Subgroups — #13128925

Order 1664.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719407	C₂	1	2	yes	maximal, complemented
3	#11719406	C₂	1	2	yes	maximal, complemented
4	#11719402	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719401	C₂	1	2	yes	maximal, complemented
6	#11719390	C₂	1	2	yes	maximal, complemented
7	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719355	C₂	1	2	yes	maximal, complemented
9	#11719354	C₂	1	2	yes	maximal
10	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719277	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719272	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719243	C₂	1	1	yes	maximal, characteristic
17	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719236	C₂	1	2	yes	maximal, complemented
20	#11719222	C₂	1	2	yes	maximal, complemented
21	#11719221	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88141	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
26	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
27	C₁₃×#126	C₂²	1	2	yes	—
28	C₁₃×#125	C₂²	1	2	yes	—
29	C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₁₃×#123	C₂²	1	2	yes	—
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#117	C₂²	1	2	yes	—
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
39	#88198	C₂²	1	1	yes	characteristic
40	#88198	C₂²	1	1	yes	characteristic
41	#88193	C₂²	1	1	yes	characteristic
42	#88189	C₂²	1	1	yes	characteristic
43	D₄×Dic₁₃	C₂²	1	2	yes	—
44	#88183	C₂²	1	2	yes	—
45	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
47	#88180	C₂²	1	2	yes	—
48	#88180	C₂²	1	1	yes	characteristic
49	#88178	C₂²	1	1	yes	characteristic
50	#88178	C₂²	1	1	yes	characteristic
51	C₂×#6101	C₂²	1	2	yes	—
52	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
53	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	1	yes	characteristic
57	#88152	C₂²	1	2	yes	—
58	#88151	C₂²	1	1	yes	characteristic
59	#88151	C₂²	1	1	yes	characteristic
60	#88150	C₂²	1	2	yes	—
61	#88150	C₂²	1	2	yes	—
62	#88146	C₂²	1	1	yes	characteristic
63	#88146	C₂²	1	2	yes	—
64	#88144	C₂²	1	1	yes	characteristic
65	#88144	C₂²	1	2	yes	—
66	#88144	C₂²	1	2	yes	—
67	#88144	C₂²	1	2	yes	—
68	#88143	C₂²	1	2	yes	—
69	#88143	C₂²	1	2	yes	—
70	#88143	C₂²	1	2	yes	—
71	#88143	C₂²	1	1	yes	characteristic
72	#88143	C₂²	1	2	yes	—
73	#88143	C₂²	1	2	yes	—
74	#88143	C₂²	1	2	yes	—
75	#88143	C₂²	1	2	yes	—
76	#88142	C₂²	1	2	yes	—
77	#88142	C₂²	1	2	yes	—
78	#88142	C₂²	1	1	yes	characteristic
79	#88142	C₂²	1	2	yes	—
80	#88142	C₂²	1	2	yes	—
81	#88141	C₂²	1	1	yes	characteristic
82	#88141	C₂²	1	1	yes	characteristic
83	#88141	C₂²	1	1	yes	characteristic
84	#88141	C₂²	1	1	yes	characteristic
85	#88141	C₂²	1	2	yes	—
86	#88141	C₂²	1	2	yes	—
87	#88141	C₂²	1	1	yes	characteristic
88	#88141	C₂²	1	1	yes	characteristic
89	#88141	C₂²	1	1	yes	characteristic
90	#88141	C₂²	1	2	yes	—
91	#88141	C₂²	1	2	yes	—
