Subgroups — #15881186

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6099	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718673	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718785	C₂	1	2	yes	maximal, complemented
4	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115609	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115041	C₂	1	2	yes	maximal, complemented
7	#13115040	C₂	1	2	yes	maximal, complemented
8	#13115007	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114876	C₂	1	2	yes	maximal, complemented
10	C₄×#88062	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	2	yes	—
15	C₂²×#6099	C₂²	1	2	yes	—
16	C₁₃×#436	—	2	1	no	—
17	C₁₃×#435	—	2	2	no	—
18	C₈×D₄×C₁₃	—	2	1	no	—
19	C₁₃×#423	C₂²	1	1	yes	characteristic
20	C₁₃×#407	C₂²	1	2	yes	—
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	#11718868	C₂²	1	2	yes	—
23	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
24	#11718785	—	2	8	no	—
25	C₂×#88062	C₂²	1	2	yes	—
26	C₂×#88062	C₂²	1	2	yes	—
27	C₂×#88062	C₂²	1	2	yes	—
28	C₂×#88062	C₂²	1	1	yes	characteristic
29	C₂×#88062	C₂²	1	2	yes	—
30	C₂×#88062	C₂²	1	1	yes	characteristic
31	#11718673	—	2	1	no	—
32	#11718673	C₄	1	2	yes	—
33	#11718673	C₄	1	2	yes	—
34	#11718673	C₄	1	4	yes	—
35	#11718672	—	2	2	no	—
36	D₄×#1055	—	2	1	no	—
37	#11718585	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₄×#6099	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	#11718150	C₂²	1	1	yes	characteristic
42	#11718150	C₂²	1	1	yes	characteristic
43	#11718150	C₂²	1	2	yes	—
44	#11718150	C₂²	1	2	yes	—
45	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	4	no	—
49	C₂×C₁₃×M₁₆	—	4	2	no	—
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
57	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	D₄	1	2	yes	—
59	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6099	—	2	2	no	—
64	C₂×#6099	—	2	4	no	—
65	C₂×#6099	—	2	4	no	—
66	C₂×#6099	—	2	4	no	—
67	C₂×#6099	—	4	2	no	—
68	C₂×#6099	C₂×C₄	1	4	yes	—
69	C₂×#6099	C₂×C₄	1	4	yes	—
70	C₂×#6099	C₂³	1	1	yes	characteristic
71	C₂×#6099	C₂³	1	2	yes	—
72	C₂×#6099	C₂³	1	1	yes	characteristic
73	C₂²×#1055	—	2	2	no	—
74	C₂²×#1055	C₂³	1	2	yes	—
75	C₂²×#1055	C₂³	1	1	yes	characteristic
76	C₂²×#1055	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	—	2	1	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	2	2	no	—
81	C₁₃×#97	—	2	1	no	—
82	C₄×C₈×C₁₃	—	2	1	no	—
83	C₂²⋊#1055	—	2	2	no	—
84	C₂²⋊#1055	—	2	2	no	—
85	C₂²⋊#1055	C₂×C₄	1	4	yes	—
86	C₂²⋊#1055	C₂×C₄	1	4	yes	—
87	#88062	—	2	4	no	—
88	#88062	—	2	4	no	—
89	#88062	—	2	4	no	—
90	#88062	—	2	2	no	—
91	#88062	—	4	2	no	—
92	#88062	D₄	1	4	yes	complemented
93	C₄⋊#1055	—	2	1	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	C₂×C₄	1	2	yes	—
96	C₄⋊#1055	C₂×C₄	1	2	yes	—
97	#88043	—	2	1	no	—
98	C₄×#1055	—	2	1	no	—
99	C₄×#1055	C₂×C₄	1	2	yes	—
100	C₄×#1055	C₂×C₄	1	2	yes	—
101	#22669	—	13	1	no	maximal, Sylow
102	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×M₁₆	—	2	1	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	1	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	1	no	—
124	C₁₃×M₁₆	—	4	4	no	—
125	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	4	4	no	—
130	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
135	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
136	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
137	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	#6099	—	2	1	no	—
142	#6099	—	2	8	no	—
143	#6099	—	2	8	no	—
144	#6099	—	2	2	no	—
145	#6099	—	2	1	no	—
146	#6099	—	2	2	no	—
147	#6099	—	2	1	no	—
148	#6099	—	4	4	no	—
