Subgroups — #15833527

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123812	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123548	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113727	C₂	1	2	yes	maximal, complemented
4	#13113721	C₂	1	2	yes	maximal, complemented
5	#13113660	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13113603	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113305	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113301	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₁₃×#529	C₂²	1	1	yes	characteristic
14	C₂×#88202	—	2	1	no	—
15	C₁₃×#501	C₄	1	1	yes	characteristic
16	C₁₃×#496	C₄	1	1	yes	characteristic
17	C₁₃×#490	C₄	1	1	yes	characteristic
18	C₁₃×#489	C₄	1	1	yes	characteristic
19	C₁₃×#469	C₄	1	2	yes	—
20	C₁₃×#468	C₄	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×D₈	C₂²	1	2	yes	—
23	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	#11718895	—	2	1	no	—
25	#11718685	C₂²	1	1	yes	characteristic
26	Q₈×#1055	C₂²	1	1	yes	characteristic
27	#11718673	—	2	1	no	—
28	#11718673	C₂²	1	1	yes	characteristic
29	#11718673	C₂²	1	2	yes	—
30	#11718672	—	2	1	no	—
31	D₄×#1055	—	2	1	no	—
32	D₄×#1055	—	2	1	no	—
33	D₄×#1055	C₂²	1	2	yes	—
34	D₄×#1055	C₂²	1	1	yes	characteristic
35	#11718661	—	2	1	no	—
36	#11718658	—	2	1	no	—
37	#11718587	C₂²	1	1	yes	characteristic
38	#11718586	C₂²	1	1	yes	characteristic
39	#11718585	C₂²	1	1	yes	characteristic
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	2	yes	—
43	D₄⋊#1055	C₂²	1	2	yes	—
44	D₄⋊#1055	C₂²	1	2	yes	—
45	#11718050	C₂²	1	2	yes	—
46	#11718049	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	C₈×#1055	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#126	—	2	1	no	—
56	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
57	C₁₃×#124	—	2	1	no	—
58	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
59	C₁₃×#123	—	2	1	no	—
60	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₃×#121	—	2	1	no	—
62	C₁₃×#121	C₂×C₄	1	2	yes	—
63	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#117	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	#88202	—	4	4	no	—
72	C₂×#6099	—	2	1	no	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	2	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	2	no	—
77	C₂²×#1055	D₄	1	1	yes	characteristic
78	C₂²×#1055	D₄	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×#103	C₂×C₄	1	2	yes	—
82	C₁₃×#102	C₂×C₄	1	2	yes	—
83	C₁₃×#102	C₂×C₄	1	2	yes	—
84	C₁₃×#102	C₂×C₄	1	2	yes	—
85	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	2	yes	—
88	C₂²⋊#1055	—	2	1	no	—
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	C₂²⋊#1055	—	2	1	no	—
92	C₂²⋊#1055	—	2	2	no	—
93	C₂²⋊#1055	—	2	2	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	C₂³	1	2	yes	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	#88043	—	2	1	no	—
102	#88043	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	#17966	—	13	1	no	maximal, Sylow
110	C₁₃×#41	—	4	2	no	—
111	C₁₃×#41	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₁₃×SD₁₆	—	2	4	no	—
126	C₁₃×D₈	—	2	4	no	—
127	C₁₃×M₁₆	—	2	4	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₃	#41	1	1	yes	characteristic
149	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
150	#6099	—	4	2	no	—
151	#6099	—	4	2	no	—
152	#6099	—	4	4	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	1	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	4	1	no	—
