Subgroups — #15831968

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123955	C₂	1	1	yes	maximal, characteristic
2	#13123950	C₂	1	1	yes	maximal, characteristic
3	C₄×#88161	C₂	1	1	yes	maximal, characteristic
4	#13113603	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113602	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113600	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113597	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113596	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113594	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113593	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113587	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113585	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113581	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88161	C₄	1	1	yes	characteristic
17	C₂×#88161	C₄	1	1	yes	characteristic
18	C₄×#6127	C₂²	1	1	yes	characteristic
19	C₁₃×#432	C₂²	1	1	yes	characteristic
20	C₁₃×#423	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	#11718789	—	2	1	no	—
23	#11718788	—	2	1	no	—
24	#11718783	C₄	1	1	yes	characteristic
25	#11718783	C₄	1	1	yes	characteristic
26	#11718587	C₂²	1	1	yes	characteristic
27	#11718585	C₂²	1	1	yes	characteristic
28	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
29	#11718498	C₂²	1	1	yes	characteristic
30	#11718498	C₂²	1	1	yes	characteristic
31	#11718497	—	2	1	no	—
32	#11718496	C₂²	1	1	yes	characteristic
33	#11718496	C₂²	1	1	yes	characteristic
34	#11718494	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	#11718489	—	2	1	no	—
39	#11718390	—	2	1	no	—
40	#11718389	—	2	1	no	—
41	#11718369	C₄	1	1	yes	characteristic
42	#11718369	C₄	1	1	yes	characteristic
43	#11718369	C₄	1	1	yes	characteristic
44	#11718369	C₄	1	1	yes	characteristic
45	#11718367	—	2	1	no	—
46	#11718362	—	2	1	no	—
47	C₄×#6094	C₂²	1	1	yes	characteristic
48	C₄×#6094	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₁₃	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	#11718071	C₂²	1	1	yes	characteristic
58	#11718071	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	C₂×C₄	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	D₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	D₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₃	Q₈	1	1	yes	characteristic
76	#88180	C₂×C₄	1	1	yes	characteristic
77	C₂×#6099	—	2	1	no	—
78	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
79	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
80	#88161	—	2	4	no	—
81	#88161	—	2	4	no	—
82	C₂×#6094	—	2	1	no	—
83	C₂×#6094	—	2	1	no	—
84	C₂×#6094	C₂×C₄	1	1	yes	characteristic
85	C₂×#6094	C₂×C₄	1	1	yes	characteristic
86	C₂×#6094	C₂×C₄	1	1	yes	characteristic
87	C₂×#6094	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₁₃	—	2	1	no	—
89	C₂×C₈×D₁₃	—	2	1	no	—
90	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
