Subgroups — #13123569

Order 1664.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718789	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#11718672	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718498	C₂	1	1	yes	maximal, characteristic, complemented
9	#11718497	C₂	1	1	yes	maximal, characteristic, complemented
10	#11718390	C₂	1	1	yes	maximal, characteristic, complemented
11	#11718387	C₂	1	1	yes	maximal, characteristic, complemented
12	#11718387	C₂	1	1	yes	maximal, characteristic, complemented
13	#11718386	C₂	1	1	yes	maximal, characteristic, complemented
14	#11718368	C₂	1	1	yes	maximal, characteristic, complemented
15	#11718367	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₃	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	D₄×Dic₁₃	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6099	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#1055	C₂²	1	1	yes	characteristic, complemented
27	M₁₆×D₁₃	—	2	4	no	—
28	C₂×#6094	—	2	4	no	—
29	C₂×#6094	C₂²	1	1	yes	characteristic
30	C₂×#6094	C₂²	1	1	yes	characteristic
31	C₂×#6094	C₂²	1	1	yes	characteristic
32	C₂×#6094	C₂²	1	1	yes	characteristic
33	C₂×#6094	C₂²	1	1	yes	characteristic, complemented
34	C₂×#6094	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
37	#88147	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₁₃	C₄	1	1	yes	characteristic
39	#88135	C₄	1	1	yes	characteristic
40	#88135	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₃	C₄	1	1	yes	characteristic
42	C₂²⋊C₄×D₁₃	C₄	1	1	yes	characteristic
43	C₄×D₅₂	C₂²	1	1	yes	characteristic
44	C₄²×D₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
51	#88060	C₂²	1	1	yes	characteristic, complemented
52	#88060	C₂²	1	1	yes	characteristic, complemented
53	#88060	C₂²	1	1	yes	characteristic, complemented
54	#88060	C₂²	1	1	yes	characteristic, complemented
55	#88054	C₂²	1	1	yes	characteristic, complemented
56	#88054	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
60	#88043	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	D₄×D₁₃	—	2	4	no	—
71	C₂×D₅₂	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₃	—	2	2	no	—
73	C₂×C₄×D₁₃	—	2	2	no	—
74	C₂×C₄×D₁₃	—	2	2	no	—
75	C₂×C₄×D₁₃	—	2	2	no	—
76	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	#6103	C₂×C₄	1	1	yes	characteristic
98	#6103	C₂×C₄	1	1	yes	characteristic
99	#6103	C₂×C₄	1	1	yes	characteristic
100	#6103	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
102	#6101	C₂×C₄	1	1	yes	characteristic
103	#6101	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
107	#6099	—	2	2	no	—
108	C₂×#1055	—	2	2	no	—
109	C₂×#1055	C₂³	1	1	yes	characteristic
110	C₂×#1055	C₂³	1	1	yes	characteristic
111	C₂×#1055	C₂³	1	1	yes	characteristic
112	C₂×#1055	C₂³	1	1	yes	characteristic
113	#6094	—	2	2	no	—
114	#6094	—	2	2	no	—
115	#6094	—	2	2	no	—
