Subgroups — #15869870

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123739	C₂	1	2	yes	maximal, complemented
2	C₂×#11718858	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123262	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115735	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115627	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115507	C₂	1	2	yes	maximal, complemented
7	#13115339	C₂	1	2	yes	maximal, complemented
8	#13114890	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114723	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114639	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3067	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#575	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	#41×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂×#88202	C₂²	1	2	yes	—
17	C₂×#88202	C₂²	1	1	yes	characteristic
18	C₁₃×#473	C₄	1	2	yes	complemented
19	C₁₃×#472	C₄	1	2	yes	complemented
20	C₁₃×#471	C₄	1	4	yes	complemented
21	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
22	C₁₃×#413	C₂²	1	2	yes	—
23	#11718901	C₂²	1	2	yes	—
24	#11718897	C₂²	1	2	yes	—
25	#11718897	C₂²	1	2	yes	—
26	C₂×#88077	C₂²	1	2	yes	—
27	#11718858	—	2	1	no	—
28	#11718858	—	2	1	no	—
29	#11718858	—	2	1	no	—
30	#11718858	—	2	1	no	—
31	#11718858	—	2	4	no	—
32	#11718857	—	2	4	no	—
33	#11718786	C₂²	1	2	yes	—
34	#11718783	—	2	1	no	—
35	#11718783	C₂²	1	1	yes	characteristic
36	#11718783	C₂²	1	2	yes	—
37	M₁₆×Dic₁₃	—	2	1	no	—
38	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂×#88059	C₂²	1	1	yes	characteristic
40	#11718767	C₂²	1	1	yes	characteristic
41	#11718762	—	2	1	no	—
42	#11718762	C₂²	1	1	yes	characteristic
43	C₂×#88055	—	2	1	no	—
44	C₂×#88055	C₂²	1	1	yes	characteristic
45	#11718151	C₂²	1	2	yes	—
46	#11718151	C₂²	1	2	yes	—
47	#11718147	C₂²	1	2	yes	—
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₁₃×#137	—	2	2	no	—
51	C₁₃×#137	C₂×C₄	1	4	yes	—
52	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
53	C₁₃×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
54	C₁₃×#135	—	2	4	no	—
55	C₁₃×#135	—	2	1	no	—
56	C₁₃×#135	—	2	1	no	—
57	C₁₃×#135	—	2	1	no	—
58	C₁₃×#135	—	2	1	no	—
59	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
61	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
62	C₁₃×#131	—	2	1	no	—
63	C₁₃×#131	—	2	1	no	—
64	C₁₃×#131	C₂×C₄	1	2	yes	—
65	C₁₃×#131	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	—	2	1	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	#88202	—	2	2	no	—
72	#88202	—	2	2	no	—
73	#88202	—	2	2	no	—
74	#88202	—	2	2	no	—
75	#88202	—	2	2	no	—
76	#88202	D₄	1	4	yes	—
77	Q₈×Dic₁₃	—	2	1	no	—
78	D₄×Dic₁₃	—	2	1	no	—
79	D₄×Dic₁₃	—	2	2	no	—
80	#88180	—	2	1	no	—
81	#88180	C₂³	1	2	yes	—
82	#88180	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₁₃	—	2	1	no	—
84	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	2	no	—
