₄×D₁₃	—	4	8	no	—
247	C₄×D₁₃	C₄×D₄	1	4	yes	—
248	C₄×D₁₃	C₄×D₄	1	4	yes	—
249	C₄×D₁₃	C₄×Q₈	1	4	yes	—
250	C₄×D₁₃	C₄×Q₈	1	4	yes	—
251	C₈×C₁₃	—	2	2	no	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	—	2	2	no	—
254	C₈×C₁₃	—	2	2	no	—
255	#1055	—	2	2	no	—
256	#1055	—	2	2	no	—
257	#1055	—	2	2	no	—
258	#1055	—	2	2	no	—
259	C₂²×M₁₆	—	13	1	no	—
260	C₂²×M₁₆	—	13	1	no	—
261	C₂³×C₈	—	13	1	no	—
262	C₂³×C₈	—	13	1	no	—
263	C₂×#117	—	13	1	no	—
264	C₂×#117	—	13	1	no	—
265	C₂²×C₄²	—	13	1	no	—
266	#424	—	13	8	no	—
267	#424	—	13	8	no	—
268	C₂×C₄⋊C₈	—	13	1	no	—
269	C₂×C₄⋊C₈	—	13	1	no	—
270	C₂×C₄⋊C₈	—	13	1	no	—
271	C₂×C₄⋊C₈	—	13	1	no	—
272	C₂×C₄⋊C₈	—	13	1	no	—
273	C₂×C₄⋊C₈	—	13	1	no	—
274	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
276	#405	—	26	4	no	—
277	#405	—	26	4	no	—
278	C₂×#97	—	13	1	no	—
279	C₂×#97	—	13	1	no	—
280	C₂×#97	—	13	1	no	—
281	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
282	C₂×C₄×C₈	—	13	1	no	—
283	C₂×C₄×C₈	—	13	1	no	—
284	C₂×C₄×C₈	—	13	1	no	—
285	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
286	C₄×C₄⋊C₄	—	13	2	no	—
287	C₄×C₄⋊C₄	—	13	2	no	—
288	C₄×C₂²⋊C₄	—	13	2	no	—
289	C₄×C₂²⋊C₄	—	13	2	no	—
290	#376	—	13	1	no	—
291	#376	C₂×D₁₃	1	1	yes	characteristic
292	C₄³	—	13	1	no	—
293	C₄³	—	13	1	no	—
294	#336	—	13	1	no	—
295	#336	—	13	1	no	—
296	#336	—	13	1	no	—
297	#336	—	13	1	no	—
298	#336	—	13	1	no	—
299	#336	—	13	1	no	—
300	#336	C₂×D₁₃	1	1	yes	characteristic
301	#336	C₂×D₁₃	1	1	yes	characteristic
302	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
303	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
304	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
305	C₂²×C₁₃	C₂×#131	1	2	yes	—
306	C₂²×C₁₃	#568	1	2	yes	—
307	C₂×D₁₃	—	2	2	no	—
308	C₂×D₁₃	—	2	2	no	—
309	C₂×D₁₃	—	2	4	no	—
310	C₂×D₁₃	—	2	4	no	—
311	C₂×D₁₃	C₄×C₄⋊C₄	1	4	yes	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
317	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
319	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
320	Dic₁₃	—	2	2	no	—
321	Dic₁₃	—	2	2	no	—
322	Dic₁₃	—	2	4	no	—
323	Dic₁₃	—	2	4	no	—
324	Dic₁₃	C₄×C₄⋊C₄	1	4	yes	—
325	C₂³×C₄	—	13	1	no	—
326	C₂³×C₄	—	13	2	no	—
327	C₂×M₁₆	—	13	4	no	—
328	C₂×M₁₆	—	13	4	no	—
329	C₂×M₁₆	—	26	2	no	—
330	C₂×M₁₆	—	26	2	no	—
331	C₂×M₁₆	—	26	2	no	—
332	C₂×M₁₆	—	26	2	no	—
333	C₂²×C₈	—	13	1	no	—
334	C₂²×C₈	—	13	1	no	—
335	C₂²×C₈	—	13	1	no	—
336	C₂²×C₈	—	13	1	no	—
337	C₂²×C₈	—	13	4	no	—
338	C₂²×C₈	—	13	4	no	—
339	C₂²×C₈	—	26	2	no	—
340	C₂²×C₈	—	26	2	no	—
341	C₂²×C₈	—	26	2	no	—
342	C₂²×C₈	—	26	2	no	—
343	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
347	#117	—	13	4	no	—
348	#117	—	13	4	no	—
349	#117	—	13	4	no	—
350	#117	—	13	4	no	—
351	C₂×C₄⋊C₄	—	13	1	no	—
352	C₂×C₄⋊C₄	—	13	1	no	—
353	C₂×C₄⋊C₄	—	13	2	no	—
354	C₂×C₂²⋊C₄	—	13	1	no	—
355	C₂×C₂²⋊C₄	—	13	1	no	—
356	C₂×C₂²⋊C₄	—	13	2	no	—
357	C₂×C₄²	—	13	1	no	—
