Subgroups — #15885429

Order 3328.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718857	C₂	1	2	yes	maximal, complemented
2	#13123580	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123404	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115665	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115542	C₂	1	2	yes	maximal, complemented
7	#13115165	C₂	1	2	yes	maximal, complemented
8	#13115113	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×#88202	C₂²	1	2	yes	—
16	C₂×#88202	C₂²	1	2	yes	—
17	C₁₃×#464	C₄	1	2	yes	complemented
18	C₁₃×#463	C₄	1	2	yes	complemented
19	C₁₃×#462	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#461	C₄	1	1	yes	characteristic, complemented
21	C₁₃×#460	C₄	1	1	yes	characteristic, complemented
22	C₁₃×#459	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₃×#416	C₂²	1	2	yes	—
25	C₂×#88077	C₂²	1	1	yes	characteristic
26	C₂×#88077	C₂²	1	2	yes	—
27	C₂×#88077	C₂²	1	2	yes	—
28	C₂×#88077	C₂²	1	1	yes	characteristic
29	#11718895	C₂²	1	2	yes	—
30	#11718857	—	2	8	no	—
31	C₂×#88059	C₂²	1	2	yes	—
32	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
33	#11718673	—	2	1	no	—
34	#11718672	—	2	2	no	—
35	D₄×#1055	—	2	1	no	—
36	#11718660	—	2	2	no	—
37	#11718660	C₂²	1	2	yes	—
38	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
39	#11718585	—	2	1	no	—
40	#11718585	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	—	2	1	no	—
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₄×#6099	C₂²	1	1	yes	characteristic
44	#11718144	C₂²	1	2	yes	—
45	#11718142	C₂²	1	2	yes	—
46	#11718124	C₂²	1	1	yes	characteristic
47	#11718124	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#41	C₂³	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
59	C₁₃×#124	C₂×C₄	1	2	yes	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#121	—	2	1	no	—
62	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	#88202	—	2	4	no	—
75	#88202	—	2	4	no	—
76	#88202	—	4	2	no	—
77	#88202	—	4	2	no	—
78	C₂×C₄×Dic₁₃	—	2	1	no	—
79	C₂×C₄×Dic₁₃	—	2	1	no	—
80	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂×#6099	—	2	2	no	—
83	C₂×#6099	—	2	2	no	—
84	C₂×#6099	C₂³	1	1	yes	characteristic
85	C₂×#6099	C₂³	1	2	yes	—
86	C₂×#6099	C₂³	1	1	yes	characteristic
87	C₂²×#1055	—	2	2	no	—
88	C₂²×#1055	—	2	2	no	—
89	C₂²×#1055	C₂³	1	2	yes	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×#103	C₂×C₄	1	2	yes	—
94	C₁₃×#103	C₂×C₄	1	2	yes	—
95	C₁₃×#102	C₂×C₄	1	2	yes	—
96	C₁₃×#102	C₂×C₄	1	2	yes	—
97	#88077	—	2	2	no	—
98	#88077	—	2	4	no	—
99	#88077	—	4	2	no	—
100	#88077	D₄	1	4	yes	complemented
101	C₂²⋊#1055	—	2	2	no	—
102	C₂²⋊#1055	—	2	2	no	—
103	#88059	—	2	4	no	—
104	C₈×Dic₁₃	—	2	4	no	—
105	C₄⋊#1055	—	2	1	no	—
106	C₄⋊#1055	—	2	1	no	—
107	C₄⋊#1055	—	2	2	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	D₄	1	2	yes	—
110	C₄⋊#1055	D₄	1	1	yes	characteristic
111	C₄⋊#1055	D₄	1	1	yes	characteristic
112	#88043	—	2	1	no	—
113	C₄×#1055	—	2	1	no	—
114	#23015	—	13	1	no	maximal, Sylow
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	C₂×D₄	1	2	yes	—
122	C₁₃×#41	#41	1	2	yes	—
123	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²×Dic₁₃	—	2	1	no	—
139	C₂²×Dic₁₃	—	2	1	no	—
