Subgroups — #15832172

Order 3328.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123798	C₂	1	1	yes	maximal, characteristic
2	#13123503	C₂	1	1	yes	maximal, characteristic
3	#13123405	C₂	1	1	yes	maximal, characteristic
4	#13113627	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113626	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113622	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113618	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113609	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113605	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113600	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113588	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113587	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88161	—	2	1	no	—
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₁₃×#432	C₂²	1	1	yes	characteristic
19	C₁₃×#423	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	#11718789	C₄	1	1	yes	characteristic
22	#11718789	C₄	1	1	yes	characteristic
23	#11718788	C₄	1	1	yes	characteristic
24	#11718788	C₄	1	1	yes	characteristic
25	#11718780	—	2	1	no	—
26	#11718586	C₂²	1	1	yes	characteristic
27	#11718586	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
29	#11718500	—	2	1	no	—
30	#11718500	—	2	1	no	—
31	#11718498	C₂²	1	1	yes	characteristic
32	#11718498	C₂²	1	1	yes	characteristic
33	#11718498	C₂²	1	1	yes	characteristic
34	#11718496	C₂²	1	1	yes	characteristic
35	#11718494	C₂²	1	1	yes	characteristic
36	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	#11718388	—	2	1	no	—
40	#11718381	—	2	1	no	—
41	#11718370	—	2	1	no	—
42	#11718369	—	2	1	no	—
43	#11718367	C₄	1	1	yes	characteristic
44	#11718367	C₄	1	1	yes	characteristic
45	#11718362	C₄	1	1	yes	characteristic
46	#11718362	C₄	1	1	yes	characteristic
47	C₄×#6094	C₂²	1	1	yes	characteristic
48	#11718346	C₂²	1	1	yes	characteristic
49	#11718346	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×#335	C₂²	1	1	yes	characteristic
53	C₁₃×#334	C₂²	1	1	yes	characteristic
54	C₁₃×#334	C₂²	1	1	yes	characteristic
55	#11718072	C₂²	1	1	yes	characteristic
56	#11718072	C₂²	1	1	yes	characteristic
57	#11718072	C₂²	1	1	yes	characteristic
58	#11718072	C₂²	1	1	yes	characteristic
59	#11718071	C₂²	1	1	yes	characteristic
60	#11718071	C₂²	1	1	yes	characteristic
61	#11718071	C₂²	1	1	yes	characteristic
62	#11718071	C₂²	1	1	yes	characteristic
63	#11718050	C₂²	1	1	yes	characteristic
64	#11718050	C₂²	1	1	yes	characteristic
65	#11718049	C₂²	1	1	yes	characteristic
66	#11718049	C₂²	1	1	yes	characteristic
67	C₂×#6127	D₄	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
76	#88180	D₄	1	1	yes	characteristic
77	C₂²×#1055	—	2	1	no	—
78	#88161	—	4	4	no	—
79	C₂×#6094	—	2	1	no	—
80	C₂×#6094	—	2	1	no	—
81	C₂×#6094	—	2	1	no	—
82	C₂×#6094	C₂×C₄	1	1	yes	characteristic
83	C₂×#6094	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₁₃	—	2	1	no	—
85	C₂×C₈×D₁₃	—	2	1	no	—
86	C₂×C₈×D₁₃	—	2	1	no	—
87	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