116	#6094	—	2	2	no	—
117	#6094	—	2	2	no	—
118	#6094	D₄	1	4	yes	complemented
119	C₈×D₁₃	—	2	2	no	—
120	C₈×D₁₃	—	2	2	no	—
121	D₄×M₁₆	—	13	1	no	maximal, Sylow
122	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₃	—	2	2	no	—
125	C₂²×D₁₃	—	2	2	no	—
126	C₂²×D₁₃	—	2	2	no	—
127	C₂²×D₁₃	—	2	2	no	—
128	C₂²×D₁₃	—	4	1	no	—
129	C₂²×D₁₃	—	4	1	no	—
130	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
133	D₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²⋊D₁₃	—	2	2	no	—
144	C₂²⋊D₁₃	M₁₆	1	4	yes	complemented
145	C₂×Dic₁₃	—	2	2	no	—
146	C₂×Dic₁₃	—	2	2	no	—
147	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	D₅₂	—	2	2	no	—
153	C₄×D₁₃	—	2	2	no	—
154	C₄×D₁₃	—	2	2	no	—
155	C₄×D₁₃	—	2	1	no	—
156	C₄×D₁₃	—	2	1	no	—
157	C₄×D₁₃	—	2	1	no	—
158	C₄×D₁₃	—	2	1	no	—
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	2	2	no	—
161	C₄×D₁₃	—	2	2	no	—
162	C₄×D₁₃	—	4	1	no	—
163	C₄×D₁₃	C₂×D₄	1	2	yes	—
164	C₄×D₁₃	#41	1	2	yes	—
165	C₈×C₁₃	—	2	1	no	—
166	C₈×C₁₃	—	2	1	no	—
167	C₈×C₁₃	—	2	1	no	—
168	C₈×C₁₃	C₂×D₄	1	2	yes	complemented
169	#1055	—	2	1	no	—
170	#1055	—	2	1	no	—
171	#1055	—	2	1	no	—
172	#1055	C₂×D₄	1	2	yes	complemented
173	C₂²×M₁₆	—	13	1	no	—
174	C₂²×M₁₆	—	13	1	no	—
175	C₂×C₄×D₄	—	13	1	no	—
176	#436	—	13	1	no	—
177	#436	—	13	1	no	—
178	#435	—	13	1	no	—
179	#435	—	13	1	no	—
180	#435	—	13	1	no	—
181	#435	D₁₃	1	1	yes	characteristic, complemented
182	C₈×D₄	—	13	1	no	—
183	C₈×D₄	—	13	1	no	—
184	#423	—	13	1	no	—
185	#407	—	13	1	no	—
186	#407	—	13	1	no	—
187	C₄×M₁₆	—	13	1	no	—
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	2	1	no	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	C₂×M₁₆	1	2	yes	complemented
194	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×D₁₃	—	2	1	no	—
196	C₂×D₁₃	—	2	1	no	—
197	C₂×D₁₃	—	2	1	no	—
198	C₂×D₁₃	—	2	1	no	—
199	C₂×D₁₃	—	2	1	no	—
200	C₂×D₁₃	—	2	1	no	—
201	C₂×D₁₃	—	2	1	no	—
202	C₂×D₁₃	—	4	4	no	—
203	C₂×D₁₃	—	4	4	no	—
204	C₂×D₁₃	C₄×D₄	1	2	yes	—
205	C₂×D₁₃	C₂×M₁₆	1	2	yes	complemented
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	Dic₁₃	—	2	1	no	—
213	Dic₁₃	—	2	1	no	—
214	Dic₁₃	—	2	1	no	—
215	Dic₁₃	C₄×D₄	1	2	yes	—
216	Dic₁₃	C₂×M₁₆	1	2	yes	complemented
217	C₂²×D₄	—	13	1	no	—
218	C₂³×C₄	—	13	1	no	—
219	C₂³×C₄	—	13	1	no	—
220	C₂×M₁₆	—	13	1	no	—
221	C₂×M₁₆	—	13	1	no	—
222	C₂×M₁₆	—	13	1	no	—
223	C₂×M₁₆	—	13	1	no	—
224	C₂×M₁₆	—	13	1	no	—
225	C₂×M₁₆	—	13	1	no	—
226	C₂×M₁₆	—	13	1	no	—
227	C₂×M₁₆	—	26	4	no	—
228	C₂×M₁₆	—	26	4	no	—
229	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
230	C₂²×C₈	—	13	1	no	—
231	C₂²×C₈	—	13	1	no	—
232	C₂²×C₈	—	13	1	no	—
233	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
234	C₄×D₄	—	13	1	no	—
235	C₄×D₄	—	13	1	no	—
236	C₄×D₄	—	13	1	no	—
237	C₄×D₄	—	13	1	no	—
238	C₄×D₄	—	13	1	no	—
239	C₄×D₄	—	13	1	no	—
240	C₄×D₄	—	13	1	no	—
241	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	13	1	no	—