140	C₁₃×Q₁₆	—	2	4	no	—
141	C₁₃×SD₁₆	—	2	4	no	—
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×D₈	—	2	4	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₁₃	—	2	4	no	—
167	C₄×Dic₁₃	—	2	1	no	—
168	C₄×Dic₁₃	—	2	1	no	—
169	C₄×Dic₁₃	—	2	1	no	—
170	C₄×Dic₁₃	—	4	2	no	—
171	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
172	#6099	—	2	1	no	—
173	#6099	—	2	2	no	—
174	#6099	—	2	1	no	—
175	#6099	—	2	2	no	—
176	#6099	—	2	1	no	—
177	#6099	—	4	4	no	—
178	#6099	—	4	4	no	—
179	#6099	C₂×D₄	1	2	yes	—
180	C₂×#1055	—	2	1	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	—	2	2	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	4	4	no	—
186	C₂×#1055	—	4	4	no	—
187	C₂×#1055	C₂×D₄	1	2	yes	—
188	C₂×#1055	C₂×D₄	1	2	yes	—
189	#3035	D₁₃	1	1	yes	characteristic
190	C₂×#443	—	13	2	no	—
191	#2935	—	13	1	no	—
192	#2906	—	13	1	no	—
193	#1962	—	13	1	no	—
194	#1950	—	13	1	no	—
195	#1937	—	13	2	no	—
196	#1876	—	13	2	no	—
197	#1866	—	13	2	no	—
198	C₄×C₄⋊C₈	—	13	1	no	—
199	C₄×#104	—	13	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	—	2	2	no	—
205	Q₈×C₁₃	—	2	2	no	—
206	Q₈×C₁₃	C₄×D₄	1	2	yes	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	1	no	—
211	D₄×C₁₃	—	2	2	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	4	2	no	—
215	D₄×C₁₃	—	8	1	no	—
216	D₄×C₁₃	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	8	1	no	—
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×Dic₁₃	—	2	2	no	—
240	C₂×Dic₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	2	no	—
242	C₂×Dic₁₃	—	2	2	no	—
243	C₂×Dic₁₃	—	4	1	no	—
244	C₂×Dic₁₃	—	4	1	no	—
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	—	2	2	no	—
247	#1055	—	2	2	no	—
248	#1055	—	2	2	no	—
249	#1055	—	2	2	no	—
250	#1055	—	4	2	no	—
251	#1055	—	4	1	no	—
252	C₂×#135	C₂×D₁₃	1	2	yes	—
253	C₂×#131	—	13	2	no	—
254	C₂×#131	—	13	2	no	—
255	#532	C₂×D₁₃	1	1	yes	characteristic
256	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
257	#464	Dic₁₃	1	2	yes	complemented
258	#463	Dic₁₃	1	2	yes	complemented
259	#462	Dic₁₃	1	1	yes	characteristic, complemented
260	#461	Dic₁₃	1	1	yes	characteristic, complemented
261	#460	Dic₁₃	1	1	yes	characteristic, complemented
262	#459	Dic₁₃	1	1	yes	characteristic, complemented
263	#443	—	26	8	no	—
264	#436	—	26	1	no	—
265	#435	—	26	2	no	—
266	C₈×D₄	—	26	1	no	—
267	C₂×#108	—	13	2	no	—
268	#424	—	13	2	no	—
269	#424	—	26	2	no	—
270	#423	—	13	1	no	—
271	#423	—	26	1	no	—
272	C₂×C₄⋊C₈	—	13	1	no	—
273	C₂×C₄⋊C₈	—	26	1	no	—
274	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
275	C₂×#104	—	13	1	no	—
276	C₂×#104	—	13	1	no	—
277	C₂×#104	—	13	2	no	—
278	C₂×#104	—	13	2	no	—
279	#416	C₂×D₁₃	1	2	yes	—
280	#408	—	13	2	no	—
281	C₄×M₁₆	—	13	1	no	—
282	C₂×C₄×C₈	—	13	2	no	—
283	C₄³	—	13	1	no	—
284	#341	—	13	2	no	—
285	#339	—	13	1	no	—
286	#339	—	13	1	no	—
287	#336	—	13	2	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
297	C₂²×C₁₃	#547	1	1	yes	characteristic
298	C₂²×C₁₃	#553	1	1	yes	characteristic
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	1	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	#443	1	2	yes	complemented