87	C₂×#6099	C₂³	1	2	yes	—
88	C₂×#6099	C₂³	1	1	yes	characteristic
89	C₂²×#1055	—	2	1	no	—
90	C₂²×#1055	—	2	2	no	—
91	C₂²×#1055	C₂³	1	1	yes	characteristic
92	C₁₃×#108	C₂×C₄	1	2	yes	complemented
93	C₁₃×#108	C₂×C₄	1	2	yes	complemented
94	C₁₃×#101	C₂×C₄	1	4	yes	complemented
95	C₁₃×#100	C₂×C₄	1	4	yes	complemented
96	#88077	—	2	4	no	—
97	#88077	—	2	2	no	—
98	#88077	—	2	2	no	—
99	#88077	—	2	4	no	—
100	#88074	—	2	4	no	—
101	#88059	—	2	1	no	—
102	#88059	—	2	1	no	—
103	#88059	—	2	4	no	—
104	#88058	—	2	1	no	—
105	#88057	—	2	1	no	—
106	#88055	—	2	1	no	—
107	#88055	—	2	1	no	—
108	#88055	—	2	1	no	—
109	#88055	—	2	2	no	—
110	#88055	D₄	1	1	yes	characteristic
111	#88055	D₄	1	1	yes	characteristic
112	#88055	D₄	1	1	yes	characteristic
113	#88055	D₄	1	1	yes	characteristic
114	C₈×Dic₁₃	—	2	1	no	—
115	C₈×Dic₁₃	—	2	1	no	—
116	C₈×Dic₁₃	—	2	1	no	—
117	C₈×Dic₁₃	—	2	2	no	—
118	#21559	—	13	1	no	maximal, Sylow
119	C₁₃×#41	—	2	1	no	—
120	C₁₃×#41	—	2	1	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	C₂²×C₄	1	2	yes	—
126	C₁₃×#41	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₁₃	—	2	2	no	—
137	C₂²×Dic₁₃	—	2	1	no	—
138	C₁₃×Q₁₆	—	2	4	no	—
139	C₁₃×Q₁₆	—	2	1	no	—
140	C₁₃×Q₁₆	—	2	1	no	—
141	C₁₃×SD₁₆	—	2	4	no	—
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×SD₁₆	—	2	2	no	—
144	C₁₃×SD₁₆	—	2	2	no	—
145	C₁₃×D₈	—	2	4	no	—
146	C₁₃×D₈	—	2	1	no	—
147	C₁₃×D₈	—	2	1	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	C₂²×C₄	1	2	yes	—
153	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
163	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	—	2	2	no	—
165	C₂²⋊Dic₁₃	—	2	2	no	—
166	C₂²⋊Dic₁₃	#41	1	2	yes	—
167	C₄⋊Dic₁₃	—	2	2	no	—
168	C₄⋊Dic₁₃	—	2	1	no	—
169	C₄⋊Dic₁₃	—	2	2	no	—
170	C₄×Dic₁₃	—	2	2	no	—
171	C₄×Dic₁₃	—	2	1	no	—
172	C₄×Dic₁₃	—	2	1	no	—
173	C₄×Dic₁₃	—	2	2	no	—
174	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
176	#6099	—	2	1	no	—
177	#6099	—	2	4	no	—
178	#6099	—	2	2	no	—
179	#6099	—	2	2	no	—
180	#6099	—	4	2	no	—
181	#6099	—	4	2	no	—
182	#6099	C₂×D₄	1	2	yes	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	4	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	—	4	2	no	—
187	C₂×#1055	—	4	2	no	—
188	C₂×#1055	C₂×D₄	1	1	yes	characteristic
189	C₂×#1055	C₂×D₄	1	1	yes	characteristic
190	C₂×#1055	C₂×D₄	1	2	yes	—
191	C₂×#1055	#41	1	2	yes	—
192	#3067	D₁₃	1	1	yes	characteristic
193	#2955	—	13	2	no	—
194	C₂×#444	—	13	1	no	—
195	#2875	—	13	1	no	—
196	#1976	—	13	1	no	—
197	#1953	—	13	1	no	—
198	#1932	—	13	2	no	—
199	#1906	—	13	2	no	—
200	#1814	—	13	1	no	—
201	#1773	—	13	1	no	—
202	#1757	—	13	2	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
206	Q₈×C₁₃	—	2	1	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	—	2	2	no	—
209	Q₈×C₁₃	C₄×D₄	1	2	yes	—