90	C₄×D₅₂	Q₈	1	1	yes	characteristic
91	#88126	D₄	1	1	yes	characteristic
92	#88126	D₄	1	1	yes	characteristic
93	C₄²×D₁₃	C₂³	1	1	yes	characteristic
94	C₄²×D₁₃	C₂³	1	1	yes	characteristic
95	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₁₃×C₂²⋊C₈	—	2	1	no	—
103	C₁₃×#97	—	2	1	no	—
104	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²⋊#1055	—	2	1	no	—
109	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
111	#88060	—	2	1	no	—
112	#88060	—	2	1	no	—
113	#88060	C₂×C₄	1	1	yes	characteristic
114	#88060	C₂×C₄	1	1	yes	characteristic
115	#88060	C₂×C₄	1	1	yes	characteristic
116	#88060	C₂×C₄	1	1	yes	characteristic
117	#88055	—	2	1	no	—
118	#88055	C₂×C₄	1	1	yes	characteristic
119	#88055	C₂×C₄	1	1	yes	characteristic
120	#88054	—	2	1	no	—
121	#88054	—	2	1	no	—
122	#88054	—	2	1	no	—
123	#88054	—	2	1	no	—
124	#88054	—	2	1	no	—
125	#88054	—	2	1	no	—
126	#88054	C₂×C₄	1	1	yes	characteristic
127	#88054	C₂×C₄	1	1	yes	characteristic
128	#88054	C₂×C₄	1	1	yes	characteristic
129	#88054	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₁₃	—	2	1	no	—
131	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
133	C₄⋊#1055	—	2	1	no	—
134	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#1055	C₂³	1	1	yes	characteristic
137	C₄⋊#1055	C₂³	1	1	yes	characteristic
138	C₄⋊#1055	C₂³	1	1	yes	characteristic
139	C₄⋊#1055	C₂³	1	1	yes	characteristic
140	C₄×#1055	—	2	1	no	—
141	C₄×#1055	C₂³	1	1	yes	characteristic
142	C₄×#1055	C₂³	1	1	yes	characteristic
143	#17830	—	13	1	no	maximal, Sylow
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
149	#6127	—	2	2	no	—
150	#6127	—	2	2	no	—
151	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
158	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
159	C₁₃×M₁₆	—	2	2	no	—
160	C₁₃×M₁₆	—	4	1	no	—
161	C₁₃×M₁₆	—	4	2	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
173	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
176	#6103	C₄⋊C₄	1	1	yes	characteristic
177	#6103	C₄⋊C₄	1	1	yes	characteristic
178	#6103	C₄⋊C₄	1	1	yes	characteristic
179	#6103	C₄⋊C₄	1	1	yes	characteristic
180	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
181	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
182	#6101	C₄⋊C₄	1	1	yes	characteristic
183	#6101	C₄⋊C₄	1	1	yes	characteristic
184	#6101	C₄⋊C₄	1	1	yes	characteristic
185	#6101	C₄⋊C₄	1	1	yes	characteristic
186	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
189	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
191	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	C₂×#1055	—	2	1	no	—
195	C₂×#1055	—	2	1	no	—
196	C₂×#1055	—	4	2	no	—
197	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
198	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
199	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
200	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
201	#6094	—	2	2	no	—
202	#6094	—	4	1	no	—
203	#6094	—	4	2	no	—
204	#6094	—	4	2	no	—
205	#6094	—	4	2	no	—
206	C₈×D₁₃	—	2	2	no	—
207	C₈×D₁₃	—	4	1	no	—
