Subgroups — #15869375

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718858	C₂	1	2	yes	maximal, complemented
2	#13123548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88202	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115756	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115486	C₂	1	2	yes	maximal, complemented
7	#13115165	C₂	1	2	yes	maximal, complemented
8	#13114856	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114706	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114683	C₂	1	2	yes	maximal, 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	1	yes	characteristic
16	C₂×#88202	C₂²	1	2	yes	—
17	C₂×#88202	C₂²	1	1	yes	characteristic
18	C₁₃×#464	C₄	1	2	yes	complemented
19	C₁₃×#463	C₄	1	2	yes	complemented
20	C₁₃×#462	C₄	1	1	yes	characteristic, complemented
21	C₁₃×#461	C₄	1	1	yes	characteristic, complemented
22	C₁₃×#460	C₄	1	1	yes	characteristic, complemented
23	C₁₃×#459	C₄	1	1	yes	characteristic, complemented
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₃×#416	C₂²	1	2	yes	—
26	C₂×#88077	C₂²	1	2	yes	—
27	C₂×#88077	C₂²	1	2	yes	—
28	C₂×#88077	C₂²	1	2	yes	—
29	#11718895	C₂²	1	2	yes	—
30	#11718858	—	2	8	no	—
31	C₂×#88059	C₂²	1	2	yes	—
32	C₂×#88055	C₂²	1	2	yes	—
33	#11718673	—	2	1	no	—
34	#11718673	—	2	1	no	—
35	D₄×#1055	—	2	1	no	—
36	D₄×#1055	—	2	1	no	—
37	#11718658	—	2	1	no	—
38	#11718658	—	2	1	no	—
39	#11718658	C₂²	1	1	yes	characteristic
40	#11718658	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
42	#11718585	C₂²	1	1	yes	characteristic
43	C₄×#6099	—	2	1	no	—
44	C₄×#6099	C₂²	1	1	yes	characteristic
45	C₂×C₄×#1055	—	2	1	no	—
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718144	C₂²	1	2	yes	—
48	#11718142	C₂²	1	2	yes	—
49	#11718124	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
52	C₁₃×#135	—	2	4	no	—
53	C₁₃×#135	—	2	4	no	—
54	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#124	C₂×C₄	1	2	yes	—
62	C₁₃×#121	—	2	1	no	—
63	C₁₃×#121	—	2	1	no	—
64	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	—	2	1	no	—
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#117	—	2	1	no	—
73	C₁₃×#117	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	#88202	—	2	2	no	—
77	#88202	—	2	2	no	—
78	#88202	—	2	2	no	—
79	#88202	—	2	4	no	—
80	#88202	—	2	4	no	—
81	#88202	D₄	1	4	yes	complemented
82	C₂×C₄⋊Dic₁₃	—	2	1	no	—
83	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	2	no	—
87	C₂×#6099	C₂³	1	2	yes	—
88	C₂×#6099	C₂³	1	1	yes	characteristic
89	C₂×#6099	C₂³	1	1	yes	characteristic
90	C₂²×#1055	—	2	1	no	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	—	2	2	no	—
93	C₂²×#1055	C₂³	1	1	yes	characteristic
94	C₂²×#1055	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
98	C₁₃×#103	C₂×C₄	1	2	yes	—
99	C₁₃×#103	C₂×C₄	1	2	yes	—
100	C₁₃×#102	C₂×C₄	1	2	yes	—
101	C₁₃×#102	C₂×C₄	1	2	yes	—
102	#88077	—	2	4	no	—
103	#88077	—	2	4	no	—
104	#88077	—	2	4	no	—
105	#88071	—	2	1	no	—
106	C₂²⋊#1055	—	2	2	no	—
107	C₂²⋊#1055	—	2	2	no	—
108	#88059	—	2	4	no	—
109	#88055	—	2	4	no	—
110	C₄⋊#1055	—	2	1	no	—
111	C₄⋊#1055	—	2	1	no	—
112	#88043	—	2	1	no	—
113	#88043	—	2	1	no	—
114	#88043	—	2	1	no	—
115	C₄×#1055	—	2	1	no	—
116	C₄×#1055	—	2	1	no	—
117	C₄×#1055	—	2	1	no	—
118	C₄×#1055	D₄	1	1	yes	characteristic
119	C₄×#1055	D₄	1	1	yes	characteristic
