Subgroups — #15834769

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125432	C₂	1	1	yes	maximal, characteristic
2	#13123582	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113748	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113726	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113714	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113698	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113670	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113665	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113646	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6104	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113252	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113249	C₂	1	1	yes	maximal, characteristic, complemented
14	#13113139	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₂²	1	1	yes	characteristic
17	C₂×#88161	—	2	1	no	—
18	#11719182	C₂²	1	1	yes	characteristic
19	C₁₃×#446	C₂²	1	1	yes	characteristic
20	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#436	—	2	1	no	—
22	C₁₃×#436	C₂²	1	1	yes	characteristic
23	C₁₃×#435	—	2	1	no	—
24	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#433	—	2	1	no	—
26	C₁₃×#431	C₂²	1	1	yes	characteristic
27	C₁₃×#405	—	2	1	no	—
28	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
29	#11718790	—	2	1	no	—
30	#11718728	C₄	1	1	yes	characteristic
31	#11718726	C₄	1	1	yes	characteristic
32	#11718719	C₄	1	1	yes	characteristic
33	#11718716	C₄	1	1	yes	characteristic
34	#11718710	C₄	1	1	yes	characteristic
35	#11718710	C₄	1	1	yes	characteristic
36	#11718700	C₄	1	1	yes	characteristic
37	#11718700	C₄	1	1	yes	characteristic
38	C₄×#6106	C₂²	1	1	yes	characteristic
39	C₄×#6106	C₂²	1	1	yes	characteristic
40	C₄×#6104	C₂²	1	1	yes	characteristic
41	C₄×#6104	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₄×#6099	C₂²	1	1	yes	characteristic
44	C₄×#6099	C₂²	1	1	yes	characteristic
45	#11718367	—	2	1	no	—
46	#11718367	—	2	1	no	—
47	#11718349	C₂²	1	1	yes	characteristic
48	#11718349	C₂²	1	1	yes	characteristic
49	C₈×D₅₂	C₂²	1	1	yes	characteristic
50	C₈×D₅₂	C₂²	1	1	yes	characteristic
51	Q₈⋊#1055	C₂²	1	1	yes	characteristic
52	Q₈⋊#1055	C₂²	1	1	yes	characteristic
53	D₄⋊#1055	C₂²	1	1	yes	characteristic
54	D₄⋊#1055	C₂²	1	1	yes	characteristic
55	#11718075	C₂²	1	1	yes	characteristic
56	#11718075	C₂²	1	1	yes	characteristic
57	#11718075	C₂²	1	1	yes	characteristic
58	#11718075	C₂²	1	1	yes	characteristic
59	#11718072	C₂²	1	1	yes	characteristic
60	#11718072	C₂²	1	1	yes	characteristic
61	#11718071	C₂²	1	1	yes	characteristic
62	#11718071	C₂²	1	1	yes	characteristic
63	#11718047	C₂²	1	1	yes	characteristic
64	#11718046	C₂²	1	1	yes	characteristic
65	#11718046	C₂²	1	1	yes	characteristic
66	C₈×#1055	C₂²	1	1	yes	characteristic
67	C₂×#6127	—	2	1	no	—
68	C₂×C₁₃×M₁₆	—	2	1	no	—
69	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₁₃×#126	—	2	1	no	—
73	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
74	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
75	C₁₃×#123	—	2	1	no	—
76	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₁₃	—	2	1	no	—
80	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#117	—	2	1	no	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×#6106	C₂×C₄	1	1	yes	characteristic