208	C₈×D₁₃	—	4	2	no	—
209	C₈×D₁₃	—	4	2	no	—
210	C₈×D₁₃	—	4	2	no	—
211	#2965	—	13	1	no	—
212	#2925	—	13	1	no	—
213	#2906	—	13	1	no	—
214	#1574	—	13	1	no	—
215	#1574	—	13	1	no	—
216	#1573	—	13	1	no	—
217	#1573	—	13	1	no	—
218	#1571	—	13	1	no	—
219	#1570	—	13	1	no	—
220	#1569	—	13	1	no	—
221	#1569	D₁₃	1	1	yes	characteristic, complemented
222	#1567	—	13	1	no	—
223	#1565	—	13	1	no	—
224	#1565	—	13	1	no	—
225	C₂×#334	—	13	1	no	—
226	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
240	C₂²⋊D₁₃	—	2	2	no	—
241	C₂²⋊D₁₃	—	2	2	no	—
242	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
248	D₅₂	—	2	2	no	—
249	C₄×D₁₃	—	2	1	no	—
250	C₄×D₁₃	—	2	1	no	—
251	C₄×D₁₃	—	2	1	no	—
252	C₄×D₁₃	—	2	1	no	—
253	C₄×D₁₃	—	2	1	no	—
254	C₄×D₁₃	—	2	1	no	—
255	C₄×D₁₃	—	4	1	no	—
256	C₄×D₁₃	—	4	1	no	—
257	C₄×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
258	C₄×D₁₃	#137	1	2	yes	—
259	Dic₂₆	—	2	2	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	#131	1	2	yes	complemented
268	#1055	—	2	1	no	—
269	#1055	—	2	1	no	—
270	#1055	—	2	1	no	—
271	#1055	—	2	1	no	—
272	#1055	—	4	1	no	—
273	#1055	—	4	1	no	—
274	#1055	—	4	1	no	—
275	#1055	—	4	1	no	—
276	C₂×#131	—	26	1	no	—
277	C₄×#41	—	13	1	no	—
278	#446	—	13	1	no	—
279	#446	—	13	1	no	—
280	#436	—	13	1	no	—
281	#436	—	13	1	no	—
282	#435	—	13	1	no	—
283	#435	—	13	1	no	—
284	#435	—	13	1	no	—
285	#435	—	13	1	no	—
286	#433	—	26	1	no	—
287	#433	—	26	1	no	—
288	#432	—	13	1	no	—
289	#432	C₂×D₁₃	1	1	yes	characteristic
290	#431	—	13	1	no	—
291	#431	—	13	1	no	—
292	#431	—	13	1	no	—
293	#431	—	13	1	no	—
294	#431	—	13	1	no	—
295	#424	—	26	1	no	—
296	#424	—	26	1	no	—
297	#424	—	26	1	no	—
298	#423	—	13	1	no	—
299	#423	—	13	1	no	—
300	#423	—	13	1	no	—
301	#423	C₂×D₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₈	—	13	1	no	—
303	C₂×C₄⋊C₈	—	13	1	no	—
304	C₂×C₄⋊C₈	—	13	1	no	—
305	C₂×C₄⋊C₈	—	13	1	no	—
306	#408	—	26	1	no	—
307	#405	—	26	1	no	—
308	C₄×M₁₆	—	13	1	no	—
309	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
310	C₂×C₄×C₈	—	13	1	no	—
311	#335	—	13	1	no	—
312	#335	—	13	1	no	—
313	#335	—	13	1	no	—
314	#335	—	13	1	no	—
315	#335	—	13	1	no	—
316	#335	—	13	1	no	—
317	#335	C₂×D₁₃	1	1	yes	characteristic
318	#335	C₂×D₁₃	1	1	yes	characteristic
319	#334	—	13	1	no	—
320	#334	—	13	1	no	—
321	#334	—	13	1	no	—
322	#334	—	13	1	no	—
323	#334	—	13	1	no	—
324	#334	—	13	1	no	—
325	#334	C₂×D₁₃	1	1	yes	characteristic
326	#334	C₂×D₁₃	1	1	yes	characteristic
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	1	no	—
334	C₂×D₁₃	—	2	1	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	#428	1	2	yes	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
342	C₄×C₁₃	#568	1	1	yes	characteristic
343	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	#428	1	2	yes	—
351	C₂×#41	—	13	1	no	—
352	#131	—	52	4	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	13	1	no	—
355	C₂×M₁₆	—	13	1	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	—	26	1	no	—
358	C₂×M₁₆	—	26	1	no	—