120	C₄×#1055	D₄	1	1	yes	characteristic
121	C₄×#1055	D₄	1	1	yes	characteristic
122	#21518	—	13	1	no	maximal, Sylow
123	C₁₃×#41	—	2	1	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	C₂×D₄	1	2	yes	—
130	C₁₃×#41	#41	1	2	yes	—
131	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₁₃	—	2	2	no	—
147	C₁₃×Q₁₆	—	2	4	no	—
148	C₁₃×SD₁₆	—	2	4	no	—
149	C₁₃×SD₁₆	—	2	4	no	—
150	C₁₃×D₈	—	2	4	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
161	C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄⋊Dic₁₃	—	4	2	no	—
174	C₄×Dic₁₃	—	2	2	no	—
175	C₄×Dic₁₃	—	2	2	no	—
176	#6099	—	2	4	no	—
177	#6099	—	2	1	no	—
178	#6099	—	2	1	no	—
179	#6099	—	2	4	no	—
180	#6099	—	2	2	no	—
181	#6099	—	2	2	no	—
182	#6099	—	4	4	no	—
183	#6099	C₂×D₄	1	2	yes	—
184	#6099	#41	1	2	yes	—
185	C₂×#1055	—	2	4	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	4	no	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	4	4	no	—
193	C₂×#1055	C₂×D₄	1	1	yes	characteristic
194	C₂×#1055	C₂×D₄	1	1	yes	characteristic
195	C₂×#1055	C₂×D₄	1	1	yes	characteristic
196	C₂×#1055	C₂×D₄	1	1	yes	characteristic
197	C₂×#1055	C₂×D₄	1	2	yes	—
198	C₂×#1055	#41	1	2	yes	—
199	#3035	D₁₃	1	1	yes	characteristic
200	C₂×#444	—	13	2	no	—
201	#2931	—	13	1	no	—
202	C₄×#131	—	13	1	no	—
203	#1980	—	13	1	no	—
204	#1950	—	13	1	no	—
205	#1929	—	13	2	no	—
206	#1876	—	13	2	no	—
207	#1806	—	13	1	no	—
208	#1770	—	13	1	no	—
209	#1765	—	13	2	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	1	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	2	2	no	—
216	Q₈×C₁₃	C₄×D₄	1	2	yes	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	1	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	4	2	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	4	2	no	—
226	D₄×C₁₃	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×Dic₁₃	—	4	2	no	—
250	C₂×Dic₁₃	—	4	2	no	—
251	C₂×Dic₁₃	—	4	2	no	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	—	2	2	no	—
254	#1055	—	2	2	no	—
255	#1055	—	2	1	no	—
256	#1055	—	2	2	no	—
257	#1055	—	2	1	no	—
258	#1055	—	4	2	no	—
259	#1055	#121	1	2	yes	—
260	#1055	#121	1	2	yes	—
261	C₂×#135	C₂×D₁₃	1	2	yes	—
262	C₂×#131	—	13	1	no	—
263	C₂×#131	—	13	1	no	—
264	C₂×#131	—	13	2	no	—
265	#532	C₂×D₁₃	1	1	yes	characteristic
266	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
267	#464	Dic₁₃	1	2	yes	complemented
268	#463	Dic₁₃	1	2	yes	complemented
269	#462	Dic₁₃	1	1	yes	characteristic, complemented
270	#461	Dic₁₃	1	1	yes	characteristic, complemented
271	#460	Dic₁₃	1	1	yes	characteristic, complemented
272	#459	Dic₁₃	1	1	yes	characteristic, complemented
273	#444	—	26	8	no	—
274	#436	—	26	1	no	—
275	#436	—	26	1	no	—
276	C₈×D₄	—	26	1	no	—
277	C₈×D₄	—	26	1	no	—
278	C₂×#108	—	13	2	no	—
279	#423	—	13	1	no	—
280	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
281	C₂×#104	—	13	2	no	—
282	C₂×#104	—	13	2	no	—
283	C₂×#104	—	13	2	no	—
284	#416	C₂×D₁₃	1	2	yes	—
285	#408	—	13	2	no	—
286	#405	—	13	1	no	—
287	#405	—	13	1	no	—
288	#405	—	26	1	no	—
289	#405	—	26	1	no	—
290	C₄×M₁₆	—	13	1	no	—
291	C₄×M₁₆	—	26	1	no	—
292	C₂×#97	—	13	2	no	—
293	C₂×C₄×C₈	—	13	1	no	—
294	C₂×C₄×C₈	—	26	1	no	—
295	C₄×C₄⋊C₄	—	13	1	no	—
296	#341	—	13	2	no	—
297	#339	—	13	2	no	—
298	#336	—	13	2	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₁₃	#529	1	1	yes	characteristic