159	C₂×#1055	—	4	2	no	—
160	C₂×#1055	—	4	4	no	—
161	C₂×#1055	C₂×D₄	1	1	yes	characteristic
162	C₂×#1055	C₂×D₄	1	1	yes	characteristic
163	C₂×#1055	C₂×D₄	1	1	yes	characteristic
164	C₂×#1055	C₂×D₄	1	1	yes	characteristic
165	#3171	D₁₃	1	1	yes	characteristic
166	#2966	—	13	1	no	—
167	#2931	—	13	1	no	—
168	#1590	—	13	2	no	—
169	#1589	—	13	2	no	—
170	#1580	—	13	2	no	—
171	SD₁₆⋊C₈	—	13	2	no	—
172	#1569	—	13	1	no	—
173	#1496	—	13	1	no	—
174	#1495	—	13	1	no	—
175	C₈×M₁₆	—	13	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂³×C₄	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	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	#131	1	4	yes	complemented
208	#1055	—	2	1	no	—
209	#1055	—	2	1	no	—
210	#1055	—	2	1	no	—
211	#1055	—	4	2	no	—
212	#1055	—	4	2	no	—
213	#1055	—	4	1	no	—
214	#1055	—	4	1	no	—
215	#1055	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×#131	—	26	1	no	—
217	#532	C₂×D₁₃	1	1	yes	characteristic
218	#529	C₂×D₁₃	1	1	yes	characteristic
219	#501	Dic₁₃	1	1	yes	characteristic
220	#496	Dic₁₃	1	1	yes	characteristic
221	#490	Dic₁₃	1	1	yes	characteristic
222	#489	Dic₁₃	1	1	yes	characteristic
223	#469	Dic₁₃	1	2	yes	—
224	#468	Dic₁₃	1	2	yes	—
225	#446	—	13	1	no	—
226	C₈×Q₈	—	13	1	no	—
227	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
228	C₄×D₈	C₂×D₁₃	1	2	yes	—
229	#436	—	13	1	no	—
230	#436	—	13	2	no	—
231	#436	—	26	1	no	—
232	#435	—	26	1	no	—
233	C₈×D₄	—	13	2	no	—
234	C₈×D₄	—	13	1	no	—
235	C₈×D₄	—	26	1	no	—
236	C₈×D₄	—	26	1	no	—
237	#433	—	26	1	no	—
238	#432	—	13	1	no	—
239	#431	—	13	1	no	—
240	#423	—	13	1	no	—
241	#408	—	26	1	no	—
242	#405	—	26	1	no	—
243	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
244	C₂×C₄×C₈	—	13	1	no	—
245	#335	—	13	2	no	—
246	#334	—	13	2	no	—
247	Q₈⋊C₈	—	13	2	no	—
248	D₄⋊C₈	—	13	2	no	—
249	D₄⋊C₈	—	13	2	no	—
250	D₄⋊C₈	—	13	2	no	—
251	#322	—	13	2	no	—
252	C₈²	—	13	2	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	1	no	—
271	C₄×C₁₃	C₂×#131	1	2	yes	—
272	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₄×C₁₃	#575	1	1	yes	characteristic
274	C₂×#41	—	2	1	no	—
275	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
276	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
277	#131	—	52	4	no	—
278	C₂×M₁₆	—	26	2	no	—
279	C₂×M₁₆	—	26	1	no	—
280	C₂×M₁₆	—	26	1	no	—
281	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
282	C₂²×C₈	—	13	1	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	26	2	no	—
285	C₂²×C₈	—	26	1	no	—
286	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
287	#127	C₂×Dic₁₃	1	1	yes	characteristic
288	#126	—	2	1	no	—
289	#125	C₂×Dic₁₃	1	1	yes	characteristic
290	#124	—	2	1	no	—
291	#124	C₂×Dic₁₃	1	1	yes	characteristic
292	#123	—	2	1	no	—
293	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
294	#121	—	2	1	no	—
295	#121	C₂×Dic₁₃	1	1	yes	characteristic
296	#121	C₂×Dic₁₃	1	2	yes	—
297	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
301	C₄×D₄	C₂²×D₁₃	1	2	yes	—
302	#117	—	2	1	no	—
303	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	#107	C₂×Dic₁₃	1	2	yes	—
305	#106	C₂×Dic₁₃	1	2	yes	—
306	C₄⋊C₈	—	13	1	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	2	no	—
309	C₄⋊C₈	—	26	1	no	—
310	C₄⋊C₈	—	26	1	no	—
311	C₄⋊C₈	—	26	1	no	—
312	C₄⋊C₈	—	26	1	no	—
313	#103	C₂×Dic₁₃	1	2	yes	—
314	#102	C₂×Dic₁₃	1	2	yes	—
315	#102	C₂×Dic₁₃	1	2	yes	—