210	D₄×C₁₃	—	2	2	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	2	2	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	1	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	4	2	no	—
217	D₄×C₁₃	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×Dic₁₃	—	2	1	no	—
231	C₂×Dic₁₃	—	2	2	no	—
232	C₂×Dic₁₃	—	2	1	no	—
233	C₂×Dic₁₃	—	4	2	no	—
234	C₂×Dic₁₃	—	8	1	no	—
235	C₂×Dic₁₃	—	8	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	4	no	—
238	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
241	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
242	#1055	—	2	2	no	—
243	#1055	—	4	2	no	—
244	#1055	#121	1	2	yes	—
245	#1055	#121	1	2	yes	—
246	#575	C₂×D₁₃	1	2	yes	—
247	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
248	C₂×#131	—	13	1	no	—
249	C₂×#131	—	13	2	no	—
250	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
251	C₄×#41	—	13	1	no	—
252	#473	Dic₁₃	1	2	yes	complemented
253	#472	Dic₁₃	1	2	yes	complemented
254	#471	Dic₁₃	1	4	yes	complemented
255	#444	—	26	1	no	—
256	#444	—	26	1	no	—
257	#444	—	26	1	no	—
258	#444	—	26	1	no	—
259	#444	—	26	4	no	—
260	#443	—	26	4	no	—
261	#430	—	13	2	no	—
262	C₂×#108	—	13	1	no	—
263	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
264	#427	—	13	1	no	—
265	#421	—	13	2	no	—
266	#421	—	13	2	no	—
267	C₂×#104	—	13	2	no	—
268	#413	C₂×D₁₃	1	2	yes	—
269	#410	—	13	2	no	—
270	#405	—	13	1	no	—
271	#405	—	13	2	no	—
272	#405	—	13	1	no	—
273	#405	—	26	1	no	—
274	#405	—	26	1	no	—
275	C₄×M₁₆	—	13	1	no	—
276	C₄×M₁₆	—	26	1	no	—
277	C₂×#97	—	13	1	no	—
278	C₂×#97	—	26	1	no	—
279	#344	—	13	2	no	—
280	#344	—	13	2	no	—
281	#339	—	13	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	8	2	no	—
287	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
288	C₂²×C₁₃	#525	1	1	yes	characteristic
289	C₂²×C₁₃	#532	1	1	yes	characteristic
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
295	C₄×C₁₃	#529	1	1	yes	characteristic
296	Dic₁₃	—	4	2	no	—
297	Dic₁₃	—	4	1	no	—
298	Dic₁₃	—	4	1	no	—
299	Dic₁₃	—	8	2	no	—
300	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
301	C₂×#41	C₂²×D₁₃	1	2	yes	—
302	#137	—	2	2	no	—
303	#137	C₂×Dic₁₃	1	4	yes	—
304	AGL(1,ℤ/8)	—	2	2	no	—
305	AGL(1,ℤ/8)	C₂×Dic₁₃	1	4	yes	—
306	#135	—	2	4	no	—
307	#135	—	2	1	no	—
308	#135	—	2	1	no	—
309	#135	—	2	1	no	—
310	#135	—	2	1	no	—
311	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic, complemented
312	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	complemented
313	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	13	4	no	—
317	#131	—	26	2	no	—
318	#131	—	26	2	no	—
319	#131	—	26	2	no	—
320	#131	—	26	2	no	—
321	#131	—	26	2	no	—
322	#131	C₂×Dic₁₃	1	2	yes	—
323	#131	C₂×Dic₁₃	1	2	yes	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	13	1	no	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂×M₁₆	—	26	1	no	—
328	C₂×M₁₆	—	26	2	no	—
329	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