307	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₁₃	#520	1	1	yes	characteristic
309	C₄×C₁₃	D₄²	1	1	yes	characteristic
310	C₄×C₁₃	#548	1	1	yes	characteristic
311	Dic₁₃	—	2	4	no	—
312	Dic₁₃	—	4	2	no	—
313	C₂×#41	C₂²×D₁₃	1	2	yes	—
314	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
315	#135	—	2	4	no	—
316	#135	—	2	4	no	—
317	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
318	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
319	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
320	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
321	#131	—	26	4	no	—
322	#131	—	26	4	no	—
323	#131	—	52	2	no	—
324	#131	—	52	2	no	—
325	C₂×M₁₆	—	13	1	no	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂×M₁₆	—	13	1	no	—
328	C₂×M₁₆	—	26	2	no	—
329	C₂×M₁₆	—	26	2	no	—
330	C₂²×C₈	—	13	2	no	—
331	C₂²×C₈	—	26	2	no	—
332	C₂²×C₈	—	26	2	no	—
333	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
334	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
335	#127	C₂×Dic₁₃	1	1	yes	characteristic
336	#124	C₂×Dic₁₃	1	2	yes	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
340	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
346	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	13	1	no	—
351	C₂×C₄²	—	13	1	no	—
352	C₂×C₄²	—	26	1	no	—
353	C₂×C₄²	—	26	1	no	—
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	#108	—	26	4	no	—
356	C₄⋊C₈	—	13	1	no	—
357	C₄⋊C₈	—	13	1	no	—
358	C₄⋊C₈	—	13	2	no	—
359	C₄⋊C₈	—	26	2	no	—
360	C₄⋊C₈	—	26	2	no	—
361	C₄⋊C₈	—	26	1	no	—
362	C₄⋊C₈	—	26	1	no	—
363	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
364	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
365	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
366	#104	—	13	4	no	—
367	#104	—	26	4	no	—
368	#104	—	26	2	no	—
369	#104	—	52	2	no	—
370	#103	C₂×Dic₁₃	1	2	yes	—
371	#103	C₂×Dic₁₃	1	2	yes	—
372	#102	C₂×Dic₁₃	1	2	yes	—
373	#102	C₂×Dic₁₃	1	2	yes	—
374	C₂²⋊C₈	—	26	2	no	—
375	C₂²⋊C₈	—	26	2	no	—
376	#97	—	26	1	no	—
377	C₄×C₈	—	26	4	no	—
378	C₄×C₈	—	26	1	no	—
379	C₂×C₁₃	—	2	1	no	—
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	4	2	no	—
382	C₂×C₁₃	—	8	2	no	—
383	C₂×C₁₃	#2361	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
385	C₂×C₁₃	#2956	1	1	yes	characteristic
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	D₄×D₁₃	1	2	yes	—
393	#41	#6129	1	2	yes	—
394	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
395	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
401	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	26	1	no	—
407	C₂²×C₄	—	26	1	no	—
408	C₂²×C₄	#6129	1	1	yes	characteristic
409	C₂²×C₄	#6129	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
411	Q₁₆	—	2	4	no	—
412	SD₁₆	—	2	4	no	—
413	SD₁₆	—	2	4	no	—
414	D₈	—	2	4	no	—
415	M₁₆	—	13	2	no	—
416	M₁₆	—	26	1	no	—
417	M₁₆	—	26	2	no	—
418	M₁₆	—	26	1	no	—
419	M₁₆	—	26	2	no	—
420	M₁₆	—	26	1	no	—
421	M₁₆	—	52	4	no	—
422	M₁₆	—	52	4	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	13	2	no	—
426	C₂×C₈	—	13	2	no	—
427	C₂×C₈	—	26	2	no	—
428	C₂×C₈	—	26	1	no	—
429	C₂×C₈	—	26	2	no	—
430	C₂×C₈	—	26	1	no	—
431	C₂×C₈	—	26	2	no	—
432	C₂×C₈	—	52	4	no	—
433	C₂×C₈	—	52	4	no	—
434	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
