Subgroups — #15834628

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123925	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123873	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#6106	C₂	1	1	yes	maximal, characteristic
4	#13113741	C₂	1	2	yes	maximal, complemented
5	#13113676	C₂	1	2	yes	maximal, complemented
6	#13113675	C₂	1	2	yes	maximal, complemented
7	#13113651	C₂	1	2	yes	maximal, complemented
8	#13113597	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113280	C₂	1	1	yes	maximal, characteristic
10	#13113123	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6106	C₄	1	1	yes	characteristic
14	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
15	C₁₃×#432	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×#88075	C₄	1	1	yes	characteristic
18	C₄×#6106	C₄	1	1	yes	characteristic
19	C₄×#6106	C₄	1	1	yes	characteristic
20	C₄×#6106	C₄	1	1	yes	characteristic
21	C₄×#6106	C₄	1	1	yes	characteristic
22	C₄×#6106	C₂²	1	1	yes	characteristic
23	C₄×#6106	C₂²	1	1	yes	characteristic
24	C₄×#6106	C₂²	1	1	yes	characteristic
25	C₄×#6106	C₂²	1	1	yes	characteristic
26	#11718685	—	2	2	no	—
27	#11718685	C₂²	1	2	yes	complemented
28	Q₈×#1055	C₂²	1	2	yes	complemented
29	C₂×#88049	C₄	1	1	yes	characteristic
30	C₂×#88048	C₄	1	1	yes	characteristic
31	#11718587	—	2	1	no	—
32	#11718587	C₂²	1	1	yes	characteristic
33	#11718586	—	2	1	no	—
34	#11718586	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	#11718499	C₂²	1	2	yes	—
37	#11718495	C₂²	1	2	yes	—
38	#11718387	—	2	1	no	—
39	D₁₃×C₂²⋊C₈	—	2	1	no	—
40	#11718367	—	2	2	no	—
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	#11718072	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718051	C₂²	1	2	yes	—
46	#11718051	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₃	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	—	2	1	no	—
55	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6106	—	2	4	no	—
64	C₂×#6106	C₂×C₄	1	1	yes	characteristic
65	C₂×#6106	C₂×C₄	1	1	yes	characteristic
66	C₂×#6106	C₂×C₄	1	1	yes	characteristic
67	C₂×#6106	C₂×C₄	1	1	yes	characteristic
68	C₂×#6103	—	2	1	no	—
69	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
71	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
72	C₂×#6094	—	2	2	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	C₄×D₅₂	—	2	1	no	—
75	C₄×D₅₂	—	2	1	no	—
76	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
77	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
78	C₄×D₅₂	C₂³	1	1	yes	characteristic
79	C₄×D₅₂	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₃×C₂²⋊C₈	—	2	1	no	—
82	C₁₃×#97	—	2	1	no	—
83	C₁₃×#97	—	2	1	no	—
84	C₄×C₈×C₁₃	C₂³	1	2	yes	—
85	#88075	C₂×C₄	1	1	yes	characteristic
86	#88075	C₂×C₄	1	1	yes	characteristic
87	#88075	C₂×C₄	1	1	yes	characteristic
88	#88075	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	D₄	1	1	yes	characteristic
91	C₂²⋊#1055	D₄	1	1	yes	characteristic
92	#88060	—	2	2	no	—
93	#88060	—	2	2	no	—
94	#88049	C₂×C₄	1	1	yes	characteristic
95	#88049	C₂×C₄	1	1	yes	characteristic
96	#88049	C₂×C₄	1	1	yes	characteristic
97	#88049	C₂×C₄	1	1	yes	characteristic
98	#88048	C₂×C₄	1	1	yes	characteristic
99	#88048	C₂×C₄	1	1	yes	characteristic
100	#88048	C₂×C₄	1	1	yes	characteristic
101	#88048	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#1055	—	2	2	no	—
103	C₄⋊#1055	—	2	2	no	—