359	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
360	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
361	C₂²×C₈	—	13	1	no	—
362	C₂²×C₈	—	13	1	no	—
363	C₂²×C₈	—	26	1	no	—
364	C₂²×C₈	—	26	1	no	—
365	C₂²×C₈	—	26	1	no	—
366	C₂²×C₈	—	26	1	no	—
367	C₄×Q₈	—	13	1	no	—
368	C₄×Q₈	—	13	1	no	—
369	C₄×D₄	—	13	1	no	—
370	C₄×D₄	—	13	1	no	—
371	C₄×D₄	—	13	1	no	—
372	C₄×D₄	—	13	1	no	—
373	C₄×D₄	—	13	1	no	—
374	C₄×D₄	—	13	1	no	—
375	#117	—	13	1	no	—
376	#117	—	13	1	no	—
377	#117	—	13	1	no	—
378	C₂×C₄²	—	13	1	no	—
379	C₂×C₄²	—	13	1	no	—
380	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	13	1	no	—
383	C₄⋊C₈	—	13	1	no	—
384	C₄⋊C₈	—	13	1	no	—
385	C₄⋊C₈	—	13	1	no	—
386	C₄⋊C₈	—	13	1	no	—
387	C₄⋊C₈	—	13	1	no	—
388	C₄⋊C₈	—	13	1	no	—
389	C₄⋊C₈	—	13	1	no	—
390	C₄⋊C₈	—	13	1	no	—
391	C₄⋊C₈	—	13	1	no	—
392	C₄⋊C₈	—	26	1	no	—
393	C₄⋊C₈	—	26	1	no	—
394	C₄⋊C₈	—	26	1	no	—
395	C₄⋊C₈	—	26	1	no	—
396	C₄⋊C₈	—	26	1	no	—
397	C₄⋊C₈	—	26	1	no	—
398	C₄⋊C₈	—	26	1	no	—
399	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
401	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	13	1	no	—
405	C₂²⋊C₈	—	13	1	no	—
406	C₂²⋊C₈	—	13	1	no	—
407	C₂²⋊C₈	—	13	1	no	—
408	C₂²⋊C₈	—	13	1	no	—
409	C₂²⋊C₈	—	13	1	no	—
410	C₂²⋊C₈	—	26	1	no	—
411	C₂²⋊C₈	—	26	1	no	—
412	C₂²⋊C₈	—	26	1	no	—
413	#97	—	2	1	no	—
414	#97	—	13	1	no	—
415	#97	—	13	1	no	—
416	#97	—	26	1	no	—
417	#97	C₄×D₁₃	1	1	yes	characteristic
418	#97	C₄×D₁₃	1	1	yes	characteristic
419	C₄×C₈	—	13	1	no	—
420	C₄×C₈	—	13	1	no	—
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	13	1	no	—
423	C₄×C₈	—	26	1	no	—
424	C₄×C₈	—	26	1	no	—
425	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
427	C₂×C₁₃	—	4	1	no	—
428	C₂×C₁₃	#2906	1	1	yes	characteristic
429	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
430	C₂×C₁₃	#2916	1	1	yes	characteristic
431	D₁₃	—	2	2	no	—
432	D₁₃	—	4	1	no	—
433	#41	—	26	2	no	—
434	#41	—	26	2	no	—
435	C₂×Q₈	—	13	1	no	—
436	C₂×D₄	—	13	1	no	—
437	C₂×D₄	—	13	1	no	—
438	C₂×D₄	—	13	1	no	—
439	C₂²×C₄	—	13	1	no	—
440	C₂²×C₄	—	13	1	no	—
441	C₂²×C₄	—	13	1	no	—
442	C₂²×C₄	—	13	1	no	—
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
446	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
447	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
448	M₁₆	—	2	2	no	—
449	M₁₆	—	4	1	no	—
450	M₁₆	—	4	2	no	—
451	M₁₆	—	26	2	no	—
452	M₁₆	—	52	1	no	—
453	M₁₆	—	52	2	no	—
454	M₁₆	—	52	2	no	—
455	M₁₆	—	52	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	13	1	no	—
461	C₂×C₈	—	13	1	no	—
462	C₂×C₈	—	13	1	no	—
463	C₂×C₈	—	13	1	no	—
464	C₂×C₈	—	26	2	no	—
465	C₂×C₈	—	26	1	no	—
466	C₂×C₈	—	26	1	no	—
467	C₂×C₈	—	26	1	no	—
468	C₂×C₈	—	26	1	no	—
469	C₂×C₈	—	52	1	no	—
470	C₂×C₈	—	52	2	no	—
471	C₂×C₈	—	52	2	no	—
472	C₂×C₈	—	52	2	no	—
473	C₂×C₈	—	52	2	no	—
474	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	1	no	—
480	C₄⋊C₄	—	13	1	no	—
481	C₄⋊C₄	—	13	1	no	—
482	C₄⋊C₄	—	13	1	no	—
483	C₄⋊C₄	—	13	1	no	—
484	C₂²⋊C₄	—	13	1	no	—
485	C₂²⋊C₄	—	13	1	no	—
486	C₂²⋊C₄	—	13	1	no	—
487	C₂²⋊C₄	—	13	1	no	—