435	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	13	2	no	—
451	C₄²	—	26	4	no	—
452	C₄²	—	26	1	no	—
453	C₄²	—	26	1	no	—
454	C₄²	—	26	1	no	—
455	C₄²	—	52	2	no	—
456	C₄²	D₄×D₁₃	1	1	yes	characteristic
457	C₄²	D₄×D₁₃	1	1	yes	characteristic
458	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
459	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
460	C₁₃	#23015	1	1	yes	characteristic, complemented, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×#6129	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	D₄×Dic₁₃	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	1	no	—
477	D₄	D₄×Dic₁₃	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	1	no	—
490	C₂×C₄	—	26	2	no	—
491	C₂×C₄	—	26	2	no	—
492	C₂×C₄	—	26	2	no	—
493	C₂×C₄	—	26	2	no	—
494	C₂×C₄	—	52	1	no	—
495	C₂×C₄	—	52	1	no	—
496	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
497	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
498	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
499	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
500	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
501	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
502	C₂×C₄	C₂×#6129	1	1	yes	characteristic
503	C₂×C₄	#88256	1	1	yes	characteristic
504	C₂×C₄	#88257	1	1	yes	characteristic
505	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	26	2	no	—
509	C₈	—	26	2	no	—
510	C₈	—	26	2	no	—
511	C₈	—	52	1	no	—
512	C₈	—	52	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	#11719316	1	1	yes	characteristic
522	C₂²	#11719323	1	1	yes	characteristic
523	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	26	4	no	—
532	C₄	—	52	2	no	—
533	C₄	#11718857	1	2	yes	complemented
534	C₄	#11719303	1	1	yes	characteristic
535	C₄	#11719314	1	1	yes	characteristic
536	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
537	C₄	#11719532	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	2	no	—
542	C₂	#13117856	1	1	yes	characteristic
543	C₂	C₂×#11718857	1	1	yes	characteristic
544	C₂	#13123746	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3035	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3035	D₁₃
hypocenter	C₁₃	#23015
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#11718857	C₂	semidirect
2. #13123580	C₂	semidirect
3. #13123404	C₂	semidirect
4. #13115665	C₂	semidirect
5. #13115612	C₂	semidirect
6. #13115542	C₂	semidirect
7. #13115165	C₂	semidirect
8. #13115113	C₂	semidirect
9. C₄⋊C₈×Dic₁₃	C₂	semidirect
10. C₄×#88077	C₂	semidirect
17. C₁₃×#464	C₄	semidirect
18. C₁₃×#463	C₄	semidirect
19. C₁₃×#462	C₄	semidirect
20. C₁₃×#461	C₄	semidirect
21. C₁₃×#460	C₄	semidirect
22. C₁₃×#459	C₄	semidirect
100. #88077	D₄	semidirect
257. #464	Dic₁₃	semidirect
258. #463	Dic₁₃	semidirect
259. #462	Dic₁₃	semidirect
260. #461	Dic₁₃	semidirect
261. #460	Dic₁₃	semidirect
262. #459	Dic₁₃	semidirect
306. C₄×C₁₃	#443	semidirect
460. C₁₃	#23015	semidirect
533. C₄	#11718857	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718857	2
#13123580	2
#13123404	2
#13115665	2
#13115612	2
#13115542	2
#13115165	2
#13115113	2
C₄⋊C₈×Dic₁₃	2
C₄×#88077	2
C₁₃×#3035	2
#23015	13