94	C₄×D₅₂	D₄	1	1	yes	characteristic
95	C₄×D₅₂	Q₈	1	1	yes	characteristic
96	#88126	C₂×C₄	1	1	yes	characteristic
97	#88126	C₂×C₄	1	1	yes	characteristic
98	C₄²×D₁₃	C₂³	1	1	yes	characteristic
99	C₄²×D₁₃	C₂³	1	1	yes	characteristic
100	C₄×Dic₂₆	D₄	1	1	yes	characteristic
101	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₂²⋊C₈	—	2	1	no	—
108	C₁₃×#97	—	2	1	no	—
109	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²⋊#1055	—	2	1	no	—
114	#88060	—	2	1	no	—
115	#88060	—	2	1	no	—
116	#88060	—	2	1	no	—
117	#88060	—	2	1	no	—
118	#88055	—	2	1	no	—
119	#88055	—	2	1	no	—
120	#88055	C₂×C₄	1	1	yes	characteristic
121	#88055	C₂×C₄	1	1	yes	characteristic
122	#88055	C₂×C₄	1	1	yes	characteristic
123	#88055	C₂×C₄	1	1	yes	characteristic
124	#88054	—	2	1	no	—
125	#88054	—	2	1	no	—
126	#88054	—	2	1	no	—
127	#88054	—	2	1	no	—
128	C₈×Dic₁₃	—	2	1	no	—
129	C₈×Dic₁₃	—	2	1	no	—
130	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#1055	—	2	1	no	—
135	C₄⋊#1055	C₂³	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	#88043	—	2	1	no	—
140	C₄×#1055	C₂×C₄	1	1	yes	characteristic
141	C₄×#1055	C₂×C₄	1	1	yes	characteristic
142	C₄×#1055	C₂³	1	1	yes	characteristic
143	C₄×#1055	C₂³	1	1	yes	characteristic
144	#17799	—	13	1	no	maximal, Sylow
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
150	#6127	—	2	2	no	—
151	#6127	—	2	2	no	—
152	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
159	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	8	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	—	2	1	no	—
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	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
174	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	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	#6103	C₄⋊C₄	1	1	yes	characteristic
181	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
182	C₄⋊Dic₁₃	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	#6101	C₄⋊C₄	1	1	yes	characteristic
187	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
192	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
193	#6099	—	8	1	no	—
194	C₂×#1055	—	2	2	no	—
195	C₂×#1055	—	2	2	no	—
196	C₂×#1055	—	2	1	no	—
197	C₂×#1055	—	2	1	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
201	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
202	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
203	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
204	#6094	—	2	2	no	—
205	#6094	—	2	2	no	—
206	#6094	—	2	2	no	—
207	#6094	—	8	1	no	—
208	#6094	—	8	1	no	—
209	#6094	M₁₆	1	4	yes	complemented
210	C₈×D₁₃	—	2	2	no	—
211	C₈×D₁₃	—	2	2	no	—
212	C₈×D₁₃	—	2	2	no	—
213	C₈×D₁₃	—	8	1	no	—
214	C₈×D₁₃	—	8	1	no	—
215	C₈×D₁₃	M₁₆	1	4	yes	complemented
216	#2989	—	13	1	no	—
217	#2989	—	13	1	no	—
218	C₄×#131	—	13	1	no	—
219	#1569	—	13	1	no	—
220	#1569	—	13	1	no	—
221	#1569	—	13	1	no	—
222	#1569	D₁₃	1	1	yes	characteristic, complemented
