Subgroups — #16785749

Order 3328.

714 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	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#13130544	C₂	1	2	yes	maximal
4	#13130529	C₂	1	2	yes	maximal
5	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
7	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	D₁₃×#117	C₂²	1	1	yes	characteristic
11	D₁₃⋊#108	—	2	1	no	—
12	D₁₃⋊#108	—	2	1	no	—
13	D₁₃⋊#108	—	2	1	no	—
14	D₁₃⋊#108	—	2	1	no	—
15	D₁₃⋊#108	—	2	1	no	—
16	D₁₃⋊#108	—	2	1	no	—
17	D₁₃⋊#108	C₄	1	2	yes	complemented
18	D₁₃⋊#108	C₄	1	2	yes	complemented
19	C₂×#88104	—	2	1	no	—
20	C₂×#88104	C₄	1	2	yes	complemented
21	C₂×#88103	—	2	1	no	—
22	C₂×#88103	C₄	1	2	yes	complemented
23	C₁₃×#405	C₄	1	1	yes	characteristic
24	#11718783	C₄	1	1	yes	characteristic
25	#11718762	C₄	1	1	yes	characteristic
26	#11718658	C₄	1	1	yes	characteristic
27	#11718369	—	2	1	no	—
28	D₁₃×#97	—	2	1	no	—
29	#11718350	—	2	1	no	—
30	C₄×C₈×D₁₃	—	2	1	no	—
31	#11718273	—	2	4	no	—
32	#11718239	—	2	4	no	—
33	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
34	C₂×#6122	—	2	2	no	—
35	C₂×#6122	—	2	2	no	—
36	D₁₃⋊M₁₆	—	2	2	no	—
37	D₁₃⋊M₁₆	—	2	2	no	—
38	D₁₃⋊M₁₆	—	2	2	no	—
39	D₁₃⋊M₁₆	—	2	2	no	—
40	D₁₃⋊M₁₆	—	2	2	no	—
41	D₁₃⋊M₁₆	—	2	2	no	—
42	D₁₃⋊M₁₆	—	2	2	no	—
43	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
44	C₂×#6118	—	2	2	no	—
45	C₂×#6118	C₂×C₄	1	4	yes	—
46	C₂×D₁₃⋊C₈	—	2	2	no	—
47	C₂×D₁₃⋊C₈	—	2	2	no	—
48	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
51	#88180	C₂×C₄	1	1	yes	characteristic
52	C₂×#6099	C₂×C₄	1	1	yes	characteristic
53	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
54	M₁₆×D₁₃	—	2	1	no	—
55	M₁₆×D₁₃	—	2	1	no	—
56	M₁₆×D₁₃	D₄	1	2	yes	—
57	M₁₆×D₁₃	Q₈	1	2	yes	—
58	C₂×#6094	—	2	1	no	—
59	C₂×C₈×D₁₃	—	2	1	no	—
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
68	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
71	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
72	#88146	—	2	1	no	—
73	C₄⋊C₄×D₁₃	—	2	1	no	—
74	C₂²⋊C₄×D₁₃	Q₈	1	2	yes	—
75	#88131	D₄	1	2	yes	—
76	#88126	—	2	1	no	—
77	C₄²×D₁₃	—	2	1	no	—
78	#88104	—	2	2	no	—
79	#88104	—	2	2	no	—
80	#88104	—	2	2	no	—
81	#88104	—	2	2	no	—
82	#88103	—	2	2	no	—
83	#88103	—	2	2	no	—
84	#88103	—	2	2	no	—
85	#88103	—	2	2	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	#88055	—	2	1	no	—
89	#88055	—	2	1	no	—
90	C₈×Dic₁₃	—	2	1	no	—
91	C₈×Dic₁₃	—	2	1	no	—
92	#88043	—	2	1	no	—
93	C₄×#1055	—	2	1	no	—
94	#10873	—	13	1	no	maximal, Sylow
95	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
108	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
109	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
110	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
111	#6122	—	2	4	no	—
112	#6122	—	4	2	no	—
113	#6122	—	4	2	no	—
114	#6122	—	4	2	no	—
115	C₂×#1057	—	2	4	no	—
116	C₂×#1057	—	4	2	no	—
117	#6118	—	2	4	no	—
118	#6118	—	2	4	no	—
119	#6118	—	2	4	no	—
120	#6118	—	4	2	no	—
121	D₁₃⋊C₈	—	2	4	no	—
122	D₁₃⋊C₈	—	4	2	no	—
123	D₁₃⋊C₈	—	4	2	no	—
124	D₁₃⋊C₈	—	4	2	no	—
125	C₁₃×M₁₆	—	2	1	no	—
126	C₁₃×M₁₆	C₄⋊C₄	1	2	yes	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₂²⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
138	#6103	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	1	no	—
140	#6101	—	2	2	no	—
141	C₄×Dic₁₃	—	2	1	no	—