84	C₂×#6106	C₂×C₄	1	1	yes	characteristic
85	C₂×#6104	C₂×C₄	1	1	yes	characteristic
86	C₂×#6104	C₂×C₄	1	1	yes	characteristic
87	#88184	—	2	1	no	—
88	#88184	C₂×C₄	1	1	yes	characteristic
89	#88184	C₂×C₄	1	1	yes	characteristic
90	C₂×#6099	—	2	1	no	—
91	C₂×#6099	C₂×C₄	1	1	yes	characteristic
92	C₂×#6099	C₂×C₄	1	1	yes	characteristic
93	C₂²×#1055	—	2	1	no	—
94	#88161	—	4	4	no	—
95	C₂×#6094	—	2	1	no	—
96	C₂×#6094	—	2	1	no	—
97	C₂×C₈×D₁₃	—	2	1	no	—
98	C₂×C₈×D₁₃	—	2	1	no	—
99	#88129	—	2	1	no	—
100	#88128	C₂×C₄	1	1	yes	characteristic
101	C₄×D₅₂	—	2	1	no	—
102	C₄×D₅₂	C₂³	1	1	yes	characteristic
103	C₄×D₅₂	C₂³	1	1	yes	characteristic
104	#88123	C₂×C₄	1	1	yes	characteristic
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₁₃×C₂²⋊C₈	—	2	1	no	—
110	C₁₃×C₂²⋊C₈	—	2	1	no	—
111	C₁₃×C₂²⋊C₈	—	2	1	no	—
112	C₁₃×#97	—	2	1	no	—
113	C₁₃×#97	D₄	1	1	yes	characteristic
114	C₁₃×#97	D₄	1	1	yes	characteristic
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	—	2	1	no	—
117	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	#88075	C₂×C₄	1	1	yes	characteristic
120	#88075	C₂×C₄	1	1	yes	characteristic
121	#88072	C₂×C₄	1	1	yes	characteristic
122	#88072	C₂×C₄	1	1	yes	characteristic
123	#88060	—	2	1	no	—
124	#88060	—	2	1	no	—
125	#88060	—	2	1	no	—
126	#88060	—	2	1	no	—
127	#88049	C₂×C₄	1	1	yes	characteristic
128	#88049	C₂×C₄	1	1	yes	characteristic
129	#88049	C₂×C₄	1	1	yes	characteristic
130	#88049	C₂×C₄	1	1	yes	characteristic
131	#88048	C₂×C₄	1	1	yes	characteristic
132	#88048	C₂×C₄	1	1	yes	characteristic
133	#88047	C₂×C₄	1	1	yes	characteristic
134	#88047	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#1055	—	2	1	no	—
136	C₄⋊#1055	C₂³	1	1	yes	characteristic
137	C₄⋊#1055	C₂³	1	1	yes	characteristic
138	#88043	—	2	1	no	—
139	#88043	C₂×C₄	1	1	yes	characteristic
140	#88043	C₂×C₄	1	1	yes	characteristic
141	C₄×#1055	C₂³	1	1	yes	characteristic
142	C₄×#1055	C₂³	1	1	yes	characteristic
143	C₄×#1055	C₂³	1	1	yes	characteristic
144	C₄×#1055	C₂³	1	1	yes	characteristic
145	#18076	—	13	1	no	maximal, Sylow
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
153	C₂×C₂²⋊D₁₃	—	2	1	no	—
154	C₂×C₂²⋊D₁₃	—	2	1	no	—
155	#6127	—	4	2	no	—
156	#6127	—	4	2	no	—
157	C₂×D₅₂	—	2	1	no	—
158	C₂×D₅₂	—	2	1	no	—
159	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₃	—	2	1	no	—
162	C₂×C₄×D₁₃	—	2	1	no	—
163	C₂×Dic₂₆	—	2	1	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	4	1	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	4	2	no	—
170	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₃	#41	1	1	yes	characteristic
189	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
190	#6106	—	2	2	no	—
191	#6106	—	4	1	no	—
192	#6104	—	2	2	no	—
193	#6104	—	4	1	no	—
194	#6103	—	2	1	no	—
195	#6103	—	2	1	no	—
196	#6103	—	2	1	no	—
197	#6103	—	2	1	no	—
198	C₄⋊Dic₁₃	—	2	1	no	—
199	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
201	#6099	—	2	2	no	—
202	#6099	—	4	1	no	—
203	#6099	—	4	2	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	2	1	no	—
206	C₂×#1055	—	2	1	no	—
207	C₂×#1055	—	2	1	no	—
208	C₂×#1055	—	4	2	no	—
209	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