316	#102	C₂×Dic₁₃	1	2	yes	—
317	C₂²⋊C₈	—	26	2	no	—
318	C₂²⋊C₈	—	26	2	no	—
319	C₂²⋊C₈	—	26	1	no	—
320	C₂²⋊C₈	—	26	1	no	—
321	C₂²⋊C₈	—	26	1	no	—
322	C₂²⋊C₈	—	26	1	no	—
323	#97	—	26	1	no	—
324	#97	—	26	1	no	—
325	#97	C₂×Dic₁₃	1	1	yes	characteristic
326	#97	C₂×Dic₁₃	1	1	yes	characteristic
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	no	—
330	C₄×C₈	—	13	1	no	—
331	C₄×C₈	—	13	2	no	—
332	C₄×C₈	—	26	1	no	—
333	C₄×C₈	C₂²×D₁₃	1	2	yes	—
334	C₂×C₁₃	—	4	1	no	—
335	C₂×C₁₃	—	8	2	no	—
336	C₂×C₁₃	—	8	1	no	—
337	C₂×C₁₃	#2931	1	1	yes	characteristic
338	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₂×C₁₃	#2955	1	1	yes	characteristic
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
349	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
353	C₂²×C₄	#6129	1	1	yes	characteristic
354	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
355	SD₁₆	—	2	4	no	—
356	D₈	—	2	4	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	52	4	no	—
359	M₁₆	—	52	2	no	—
360	M₁₆	—	52	2	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	13	1	no	—
363	C₂×C₈	—	13	1	no	—
364	C₂×C₈	—	13	1	no	—
365	C₂×C₈	—	26	2	no	—
366	C₂×C₈	—	26	1	no	—
367	C₂×C₈	—	26	1	no	—
368	C₂×C₈	—	26	2	no	—
369	C₂×C₈	—	26	2	no	—
370	C₂×C₈	—	52	1	no	—
371	C₂×C₈	—	52	4	no	—
372	C₂×C₈	—	52	2	no	—
373	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
374	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
382	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	D₄×D₁₃	1	1	yes	characteristic
392	C₄²	#6129	1	1	yes	characteristic
393	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
394	C₄²	C₂³×D₁₃	1	1	yes	characteristic
395	C₁₃	#17966	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	2	1	no	—
397	C₂³	—	2	2	no	—
398	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
421	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
422	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#6129	1	1	yes	characteristic
425	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	13	2	no	—
428	C₈	—	26	1	no	—
429	C₈	—	26	1	no	—
430	C₈	—	26	1	no	—
431	C₈	—	52	2	no	—
432	C₈	—	52	2	no	—
433	C₈	—	52	1	no	—
434	C₈	—	52	1	no	—
435	C₈	#88202	1	4	yes	complemented
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₄	#11719478	1	1	yes	characteristic
456	C₄	C₂×#88202	1	2	yes	—
457	C₂	—	4	1	no	—
458	C₂	—	8	2	no	—
459	C₂	—	8	1	no	—
460	C₂	#13123548	1	1	yes	characteristic
461	C₂	AGL(1,ℤ/8)×Dic₁₃	1	1	yes	characteristic
462	C₂	#13123739	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3171	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3171	D₁₃
hypocenter	C₁₃	#17966
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3171

Complements

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

N	H ≅ G/N	type
1. #13123812	C₂	semidirect
2. #13123548	C₂	semidirect
3. #13113727	C₂	semidirect
4. #13113721	C₂	semidirect
5. #13113660	C₂	semidirect
6. SD₁₆⋊#1055	C₂	semidirect
7. #13113603	C₂	semidirect
8. #13113305	C₂	semidirect
9. #13113301	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
207. C₈×C₁₃	#131	semidirect
395. C₁₃	#17966	semidirect
435. C₈	#88202	semidirect

Maximal subgroups

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

subgroup	index
#13123812	2
#13123548	2
#13113727	2
#13113721	2
#13113660	2
SD₁₆⋊#1055	2
#13113603	2
#13113305	2
#13113301	2
M₁₆×#1055	2
C₁₃×#3171	2
#17966	13