149	#6099	C₂×D₄	1	2	yes	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	2	1	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	4	4	no	—
158	C₂×#1055	C₂²×C₄	1	2	yes	—
159	C₂×#1055	C₂²×C₄	1	4	yes	—
160	C₂×#1055	C₂²×C₄	1	2	yes	—
161	C₂×#1055	C₂×D₄	1	2	yes	—
162	C₂×#1055	#41	1	2	yes	—
163	D₄×M₁₆	—	13	1	no	—
164	D₄×M₁₆	D₁₃	1	1	yes	characteristic
165	C₂×#436	—	13	1	no	—
166	C₂×#430	—	13	2	no	—
167	#1950	—	13	1	no	—
168	#1950	—	13	1	no	—
169	#1855	—	13	2	no	—
170	#1855	—	13	2	no	—
171	#1848	—	13	1	no	—
172	#1811	—	13	2	no	—
173	C₄×#108	—	13	1	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
180	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₁₃	—	2	2	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	#1055	—	2	4	no	—
212	#1055	—	2	2	no	—
213	#1055	—	2	2	no	—
214	#1055	—	4	2	no	—
215	#1055	—	4	1	no	—
216	#1055	C₄×D₄	1	4	yes	—
217	C₂²×M₁₆	—	13	2	no	—
218	C₂²×M₁₆	—	13	2	no	—
219	C₂²×M₁₆	C₂×D₁₃	1	2	yes	—
220	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
221	#436	—	2	1	no	—
222	#436	—	13	2	no	—
223	#436	—	13	2	no	—
224	#436	—	13	4	no	—
225	#436	—	26	1	no	—
226	#435	—	2	2	no	—
227	#435	—	26	2	no	—
228	C₈×D₄	—	2	1	no	—
229	C₈×D₄	—	26	1	no	—
230	#430	—	26	8	no	—
231	C₂×#108	—	13	1	no	—
232	C₂×#108	—	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	#423	—	13	1	no	—
238	#423	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₄⋊C₈	—	13	1	no	—
240	#407	—	13	2	no	—
241	#407	C₂×D₁₃	1	2	yes	—
242	C₂×C₂²⋊C₈	—	13	2	no	—
243	C₄×M₁₆	—	13	1	no	—
244	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
245	C₂×C₄×C₈	—	13	1	no	—
246	#341	—	13	2	no	—
247	#341	—	13	2	no	—
248	#341	—	13	1	no	—
249	#341	—	13	1	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
262	C₂²×C₁₃	#554	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	#430	1	2	yes	complemented
269	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₁₃	#520	1	1	yes	characteristic
271	C₄×C₁₃	D₄²	1	1	yes	characteristic
272	C₄×C₁₃	#547	1	1	yes	characteristic
273	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	—	4	2	no	—
278	C₂×M₁₆	—	13	4	no	—
279	C₂×M₁₆	—	13	4	no	—
280	C₂×M₁₆	—	13	1	no	—
281	C₂×M₁₆	—	13	2	no	—
282	C₂×M₁₆	—	13	1	no	—
283	C₂×M₁₆	—	26	4	no	—
284	C₂×M₁₆	—	26	4	no	—
285	C₂×M₁₆	—	26	2	no	—
286	C₂×M₁₆	—	26	4	no	—
287	C₂×M₁₆	—	52	2	no	—
288	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
289	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
290	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	13	1	no	—
293	C₂²×C₈	—	13	2	no	—
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	26	2	no	—
296	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
297	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
298	C₄×D₄	C₄×D₁₃	1	2	yes	—
299	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
300	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
301	C₄×D₄	C₂²⋊D₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	Dic₂₆	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	Dic₂₆	1	2	yes	—
304	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
305	#108	—	13	4	no	—
306	#108	—	26	4	no	—
307	#108	—	26	2	no	—
308	#108	—	26	4	no	—
309	#108	—	26	4	no	—
310	#108	—	52	2	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	—	13	2	no	—
314	C₄⋊C₈	—	13	2	no	—
315	C₄⋊C₈	—	26	1	no	—
316	C₄⋊C₈	—	26	1	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	13	4	no	—
320	C₂²⋊C₈	—	13	4	no	—
321	C₂²⋊C₈	—	26	2	no	—
322	C₂²⋊C₈	—	26	2	no	—
323	#97	—	2	1	no	—
324	#97	—	26	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	13	2	no	—
327	C₄×C₈	—	13	2	no	—
328	C₄×C₈	—	26	1	no	—
329	C₂×C₁₃	—	2	1	no	—
330	C₂×C₁₃	—	2	1	no	—
331	C₂×C₁₃	—	4	2	no	—
332	C₂×C₁₃	—	4	2	no	—
333	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