210	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
211	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
212	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
213	#6094	—	4	2	no	—
214	#6094	—	4	2	no	—
215	C₈×D₁₃	—	4	2	no	—
216	C₈×D₁₃	—	4	2	no	—
217	#3171	—	13	1	no	—
218	#2969	D₁₃	1	1	yes	characteristic, complemented
219	#2935	—	13	1	no	—
220	#1594	—	13	1	no	—
221	#1590	—	13	1	no	—
222	#1588	—	13	1	no	—
223	#1586	—	13	1	no	—
224	#1582	—	13	1	no	—
225	#1581	—	13	1	no	—
226	SD₁₆⋊C₈	—	13	1	no	—
227	C₈×D₈	—	13	1	no	—
228	#1565	—	13	1	no	—
229	#1484	—	13	1	no	—
230	#1483	—	13	1	no	—
231	#1455	—	13	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
234	C₂²×D₁₃	—	2	1	no	—
235	C₂²×D₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	8	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂×Dic₁₃	—	2	1	no	—
260	C₂×Dic₁₃	—	2	1	no	—
261	D₅₂	—	2	1	no	—
262	D₅₂	—	2	1	no	—
263	D₅₂	—	2	1	no	—
264	D₅₂	—	2	1	no	—
265	D₅₂	—	4	2	no	—
266	D₅₂	—	8	1	no	—
267	C₄×D₁₃	—	4	1	no	—
268	C₄×D₁₃	—	4	1	no	—
269	C₄×D₁₃	—	4	1	no	—
270	C₄×D₁₃	—	4	1	no	—
271	Dic₂₆	—	4	2	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
278	#1055	—	2	2	no	—
279	#1055	—	2	1	no	—
280	#1055	—	2	1	no	—
281	#1055	—	2	1	no	—
282	#1055	—	4	1	no	—
283	#1055	—	4	1	no	—
284	#1055	—	4	1	no	—
285	#1055	#131	1	2	yes	complemented
286	C₂×#131	—	26	1	no	—
287	#532	—	13	1	no	—
288	#529	C₂×D₁₃	1	1	yes	characteristic
289	#501	—	13	1	no	—
290	#496	—	13	1	no	—
291	#490	—	13	1	no	—
292	#489	—	13	1	no	—
293	#469	—	13	1	no	—
294	#469	—	13	1	no	—
295	#468	—	13	1	no	—
296	#468	—	13	1	no	—
297	#446	C₂×D₁₃	1	1	yes	characteristic
298	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
299	C₄×SD₁₆	—	13	1	no	—
300	C₄×SD₁₆	—	13	1	no	—
301	C₄×D₈	—	13	1	no	—
302	C₄×D₈	—	13	1	no	—
303	#436	—	2	1	no	—
304	#436	—	13	1	no	—
305	#436	—	13	1	no	—
306	#436	C₂×D₁₃	1	1	yes	characteristic
307	#435	—	2	1	no	—
308	#435	—	26	1	no	—
309	#435	—	26	1	no	—
310	C₈×D₄	—	13	1	no	—
311	C₈×D₄	—	13	1	no	—
312	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
313	#433	—	2	1	no	—
314	#431	C₂×D₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₈	—	13	1	no	—
316	#408	—	26	1	no	—
317	#405	—	2	1	no	—
318	C₄×M₁₆	—	13	1	no	—
319	C₄×M₁₆	—	13	1	no	—
320	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
321	#335	—	13	1	no	—
322	#335	—	13	1	no	—
323	#334	—	13	1	no	—
324	#334	—	13	1	no	—
325	Q₈⋊C₈	—	13	1	no	—
326	Q₈⋊C₈	—	13	1	no	—
327	D₄⋊C₈	—	13	1	no	—
328	D₄⋊C₈	—	13	1	no	—
329	D₄⋊C₈	—	13	1	no	—
330	D₄⋊C₈	—	13	1	no	—
331	D₄⋊C₈	—	13	1	no	—
332	D₄⋊C₈	—	13	1	no	—
333	#322	—	13	1	no	—
334	#322	—	13	1	no	—
335	#322	—	13	1	no	—
336	C₈²	—	13	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂×D₁₃	—	4	1	no	—
345	C₂×D₁₃	—	4	1	no	—
346	C₂×D₁₃	—	4	1	no	—
347	C₂×D₁₃	—	4	1	no	—
348	C₂×D₁₃	—	4	1	no	—
349	C₂×D₁₃	—	4	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
358	C₄×C₁₃	#568	1	1	yes	characteristic
359	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₄×C₁₃	#575	1	1	yes	characteristic
361	Dic₁₃	—	4	1	no	—
362	Dic₁₃	—	4	1	no	—
363	C₂×#41	—	26	1	no	—
364	C₂×SD₁₆	—	13	1	no	—
365	C₂×SD₁₆	—	13	1	no	—
366	C₂×D₈	—	13	1	no	—
367	C₂×D₈	—	13	1	no	—