223	#1568	—	13	1	no	—
224	#1568	—	13	1	no	—
225	#1567	—	13	1	no	—
226	#1567	—	13	1	no	—
227	#1565	—	13	1	no	—
228	#1565	—	13	1	no	—
229	#1564	—	13	1	no	—
230	C₂×#335	—	13	1	no	—
231	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
245	C₂²⋊D₁₃	—	2	2	no	—
246	C₂²⋊D₁₃	—	2	2	no	—
247	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
253	D₅₂	—	2	2	no	—
254	C₄×D₁₃	—	2	1	no	—
255	C₄×D₁₃	—	2	1	no	—
256	C₄×D₁₃	—	2	1	no	—
257	C₄×D₁₃	—	2	1	no	—
258	C₄×D₁₃	—	2	1	no	—
259	C₄×D₁₃	—	2	1	no	—
260	C₄×D₁₃	—	4	1	no	—
261	C₄×D₁₃	—	4	1	no	—
262	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
263	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
264	Dic₂₆	—	2	2	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
272	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
273	#1055	—	2	1	no	—
274	#1055	—	2	1	no	—
275	#1055	—	4	1	no	—
276	#1055	—	4	1	no	—
277	#1055	—	4	1	no	—
278	#1055	—	4	1	no	—
279	#1055	C₂×M₁₆	1	2	yes	—
280	#1055	C₂×M₁₆	1	2	yes	—
281	C₂×#131	—	13	1	no	—
282	C₂×#131	—	13	1	no	—
283	C₄×#41	—	13	1	no	—
284	#446	—	26	1	no	—
285	#446	—	26	1	no	—
286	#436	—	26	1	no	—
287	#436	—	26	1	no	—
288	#435	—	26	1	no	—
289	#435	—	26	1	no	—
290	#435	—	26	1	no	—
291	#435	—	26	1	no	—
292	#432	—	13	1	no	—
293	#432	—	13	1	no	—
294	#432	—	13	1	no	—
295	#432	C₂×D₁₃	1	1	yes	characteristic
296	#431	—	13	1	no	—
297	#431	—	13	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	#405	—	13	1	no	—
305	#405	—	13	1	no	—
306	#405	—	13	1	no	—
307	#405	—	13	1	no	—
308	#405	—	13	1	no	—
309	#405	—	13	1	no	—
310	C₄×M₁₆	—	13	1	no	—
311	C₄×M₁₆	—	13	1	no	—
312	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
313	C₂×C₄×C₈	—	13	1	no	—
314	C₂×C₄×C₈	—	13	1	no	—
315	C₂×C₄×C₈	—	13	1	no	—
316	#335	—	13	1	no	—
317	#335	—	13	1	no	—
318	#335	—	13	1	no	—
319	#335	—	13	1	no	—
320	#335	—	13	1	no	—
321	#335	—	13	1	no	—
322	#335	—	13	1	no	—
323	#335	—	13	1	no	—
324	#335	C₂×D₁₃	1	1	yes	characteristic
325	#335	C₂×D₁₃	1	1	yes	characteristic
326	#334	—	13	1	no	—
327	#334	—	13	1	no	—
328	#334	—	13	1	no	—
329	#334	—	13	1	no	—
330	#334	C₂×D₁₃	1	1	yes	characteristic
331	#334	C₂×D₁₃	1	1	yes	characteristic
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	1	no	—
341	C₂×D₁₃	#423	1	2	yes	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
347	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
348	C₄×C₁₃	#576	1	1	yes	characteristic
349	C₄×C₁₃	#578	1	1	yes	characteristic
350	Dic₁₃	—	2	1	no	—
351	Dic₁₃	—	2	1	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	2	1	no	—
355	Dic₁₃	#423	1	2	yes	—
356	C₂×#41	—	13	1	no	—
357	#131	—	26	4	no	—
358	#131	—	26	4	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	13	1	no	—
361	C₂×M₁₆	—	13	1	no	—
362	C₂×M₁₆	—	13	1	no	—
363	C₂×M₁₆	—	13	1	no	—
364	C₂×M₁₆	—	26	1	no	—
365	C₂×M₁₆	—	26	1	no	—
366	C₂×M₁₆	—	26	1	no	—
367	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