104	C₄⋊#1055	D₄	1	2	yes	—
105	C₄⋊#1055	C₂³	1	2	yes	—
106	#88043	—	2	1	no	—
107	#88043	—	2	2	no	—
108	C₄×#1055	—	2	2	no	—
109	C₄×#1055	C₂×C₄	1	1	yes	characteristic
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂³	1	1	yes	characteristic
112	C₄×#1055	C₂³	1	1	yes	characteristic
113	C₄×#1055	C₂³	1	2	yes	—
114	#18060	—	13	1	no	maximal, Sylow
115	C₂³×D₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	1	no	—
119	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×Dic₁₃	—	2	1	no	—
127	C₂×D₅₂	—	2	2	no	—
128	C₂×D₅₂	—	2	1	no	—
129	C₂×D₅₂	—	4	1	no	—
130	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₁₃	—	2	1	no	—
133	C₂×C₄×D₁₃	—	2	1	no	—
134	C₂×C₄×D₁₃	—	2	1	no	—
135	C₂×C₄×D₁₃	—	2	1	no	—
136	C₂×C₄×D₁₃	—	8	2	no	—
137	C₁₃×M₁₆	—	4	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃	#41	1	1	yes	characteristic
154	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
155	#6106	—	2	2	no	—
156	#6106	—	2	2	no	—
157	#6106	—	2	2	no	—
158	#6106	M₁₆	1	4	yes	complemented
159	#6103	—	2	1	no	—
160	#6103	—	2	1	no	—
161	#6103	—	2	1	no	—
162	#6103	—	2	1	no	—
163	C₄⋊Dic₁₃	—	2	1	no	—
164	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×#1055	—	2	2	no	—
167	C₂×#1055	—	2	2	no	—
168	C₂×#1055	—	4	1	no	—
169	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
170	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
171	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
172	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
173	C₂×#1055	C₂×D₄	1	2	yes	—
174	C₂×#1055	C₂×D₄	1	2	yes	—
175	#6094	—	8	2	no	—
176	C₈×D₁₃	—	8	2	no	—
177	#2984	—	13	1	no	—
178	#2974	—	13	1	no	—
179	C₂×C₄×SD₁₆	—	13	1	no	—
180	#1592	—	13	2	no	—
181	#1583	—	13	2	no	—
182	#1582	—	13	2	no	—
183	SD₁₆⋊C₈	—	13	2	no	—
184	#1568	—	13	1	no	—
185	#1491	D₁₃	1	1	yes	characteristic, complemented
186	#1490	—	13	1	no	—
187	#1451	—	13	1	no	—
188	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂²×D₁₃	—	2	1	no	—
190	C₂²×D₁₃	—	2	1	no	—
191	C₂²×D₁₃	—	4	2	no	—
192	C₂²×D₁₃	—	4	2	no	—
193	C₂²×D₁₃	—	8	1	no	—
194	Q₈×C₁₃	—	2	1	no	—
195	Q₈×C₁₃	—	2	1	no	—
196	Q₈×C₁₃	—	2	1	no	—
197	Q₈×C₁₃	—	4	2	no	—
198	Q₈×C₁₃	C₂×M₁₆	1	2	yes	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×Dic₁₃	—	2	1	no	—
216	C₂×Dic₁₃	—	2	1	no	—
217	C₂×Dic₁₃	—	8	1	no	—
218	D₅₂	—	2	1	no	—
219	D₅₂	—	2	1	no	—
220	D₅₂	—	2	1	no	—
221	D₅₂	—	4	2	no	—
222	D₅₂	C₂×M₁₆	1	2	yes	—
223	C₄×D₁₃	—	4	2	no	—
224	C₄×D₁₃	—	4	2	no	—
225	C₄×D₁₃	—	8	1	no	—
226	C₄×D₁₃	—	8	1	no	—
227	C₈×C₁₃	—	4	2	no	—
228	C₈×C₁₃	—	4	2	no	—
229	#1055	—	2	1	no	—
230	#1055	—	2	1	no	—
231	#1055	—	2	1	no	—
232	#1055	—	2	2	no	—
233	#1055	—	2	2	no	—
234	#1055	—	4	2	no	—
235	#1055	C₂×M₁₆	1	2	yes	—
236	C₂²×SD₁₆	—	13	1	no	—
237	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
238	C₂×C₄×D₄	—	13	1	no	—
239	#446	—	13	2	no	—
240	#446	—	26	2	no	—
241	C₈×Q₈	—	13	2	no	—
242	C₄×SD₁₆	—	13	1	no	—
243	C₄×SD₁₆	—	13	1	no	—
244	C₄×SD₁₆	—	13	1	no	—
245	C₄×SD₁₆	—	13	1	no	—
246	C₄×SD₁₆	—	13	1	no	—
247	C₄×SD₁₆	—	13	1	no	—
248	C₄×SD₁₆	—	13	1	no	—
249	C₄×SD₁₆	—	13	1	no	—
250	#436	—	13	2	no	—
251	#435	—	26	2	no	—
252	C₈×D₄	—	13	2	no	—
253	#432	—	13	1	no	—
254	#432	—	26	1	no	—
255	#432	C₂×D₁₃	1	1	yes	characteristic
256	#431	—	13	1	no	—
257	#431	—	26	1	no	—
258	C₂×#106	—	13	1	no	—
259	C₂×#103	—	13	1	no	—
260	C₂×#102	—	13	1	no	—
261	#407	—	26	1	no	—
262	C₂×C₂²⋊C₈	—	26	1	no	—