358	C₂×C₄²	—	13	1	no	—
359	C₂×C₄²	—	13	2	no	—
360	C₂×C₄²	—	13	2	no	—
361	C₂×C₄²	—	13	2	no	—
362	C₂×C₄²	—	13	1	no	—
363	C₂×C₄²	—	13	2	no	—
364	C₂×C₄²	—	13	2	no	—
365	C₂×C₄²	—	26	2	no	—
366	C₂×C₄²	—	26	2	no	—
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
370	C₄⋊C₈	—	13	4	no	—
371	C₄⋊C₈	—	13	4	no	—
372	C₄⋊C₈	—	13	4	no	—
373	C₄⋊C₈	—	13	4	no	—
374	C₄⋊C₈	—	13	4	no	—
375	C₄⋊C₈	—	13	4	no	—
376	C₄⋊C₈	C₄×D₁₃	1	4	yes	complemented
377	C₄⋊C₈	C₄×D₁₃	1	4	yes	complemented
378	#97	—	2	2	no	—
379	#97	—	26	2	no	—
380	#97	—	26	2	no	—
381	#97	—	26	2	no	—
382	C₄×C₈	—	2	2	no	—
383	C₄×C₈	—	26	2	no	—
384	C₄×C₈	—	26	2	no	—
385	C₄×C₈	—	26	2	no	—
386	#95	—	13	2	no	—
387	#95	—	13	2	no	—
388	#95	C₄×D₁₃	1	2	yes	—
389	#95	C₄×D₁₃	1	2	yes	—
390	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
391	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
392	C₂×C₁₃	#2875	1	1	yes	characteristic
393	C₂×C₁₃	#2906	1	2	yes	—
394	C₂×C₁₃	#2924	1	2	yes	—
395	D₁₃	—	2	4	no	—
396	C₂⁴	—	13	1	no	—
397	C₂²×C₄	—	13	1	no	—
398	C₂²×C₄	—	13	2	no	—
399	C₂²×C₄	—	13	2	no	—
400	C₂²×C₄	—	13	2	no	—
401	C₂²×C₄	—	13	2	no	—
402	C₂²×C₄	—	13	2	no	—
403	C₂²×C₄	—	13	2	no	—
404	C₂²×C₄	—	13	1	no	—
405	C₂²×C₄	—	13	1	no	—
406	C₂²×C₄	—	13	2	no	—
407	C₂²×C₄	—	13	2	no	—
408	C₂²×C₄	—	26	4	no	—
409	C₂²×C₄	—	26	4	no	—
410	C₂²×C₄	—	52	2	no	—
411	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
412	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
415	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
416	M₁₆	—	26	8	no	—
417	M₁₆	—	26	8	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	13	2	no	—
427	C₂×C₈	—	13	2	no	—
428	C₂×C₈	—	13	2	no	—
429	C₂×C₈	—	13	2	no	—
430	C₂×C₈	—	26	8	no	—
431	C₂×C₈	—	26	8	no	—
432	C₂×C₈	—	26	1	no	—
433	C₂×C₈	—	26	1	no	—
434	C₂×C₈	—	26	1	no	—
435	C₂×C₈	—	26	1	no	—
436	C₂×C₈	—	26	1	no	—
437	C₂×C₈	—	26	1	no	—
438	C₂×C₈	—	26	1	no	—
439	C₂×C₈	—	26	1	no	—
440	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
441	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
442	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
443	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
444	C₄⋊C₄	—	13	4	no	—
445	C₄⋊C₄	—	13	4	no	—
446	C₄⋊C₄	—	13	8	no	—
447	C₂²⋊C₄	—	13	4	no	—
448	C₂²⋊C₄	—	13	4	no	—
449	C₂²⋊C₄	—	13	8	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	13	2	no	—
453	C₄²	—	13	2	no	—
454	C₄²	—	13	2	no	—
455	C₄²	—	13	2	no	—
456	C₄²	—	26	4	no	—
457	C₄²	—	26	4	no	—
458	C₄²	—	26	4	no	—
459	C₄²	—	26	1	no	—
460	C₄²	—	26	1	no	—
461	C₄²	—	52	2	no	—
462	C₄²	—	52	2	no	—
463	C₄²	C₂×C₄×D₁₃	1	2	yes	—
464	C₄²	C₂×C₄×D₁₃	1	2	yes	—
465	C₄²	D₄×D₁₃	1	2	yes	—
466	C₄²	Q₈×D₁₃	1	2	yes	—
467	C₁₃	#20430	1	1	yes	characteristic, complemented, Sylow
468	C₂³	—	13	2	no	—
469	C₂³	—	13	2	no	—
470	C₂³	—	13	2	no	—
471	C₂³	—	26	2	no	—
472	C₂³	—	26	2	no	—
473	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	13	2	no	—