330	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	13	1	no	—
333	C₂²×C₈	—	26	1	no	—
334	C₂²×C₈	—	26	2	no	—
335	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
336	C₄×Q₈	—	26	1	no	—
337	C₄×D₄	—	26	2	no	—
338	C₄×D₄	—	26	1	no	—
339	#117	—	13	1	no	—
340	#117	—	13	2	no	—
341	#117	—	26	1	no	—
342	C₂×C₄²	—	13	1	no	—
343	C₂×C₄²	—	26	1	no	—
344	#108	—	26	4	no	—
345	#108	—	26	1	no	—
346	#108	—	26	1	no	—
347	#108	C₂×Dic₁₃	1	2	yes	complemented
348	#108	C₂×Dic₁₃	1	2	yes	complemented
349	#107	—	26	1	no	—
350	#106	—	26	1	no	—
351	#104	—	26	2	no	—
352	#104	—	26	2	no	—
353	#104	—	26	4	no	—
354	#104	—	26	4	no	—
355	#101	C₂×Dic₁₃	1	4	yes	complemented
356	#100	C₂×Dic₁₃	1	4	yes	complemented
357	#99	—	26	4	no	—
358	#97	—	13	1	no	—
359	#97	—	13	1	no	—
360	#97	—	13	1	no	—
361	#97	—	13	1	no	—
362	#97	—	26	1	no	—
363	#97	—	26	1	no	—
364	#97	—	26	2	no	—
365	#97	—	26	1	no	—
366	C₄×C₈	—	26	1	no	—
367	C₄×C₈	—	26	1	no	—
368	C₄×C₈	—	26	2	no	—
369	C₄×C₈	—	26	1	no	—
370	C₂×C₁₃	—	2	1	no	—
371	C₂×C₁₃	—	2	1	no	—
372	C₂×C₁₃	—	2	1	no	—
373	C₂×C₁₃	—	4	2	no	—
374	C₂×C₁₃	—	8	2	no	—
375	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	2	2	no	—
382	#41	D₄×D₁₃	1	2	yes	—
383	#41	C₂²×Dic₁₃	1	2	yes	—
384	C₂×Q₈	#6129	1	1	yes	characteristic
385	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	#6129	1	1	yes	characteristic
389	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	26	2	no	—
393	C₂²×C₄	—	26	1	no	—
394	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
395	Q₁₆	—	2	4	no	—
396	Q₁₆	—	2	1	no	—
397	Q₁₆	—	2	1	no	—
398	SD₁₆	—	2	4	no	—
399	SD₁₆	—	2	4	no	—
400	SD₁₆	—	2	2	no	—
401	SD₁₆	—	2	2	no	—
402	D₈	—	2	4	no	—
403	D₈	—	2	1	no	—
404	D₈	—	2	1	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	13	2	no	—
410	M₁₆	—	26	4	no	—
411	M₁₆	—	26	1	no	—
412	M₁₆	—	26	2	no	—
413	M₁₆	—	26	2	no	—
414	M₁₆	—	52	2	no	—
415	M₁₆	—	52	2	no	—
416	M₁₆	C₂²×Dic₁₃	1	2	yes	—
417	M₁₆	C₂²×Dic₁₃	1	4	yes	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	13	1	no	—
423	C₂×C₈	—	13	2	no	—
424	C₂×C₈	—	13	1	no	—
425	C₂×C₈	—	13	2	no	—
426	C₂×C₈	—	26	4	no	—
427	C₂×C₈	—	26	1	no	—
428	C₂×C₈	—	26	2	no	—
429	C₂×C₈	—	52	2	no	—
430	C₂×C₈	—	52	2	no	—
431	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
432	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
433	C₂×C₈	#6129	1	1	yes	characteristic
434	C₂×C₈	#6129	1	1	yes	characteristic
435	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
436	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
437	C₄⋊C₄	—	26	2	no	—
438	C₄⋊C₄	—	26	1	no	—
439	C₄⋊C₄	—	26	2	no	—
440	C₂²⋊C₄	—	13	2	no	—
441	C₂²⋊C₄	—	26	2	no	—
442	C₂²⋊C₄	—	26	2	no	—
443	C₄²	—	13	1	no	—
444	C₄²	—	13	1	no	—
445	C₄²	—	26	2	no	—
446	C₄²	—	26	1	no	—
447	C₄²	—	26	1	no	—
448	C₄²	—	26	2	no	—
449	C₁₃	#21559	1	1	yes	characteristic, complemented, Sylow
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	#41×D₁₃	1	1	yes	characteristic