92	#88141	C₂²	1	2	yes	—
93	#88140	C₂²	1	1	yes	characteristic
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	1	yes	characteristic
96	#88135	C₂²	1	2	yes	—
97	#88135	C₂²	1	2	yes	—
98	#88133	C₂²	1	2	yes	—
99	#88133	C₂²	1	1	yes	characteristic
100	#88133	C₂²	1	2	yes	—
101	#88133	C₂²	1	2	yes	—
102	#88132	C₂²	1	1	yes	characteristic
103	#88132	C₂²	1	2	yes	—
104	#88132	C₂²	1	2	yes	—
105	#88132	C₂²	1	2	yes	—
106	#88132	C₂²	1	2	yes	—
107	#88132	C₂²	1	2	yes	—
108	#88131	C₂²	1	2	yes	—
109	#88131	C₂²	1	2	yes	—
110	#88131	C₂²	1	2	yes	—
111	#88130	C₂²	1	2	yes	—
112	#88126	C₂²	1	2	yes	—
113	#88126	C₂²	1	1	yes	characteristic
114	#88124	C₂²	1	2	yes	—
115	#88123	C₂²	1	1	yes	characteristic
116	C₄×Dic₂₆	C₂²	1	2	yes	—
117	C₄×Dic₂₆	C₂²	1	2	yes	—
118	C₄×Dic₂₆	C₂²	1	2	yes	—
119	C₄×Dic₂₆	C₂²	1	2	yes	—
120	C₄×Dic₂₆	C₂²	1	2	yes	—
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	Q₈×D₁₃	—	2	4	no	—
135	C₂×C₄×D₁₃	C₂³	1	2	yes	—
136	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₆	—	2	4	no	—
138	C₂×Dic₂₆	—	2	4	no	—
139	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
140	C₂×Dic₂₆	C₂³	1	2	yes	—
141	C₂×Dic₂₆	C₂³	1	2	yes	—
142	C₂×Dic₂₆	C₂³	1	2	yes	—
143	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₂₆	C₂³	1	2	yes	—
146	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₄²×C₁₃	C₂³	1	2	yes	—
163	C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
166	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
167	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	#6103	C₂³	1	1	yes	characteristic
172	#6103	C₂³	1	2	yes	—
173	#6103	C₂³	1	1	yes	characteristic
174	#6103	C₂³	1	1	yes	characteristic
175	#6103	C₂³	1	2	yes	—
176	#6103	C₂³	1	2	yes	—
177	#6103	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₁₃	C₂³	1	2	yes	—
183	C₄⋊Dic₁₃	C₂³	1	2	yes	—
184	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₁₃	C₂³	1	2	yes	—
186	C₄⋊Dic₁₃	C₂³	1	2	yes	—
187	C₄⋊Dic₁₃	C₂³	1	2	yes	—
188	#6101	C₂³	1	2	yes	—
189	#6101	C₂³	1	1	yes	characteristic
190	#6101	C₂³	1	1	yes	characteristic
191	#6101	C₂³	1	2	yes	—
192	#6101	C₂³	1	2	yes	—
193	#6101	C₂³	1	2	yes	—
194	#6101	C₂³	1	2	yes	—
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	2	yes	—
197	#6101	C₂³	1	2	yes	—
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	2	yes	—
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	C₄×Dic₁₃	C₂³	1	2	yes	—
211	C₄×Dic₁₃	C₂³	1	2	yes	—
212	C₄×Dic₁₃	C₂³	1	2	yes	—
213	C₄×Dic₁₃	C₂³	1	2	yes	—
214	C₄×Dic₁₃	C₂³	1	2	yes	—
215	C₄×Dic₁₃	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	#3523	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²⋊D₁₃	—	2	2	no	—
244	C₂²⋊D₁₃	—	2	2	no	—
245	C₂×Dic₁₃	—	2	2	no	—
246	C₂×Dic₁₃	—	2	4	no	—
247	C₂×Dic₁₃	—	2	4	no	—
248	C₂×Dic₁₃	—	2	2	no	—
249	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₃	C₂⁴	1	2	yes	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₄×D₁₃	—	2	2	no	—
