Subgroups — #15863094

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718554	C₂	1	1	yes	maximal, characteristic
2	#13123424	C₂	1	1	yes	maximal, characteristic
3	#13123252	C₂	1	1	yes	maximal, characteristic
4	#13114961	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114960	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114959	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114958	C₂	1	2	yes	maximal, complemented
8	#13114957	C₂	1	2	yes	maximal, complemented
9	D₁₃×#344	C₂	1	2	yes	maximal
10	D₁₃×H(3,ℤ/4)	C₂	1	2	yes	maximal
11	C₁₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6094	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	D₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
18	C₁₃×#427	C₂²	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	1	yes	characteristic
20	C₂×#88062	C₂²	1	2	yes	—
21	#11718783	C₂²	1	1	yes	characteristic
22	C₂×#88059	C₂²	1	1	yes	characteristic
23	#11718767	C₂²	1	1	yes	characteristic
24	#11718762	C₂²	1	1	yes	characteristic
25	#11718659	C₂²	1	2	yes	—
26	#11718658	C₂²	1	1	yes	characteristic
27	#11718554	—	2	2	no	—
28	#11718554	—	2	2	no	—
29	#11718542	—	2	2	no	—
30	#11718522	—	2	2	no	—
31	#11718369	C₄	1	2	yes	complemented
32	#11718368	C₄	1	2	yes	complemented
33	#11718350	C₄	1	2	yes	complemented
34	C₄×#6094	C₄	1	2	yes	complemented
35	C₁₃×#344	C₂²	1	2	yes	—
36	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	—
37	#11718151	C₂²	1	2	yes	—
38	#11718149	C₂²	1	2	yes	—
39	#11718148	C₂²	1	2	yes	—
40	#11718125	C₂²	1	2	yes	—
41	#11718123	C₂²	1	2	yes	—
42	#11718123	C₂²	1	2	yes	—
43	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
45	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×#117	C₂³	1	2	yes	—
48	C₁₃×#117	C₂³	1	1	yes	characteristic
49	#88180	C₂³	1	2	yes	—
50	#88180	C₂³	1	1	yes	characteristic
51	C₂×#6099	C₂³	1	2	yes	—
52	C₂×#6099	C₂³	1	1	yes	characteristic
53	C₂²×#1055	C₂³	1	1	yes	characteristic
54	M₁₆×D₁₃	—	2	2	no	—
55	M₁₆×D₁₃	—	2	2	no	—
56	M₁₆×D₁₃	—	2	2	no	—
57	M₁₆×D₁₃	—	2	2	no	—
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	—	2	2	no	—
60	C₂×#6094	—	2	2	no	—
61	C₂×#6094	C₂×C₄	1	2	yes	—
62	C₂×#6094	C₂×C₄	1	1	yes	characteristic
63	C₂×#6094	C₂×C₄	1	1	yes	characteristic
64	C₂×#6094	C₂×C₄	1	1	yes	characteristic
65	C₂×#6094	C₂×C₄	1	1	yes	characteristic
66	C₂×#6094	D₄	1	2	yes	—
67	C₂×#6094	D₄	1	2	yes	—
68	C₂×#6094	Q₈	1	2	yes	—
69	C₂×#6094	Q₈	1	2	yes	—
70	C₂×C₈×D₁₃	—	2	2	no	—
71	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
72	#88146	—	2	1	no	—
73	#88146	—	2	2	no	—
74	C₄⋊C₄×D₁₃	—	2	1	no	—
75	C₄⋊C₄×D₁₃	—	2	2	no	—
76	C₂²⋊C₄×D₁₃	—	2	1	no	—
77	C₂²⋊C₄×D₁₃	—	2	2	no	—
78	#88131	—	2	1	no	—
79	#88131	—	2	2	no	—
80	#88126	—	2	2	no	—
81	#88126	C₂×C₄	1	2	yes	—
82	C₄²×D₁₃	—	2	2	no	—
83	C₄²×D₁₃	C₂×C₄	1	2	yes	—
84	C₁₃×#108	—	2	1	no	—
85	C₁₃×#108	—	2	1	no	—
86	C₁₃×#107	—	2	1	no	—
87	C₁₃×#106	—	2	1	no	—
88	C₁₃×#97	C₂×C₄	1	2	yes	complemented
89	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
90	#88062	—	2	4	no	—
91	#88059	—	2	1	no	—
92	#88059	—	2	1	no	—
93	#88058	—	2	1	no	—
94	#88057	—	2	1	no	—
95	#88055	C₂×C₄	1	2	yes	complemented
96	#88055	C₂×C₄	1	2	yes	complemented
97	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
98	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