368	#131	—	52	4	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	13	1	no	—
371	C₂×M₁₆	—	13	1	no	—
372	C₂×M₁₆	—	26	1	no	—
373	C₂×M₁₆	—	26	1	no	—
374	C₂×M₁₆	—	26	1	no	—
375	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
376	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	26	1	no	—
379	C₂²×C₈	—	26	1	no	—
380	C₂²×C₈	—	26	1	no	—
381	C₄⋊Q₈	—	13	1	no	—
382	#127	—	13	1	no	—
383	#126	—	2	1	no	—
384	#125	C₄×D₁₃	1	1	yes	characteristic
385	#124	—	26	1	no	—
386	#124	C₄×D₁₃	1	1	yes	characteristic
387	#123	—	2	1	no	—
388	C₂²⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
389	#121	—	13	1	no	—
390	#121	—	13	1	no	—
391	#121	—	26	1	no	—
392	#121	C₄×D₁₃	1	1	yes	characteristic
393	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	13	1	no	—
396	C₄×D₄	—	13	1	no	—
397	C₄×D₄	—	26	1	no	—
398	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
399	#117	—	2	1	no	—
400	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
401	#107	—	13	1	no	—
402	#107	—	13	1	no	—
403	#106	—	13	1	no	—
404	#106	—	13	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	13	1	no	—
408	C₄⋊C₈	—	13	1	no	—
409	C₄⋊C₈	—	26	1	no	—
410	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
412	#103	—	13	1	no	—
413	#103	—	13	1	no	—
414	#102	—	13	1	no	—
415	#102	—	13	1	no	—
416	#102	—	13	1	no	—
417	#102	—	13	1	no	—
418	#102	—	13	1	no	—
419	#102	—	13	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	—	26	1	no	—
424	C₂²⋊C₈	—	26	1	no	—
425	C₂²⋊C₈	—	26	1	no	—
426	C₂²⋊C₈	—	26	1	no	—
427	#97	—	2	1	no	—
428	#97	—	13	1	no	—
429	#97	—	13	1	no	—
430	#97	—	26	1	no	—
431	#97	C₂²⋊D₁₃	1	1	yes	characteristic
432	#97	C₂²⋊D₁₃	1	1	yes	characteristic
433	C₄×C₈	—	2	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	13	1	no	—
436	C₄×C₈	—	13	1	no	—
437	C₄×C₈	—	13	1	no	—
438	C₄×C₈	—	13	1	no	—
439	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
440	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
441	C₂×C₁₃	—	4	1	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	#2935	1	1	yes	characteristic
444	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂×C₁₃	#2956	1	1	yes	characteristic
446	D₁₃	—	8	1	no	—
447	D₁₃	—	8	1	no	—
448	#41	—	52	2	no	—
449	#41	—	52	2	no	—
450	C₂×Q₈	—	26	1	no	—
451	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	13	1	no	—
454	C₂×D₄	—	13	1	no	—
455	C₂×D₄	—	26	1	no	—
456	C₂×D₄	—	26	1	no	—
457	C₂×D₄	—	26	1	no	—
458	C₂×D₄	—	26	1	no	—
459	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	26	1	no	—
462	C₂²×C₄	—	26	1	no	—
463	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
464	C₂²×C₄	#6127	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
466	SD₁₆	—	26	2	no	—
467	SD₁₆	—	52	1	no	—
468	D₈	—	26	2	no	—
469	D₈	—	52	1	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	2	no	—
473	M₁₆	—	26	2	no	—
474	M₁₆	—	52	2	no	—
475	M₁₆	—	52	1	no	—
476	M₁₆	—	52	2	no	—
477	M₁₆	—	52	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	13	1	no	—
482	C₂×C₈	—	13	1	no	—
483	C₂×C₈	—	13	1	no	—
484	C₂×C₈	—	13	1	no	—
485	C₂×C₈	—	26	1	no	—
486	C₂×C₈	—	26	1	no	—
487	C₂×C₈	—	26	1	no	—
488	C₂×C₈	—	26	1	no	—
489	C₂×C₈	—	52	2	no	—
490	C₂×C₈	—	52	2	no	—
491	C₂×C₈	—	52	2	no	—
492	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