488	C₂²⋊C₄	—	13	1	no	—
489	C₂²⋊C₄	—	13	1	no	—
490	C₄²	—	13	1	no	—
491	C₄²	—	13	1	no	—
492	C₄²	—	13	1	no	—
493	C₄²	—	13	1	no	—
494	C₄²	—	13	1	no	—
495	C₄²	—	13	1	no	—
496	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
497	C₄²	D₄×D₁₃	1	1	yes	characteristic
498	C₄²	Q₈×D₁₃	1	1	yes	characteristic
499	C₄²	C₂³×D₁₃	1	1	yes	characteristic
500	C₁₃	#17830	1	1	yes	characteristic, complemented, Sylow
501	C₂³	—	13	1	no	—
502	C₂³	—	13	1	no	—
503	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
504	Q₈	—	26	2	no	—
505	D₄	—	26	2	no	—
506	D₄	—	26	2	no	—
507	D₄	—	26	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	13	1	no	—
514	C₂×C₄	—	13	2	no	—
515	C₂×C₄	—	13	2	no	—
516	C₂×C₄	—	13	1	no	—
517	C₂×C₄	—	13	1	no	—
518	C₂×C₄	—	13	1	no	—
519	C₂×C₄	—	13	1	no	—
520	C₂×C₄	—	13	1	no	—
521	C₂×C₄	—	26	1	no	—
522	C₂×C₄	—	26	1	no	—
523	C₂×C₄	—	26	1	no	—
524	C₂×C₄	—	26	1	no	—
525	C₂×C₄	—	26	1	no	—
526	C₂×C₄	—	26	1	no	—
527	C₂×C₄	—	52	1	no	—
528	C₂×C₄	—	52	1	no	—
529	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
530	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
531	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
534	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	26	1	no	—
543	C₈	—	26	1	no	—
544	C₈	—	26	1	no	—
545	C₈	—	26	1	no	—
546	C₈	—	52	1	no	—
547	C₈	—	52	1	no	—
548	C₈	—	52	1	no	—
549	C₈	—	52	1	no	—
550	C₈	#88161	1	2	yes	complemented
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	13	2	no	—
555	C₂²	—	26	1	no	—
556	C₂²	—	26	1	no	—
557	C₂²	—	26	1	no	—
558	C₂²	—	26	1	no	—
559	C₂²	—	26	1	no	—
560	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	13	2	no	—
566	C₄	—	26	1	no	—
567	C₄	—	26	1	no	—
568	C₄	—	26	1	no	—
569	C₄	—	26	1	no	—
570	C₄	—	26	1	no	—
571	C₄	C₂×#88161	1	1	yes	characteristic
572	C₄	#11719450	1	1	yes	characteristic
573	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
574	C₄	D₁₃×#137	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	26	2	no	—
577	C₂	—	52	1	no	—
578	C₂	#13123405	1	1	yes	characteristic
579	C₂	D₁₃×#428	1	1	yes	characteristic
580	C₂	#13123446	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1569	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1569	D₁₃
hypocenter	C₁₃	#17830
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #13113627	C₂	semidirect
5. #13113626	C₂	semidirect
6. #13113622	C₂	semidirect
7. #13113618	C₂	semidirect
8. #13113609	C₂	semidirect
9. #13113605	C₂	semidirect
10. #13113600	C₂	semidirect
11. #13113593	C₂	semidirect
12. #13113588	C₂	semidirect
13. #13113587	C₂	semidirect
14. D₁₃×#334	C₂	semidirect
15. C₁₃×#1569	C₂	semidirect
221. #1569	D₁₃	semidirect
267. C₈×C₁₃	#131	semidirect
500. C₁₃	#17830	semidirect
550. C₈	#88161	semidirect

Maximal subgroups

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

subgroup	index
#13123798	2
#13123503	2
#13123405	2
#13113627	2
#13113626	2
#13113622	2
#13113618	2
#13113609	2
#13113605	2
#13113600	2
#13113593	2
#13113588	2
#13113587	2
D₁₃×#334	2
C₁₃×#1569	2
#17830	13