261	C₄×D₁₃	—	2	4	no	—
262	Dic₂₆	—	2	2	no	—
263	Dic₂₆	—	2	2	no	—
264	Dic₂₆	—	2	4	no	—
265	Dic₂₆	—	2	4	no	—
266	Dic₂₆	—	2	4	no	—
267	Dic₂₆	—	2	2	no	—
268	Dic₂₆	—	2	4	no	—
269	Dic₂₆	#41	1	4	yes	—
270	#557	—	13	1	no	—
271	#557	—	13	2	no	—
272	#557	—	13	1	no	—
273	#556	—	13	2	no	—
274	#556	—	13	1	no	—
275	#552	—	13	2	no	—
276	#552	—	13	2	no	—
277	#552	—	13	1	no	—
278	#552	D₁₃	1	1	yes	characteristic, complemented
279	D₄×Q₈	—	13	1	no	—
280	D₄×Q₈	—	13	1	no	—
281	D₄×Q₈	—	13	1	no	—
282	#541	—	13	2	no	—
283	#541	—	13	2	no	—
284	#541	—	13	1	no	—
285	#541	—	13	1	no	—
286	#533	—	13	1	no	—
287	#533	—	13	2	no	—
288	#529	—	13	2	no	—
289	#529	—	13	1	no	—
290	#519	—	13	1	no	—
291	#519	—	13	1	no	—
292	C₂×C₄×Q₈	—	13	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	—	2	1	no	—
295	C₂²×C₁₃	—	2	1	no	—
296	C₂²×C₁₃	—	2	1	no	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
299	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₃	—	2	1	no	—
301	C₂×D₁₃	—	2	1	no	—
302	C₂×D₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	C₂×#41	1	2	yes	—
312	Dic₁₃	—	2	1	no	—
313	Dic₁₃	—	2	2	no	—
314	Dic₁₃	—	2	2	no	—
315	Dic₁₃	—	2	1	no	—
316	Dic₁₃	—	2	2	no	—
317	Dic₁₃	—	2	1	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	—	2	1	no	—
320	Dic₁₃	—	2	1	no	—
321	Dic₁₃	C₂×#41	1	4	yes	—
322	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
323	C₂²×Q₈	—	13	1	no	—
324	C₂²×Q₈	—	13	1	no	—
325	C₂²×Q₈	—	13	1	no	—
326	C₄⋊Q₈	—	13	1	no	—
327	C₄⋊Q₈	—	13	1	no	—
328	C₄⋊Q₈	—	13	2	no	—
329	C₄⋊Q₈	—	13	2	no	—
330	C₄⋊Q₈	—	13	1	no	—
331	C₄⋊Q₈	—	13	2	no	—
332	C₄⋊Q₈	—	13	2	no	—
333	C₄⋊Q₈	—	13	1	no	—
334	#126	—	13	2	no	—
335	#126	—	13	1	no	—
336	#126	—	13	2	no	—
337	#126	—	13	2	no	—
338	#126	—	13	1	no	—
339	#126	—	13	2	no	—
340	#126	—	13	2	no	—
341	#126	—	13	2	no	—
342	#126	—	13	2	no	—
343	#126	C₂×D₁₃	1	2	yes	—
344	#125	—	13	1	no	—
345	#125	—	13	2	no	—
346	#125	—	13	2	no	—
347	#125	—	13	2	no	—
348	#125	—	13	2	no	—
349	#125	—	13	2	no	—
350	#125	—	13	2	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	—	13	1	no	—
356	#125	—	13	2	no	—
357	#125	C₂×D₁₃	1	1	yes	characteristic
358	#125	C₂×D₁₃	1	2	yes	—
359	#124	—	13	1	no	—
360	#124	—	13	2	no	—
361	#123	—	13	1	no	—
362	#123	—	13	2	no	—
363	#123	—	13	1	no	—
364	#123	C₂×D₁₃	1	2	yes	—
365	C₂²⋊Q₈	—	13	1	no	—
366	C₂²⋊Q₈	—	13	1	no	—
367	C₂²⋊Q₈	—	13	2	no	—
368	C₂²⋊Q₈	—	13	1	no	—
369	C₂²⋊Q₈	—	13	2	no	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	2	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
378	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
379	#121	—	13	1	no	—
380	C₄×Q₈	—	13	1	no	—
381	C₄×Q₈	—	13	1	no	—
382	C₄×Q₈	—	13	2	no	—
383	C₄×Q₈	—	13	1	no	—
384	C₄×Q₈	—	13	1	no	—
385	C₄×Q₈	—	13	2	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	1	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	—	13	2	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	2	no	—