99	#88048	—	2	2	no	—
100	#88047	—	2	2	no	—
101	#88043	C₂×C₄	1	2	yes	complemented
102	C₄×#1055	C₂×C₄	1	2	yes	complemented
103	#20757	—	13	1	no	maximal, Sylow
104	C₂³×D₁₃	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₁₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₁₃	—	2	2	no	—
108	C₂×C₄×D₁₃	—	4	2	no	—
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
112	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
113	C₂×C₄×D₁₃	#41	1	2	yes	—
114	C₂×C₄×D₁₃	#41	1	2	yes	—
115	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
117	C₁₃×M₁₆	—	2	1	no	—
118	C₁₃×M₁₆	—	2	1	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂²⋊Dic₁₃	—	2	1	no	—
136	C₂²⋊Dic₁₃	—	2	2	no	—
137	#6103	—	2	2	no	—
138	#6103	—	4	2	no	—
139	C₄⋊Dic₁₃	—	2	1	no	—
140	C₄⋊Dic₁₃	—	2	2	no	—
141	#6101	—	2	2	no	—
142	#6101	—	4	2	no	—
143	C₄×Dic₁₃	—	2	2	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	—	4	2	no	—
146	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
147	#6099	—	2	1	no	—
148	#6099	—	2	1	no	—
149	#6099	—	2	2	no	—
150	#6099	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	C₂²×C₄	1	2	yes	—
153	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
154	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂×D₄	1	2	yes	—
156	C₂×#1055	C₂×Q₈	1	2	yes	—
157	#6094	—	2	4	no	—
158	#6094	—	4	2	no	—
159	#6094	—	4	2	no	—
160	#6094	C₄⋊C₄	1	2	yes	—
161	#6094	C₄⋊C₄	1	2	yes	—
162	#6094	C₄⋊C₄	1	2	yes	—
163	#6094	C₄⋊C₄	1	2	yes	—
164	#6094	C₄⋊C₄	1	2	yes	—
165	#6094	C₄⋊C₄	1	2	yes	—
166	#6094	C₄⋊C₄	1	2	yes	—
167	#6094	C₄⋊C₄	1	2	yes	—
168	C₈×D₁₃	—	2	4	no	—
169	C₈×D₁₃	—	4	2	no	—
170	C₈×D₁₃	—	4	2	no	—
171	C₂×#430	—	13	1	no	—
172	#2911	—	13	1	no	—
173	#2873	—	13	1	no	—
174	#1833	—	13	1	no	—
175	#1833	—	13	1	no	—
176	#1833	—	13	1	no	—
177	#1833	—	13	2	no	—
178	#1833	—	13	2	no	—
179	#1833	D₁₃	1	1	yes	characteristic, complemented
180	C₂×#344	—	13	2	no	—
181	C₂×H(3,ℤ/4)	—	13	2	no	—
182	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂²×D₁₃	—	8	1	no	—
184	C₂²×D₁₃	#117	1	1	yes	characteristic
185	C₂²×D₁₃	#117	1	1	yes	characteristic
186	C₂²×D₁₃	#124	1	2	yes	—
187	C₂²×D₁₃	#125	1	2	yes	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	4	2	no	—
198	C₂×Dic₁₃	#117	1	1	yes	characteristic
199	C₂×Dic₁₃	#117	1	1	yes	characteristic
200	C₂×Dic₁₃	#124	1	2	yes	—
201	C₂×Dic₁₃	#125	1	2	yes	—
202	C₄×D₁₃	—	8	2	no	—
203	C₄×D₁₃	—	8	4	no	—
204	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₄×D₁₃	#117	1	2	yes	—
207	C₄×D₁₃	#117	1	2	yes	—
208	C₄×D₁₃	#124	1	2	yes	—
209	C₄×D₁₃	#124	1	2	yes	—
210	C₄×D₁₃	#125	1	2	yes	—
211	C₄×D₁₃	#125	1	2	yes	—
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	—	4	2	no	—
214	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
218	#1055	—	2	2	no	—
219	#1055	—	4	2	no	—
220	#1055	C₂×C₄⋊C₄	1	2	yes	—
221	#1055	C₂×C₄⋊C₄	1	2	yes	—
222	C₂²×M₁₆	—	13	1	no	—
223	C₂²×M₁₆	—	13	1	no	—
224	C₂²×M₁₆	—	13	2	no	—
225	C₂×#117	—	13	1	no	—
226	C₂×#117	—	13	2	no	—
227	#430	—	26	2	no	—
228	#430	—	26	2	no	—
229	C₂×#108	—	13	2	no	—
230	C₂×#108	—	13	1	no	—
231	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
232	#428	—	26	2	no	—
233	#428	—	26	2	no	—
234	#427	—	13	1	no	—
235	#427	—	13	2	no	—
236	#427	C₂×D₁₃	1	1	yes	characteristic
237	#405	—	13	1	no	—
238	#405	—	13	1	no	—
239	#405	—	13	1	no	—