243	C₂×C₂²⋊C₄	—	13	1	no	—
244	C₂×C₂²⋊C₄	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₄⋊C₈	—	13	1	no	—
247	C₄⋊C₈	—	13	1	no	—
248	C₄⋊C₈	—	13	1	no	—
249	C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
250	C₂²⋊C₈	—	13	1	no	—
251	C₂²⋊C₈	—	13	1	no	—
252	C₂²⋊C₈	—	13	1	no	—
253	C₂²⋊C₈	—	13	1	no	—
254	C₂²⋊C₈	—	13	1	no	—
255	C₂²⋊C₈	—	13	1	no	—
256	C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
257	C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
258	#97	—	13	1	no	—
259	#97	C₂×D₁₃	1	1	yes	characteristic, complemented
260	C₄×C₈	—	13	1	no	—
261	C₄×C₈	—	13	1	no	—
262	C₂×C₁₃	—	2	2	no	—
263	C₂×C₁₃	—	4	1	no	—
264	C₂×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
266	C₂×C₁₃	#568	1	1	yes	characteristic
267	D₁₃	—	2	2	no	—
268	D₁₃	—	2	2	no	—
269	D₁₃	—	4	1	no	—
270	C₂⁴	—	13	1	no	—
271	C₂⁴	—	13	1	no	—
272	C₂×D₄	—	13	1	no	—
273	C₂×D₄	—	13	1	no	—
274	C₂×D₄	—	13	1	no	—
275	C₂×D₄	—	26	4	no	—
276	C₂×D₄	C₄×D₁₃	1	1	yes	characteristic
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	26	2	no	—
289	C₂²×C₄	—	26	2	no	—
290	C₂²×C₄	—	26	2	no	—
291	C₂²×C₄	—	26	2	no	—
292	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
294	M₁₆	—	2	2	no	—
295	M₁₆	—	13	4	no	—
296	M₁₆	—	26	2	no	—
297	M₁₆	—	26	2	no	—
298	M₁₆	—	26	2	no	—
299	M₁₆	—	26	2	no	—
300	M₁₆	—	26	2	no	—
301	M₁₆	—	26	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	13	1	no	—
304	C₂×C₈	—	13	1	no	—
305	C₂×C₈	—	13	1	no	—
306	C₂×C₈	—	13	1	no	—
307	C₂×C₈	—	26	2	no	—
308	C₂×C₈	—	26	2	no	—
309	C₂×C₈	—	26	2	no	—
310	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
314	C₄⋊C₄	—	13	1	no	—
315	C₄⋊C₄	—	13	1	no	—
316	C₄⋊C₄	—	13	1	no	—
317	C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
318	C₂²⋊C₄	—	13	1	no	—
319	C₂²⋊C₄	—	13	1	no	—
320	C₂²⋊C₄	—	13	1	no	—
321	C₂²⋊C₄	—	13	1	no	—
322	C₂²⋊C₄	—	13	1	no	—
323	C₂²⋊C₄	—	13	1	no	—
324	C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
325	C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
326	C₄²	—	13	1	no	—
327	C₄²	—	13	1	no	—
328	C₄²	—	13	1	no	—
329	C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	C₁₃	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
331	C₂³	—	13	1	no	—
332	C₂³	—	13	1	no	—
333	C₂³	—	13	1	no	—
334	C₂³	—	26	2	no	—
335	C₂³	—	26	2	no	—
336	C₂³	—	26	2	no	—
337	C₂³	—	26	2	no	—
338	C₂³	—	52	1	no	—
339	C₂³	—	52	1	no	—
340	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	13	4	no	—
344	D₄	—	26	2	no	—
345	D₄	—	26	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	13	1	no	—
351	C₂×C₄	—	13	1	no	—
352	C₂×C₄	—	13	2	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	1	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	1	no	—
366	C₂×C₄	—	26	1	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	52	1	no	—
369	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	13	2	no	—