392	C₄×Q₈	—	13	2	no	—
393	C₄×Q₈	—	13	2	no	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	2	no	—
397	C₄×Q₈	—	13	1	no	—
398	C₄×Q₈	—	13	2	no	—
399	C₄×Q₈	—	13	2	no	—
400	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
407	#117	—	13	1	no	—
408	#117	—	13	2	no	—
409	#117	—	13	2	no	—
410	#117	—	13	1	no	—
411	#117	—	13	2	no	—
412	#117	—	13	2	no	—
413	#117	—	13	2	no	—
414	#117	—	13	1	no	—
415	#117	—	13	2	no	—
416	#117	C₂×D₁₃	1	1	yes	characteristic
417	#117	C₂×D₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	—	13	2	no	—
419	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
420	C₂×C₄²	—	13	1	no	—
421	C₂×C₄²	—	13	2	no	—
422	C₂×C₁₃	—	2	2	no	—
423	C₂×C₁₃	—	4	1	no	—
424	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
425	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	D₁₃	—	4	1	no	—
428	C₂×Q₈	—	13	1	no	—
429	C₂×Q₈	—	13	2	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×Q₈	—	13	2	no	—
432	C₂×Q₈	—	13	2	no	—
433	C₂×Q₈	—	13	2	no	—
434	C₂×Q₈	—	13	1	no	—
435	C₂×Q₈	—	13	1	no	—
436	C₂×Q₈	—	26	4	no	—
437	C₂×Q₈	—	26	4	no	—
438	C₂×Q₈	—	26	4	no	—
439	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
440	C₂×D₄	—	13	1	no	—
441	C₂×D₄	—	13	1	no	—
442	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	1	no	—
445	C₂²×C₄	—	13	2	no	—
446	C₂²×C₄	—	13	2	no	—
447	C₂²×C₄	—	13	2	no	—
448	C₂²×C₄	—	13	1	no	—
449	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
450	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
452	C₄⋊C₄	—	13	2	no	—
453	C₄⋊C₄	—	13	2	no	—
454	C₄⋊C₄	—	13	2	no	—
455	C₄⋊C₄	—	13	2	no	—
456	C₄⋊C₄	—	13	2	no	—
457	C₄⋊C₄	—	13	2	no	—
458	C₄⋊C₄	—	13	1	no	—
459	C₄⋊C₄	—	13	2	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	13	2	no	—
462	C₄⋊C₄	—	13	1	no	—
463	C₄⋊C₄	—	13	1	no	—
464	C₄⋊C₄	—	13	2	no	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	2	no	—
467	C₄⋊C₄	—	13	2	no	—
468	C₄⋊C₄	—	13	2	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	2	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	1	no	—
473	C₄⋊C₄	—	13	2	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	2	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	1	no	—
483	C₄⋊C₄	—	13	1	no	—
484	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
494	C₂²⋊C₄	—	13	1	no	—
495	C₂²⋊C₄	—	13	1	no	—
496	C₂²⋊C₄	—	13	1	no	—
497	C₂²⋊C₄	—	13	2	no	—
498	C₂²⋊C₄	—	13	1	no	—
499	C₂²⋊C₄	—	13	2	no	—
500	C₂²⋊C₄	—	13	1	no	—
501	C₂²⋊C₄	—	13	1	no	—
502	C₂²⋊C₄	—	13	2	no	—
503	C₂²⋊C₄	—	13	1	no	—
504	C₂²⋊C₄	—	13	2	no	—
505	C₂²⋊C₄	—	13	1	no	—
506	C₂²⋊C₄	—	13	2	no	—
507	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
512	C₄²	—	13	2	no	—
513	C₄²	—	13	1	no	—
514	C₄²	—	13	2	no	—
515	C₄²	—	13	1	no	—
516	C₄²	—	13	1	no	—
517	C₄²	—	13	2	no	—
518	C₄²	—	13	1	no	—
519	C₄²	—	13	2	no	—
520	C₄²	—	13	2	no	—
521	C₄²	—	13	2	no	—
522	C₄²	—	13	2	no	—
523	C₄²	—	13	2	no	—
524	C₄²	—	13	2	no	—