263	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
264	C₂×C₄×C₈	—	13	1	no	—
265	#335	—	13	2	no	—
266	#334	—	13	2	no	—
267	Q₈⋊C₈	C₂×D₁₃	1	2	yes	complemented
268	Q₈⋊C₈	C₂×D₁₃	1	2	yes	complemented
269	D₄⋊C₈	—	13	2	no	—
270	D₄⋊C₈	—	13	2	no	—
271	#322	—	13	2	no	—
272	#322	—	13	2	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	#444	1	2	yes	—
276	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂×D₁₃	—	2	2	no	—
278	C₂×D₁₃	—	4	1	no	—
279	C₂×D₁₃	—	4	1	no	—
280	C₂×D₁₃	—	4	1	no	—
281	C₂×D₁₃	—	4	1	no	—
282	C₂×D₁₃	—	4	1	no	—
283	C₂×D₁₃	—	8	4	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
293	C₄×C₁₃	#568	1	1	yes	characteristic
294	C₄×C₁₃	#577	1	2	yes	—
295	Dic₁₃	—	4	1	no	—
296	Dic₁₃	—	4	1	no	—
297	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
298	C₂²×D₄	—	13	1	no	—
299	C₂³×C₄	—	26	1	no	—
300	C₂×SD₁₆	—	13	1	no	—
301	C₂×SD₁₆	—	13	1	no	—
302	C₂×SD₁₆	—	13	1	no	—
303	C₂×SD₁₆	—	13	1	no	—
304	C₂×SD₁₆	—	26	4	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	—	26	2	no	—
307	C₂²×C₈	—	13	1	no	—
308	C₂²×C₈	—	13	1	no	—
309	C₂²×C₈	—	26	2	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
313	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
314	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
316	C₄×D₄	—	13	1	no	—
317	C₄×D₄	—	13	1	no	—
318	C₄×D₄	—	13	1	no	—
319	C₄×D₄	—	13	1	no	—
320	C₄×D₄	—	26	1	no	—
321	C₄×D₄	—	26	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	13	1	no	—
324	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	26	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
328	#106	—	13	1	no	—
329	#106	—	13	1	no	—
330	#106	—	13	1	no	—
331	#106	—	13	1	no	—
332	C₄⋊C₈	—	13	2	no	—
333	C₄⋊C₈	—	13	2	no	—
334	C₄⋊C₈	—	26	2	no	—
335	C₄⋊C₈	—	26	2	no	—
336	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
337	#103	—	13	1	no	—
338	#103	—	13	1	no	—
339	#103	—	13	1	no	—
340	#103	—	13	1	no	—
341	#102	—	13	1	no	—
342	#102	—	13	1	no	—
343	#102	—	13	1	no	—
344	#102	—	13	1	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	13	1	no	—
347	C₂²⋊C₈	—	13	1	no	—
348	C₂²⋊C₈	—	26	2	no	—
349	C₂²⋊C₈	—	26	2	no	—
350	C₂²⋊C₈	—	26	1	no	—
351	#97	—	2	1	no	—
352	#97	—	2	1	no	—
353	#97	—	26	2	no	—
354	#97	—	26	1	no	—
355	C₄×C₈	—	13	1	no	—
356	C₄×C₈	—	13	1	no	—
357	C₄×C₈	—	13	1	no	—
358	C₄×C₈	—	13	1	no	—
359	C₄×C₈	—	13	2	no	—
360	C₄×C₈	—	26	2	no	—
361	C₄×C₈	C₂²×D₁₃	1	2	yes	—
362	C₂×C₁₃	—	2	2	no	—
363	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
364	C₂×C₁₃	#2949	1	1	yes	characteristic
365	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
366	D₁₃	—	4	2	no	—
367	D₁₃	—	8	1	no	—
368	C₂⁴	—	26	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	1	no	—
372	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₂×D₄	—	13	1	no	—
375	C₂×D₄	—	13	1	no	—
376	C₂×D₄	—	26	2	no	—
377	C₂×D₄	—	26	1	no	—
378	C₂×D₄	—	52	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	26	1	no	—
382	C₂²×C₄	—	26	1	no	—
383	C₂²×C₄	—	26	1	no	—
384	C₂²×C₄	—	26	1	no	—
385	C₂²×C₄	—	26	1	no	—
386	C₂²×C₄	—	104	2	no	—
387	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
388	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
389	C₂²×C₄	#6129	1	1	yes	characteristic
390	SD₁₆	—	13	4	no	—
391	SD₁₆	—	26	2	no	—
392	SD₁₆	—	26	2	no	—
393	SD₁₆	—	26	2	no	—
394	M₁₆	—	4	2	no	—
395	M₁₆	—	104	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	13	1	no	—