335	C₂×C₁₃	#2916	1	1	yes	characteristic
336	C₂⁴	C₂×Dic₂₆	1	2	yes	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	#6101	1	1	yes	characteristic
339	C₂×D₄	#6101	1	1	yes	characteristic
340	C₂×D₄	#6101	1	2	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
346	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
347	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
349	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
350	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
351	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
352	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	4	no	—
359	M₁₆	—	13	2	no	—
360	M₁₆	—	26	8	no	—
361	M₁₆	—	26	8	no	—
362	M₁₆	—	26	1	no	—
363	M₁₆	—	26	2	no	—
364	M₁₆	—	26	2	no	—
365	M₁₆	—	26	1	no	—
366	M₁₆	—	26	1	no	—
367	M₁₆	—	52	4	no	—
368	M₁₆	D₄×D₁₃	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	13	2	no	—
374	C₂×C₈	—	13	2	no	—
375	C₂×C₈	—	13	2	no	—
376	C₂×C₈	—	13	2	no	—
377	C₂×C₈	—	13	4	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	—	26	1	no	—
380	C₂×C₈	—	26	2	no	—
381	C₂×C₈	—	26	1	no	—
382	C₂×C₈	—	26	1	no	—
383	C₂×C₈	—	26	1	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	52	4	no	—
386	C₄⋊C₄	#6101	1	2	yes	—
387	C₄⋊C₄	#6101	1	1	yes	characteristic
388	C₄⋊C₄	#6101	1	1	yes	characteristic
389	C₂²⋊C₄	#6101	1	2	yes	—
390	C₂²⋊C₄	#6101	1	2	yes	—
391	C₂²⋊C₄	#6101	1	2	yes	—
392	C₂²⋊C₄	#6101	1	2	yes	—
393	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
394	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
395	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
396	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
397	C₁₃	#22669	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂×#6101	1	2	yes	—
403	C₂³	C₂×#6101	1	2	yes	—
404	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	C₂×#6101	1	1	yes	characteristic
421	C₂×C₄	C₂×#6101	1	1	yes	characteristic
422	C₂×C₄	C₂×#6101	1	1	yes	characteristic
423	C₂×C₄	C₂×#6101	1	2	yes	—
424	C₂×C₄	C₂×#6101	1	2	yes	—
425	C₂×C₄	C₂×#6101	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
428	C₂×C₄	#88251	1	1	yes	characteristic
429	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
430	C₂×C₄	#88257	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	13	4	no	—
436	C₈	—	26	4	no	—
437	C₈	—	26	2	no	—
438	C₈	—	26	2	no	—
439	C₈	—	52	2	no	—
440	C₈	—	52	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	D₄×Dic₂₆	1	1	yes	characteristic
452	C₂²	#11719244	1	1	yes	characteristic
453	C₂²	C₂²×#6101	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	#11718785	1	2	yes	complemented
460	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
461	C₄	#11719251	1	1	yes	characteristic
462	C₄	D₄×C₂²⋊D₁₃	1	1	yes	characteristic
463	C₄	#11719529	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	4	2	no	—
467	C₂	—	4	2	no	—
468	C₂	D₄×#6101	1	1	yes	characteristic
469	C₂	C₂×#11718785	1	1	yes	characteristic
470	C₂	#13123445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	D₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	D₄×M₁₆	D₁₃
hypocenter	C₁₃	#22669
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#11718785	C₂	semidirect
4. #13115611	C₂	semidirect
5. #13115609	C₂	semidirect
6. #13115041	C₂	semidirect
7. #13115040	C₂	semidirect
8. #13115007	C₂	semidirect
9. #13114876	C₂	semidirect
10. C₄×#88062	C₂	semidirect
92. #88062	D₄	semidirect
268. C₄×C₁₃	#430	semidirect
397. C₁₃	#22669	semidirect
459. C₄	#11718785	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6099	2
C₂×#11718673	2
C₂×#11718785	2
#13115611	2
#13115609	2
#13115041	2
#13115040	2
#13115007	2
#13114876	2
C₄×#88062	2
D₄×C₁₃×M₁₆	2
#22669	13