453	Q₈	—	2	1	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	D₄×Dic₁₃	1	2	yes	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	1	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	D₄×Dic₁₃	1	2	yes	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	26	1	no	—
472	C₂×C₄	—	26	1	no	—
473	C₂×C₄	—	26	2	no	—
474	C₂×C₄	—	52	2	no	—
475	C₂×C₄	—	104	1	no	—
476	C₂×C₄	—	104	2	no	—
477	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂×#6129	1	1	yes	characteristic
480	C₂×C₄	C₂×#6129	1	1	yes	characteristic
481	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	4	no	—
485	C₈	—	13	2	no	—
486	C₈	—	13	2	no	—
487	C₈	—	26	2	no	—
488	C₈	—	52	2	no	—
489	C₈	D₄×Dic₁₃	1	1	yes	characteristic
490	C₈	D₄×Dic₁₃	1	1	yes	characteristic
491	C₈	D₄×Dic₁₃	1	1	yes	characteristic
492	C₈	D₄×Dic₁₃	1	1	yes	characteristic
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	#11719301	1	1	yes	characteristic
499	C₂²	#11719311	1	1	yes	characteristic
500	C₂²	#41×Dic₁₃	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	52	1	no	—
504	C₄	—	52	2	no	—
505	C₄	—	52	1	no	—
506	C₄	—	104	2	no	—
507	C₄	#11719305	1	1	yes	characteristic
508	C₄	D₁₃×#121	1	1	yes	characteristic
509	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
510	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	2	no	—
515	C₂	—	8	2	no	—
516	C₂	#121×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#121
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3067	C₂
socle	C₂×C₁₃	C₄×#121
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3067	D₁₃
hypocenter	C₁₃	#21559
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #13123739	C₂	semidirect
2. C₂×#11718858	C₂	semidirect
3. #13123262	C₂	semidirect
4. #13115735	C₂	semidirect
5. #13115627	C₂	semidirect
6. #13115507	C₂	semidirect
7. #13115339	C₂	semidirect
8. #13114890	C₂	semidirect
9. #13114723	C₂	semidirect
10. #13114639	C₂	semidirect
18. C₁₃×#473	C₄	semidirect
19. C₁₃×#472	C₄	semidirect
20. C₁₃×#471	C₄	semidirect
59. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
60. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
61. C₂×C₁₃×D₈	C₂×C₄	semidirect
92. C₁₃×#108	C₂×C₄	semidirect
93. C₁₃×#108	C₂×C₄	semidirect
94. C₁₃×#101	C₂×C₄	semidirect
95. C₁₃×#100	C₂×C₄	semidirect
252. #473	Dic₁₃	semidirect
253. #472	Dic₁₃	semidirect
254. #471	Dic₁₃	semidirect
311. C₂×Q₁₆	C₂×Dic₁₃	semidirect
312. C₂×SD₁₆	C₂×Dic₁₃	semidirect
313. C₂×D₈	C₂×Dic₁₃	semidirect
347. #108	C₂×Dic₁₃	semidirect
348. #108	C₂×Dic₁₃	semidirect
355. #101	C₂×Dic₁₃	semidirect
356. #100	C₂×Dic₁₃	semidirect
449. C₁₃	#21559	semidirect

Maximal subgroups

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

subgroup	index
#13123739	2
C₂×#11718858	2
#13123262	2
#13115735	2
#13115627	2
#13115507	2
#13115339	2
#13114890	2
#13114723	2
#13114639	2
C₁₃×#3067	2
#21559	13