240	#405	—	13	2	no	—
241	#405	—	13	2	no	—
242	#405	C₂×D₁₃	1	1	yes	characteristic
243	C₄×M₁₆	—	13	2	no	—
244	C₄×M₁₆	—	13	2	no	—
245	#344	—	13	2	no	—
246	#344	—	13	2	no	—
247	#344	—	13	2	no	—
248	#344	C₂×D₁₃	1	2	yes	—
249	H(3,ℤ/4)	—	13	2	no	—
250	H(3,ℤ/4)	—	13	2	no	—
251	H(3,ℤ/4)	—	13	2	no	—
252	H(3,ℤ/4)	C₂×D₁₃	1	2	yes	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
257	C₂×D₁₃	—	4	1	no	—
258	C₂×D₁₃	—	4	2	no	—
259	C₂×D₁₃	—	4	1	no	—
260	C₂×D₁₃	—	4	2	no	—
261	C₂×D₁₃	#382	1	2	yes	—
262	C₂×D₁₃	#382	1	2	yes	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
267	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
268	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
269	Dic₁₃	—	4	2	no	—
270	Dic₁₃	—	8	2	no	—
271	Dic₁₃	#382	1	2	yes	—
272	Dic₁₃	#382	1	2	yes	—
273	C₂³×C₄	—	13	1	no	—
274	C₂×M₁₆	—	13	1	no	—
275	C₂×M₁₆	—	13	1	no	—
276	C₂×M₁₆	—	13	1	no	—
277	C₂×M₁₆	—	13	1	no	—
278	C₂×M₁₆	—	13	1	no	—
279	C₂×M₁₆	—	13	2	no	—
280	C₂×M₁₆	—	13	2	no	—
281	C₂×M₁₆	—	13	2	no	—
282	C₂×M₁₆	—	13	2	no	—
283	C₂×M₁₆	—	13	2	no	—
284	C₂×M₁₆	—	13	2	no	—
285	C₂×M₁₆	—	26	2	no	—
286	C₂×M₁₆	—	26	2	no	—
287	C₂×M₁₆	—	26	2	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	C₂²×D₁₃	1	2	yes	—
293	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	13	2	no	—
296	C₂²×C₈	—	26	2	no	—
297	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
298	#117	—	13	1	no	—
299	#117	—	13	2	no	—
300	#117	—	13	2	no	—
301	#117	—	26	2	no	—
302	#117	—	26	1	no	—
303	#117	—	26	1	no	—
304	#117	—	26	2	no	—
305	#117	—	26	2	no	—
306	#117	C₂²×D₁₃	1	2	yes	—
307	#117	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	—	26	1	no	—
309	C₂×C₄⋊C₄	—	26	2	no	—
310	C₂×C₂²⋊C₄	—	26	1	no	—
311	C₂×C₂²⋊C₄	—	26	2	no	—
312	C₂×C₄²	—	13	2	no	—
313	C₂×C₄²	—	26	2	no	—
314	#108	—	2	1	no	—
315	#108	—	2	1	no	—
316	#108	—	26	4	no	—
317	#108	—	26	1	no	—
318	#108	—	26	1	no	—
319	#107	—	2	1	no	—
320	#107	—	26	2	no	—
321	#107	—	26	1	no	—
322	#106	—	2	1	no	—
323	#106	—	26	2	no	—
324	#106	—	26	1	no	—
325	#97	—	13	2	no	—
326	#97	—	13	2	no	—
327	#97	—	13	2	no	—
328	#97	C₄×D₁₃	1	2	yes	complemented
329	C₄×C₈	—	13	2	no	—
330	C₄×C₈	—	13	2	no	—
331	C₄×C₈	—	13	2	no	—
332	C₄×C₈	C₄×D₁₃	1	2	yes	complemented
333	C₂×C₁₃	—	2	1	no	—
334	C₂×C₁₃	—	2	1	no	—
335	C₂×C₁₃	—	2	1	no	—
336	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
337	D₁₃	—	2	2	no	—
338	D₁₃	—	2	2	no	—
339	C₂⁴	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	2	no	—
344	C₂²×C₄	—	13	2	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	2	no	—
349	C₂²×C₄	—	26	2	no	—
350	C₂²×C₄	—	52	2	no	—
351	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	13	2	no	—
357	M₁₆	—	13	2	no	—
358	M₁₆	—	13	2	no	—
359	M₁₆	—	13	2	no	—
360	M₁₆	—	13	2	no	—
361	M₁₆	—	13	2	no	—
362	M₁₆	—	13	2	no	—
363	M₁₆	—	13	2	no	—
364	M₁₆	—	26	4	no	—
365	M₁₆	—	26	1	no	—
366	M₁₆	—	26	1	no	—
367	M₁₆	—	26	2	no	—
368	M₁₆	—	26	2	no	—
369	M₁₆	—	52	2	no	—
370	M₁₆	—	52	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	2	no	—
375	C₂×C₈	—	13	2	no	—
376	C₂×C₈	—	13	2	no	—
377	C₂×C₈	—	26	4	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	—	52	2	no	—
380	C₂×C₈	—	52	2	no	—
381	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
382	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