493	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
494	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
495	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	13	1	no	—
501	C₄⋊C₄	—	13	1	no	—
502	C₄⋊C₄	—	26	1	no	—
503	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	26	1	no	—
511	C₂²⋊C₄	—	26	1	no	—
512	C₂²⋊C₄	—	26	1	no	—
513	C₂²⋊C₄	—	26	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
516	C₄²	#6127	1	1	yes	characteristic
517	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
518	C₄²	C₂³×D₁₃	1	1	yes	characteristic
519	C₁₃	#18076	1	1	yes	characteristic, complemented, Sylow
520	C₂³	—	2	1	no	—
521	C₂³	—	26	1	no	—
522	C₂³	—	26	1	no	—
523	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
524	Q₈	—	2	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	52	2	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	26	1	no	—
531	D₄	—	26	1	no	—
532	D₄	—	26	1	no	—
533	D₄	—	26	1	no	—
534	D₄	—	52	2	no	—
535	D₄	—	52	2	no	—
536	D₄	—	52	2	no	—
537	D₄	—	104	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	26	1	no	—
549	C₂×C₄	—	26	1	no	—
550	C₂×C₄	—	52	1	no	—
551	C₂×C₄	—	52	1	no	—
552	C₂×C₄	—	52	1	no	—
553	C₂×C₄	—	52	1	no	—
554	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
555	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂×#6127	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	13	2	no	—
566	C₈	—	26	2	no	—
567	C₈	—	26	1	no	—
568	C₈	—	26	1	no	—
569	C₈	—	26	1	no	—
570	C₈	—	52	1	no	—
571	C₈	—	52	1	no	—
572	C₈	—	52	1	no	—
573	C₈	#88203	1	2	yes	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	52	1	no	—
581	C₂²	—	52	1	no	—
582	C₂²	—	52	1	no	—
583	C₂²	—	52	1	no	—
584	C₂²	—	52	1	no	—
585	C₂²	—	52	1	no	—
586	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	52	1	no	—
595	C₄	—	52	1	no	—
596	C₄	D₁₃×#131	1	1	yes	characteristic
597	C₄	#11719455	1	1	yes	characteristic
598	C₄	C₂×#88203	1	1	yes	characteristic
599	C₄	#11719527	1	1	yes	characteristic
600	C₂	—	4	1	no	—
601	C₂	—	8	1	no	—
602	C₂	—	104	1	no	—
603	C₂	—	104	1	no	—
604	C₂	#13123578	1	1	yes	characteristic
605	C₂	C₄×#88203	1	1	yes	characteristic
606	C₂	#13123743	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2969	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125432	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2969	D₁₃
hypocenter	C₁₃	#18076
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2969

Complements

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

N	H ≅ G/N	type
2. #13123582	C₂	semidirect
3. #13113748	C₂	semidirect
4. #13113726	C₂	semidirect
5. #13113714	C₂	semidirect
6. #13113698	C₂	semidirect
7. #13113670	C₂	semidirect
8. #13113665	C₂	semidirect
9. #13113646	C₂	semidirect
10. C₈×#6104	C₂	semidirect
11. #13113589	C₂	semidirect
12. #13113252	C₂	semidirect
13. #13113249	C₂	semidirect
14. #13113139	C₂	semidirect
15. C₁₃×#2969	C₂	semidirect
218. #2969	D₁₃	semidirect
285. #1055	#131	semidirect
519. C₁₃	#18076	semidirect

Maximal subgroups

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

subgroup	index
#13125432	2
#13123582	2
#13113748	2
#13113726	2
#13113714	2
#13113698	2
#13113670	2
#13113665	2
#13113646	2
C₈×#6104	2
#13113589	2
#13113252	2
#13113249	2
#13113139	2
C₁₃×#2969	2
#18076	13