Subgroups — #16794973

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131758	C₂	1	2	yes	maximal
2	#13130401	C₂	1	2	yes	maximal, complemented
3	#13130400	C₂	1	2	yes	maximal, complemented
4	#13130399	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130396	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130395	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130393	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130388	C₂	1	2	yes	maximal, complemented
9	#13130384	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃⋊#335	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123258	C₂	1	1	yes	maximal, characteristic
12	C₂×#88161	C₄	1	1	yes	characteristic
13	C₂×#88155	C₄	1	1	yes	characteristic
14	#11719227	C₂²	1	1	yes	characteristic
15	#11719130	C₂²	1	2	yes	—
16	#11719129	C₂²	1	2	yes	—
17	#11719078	—	2	2	no	—
18	#11719075	—	2	2	no	—
19	#11719066	—	2	2	no	—
20	#11719065	—	2	2	no	—
21	#11719054	C₂²	1	2	yes	—
22	#11719052	C₂²	1	2	yes	—
23	#11719051	C₂²	1	2	yes	—
24	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
25	C₁₃×#405	C₄	1	1	yes	characteristic
26	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718658	C₄	1	1	yes	characteristic
29	#11718369	C₄	1	1	yes	characteristic
30	#11718369	C₄	1	1	yes	characteristic
31	#11718368	C₂²	1	1	yes	characteristic
32	#11718368	C₂²	1	1	yes	characteristic
33	#11718350	C₄	1	1	yes	characteristic
34	#11718350	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	#11718256	C₂²	1	1	yes	characteristic
38	#11718256	C₂²	1	1	yes	characteristic
39	#11718256	C₂²	1	1	yes	characteristic
40	#11718256	C₂²	1	1	yes	characteristic
41	#11718256	C₂²	1	2	yes	—
42	#11718255	C₂²	1	2	yes	—
43	#11718254	C₂²	1	2	yes	—
44	#11718254	C₂²	1	2	yes	—
45	#11718253	C₂²	1	2	yes	—
46	#11718253	C₂²	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₂×#6122	—	2	2	no	—
49	C₂×#6118	—	2	2	no	—
50	C₂×D₁₃⋊C₈	—	2	2	no	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂×C₄	1	1	yes	characteristic
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	#88161	—	2	4	no	—
58	#88155	—	2	4	no	—
59	C₂×#6094	C₂×C₄	1	1	yes	characteristic
60	C₂×#6094	C₂×C₄	1	1	yes	characteristic
61	C₂×#6094	C₂×C₄	1	1	yes	characteristic
62	C₂×#6094	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	#88147	D₄	1	1	yes	characteristic
68	#88147	Q₈	1	1	yes	characteristic
69	#88141	D₄	1	1	yes	characteristic
70	#88141	Q₈	1	1	yes	characteristic
71	#88135	D₄	1	1	yes	characteristic
72	#88135	D₄	1	1	yes	characteristic
73	#88135	Q₈	1	1	yes	characteristic
74	#88135	Q₈	1	1	yes	characteristic
75	#88126	C₂×C₄	1	1	yes	characteristic
76	#88126	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₃	C₂³	1	1	yes	characteristic
78	C₄²×D₁₃	C₂³	1	1	yes	characteristic
79	C₂²⋊#1057	—	2	2	no	—
80	#88112	—	2	2	no	—
81	#88112	—	2	2	no	—
82	#88111	—	2	2	no	—
83	#88111	—	2	2	no	—
84	#88110	—	2	2	no	—
85	#88110	—	2	2	no	—
86	C₄⋊#1057	—	2	2	no	—
87	C₄⋊#1057	C₂³	1	2	yes	—
88	C₄⋊#1057	C₂³	1	2	yes	—
89	C₄⋊#1057	C₂³	1	2	yes	—
90	C₄⋊#1057	C₂³	1	2	yes	—
91	C₄×#1057	—	2	2	no	—
92	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
96	#88055	C₂×C₄	1	1	yes	characteristic
97	#88055	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