142	C₄×Dic₁₃	—	2	2	no	—
143	#6099	—	2	1	no	—
144	#6099	C₄⋊C₄	1	2	yes	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	C₄²	1	1	yes	characteristic
147	C₂×#1055	C₄²	1	1	yes	characteristic
148	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
151	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
152	#6094	—	2	2	no	—
153	#6094	—	2	2	no	—
154	C₈×D₁₃	—	2	2	no	—
155	C₈×D₁₃	—	2	2	no	—
156	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
165	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
166	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
167	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
168	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
169	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
170	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
171	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
172	C₂²×#108	—	13	1	no	—
173	C₂²×#108	—	13	1	no	—
174	C₂×#405	—	13	1	no	—
175	C₂×#344	—	13	2	no	—
176	#1738	—	13	2	no	—
177	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×D₁₃	—	4	2	no	—
179	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
180	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
181	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
184	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
192	C₂×Dic₁₃	—	2	2	no	—
193	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
195	C₂×Dic₁₃	#121	1	1	yes	characteristic
196	C₂×Dic₁₃	#121	1	1	yes	characteristic
197	C₂×Dic₁₃	#127	1	1	yes	characteristic
198	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
199	C₄×D₁₃	—	4	4	no	—
200	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
205	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
206	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
207	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
208	C₄×D₁₃	#121	1	1	yes	characteristic
209	C₄×D₁₃	#121	1	1	yes	characteristic
210	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
211	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×D₁₃	#124	1	1	yes	characteristic
213	C₄×D₁₃	#124	1	1	yes	characteristic
214	C₄×D₁₃	#125	1	1	yes	characteristic
215	C₄×D₁₃	#125	1	1	yes	characteristic
216	#1057	—	4	4	no	—
217	#1057	—	4	4	no	—
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	#95	1	1	yes	characteristic
220	C₈×C₁₃	#95	1	1	yes	characteristic
221	C₈×C₁₃	#95	1	1	yes	characteristic
222	C₈×C₁₃	#95	1	1	yes	characteristic
223	#1055	—	2	2	no	—
224	#1055	#95	1	1	yes	characteristic
225	#1055	#95	1	1	yes	characteristic
226	#1055	#95	1	1	yes	characteristic
227	#1055	#95	1	1	yes	characteristic
228	C₂²×M₁₆	—	13	1	no	—
229	C₂²×M₁₆	—	13	2	no	—
230	C₂²×M₁₆	—	13	2	no	—
231	C₂³×C₈	—	13	1	no	—
232	C₂×#117	—	13	1	no	—
233	C₂×#108	—	13	2	no	—
234	C₂×#108	—	13	2	no	—
235	C₂×#108	—	13	2	no	—
236	C₂×#108	—	13	2	no	—
237	C₂×#108	—	26	1	no	—
238	C₂×#108	—	26	1	no	—
239	C₂×#108	—	26	1	no	—
240	C₂×#108	—	26	1	no	—
241	C₂×#108	—	26	1	no	—
242	C₂×#108	—	26	1	no	—
243	C₂×#108	—	26	1	no	—
244	C₂×#108	—	26	1	no	—
245	#405	—	13	1	no	—
246	#405	—	13	1	no	—
247	#405	—	13	1	no	—
248	#405	—	26	1	no	—
249	#405	—	26	1	no	—
250	#405	#261	1	1	yes	characteristic
251	C₂×#97	—	26	1	no	—
252	C₂×C₄×C₈	—	26	1	no	—
253	#344	—	26	4	no	—