309	C₂²×C₁₃	#532	1	1	yes	characteristic
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	4	1	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	#444	1	2	yes	complemented
318	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
319	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
320	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
321	C₄×C₁₃	#525	1	1	yes	characteristic
322	Dic₁₃	—	8	2	no	—
323	C₂×#41	C₂²×D₁₃	1	2	yes	—
324	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
325	#135	—	2	4	no	—
326	#135	—	2	4	no	—
327	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
328	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
329	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
330	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
331	#131	—	13	4	no	—
332	#131	—	26	2	no	—
333	#131	—	26	4	no	—
334	#131	—	26	4	no	—
335	#131	—	26	2	no	—
336	#131	—	26	2	no	—
337	C₂×M₁₆	—	13	1	no	—
338	C₂×M₁₆	—	13	1	no	—
339	C₂×M₁₆	—	13	2	no	—
340	C₂×M₁₆	—	26	1	no	—
341	C₂×M₁₆	—	26	1	no	—
342	C₂×M₁₆	—	26	2	no	—
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	13	1	no	—
345	C₂²×C₈	—	26	1	no	—
346	C₂²×C₈	—	26	1	no	—
347	C₂²×C₈	—	26	2	no	—
348	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
349	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
350	#127	C₂×Dic₁₃	1	1	yes	characteristic
351	#124	C₂×Dic₁₃	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
355	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
361	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
362	#117	—	2	1	no	—
363	#117	C₂²×D₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	—	26	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	13	2	no	—
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	#108	—	26	4	no	—
369	C₄⋊C₈	—	26	1	no	—
370	C₄⋊C₈	—	26	1	no	—
371	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
372	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
373	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
374	#104	—	26	4	no	—
375	#104	—	26	4	no	—
376	#104	—	26	4	no	—
377	#103	C₂×Dic₁₃	1	2	yes	—
378	#103	C₂×Dic₁₃	1	2	yes	—
379	#102	C₂×Dic₁₃	1	2	yes	—
380	#102	C₂×Dic₁₃	1	2	yes	—
381	C₂²⋊C₈	—	26	2	no	—
382	C₂²⋊C₈	—	26	2	no	—
383	#97	—	26	1	no	—
384	#97	—	26	1	no	—
385	#97	—	26	4	no	—
386	#97	—	26	1	no	—
387	C₄×C₈	—	13	1	no	—
388	C₄×C₈	—	13	1	no	—
389	C₄×C₈	—	13	1	no	—
390	C₄×C₈	—	13	1	no	—
391	C₄×C₈	—	26	1	no	—
392	C₄×C₈	—	26	1	no	—
393	C₄×C₈	—	26	1	no	—
394	#95	—	26	1	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	4	2	no	—
398	C₂×C₁₃	—	8	2	no	—
399	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
401	C₂×C₁₃	#2955	1	1	yes	characteristic
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	D₄×D₁₃	1	2	yes	—
409	#41	#6129	1	2	yes	—
410	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
411	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
417	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	26	2	no	—
423	C₂²×C₄	#6129	1	1	yes	characteristic
424	C₂²×C₄	#6129	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
426	Q₁₆	—	2	4	no	—
427	SD₁₆	—	2	4	no	—
428	SD₁₆	—	2	4	no	—
429	D₈	—	2	4	no	—
430	M₁₆	—	13	2	no	—
431	M₁₆	—	13	2	no	—
432	M₁₆	—	26	4	no	—
433	M₁₆	—	26	4	no	—