102	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
103	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
104	#88043	C₂×C₄	1	1	yes	characteristic
105	#88043	C₂×C₄	1	1	yes	characteristic
106	C₄×#1055	C₂×C₄	1	1	yes	characteristic
107	C₄×#1055	C₂×C₄	1	1	yes	characteristic
108	#17799	—	13	1	no	maximal, Sylow
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
114	#6127	—	2	2	no	—
115	#6127	—	2	2	no	—
116	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
123	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
124	#6122	—	8	2	no	—
125	C₂×#1057	—	2	2	no	—
126	C₂×#1057	—	2	2	no	—
127	C₂×#1057	—	2	2	no	—
128	C₂×#1057	—	2	2	no	—
129	#6118	—	8	2	no	—
130	D₁₃⋊C₈	—	8	2	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
140	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	#6103	C₄⋊C₄	1	1	yes	characteristic
144	#6103	C₄⋊C₄	1	1	yes	characteristic
145	#6103	C₄⋊C₄	1	1	yes	characteristic
146	#6103	C₄⋊C₄	1	1	yes	characteristic
147	#6101	C₄⋊C₄	1	1	yes	characteristic
148	#6101	C₄⋊C₄	1	1	yes	characteristic
149	#6101	C₄⋊C₄	1	1	yes	characteristic
150	#6101	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
159	#6099	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
162	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
163	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
164	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
165	#6094	—	2	2	no	—
166	#6094	—	2	2	no	—
167	#6094	—	2	2	no	—
168	#6094	M₁₆	1	4	yes	complemented
169	C₈×D₁₃	—	2	2	no	—
170	C₈×D₁₃	—	2	2	no	—
171	C₈×D₁₃	—	2	2	no	—
172	C₈×D₁₃	M₁₆	1	4	yes	complemented
173	#2989	—	13	2	no	—
174	C₄×#131	—	13	1	no	—
175	#1569	—	13	2	no	—
176	#1569	—	13	2	no	—
177	#1568	—	13	1	no	—
178	#1568	—	13	1	no	—
179	#1567	—	13	1	no	—
180	#1567	—	13	1	no	—
181	#1565	—	13	2	no	—
182	#1564	—	13	1	no	—
183	C₂×#335	—	13	1	no	—
184	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂²⋊D₁₃	—	2	2	no	—
196	C₂²⋊D₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	1	no	—
198	C₂×Dic₁₃	—	2	1	no	—
199	C₂×Dic₁₃	—	4	1	no	—
200	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
206	D₅₂	—	2	2	no	—
207	C₄×D₁₃	—	2	1	no	—
208	C₄×D₁₃	—	2	1	no	—
209	C₄×D₁₃	—	2	1	no	—
210	C₄×D₁₃	—	2	1	no	—
211	C₄×D₁₃	—	2	1	no	—
212	C₄×D₁₃	—	2	1	no	—
213	C₄×D₁₃	—	4	1	no	—
214	C₄×D₁₃	—	4	1	no	—
215	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
216	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
217	Dic₂₆	—	2	2	no	—
218	#1057	—	4	2	no	—
219	#1057	—	4	2	no	—
220	#1057	—	4	2	no	—
221	#1057	—	4	2	no	—
222	C₈×C₁₃	—	2	1	no	—
223	C₈×C₁₃	—	2	1	no	—
224	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
225	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
226	#1055	—	2	1	no	—
227	#1055	—	2	1	no	—
228	#1055	C₂×M₁₆	1	2	yes	—
229	#1055	C₂×M₁₆	1	2	yes	—
230	C₂×#131	—	13	1	no	—
231	C₂×#131	—	13	1	no	—
232	C₄×#41	—	13	1	no	—
233	#446	—	26	2	no	—
234	#436	—	26	2	no	—
235	#435	—	26	2	no	—
236	#435	—	26	2	no	—
237	#432	—	13	2	no	—
238	#432	—	13	2	no	—
239	#431	—	13	2	no	—
240	#423	—	13	2	no	—
241	#423	—	13	2	no	—
242	C₂×C₄⋊C₈	—	13	2	no	—
243	#405	—	13	1	no	—
244	#405	—	13	1	no	—
245	#405	—	13	1	no	—
246	#405	—	13	1	no	—
247	#405	—	13	1	no	—
248	#405	#261	1	1	yes	characteristic