400	C₂×C₈	—	13	1	no	—
401	C₂×C₈	—	13	1	no	—
402	C₂×C₈	—	13	2	no	—
403	C₂×C₈	—	13	2	no	—
404	C₂×C₈	—	26	2	no	—
405	C₂×C₈	—	26	2	no	—
406	C₂×C₈	—	52	1	no	—
407	C₂×C₈	—	104	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	13	1	no	—
414	C₄⋊C₄	—	13	1	no	—
415	C₄⋊C₄	—	26	1	no	—
416	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
418	C₂²⋊C₄	—	26	1	no	—
419	C₂²⋊C₄	—	26	1	no	—
420	C₂²⋊C₄	—	26	1	no	—
421	C₂²⋊C₄	—	26	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
427	C₄²	D₄×D₁₃	1	1	yes	characteristic
428	C₄²	#6129	1	1	yes	characteristic
429	C₄²	C₂³×D₁₃	1	1	yes	characteristic
430	C₁₃	#18060	1	1	yes	characteristic, complemented, Sylow
431	C₂³	—	26	1	no	—
432	C₂³	—	26	1	no	—
433	C₂³	—	52	2	no	—
434	C₂³	—	52	2	no	—
435	C₂³	—	104	1	no	—
436	C₂³	#88135	1	1	yes	characteristic
437	Q₈	—	2	1	no	—
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	4	2	no	—
441	Q₈	M₁₆×D₁₃	1	2	yes	—
442	D₄	—	13	2	no	—
443	D₄	—	26	1	no	—
444	D₄	—	26	1	no	—
445	D₄	—	26	1	no	—
446	D₄	—	52	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	26	1	no	—
458	C₂×C₄	—	26	1	no	—
459	C₂×C₄	—	52	2	no	—
460	C₂×C₄	—	52	2	no	—
461	C₂×C₄	—	104	1	no	—
462	C₂×C₄	—	104	1	no	—
463	C₂×C₄	—	104	1	no	—
464	C₂×C₄	#88135	1	1	yes	characteristic
465	C₂×C₄	#88135	1	1	yes	characteristic
466	C₂×C₄	#88135	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂×#6129	1	1	yes	characteristic
470	C₈	—	4	2	no	—
471	C₈	—	4	2	no	—
472	C₈	—	13	2	no	—
473	C₈	—	26	1	no	—
474	C₈	—	26	1	no	—
475	C₈	—	26	1	no	—
476	C₈	—	26	2	no	—
477	C₈	—	26	2	no	—
478	C₈	—	52	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	26	2	no	—
482	C₂²	—	52	1	no	—
483	C₂²	—	52	1	no	—
484	C₂²	—	52	1	no	—
485	C₂²	—	52	1	no	—
486	C₂²	—	52	1	no	—
487	C₂²	—	104	4	no	—
488	C₂²	#11718484	1	2	yes	—
489	C₂²	C₂×#88135	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	52	1	no	—
499	C₄	—	52	1	no	—
500	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
501	C₄	#11719450	1	1	yes	characteristic
502	C₄	#11719483	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	52	2	no	—
505	C₂	—	104	1	no	—
506	C₂	#13123568	1	1	yes	characteristic
507	C₂	#13123691	1	1	yes	characteristic
508	C₂	C₂×#11718484	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×#1491	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1491	D₁₃
hypocenter	C₁₃	#18060
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1491

Complements

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

N	H ≅ G/N	type
1. #13123925	C₂	semidirect
4. #13113741	C₂	semidirect
5. #13113676	C₂	semidirect
6. #13113675	C₂	semidirect
7. #13113651	C₂	semidirect
8. #13113597	C₂	semidirect
10. #13113123	C₂	semidirect
11. C₁₃×#1491	C₂	semidirect
27. #11718685	C₂²	semidirect
28. Q₈×#1055	C₂²	semidirect
41. C₁₃×Q₈⋊C₈	C₂²	semidirect
42. C₁₃×Q₈⋊C₈	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718071	C₂²	semidirect
47. #11718046	C₂²	semidirect
48. #11718046	C₂²	semidirect
158. #6106	M₁₆	semidirect
185. #1491	D₁₃	semidirect
267. Q₈⋊C₈	C₂×D₁₃	semidirect
268. Q₈⋊C₈	C₂×D₁₃	semidirect
430. C₁₃	#18060	semidirect

Maximal subgroups

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

subgroup	index
#13123925	2
#13123873	2
C₂×C₄×#6106	2
#13113741	2
#13113676	2
#13113675	2
#13113651	2
#13113597	2
#13113280	2
#13113123	2
C₁₃×#1491	2
#18060	13