434	M₁₆	—	26	1	no	—
435	M₁₆	—	26	1	no	—
436	M₁₆	—	26	2	no	—
437	M₁₆	—	26	2	no	—
438	M₁₆	—	52	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	13	2	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	13	2	no	—
445	C₂×C₈	—	13	1	no	—
446	C₂×C₈	—	13	1	no	—
447	C₂×C₈	—	26	4	no	—
448	C₂×C₈	—	26	4	no	—
449	C₂×C₈	—	26	1	no	—
450	C₂×C₈	—	26	1	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	52	4	no	—
455	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
456	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	52	2	no	—
462	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	26	2	no	—
473	C₄²	—	26	2	no	—
474	C₄²	D₄×D₁₃	1	1	yes	characteristic
475	C₄²	D₄×D₁₃	1	1	yes	characteristic
476	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
477	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
478	C₁₃	#21518	1	1	yes	characteristic, complemented, Sylow
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×#6129	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	D₄×Dic₁₃	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	D₄×Dic₁₃	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	52	2	no	—
509	C₂×C₄	—	52	2	no	—
510	C₂×C₄	—	52	2	no	—
511	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
512	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
513	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
514	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂×#6129	1	1	yes	characteristic
518	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
519	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	13	2	no	—
524	C₈	—	13	2	no	—
525	C₈	—	26	2	no	—
526	C₈	—	26	1	no	—
527	C₈	—	26	1	no	—
528	C₈	—	26	2	no	—
529	C₈	—	52	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	#11719301	1	1	yes	characteristic
539	C₂²	#11719305	1	1	yes	characteristic
540	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	104	2	no	—
549	C₄	#11718858	1	2	yes	complemented
550	C₄	D₁₃×#121	1	1	yes	characteristic
551	C₄	#11719311	1	1	yes	characteristic
552	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
553	C₄	#41×Dic₁₃	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	#121×Dic₁₃	1	1	yes	characteristic
559	C₂	C₂×#11718858	1	1	yes	characteristic
560	C₂	#13123739	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	#21518
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×#11718858	C₂	semidirect
2. #13123548	C₂	semidirect
3. C₄×#88202	C₂	semidirect
4. #13115756	C₂	semidirect
5. #13115612	C₂	semidirect
6. #13115486	C₂	semidirect
7. #13115165	C₂	semidirect
8. #13114856	C₂	semidirect
9. #13114706	C₂	semidirect
10. #13114683	C₂	semidirect
18. C₁₃×#464	C₄	semidirect
19. C₁₃×#463	C₄	semidirect
20. C₁₃×#462	C₄	semidirect
21. C₁₃×#461	C₄	semidirect
22. C₁₃×#460	C₄	semidirect
23. C₁₃×#459	C₄	semidirect
81. #88202	D₄	semidirect
267. #464	Dic₁₃	semidirect
268. #463	Dic₁₃	semidirect
269. #462	Dic₁₃	semidirect
270. #461	Dic₁₃	semidirect
271. #460	Dic₁₃	semidirect
272. #459	Dic₁₃	semidirect
317. C₄×C₁₃	#444	semidirect
478. C₁₃	#21518	semidirect
549. C₄	#11718858	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718858	2
#13123548	2
C₄×#88202	2
#13115756	2
#13115612	2
#13115486	2
#13115165	2
#13114856	2
#13114706	2
#13114683	2
C₁₃×#3035	2
#21518	13