254	#341	—	26	4	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₁₃	#380	1	1	yes	characteristic
258	C₂²×C₁₃	#384	1	1	yes	characteristic
259	C₂×D₁₃	—	2	2	no	—
260	C₂×D₁₃	—	2	2	no	—
261	C₂×D₁₃	—	2	2	no	—
262	C₂×D₁₃	—	4	1	no	—
263	C₂×D₁₃	—	4	1	no	—
264	C₂×D₁₃	—	4	1	no	—
265	C₂×D₁₃	#389	1	1	yes	characteristic
266	C₂×D₁₃	#389	1	1	yes	characteristic
267	C₂×D₁₃	#391	1	1	yes	characteristic
268	C₂×D₁₃	#391	1	1	yes	characteristic
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
271	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
272	C₄×C₁₃	#380	1	1	yes	characteristic
273	C₄×C₁₃	#382	1	1	yes	characteristic
274	Dic₁₃	—	4	2	no	—
275	Dic₁₃	#389	1	1	yes	characteristic
276	Dic₁₃	#389	1	1	yes	characteristic
277	Dic₁₃	#390	1	1	yes	characteristic
278	Dic₁₃	#390	1	1	yes	characteristic
279	C₂³×C₄	—	13	1	no	—
280	C₂×M₁₆	—	13	1	no	—
281	C₂×M₁₆	—	13	2	no	—
282	C₂×M₁₆	—	13	2	no	—
283	C₂×M₁₆	—	13	4	no	—
284	C₂×M₁₆	—	13	4	no	—
285	C₂×M₁₆	—	26	1	no	—
286	C₂×M₁₆	—	26	1	no	—
287	C₂×M₁₆	—	26	1	no	—
288	C₂×M₁₆	—	26	2	no	—
289	C₂×M₁₆	—	26	2	no	—
290	C₂×M₁₆	—	26	2	no	—
291	C₂×M₁₆	—	26	2	no	—
292	C₂×M₁₆	—	26	2	no	—
293	C₂×M₁₆	—	26	2	no	—
294	C₂×M₁₆	—	26	2	no	—
295	C₂×M₁₆	—	26	2	no	—
296	C₂×M₁₆	—	26	2	no	—
297	C₂×M₁₆	—	26	2	no	—
298	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
299	C₂²×C₈	—	13	1	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	—	13	1	no	—
305	C₂²×C₈	—	13	1	no	—
306	C₂²×C₈	—	13	1	no	—
307	C₂²×C₈	—	13	1	no	—
308	C₂²×C₈	—	13	1	no	—
309	C₂²×C₈	—	13	1	no	—
310	C₂²×C₈	—	13	1	no	—
311	C₂²×C₈	—	13	1	no	—
312	C₂²×C₈	—	26	1	no	—
313	C₂²×C₈	—	26	2	no	—
314	C₂²×C₈	—	26	2	no	—
315	C₂²×C₈	C₂×#261	1	1	yes	characteristic
316	#117	—	13	1	no	—
317	#117	—	13	2	no	—
318	#117	—	26	1	no	—
319	#117	—	26	1	no	—
320	#117	C₂×#261	1	1	yes	characteristic
321	C₂×C₄⋊C₄	—	26	1	no	—
322	C₂×C₂²⋊C₄	—	13	2	no	—
323	C₂×C₄²	—	26	1	no	—
324	#108	—	26	2	no	—
325	#108	—	26	2	no	—
326	#108	—	26	2	no	—
327	#108	—	26	2	no	—
328	#108	—	26	2	no	—
329	#108	—	26	2	no	—
330	#108	—	26	2	no	—
331	#108	—	26	2	no	—
332	#97	—	2	1	no	—
333	#97	—	26	1	no	—
334	#97	—	26	1	no	—
335	#97	—	26	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	26	1	no	—
338	C₄×C₈	—	26	1	no	—
339	C₄×C₈	—	26	1	no	—
340	C₂×C₁₃	—	2	1	no	—
341	C₂×C₁₃	—	2	1	no	—
342	C₂×C₁₃	—	2	1	no	—
343	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
344	D₁₃	—	2	1	no	—
345	D₁₃	—	2	1	no	—
346	D₁₃	—	2	1	no	—
347	D₁₃	#1953	1	2	yes	—
348	C₂⁴	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	26	2	no	—
363	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
364	M₁₆	—	2	1	no	—
365	M₁₆	—	13	2	no	—
366	M₁₆	—	26	2	no	—
367	M₁₆	—	26	2	no	—
368	M₁₆	—	26	1	no	—
369	M₁₆	—	26	4	no	—
370	M₁₆	—	26	4	no	—
371	M₁₆	—	26	4	no	—
372	M₁₆	—	26	4	no	—
373	M₁₆	—	52	2	no	—
374	M₁₆	—	52	2	no	—
375	M₁₆	—	52	2	no	—
376	M₁₆	—	52	2	no	—
377	M₁₆	C₄⋊#261	1	2	yes	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	13	1	no	—
385	C₂×C₈	—	13	1	no	—
386	C₂×C₈	—	13	1	no	—
387	C₂×C₈	—	13	1	no	—
388	C₂×C₈	—	13	1	no	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	13	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	13	1	no	—
393	C₂×C₈	—	13	1	no	—
394	C₂×C₈	—	13	1	no	—
395	C₂×C₈	—	13	1	no	—
396	C₂×C₈	—	13	1	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	13	1	no	—
400	C₂×C₈	—	13	1	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	1	no	—