482	C₂×C₄	—	13	2	no	—
483	C₂×C₄	—	13	2	no	—
484	C₂×C₄	—	13	4	no	—
485	C₂×C₄	—	13	4	no	—
486	C₂×C₄	—	13	4	no	—
487	C₂×C₄	—	13	4	no	—
488	C₂×C₄	—	13	2	no	—
489	C₂×C₄	—	13	2	no	—
490	C₂×C₄	—	13	4	no	—
491	C₂×C₄	—	13	4	no	—
492	C₂×C₄	—	26	2	no	—
493	C₂×C₄	—	26	2	no	—
494	C₂×C₄	—	26	2	no	—
495	C₂×C₄	—	26	2	no	—
496	C₂×C₄	—	26	2	no	—
497	C₂×C₄	—	26	2	no	—
498	C₂×C₄	—	52	8	no	—
499	C₂×C₄	C₄²×D₁₃	1	2	yes	—
500	C₂×C₄	C₄²×D₁₃	1	2	yes	—
501	C₂×C₄	C₄⋊C₄×D₁₃	1	4	yes	—
502	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
506	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
507	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₈	—	2	2	no	—
512	C₈	—	26	2	no	—
513	C₈	—	26	2	no	—
514	C₈	—	26	2	no	—
515	C₈	—	26	2	no	—
516	C₂²	—	13	4	no	—
517	C₂²	—	26	4	no	—
518	C₂²	—	26	4	no	—
519	C₂²	—	26	2	no	—
520	C₂²	—	26	2	no	—
521	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
522	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
523	C₂²	D₁₃×#117	1	1	yes	characteristic
524	C₂²	D₁₃×#131	1	2	yes	—
525	C₂²	#11719455	1	2	yes	—
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	13	4	no	—
531	C₄	—	26	4	no	—
532	C₄	—	26	4	no	—
533	C₄	—	26	2	no	—
534	C₄	—	26	2	no	—
535	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
536	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
537	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
538	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
539	C₂	—	26	4	no	—
540	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
541	C₂	#13123258	1	1	yes	characteristic
542	C₂	#13123263	1	1	yes	characteristic
543	C₂	#13123403	1	2	yes	—
544	C₂	#13123492	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1768	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1768	D₁₃
hypocenter	C₁₃	#20430
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1768

Complements

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

N	H ≅ G/N	type
6. #13114693	C₂	semidirect
7. #13114692	C₂	semidirect
8. #13114692	C₂	semidirect
9. #13114691	C₂	semidirect
10. #13114690	C₂	semidirect
11. C₄⋊C₈×Dic₁₃	C₂	semidirect
12. C₄×#88054	C₂	semidirect
15. C₁₃×#1768	C₂	semidirect
43. #11718500	C₄	semidirect
44. #11718500	C₄	semidirect
104. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
105. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
114. #88054	C₂×C₄	semidirect
115. #88054	C₂×C₄	semidirect
116. #88054	C₂×C₄	semidirect
117. #88054	C₂×C₄	semidirect
120. C₄⋊#1055	C₂×C₄	semidirect
121. C₄⋊#1055	C₂×C₄	semidirect
204. #1768	D₁₃	semidirect
376. C₄⋊C₈	C₄×D₁₃	semidirect
377. C₄⋊C₈	C₄×D₁₃	semidirect
467. C₁₃	#20430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718500	2
C₂×#11718369	2
C₂×#11718350	2
#13117175	2
#13114693	2
#13114692	2
#13114691	2
#13114690	2
C₄⋊C₈×Dic₁₃	2
C₄×#88054	2
#13114528	2
D₁₃×#336	2
C₁₃×#1768	2
#20430	13