386	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
387	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	26	2	no	—
391	C₄⋊C₄	—	26	1	no	—
392	C₄⋊C₄	—	26	2	no	—
393	C₄⋊C₄	—	52	2	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	26	2	no	—
397	C₂²⋊C₄	—	26	1	no	—
398	C₂²⋊C₄	—	26	2	no	—
399	C₂²⋊C₄	—	52	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	13	2	no	—
402	C₄²	—	26	2	no	—
403	C₄²	—	26	2	no	—
404	C₄²	—	52	2	no	—
405	C₄²	C₂×C₄×D₁₃	1	2	yes	—
406	C₁₃	#20757	1	1	yes	characteristic, complemented, Sylow
407	C₂³	—	13	1	no	—
408	C₂³	—	13	1	no	—
409	C₂³	—	13	2	no	—
410	C₂³	—	13	2	no	—
411	C₂³	—	104	1	no	—
412	C₂³	#41×D₁₃	1	1	yes	characteristic
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	13	2	no	—
418	C₂×C₄	—	13	2	no	—
419	C₂×C₄	—	13	2	no	—
420	C₂×C₄	—	13	2	no	—
421	C₂×C₄	—	13	2	no	—
422	C₂×C₄	—	13	2	no	—
423	C₂×C₄	—	13	2	no	—
424	C₂×C₄	—	13	2	no	—
425	C₂×C₄	—	13	2	no	—
426	C₂×C₄	—	13	2	no	—
427	C₂×C₄	—	26	2	no	—
428	C₂×C₄	—	52	2	no	—
429	C₂×C₄	—	104	2	no	—
430	C₂×C₄	—	104	4	no	—
431	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
434	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
435	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
436	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	13	2	no	—
440	C₈	—	13	2	no	—
441	C₈	—	26	2	no	—
442	C₈	—	52	2	no	—
443	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
444	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
445	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
446	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
447	C₂²	—	4	1	no	—
448	C₂²	—	13	2	no	—
449	C₂²	—	13	2	no	—
450	C₂²	—	52	1	no	—
451	C₂²	—	52	2	no	—
452	C₂²	—	52	1	no	—
453	C₂²	—	52	2	no	—
454	C₂²	D₁₃×#117	1	1	yes	characteristic
455	C₂²	D₁₃×#124	1	1	yes	characteristic
456	C₂²	D₁₃×#125	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	13	2	no	—
460	C₄	—	13	2	no	—
461	C₄	—	52	2	no	—
462	C₄	—	104	2	no	—
463	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
464	C₄	D₁₃×#117	1	1	yes	characteristic
465	C₄	D₁₃×#124	1	1	yes	characteristic
466	C₄	D₁₃×#125	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	26	2	no	—
471	C₂	—	26	2	no	—
472	C₂	D₁₃×#382	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#117
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1833	C₂
socle	C₂×C₁₃	C₂×#382
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1833	D₁₃
hypocenter	C₁₃	#20757
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #13114961	C₂	semidirect
5. #13114960	C₂	semidirect
6. #13114959	C₂	semidirect
7. #13114958	C₂	semidirect
8. #13114957	C₂	semidirect
11. C₁₃×#1833	C₂	semidirect
31. #11718369	C₄	semidirect
32. #11718368	C₄	semidirect
33. #11718350	C₄	semidirect
34. C₄×#6094	C₄	semidirect
88. C₁₃×#97	C₂×C₄	semidirect
89. C₄×C₈×C₁₃	C₂×C₄	semidirect
95. #88055	C₂×C₄	semidirect
96. #88055	C₂×C₄	semidirect
97. C₈×Dic₁₃	C₂×C₄	semidirect
98. C₈×Dic₁₃	C₂×C₄	semidirect
101. #88043	C₂×C₄	semidirect
102. C₄×#1055	C₂×C₄	semidirect
179. #1833	D₁₃	semidirect
328. #97	C₄×D₁₃	semidirect
332. C₄×C₈	C₄×D₁₃	semidirect
406. C₁₃	#20757	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718554	2
#13123424	2
#13123252	2
#13114961	2
#13114960	2
#13114959	2
#13114958	2
#13114957	2
D₁₃×#344	2
D₁₃×H(3,ℤ/4)	2
C₁₃×#1833	2
#20757	13