378	C₈	—	26	1	no	—
379	C₈	—	26	1	no	—
380	C₈	—	26	1	no	—
381	C₈	D₄×D₁₃	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	13	2	no	—
388	C₂²	—	13	2	no	—
389	C₂²	—	26	1	no	—
390	C₂²	—	26	1	no	—
391	C₂²	—	26	1	no	—
392	C₂²	—	26	1	no	—
393	C₂²	—	26	1	no	—
394	C₂²	—	26	1	no	—
395	C₂²	—	26	1	no	—
396	C₂²	—	52	4	no	—
397	C₂²	—	52	4	no	—
398	C₂²	M₁₆×D₁₃	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	13	2	no	—
405	C₄	—	13	2	no	—
406	C₄	—	26	1	no	—
407	C₄	—	26	1	no	—
408	C₄	—	26	1	no	—
409	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
410	C₄	#41×D₁₃	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	26	2	no	—
414	C₂	—	26	2	no	—
415	C₂	—	52	1	no	—
416	C₂	C₄×D₄×D₁₃	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₁₃	1	1	yes	characteristic
418	C₂	#11719455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₄
Fitting	C₁₃×#435	C₂
prime radical	C₂×D₄×D₁₃	C₄
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	#435	D₁₃
hypocenter	C₁₃	D₄×M₁₆
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₁₃	C₂	semidirect
2. C₂²×#6094	C₂	semidirect
4. C₁₃×#435	C₂	semidirect
5. #11718789	C₂	semidirect
6. C₈×C₂²⋊D₁₃	C₂	semidirect
7. #11718672	C₂	semidirect
8. #11718498	C₂	semidirect
9. #11718497	C₂	semidirect
10. #11718390	C₂	semidirect
11. #11718387	C₂	semidirect
12. #11718387	C₂	semidirect
13. #11718386	C₂	semidirect
14. #11718368	C₂	semidirect
15. #11718367	C₂	semidirect
19. C₂×C₁₃×M₁₆	C₂²	semidirect
20. C₂²×C₈×C₁₃	C₂²	semidirect
25. C₂×#6099	C₂²	semidirect
26. C₂²×#1055	C₂²	semidirect
33. C₂×#6094	C₂²	semidirect
34. C₂×#6094	C₂²	semidirect
35. C₂×C₈×D₁₃	C₂²	semidirect
36. C₂×C₈×D₁₃	C₂²	semidirect
45. C₁₃×C₄⋊C₈	C₂²	semidirect
46. C₁₃×C₂²⋊C₈	C₂²	semidirect
47. C₁₃×C₂²⋊C₈	C₂²	semidirect
48. C₁₃×#97	C₂²	semidirect
49. C₂²⋊#1055	C₂²	semidirect
50. C₂²⋊#1055	C₂²	semidirect
51. #88060	C₂²	semidirect
52. #88060	C₂²	semidirect
53. #88060	C₂²	semidirect
54. #88060	C₂²	semidirect
55. #88054	C₂²	semidirect
56. #88054	C₂²	semidirect
57. C₈×Dic₁₃	C₂²	semidirect
58. C₈×Dic₁₃	C₂²	semidirect
59. C₄⋊#1055	C₂²	semidirect
60. #88043	C₂²	semidirect
118. #6094	D₄	semidirect
144. C₂²⋊D₁₃	M₁₆	semidirect
168. C₈×C₁₃	C₂×D₄	semidirect
172. #1055	C₂×D₄	semidirect
181. #435	D₁₃	semidirect
193. C₂²×C₁₃	C₂×M₁₆	semidirect
205. C₂×D₁₃	C₂×M₁₆	semidirect
216. Dic₁₃	C₂×M₁₆	semidirect
229. C₂×M₁₆	C₂×D₁₃	semidirect
233. C₂²×C₈	C₂×D₁₃	semidirect
249. C₄⋊C₈	C₂×D₁₃	semidirect
256. C₂²⋊C₈	C₂×D₁₃	semidirect
257. C₂²⋊C₈	C₂×D₁₃	semidirect
259. #97	C₂×D₁₃	semidirect
330. C₁₃	D₄×M₁₆	semidirect
381. C₈	D₄×D₁₃	semidirect
398. C₂²	M₁₆×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₃	2
C₂²×#6094	2
C₄×D₄×D₁₃	2
C₁₃×#435	2
#11718789	2
C₈×C₂²⋊D₁₃	2
#11718672	2
#11718498	2
#11718497	2
#11718390	2
#11718387	2
#11718386	2
#11718368	2
#11718367	2
D₄×M₁₆	13