525	C₄²	—	13	2	no	—
526	C₄²	—	13	1	no	—
527	C₄²	C₂²×D₁₃	1	2	yes	—
528	C₄²	C₂²×D₁₃	1	1	yes	characteristic
529	C₄²	C₂²×D₁₃	1	2	yes	—
530	C₁₃	#3523	1	1	yes	characteristic, complemented, Sylow
531	C₂³	—	13	1	no	—
532	C₂³	C₂³×D₁₃	1	1	yes	characteristic
533	C₂³	C₂³×D₁₃	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	13	4	no	—
536	Q₈	—	26	4	no	—
537	Q₈	—	26	2	no	—
538	Q₈	—	26	4	no	—
539	Q₈	—	26	4	no	—
540	Q₈	—	26	4	no	—
541	Q₈	—	26	2	no	—
542	Q₈	—	26	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	26	2	no	—
545	D₄	—	26	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	13	1	no	—
550	C₂×C₄	—	13	2	no	—
551	C₂×C₄	—	13	1	no	—
552	C₂×C₄	—	13	1	no	—
553	C₂×C₄	—	13	1	no	—
554	C₂×C₄	—	13	2	no	—
555	C₂×C₄	—	13	1	no	—
556	C₂×C₄	—	13	1	no	—
557	C₂×C₄	—	13	2	no	—
558	C₂×C₄	—	13	1	no	—
559	C₂×C₄	—	13	2	no	—
560	C₂×C₄	—	26	4	no	—
561	C₂×C₄	—	26	2	no	—
562	C₂×C₄	—	26	4	no	—
563	C₂×C₄	—	26	4	no	—
564	C₂×C₄	—	26	2	no	—
565	C₂×C₄	—	26	2	no	—
566	C₂×C₄	C₂³×D₁₃	1	2	yes	—
567	C₂×C₄	C₂³×D₁₃	1	2	yes	—
568	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₃	1	2	yes	—
570	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₃	1	2	yes	—
572	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	26	1	no	—
581	C₂²	—	26	1	no	—
582	C₂²	—	26	1	no	—
583	C₂²	#88257	1	2	yes	—
584	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	13	4	no	—
594	C₄	—	13	2	no	—
595	C₄	—	26	1	no	—
596	C₄	—	26	2	no	—
597	C₄	—	26	2	no	—
598	C₄	—	26	1	no	—
599	C₄	—	26	1	no	—
600	C₄	—	26	1	no	—
601	C₄	—	26	1	no	—
602	C₄	—	26	1	no	—
603	C₄	—	26	2	no	—
604	C₄	#41×D₁₃	1	2	yes	—
605	C₂	—	2	2	no	—
606	C₂	—	4	1	no	—
607	C₂	—	52	1	no	—
608	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
609	C₂	C₂×#88257	1	1	yes	characteristic
610	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#552	C₂
prime radical	#88193	C₂²
hypercenter	#552	D₁₃
hypocenter	C₁₃	#3523
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₃×#552	C₂	semidirect
2. #11719407	C₂	semidirect
3. #11719406	C₂	semidirect
4. #11719402	C₂	semidirect
5. #11719401	C₂	semidirect
6. #11719390	C₂	semidirect
7. #11719390	C₂	semidirect
8. #11719355	C₂	semidirect
10. #11719337	C₂	semidirect
11. #11719337	C₂	semidirect
12. #11719330	C₂	semidirect
13. #11719327	C₂	semidirect
14. #11719277	C₂	semidirect
15. #11719272	C₂	semidirect
17. D₄×Dic₂₆	C₂	semidirect
18. #11719238	C₂	semidirect
19. #11719236	C₂	semidirect
20. #11719222	C₂	semidirect
21. #11719221	C₂	semidirect
22. #11719218	C₂	semidirect
23. C₂×#88141	C₂	semidirect
278. #552	D₁₃	semidirect
530. C₁₃	#3523	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#552	2
#11719407	2
#11719406	2
#11719402	2
#11719401	2
#11719390	2
#11719355	2
#11719354	2
#11719337	2
#11719330	2
#11719327	2
#11719277	2
#11719272	2
#11719243	2
D₄×Dic₂₆	2
#11719238	2
#11719236	2
#11719222	2
#11719221	2
#11719218	2
C₂×#88141	2
#3523	13