404	C₂×C₈	—	26	4	no	—
405	C₂×C₈	—	26	4	no	—
406	C₂×C₈	—	52	2	no	—
407	C₂×C₈	—	52	2	no	—
408	C₂×C₈	—	52	2	no	—
409	C₂×C₈	—	52	2	no	—
410	C₂×C₈	C₄×#261	1	1	yes	characteristic
411	C₂×C₈	C₄×#261	1	1	yes	characteristic
412	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
413	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
414	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
415	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	26	2	no	—
418	C₄⋊C₄	—	26	1	no	—
419	C₂²⋊C₄	—	13	2	no	—
420	C₂²⋊C₄	—	26	2	no	—
421	C₂²⋊C₄	C₄⋊#261	1	2	yes	—
422	C₄²	—	2	1	no	—
423	C₄²	—	26	2	no	—
424	C₄²	—	26	1	no	—
425	C₁₃	#10873	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	13	1	no	—
427	C₂³	—	13	1	no	—
428	C₂³	—	13	1	no	—
429	C₂³	—	13	1	no	—
430	C₂³	—	13	1	no	—
431	C₂³	—	13	1	no	—
432	C₂³	—	52	2	no	—
433	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	13	1	no	—
445	C₂×C₄	—	13	1	no	—
446	C₂×C₄	—	13	1	no	—
447	C₂×C₄	—	13	1	no	—
448	C₂×C₄	—	13	1	no	—
449	C₂×C₄	—	13	1	no	—
450	C₂×C₄	—	13	1	no	—
451	C₂×C₄	—	13	1	no	—
452	C₂×C₄	—	13	1	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	13	1	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	26	2	no	—
458	C₂×C₄	—	52	4	no	—
459	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
460	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
461	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
462	C₂×C₄	#88237	1	1	yes	characteristic
463	C₂×C₄	#88237	1	1	yes	characteristic
464	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	13	1	no	—
467	C₈	—	13	1	no	—
468	C₈	—	13	1	no	—
469	C₈	—	13	1	no	—
470	C₈	—	26	2	no	—
471	C₈	—	52	4	no	—
472	C₈	—	52	4	no	—
473	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
474	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
475	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
476	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
477	C₂²	—	4	1	no	—
478	C₂²	—	13	1	no	—
479	C₂²	—	13	1	no	—
480	C₂²	—	13	1	no	—
481	C₂²	—	13	1	no	—
482	C₂²	—	26	2	no	—
483	C₂²	—	26	2	no	—
484	C₂²	—	26	2	no	—
485	C₂²	—	52	1	no	—
486	C₂²	—	52	1	no	—
487	C₂²	—	52	1	no	—
488	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
489	C₂²	#11719059	1	1	yes	characteristic
490	C₂²	#11719136	1	1	yes	characteristic
491	C₄	—	4	2	no	—
492	C₄	—	13	1	no	—
493	C₄	—	13	1	no	—
494	C₄	—	13	1	no	—
495	C₄	—	13	1	no	—
496	C₄	—	52	2	no	—
497	C₄	C₄×C₄⋊#261	1	1	yes	characteristic
498	C₄	#11719060	1	1	yes	characteristic
499	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
500	C₄	#11719136	1	1	yes	characteristic
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	13	2	no	—
505	C₂	—	26	1	no	—
506	C₂	—	26	1	no	—
507	C₂	—	26	1	no	—
508	C₂	#13130014	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11719136
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×#405	C₄
socle	C₂×C₁₃	C₄⋊#95
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×D₁₃	C₂³
hypercenter	#405	#261
hypocenter	C₁₃	#10873
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
17. D₁₃⋊#108	C₄	semidirect
18. D₁₃⋊#108	C₄	semidirect
20. C₂×#88104	C₄	semidirect
22. C₂×#88103	C₄	semidirect
425. C₁₃	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊#108	2
#13130544	2
#13130529	2
D₁₃×#405	2
#10873	13