368	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
369	C₂²×C₈	—	13	1	no	—
370	C₂²×C₈	—	13	1	no	—
371	C₂²×C₈	—	13	1	no	—
372	C₂²×C₈	—	13	1	no	—
373	C₂²×C₈	—	13	1	no	—
374	C₂²×C₈	—	13	1	no	—
375	C₂²×C₈	—	26	1	no	—
376	C₂²×C₈	—	26	1	no	—
377	C₄×Q₈	—	13	1	no	—
378	C₄×Q₈	—	13	1	no	—
379	C₄×D₄	—	13	1	no	—
380	C₄×D₄	—	13	1	no	—
381	C₄×D₄	—	13	1	no	—
382	C₄×D₄	—	13	1	no	—
383	C₄×D₄	—	13	1	no	—
384	C₄×D₄	—	13	1	no	—
385	#117	—	13	1	no	—
386	#117	—	13	1	no	—
387	#117	—	13	1	no	—
388	C₂×C₄²	—	13	1	no	—
389	C₂×C₄²	—	13	1	no	—
390	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	13	1	no	—
393	C₄⋊C₈	—	13	1	no	—
394	C₄⋊C₈	—	13	1	no	—
395	C₄⋊C₈	—	13	1	no	—
396	C₄⋊C₈	—	26	1	no	—
397	C₄⋊C₈	—	26	1	no	—
398	C₄⋊C₈	—	26	1	no	—
399	C₄⋊C₈	—	26	1	no	—
400	C₄⋊C₈	—	26	1	no	—
401	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
403	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	26	1	no	—
407	C₂²⋊C₈	—	26	1	no	—
408	C₂²⋊C₈	—	26	1	no	—
409	C₂²⋊C₈	—	26	1	no	—
410	C₂²⋊C₈	—	26	1	no	—
411	#97	—	2	1	no	—
412	#97	—	13	1	no	—
413	#97	—	13	1	no	—
414	#97	—	13	1	no	—
415	#97	—	13	1	no	—
416	#97	—	26	1	no	—
417	#97	—	26	1	no	—
418	#97	—	26	1	no	—
419	#97	C₄×D₁₃	1	1	yes	characteristic
420	#97	C₄×D₁₃	1	1	yes	characteristic
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	13	1	no	—
423	C₄×C₈	—	13	1	no	—
424	C₄×C₈	—	13	1	no	—
425	C₄×C₈	—	13	1	no	—
426	C₄×C₈	—	13	1	no	—
427	C₄×C₈	—	13	1	no	—
428	C₄×C₈	—	13	1	no	—
429	C₄×C₈	—	26	1	no	—
430	C₄×C₈	—	26	1	no	—
431	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
433	C₂×C₁₃	—	4	1	no	—
434	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
435	C₂×C₁₃	#2913	1	1	yes	characteristic
436	C₂×C₁₃	#2916	1	1	yes	characteristic
437	D₁₃	—	2	2	no	—
438	D₁₃	—	4	1	no	—
439	#41	—	26	2	no	—
440	#41	—	26	2	no	—
441	C₂×Q₈	—	13	1	no	—
442	C₂×D₄	—	13	1	no	—
443	C₂×D₄	—	13	1	no	—
444	C₂×D₄	—	13	1	no	—
445	C₂²×C₄	—	13	1	no	—
446	C₂²×C₄	—	13	1	no	—
447	C₂²×C₄	—	13	1	no	—
448	C₂²×C₄	—	13	1	no	—
449	C₂²×C₄	—	13	1	no	—
450	C₂²×C₄	—	13	1	no	—
451	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
453	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	8	1	no	—
457	M₁₆	—	13	4	no	—
458	M₁₆	—	26	2	no	—
459	M₁₆	—	26	2	no	—
460	M₁₆	—	26	2	no	—
461	M₁₆	—	104	1	no	—
462	M₁₆	—	104	1	no	—
463	M₁₆	—	104	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	13	1	no	—
469	C₂×C₈	—	13	1	no	—
470	C₂×C₈	—	13	4	no	—
471	C₂×C₈	—	13	1	no	—
472	C₂×C₈	—	13	1	no	—
473	C₂×C₈	—	26	2	no	—
474	C₂×C₈	—	26	2	no	—
475	C₂×C₈	—	26	2	no	—
476	C₂×C₈	—	26	2	no	—
477	C₂×C₈	—	26	2	no	—
478	C₂×C₈	—	26	1	no	—
479	C₂×C₈	—	26	1	no	—
480	C₂×C₈	—	26	1	no	—
481	C₂×C₈	—	26	1	no	—
482	C₂×C₈	—	104	1	no	—
483	C₂×C₈	—	104	1	no	—
484	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₂²⋊C₄	—	13	1	no	—
495	C₂²⋊C₄	—	13	1	no	—
496	C₂²⋊C₄	—	13	1	no	—
497	C₂²⋊C₄	—	13	1	no	—
498	C₂²⋊C₄	—	13	1	no	—
499	C₂²⋊C₄	—	13	1	no	—
500	C₄²	—	13	1	no	—
501	C₄²	—	13	1	no	—
502	C₄²	—	13	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	—	13	1	no	—
505	C₄²	—	13	1	no	—
506	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
507	C₄²	D₄×D₁₃	1	1	yes	characteristic
508	C₄²	Q₈×D₁₃	1	1	yes	characteristic
509	C₄²	C₂³×D₁₃	1	1	yes	characteristic
510	C₁₃	#17799	1	1	yes	characteristic, complemented, Sylow
511	C₂³	—	13	1	no	—
512	C₂³	—	13	1	no	—
513	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
514	Q₈	—	26	2	no	—
515	D₄	—	26	2	no	—
516	D₄	—	26	2	no	—
517	D₄	—	26	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	13	1	no	—
524	C₂×C₄	—	13	2	no	—
525	C₂×C₄	—	13	2	no	—
526	C₂×C₄	—	13	1	no	—
527	C₂×C₄	—	13	1	no	—
528	C₂×C₄	—	13	1	no	—
529	C₂×C₄	—	13	1	no	—
530	C₂×C₄	—	13	1	no	—
531	C₂×C₄	—	26	1	no	—
532	C₂×C₄	—	26	1	no	—
533	C₂×C₄	—	26	1	no	—
534	C₂×C₄	—	26	1	no	—
535	C₂×C₄	—	26	1	no	—
536	C₂×C₄	—	26	1	no	—
537	C₂×C₄	—	52	1	no	—
538	C₂×C₄	—	52	1	no	—
539	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
540	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
541	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	13	2	no	—
552	C₈	—	13	2	no	—
553	C₈	—	26	1	no	—
554	C₈	—	26	1	no	—
555	C₈	—	52	1	no	—
556	C₈	—	52	1	no	—
557	C₈	—	52	1	no	—
558	C₈	—	52	1	no	—
559	C₈	M₁₆×D₁₃	1	2	yes	—
560	C₈	M₁₆×D₁₃	1	2	yes	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	13	2	no	—
565	C₂²	—	26	1	no	—
566	C₂²	—	26	1	no	—
567	C₂²	—	26	1	no	—
568	C₂²	—	26	1	no	—
569	C₂²	—	26	1	no	—
570	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	13	2	no	—
576	C₄	—	26	1	no	—
577	C₄	—	26	1	no	—
578	C₄	—	26	1	no	—
579	C₄	—	26	1	no	—
580	C₄	—	26	1	no	—
581	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
582	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
583	C₄	#11719479	1	1	yes	characteristic
584	C₄	#11719484	1	1	yes	characteristic
585	C₂	—	4	1	no	—
586	C₂	—	26	2	no	—
587	C₂	—	52	1	no	—
588	C₂	D₁₃×#423	1	1	yes	characteristic
589	C₂	#13123435	1	1	yes	characteristic
590	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	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1569	D₁₃
hypocenter	C₁₃	#17799
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. #13113603	C₂	semidirect
5. #13113602	C₂	semidirect
6. #13113600	C₂	semidirect
7. #13113597	C₂	semidirect
8. #13113596	C₂	semidirect
9. #13113594	C₂	semidirect
10. #13113593	C₂	semidirect
11. #13113587	C₂	semidirect
12. #13113585	C₂	semidirect
13. #13113581	C₂	semidirect
14. D₁₃×#335	C₂	semidirect
15. C₁₃×#1569	C₂	semidirect
209. #6094	M₁₆	semidirect
215. C₈×D₁₃	M₁₆	semidirect
222. #1569	D₁₃	semidirect
510. C₁₃	#17799	semidirect

Maximal subgroups

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

subgroup	index
#13123955	2
#13123950	2
C₄×#88161	2
#13113603	2
#13113602	2
#13113600	2
#13113597	2
#13113596	2
#13113594	2
#13113593	2
#13113587	2
#13113585	2
#13113581	2
D₁₃×#335	2
C₁₃×#1569	2
#17799	13