249	C₄×M₁₆	—	13	1	no	—
250	C₄×M₁₆	—	13	1	no	—
251	C₄×M₁₆	—	13	1	no	—
252	C₂×C₄×C₈	—	13	1	no	—
253	C₂×C₄×C₈	—	13	1	no	—
254	C₂×C₄×C₈	—	13	1	no	—
255	#335	—	13	1	no	—
256	#335	—	13	1	no	—
257	#335	—	13	2	no	—
258	#335	—	13	1	no	—
259	#335	—	13	1	no	—
260	#335	—	13	2	no	—
261	#335	—	13	2	no	—
262	#334	—	13	2	no	—
263	#334	—	13	2	no	—
264	#334	—	13	2	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₂×D₁₃	—	2	1	no	—
270	C₂×D₁₃	—	2	1	no	—
271	C₂×D₁₃	—	2	1	no	—
272	C₂×D₁₃	—	2	1	no	—
273	C₂×D₁₃	—	2	1	no	—
274	C₂×D₁₃	#423	1	2	yes	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
281	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
282	Dic₁₃	—	2	1	no	—
283	Dic₁₃	—	2	1	no	—
284	Dic₁₃	—	2	1	no	—
285	Dic₁₃	—	2	1	no	—
286	Dic₁₃	#423	1	2	yes	—
287	Dic₁₃	#576	1	1	yes	characteristic
288	Dic₁₃	#578	1	1	yes	characteristic
289	C₂×#41	—	13	1	no	—
290	#131	—	26	4	no	—
291	#131	—	26	4	no	—
292	C₂×M₁₆	—	13	1	no	—
293	C₂×M₁₆	—	13	1	no	—
294	C₂×M₁₆	—	13	1	no	—
295	C₂×M₁₆	—	13	1	no	—
296	C₂×M₁₆	—	13	1	no	—
297	C₂×M₁₆	—	26	2	no	—
298	C₂×M₁₆	—	26	2	no	—
299	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	—	13	1	no	—
305	C₂²×C₈	—	26	2	no	—
306	C₂²×C₈	C₂×#261	1	1	yes	characteristic
307	C₄×Q₈	—	13	1	no	—
308	C₄×Q₈	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	—	13	1	no	—
312	C₄×D₄	—	13	1	no	—
313	C₄×D₄	—	13	1	no	—
314	C₄×D₄	—	13	1	no	—
315	#117	—	13	1	no	—
316	#117	—	13	1	no	—
317	#117	C₂×#261	1	1	yes	characteristic
318	C₂×C₄²	—	13	1	no	—
319	C₂×C₄²	—	13	1	no	—
320	C₂×C₄²	—	13	1	no	—
321	C₄⋊C₈	—	13	2	no	—
322	C₄⋊C₈	—	13	2	no	—
323	C₄⋊C₈	—	13	2	no	—
324	C₄⋊C₈	—	13	2	no	—
325	C₄⋊C₈	—	26	2	no	—
326	C₄⋊C₈	—	26	2	no	—
327	C₄⋊C₈	—	26	2	no	—
328	C₂²⋊C₈	—	26	2	no	—
329	C₂²⋊C₈	—	26	2	no	—
330	C₂²⋊C₈	—	26	2	no	—
331	#97	—	13	1	no	—
332	#97	—	13	1	no	—
333	#97	—	13	1	no	—
334	#97	—	13	1	no	—
335	#97	—	26	2	no	—
336	#97	—	26	2	no	—
337	#97	C₂×#261	1	1	yes	characteristic
338	#97	C₂×#261	1	1	yes	characteristic
339	C₄×C₈	—	13	1	no	—
340	C₄×C₈	—	13	1	no	—
341	C₄×C₈	—	13	1	no	—
342	C₄×C₈	—	13	1	no	—
343	C₄×C₈	—	13	1	no	—
344	C₄×C₈	—	13	1	no	—
345	C₄×C₈	—	13	1	no	—
346	C₄×C₈	—	13	1	no	—
347	C₄×C₈	—	26	2	no	—
348	C₄×C₈	C₂×#261	1	1	yes	characteristic
349	C₄×C₈	C₂×#261	1	1	yes	characteristic
350	C₂×C₁₃	—	4	1	no	—
351	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
352	C₂×C₁₃	#2913	1	1	yes	characteristic
353	C₂×C₁₃	#2916	1	1	yes	characteristic
354	D₁₃	—	2	2	no	—
355	D₁₃	—	4	1	no	—
356	#41	—	26	2	no	—
357	#41	—	26	2	no	—
358	C₂×Q₈	—	13	1	no	—
359	C₂×D₄	—	13	1	no	—
360	C₂×D₄	—	13	1	no	—
361	C₂×D₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	1	no	—
365	C₂²×C₄	—	13	1	no	—
366	C₂²×C₄	—	13	1	no	—
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
371	M₁₆	—	2	2	no	—
372	M₁₆	—	13	4	no	—
373	M₁₆	—	26	2	no	—
374	M₁₆	—	26	2	no	—
375	M₁₆	—	26	2	no	—
376	M₁₆	—	26	2	no	—
377	M₁₆	—	104	2	no	—
378	M₁₆	—	104	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	4	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	13	1	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₂×C₈	—	26	2	no	—
389	C₂×C₈	—	26	2	no	—
390	C₂×C₈	—	26	2	no	—
391	C₂×C₈	—	26	2	no	—
392	C₂×C₈	—	26	2	no	—
393	C₂×C₈	—	104	2	no	—
394	C₂×C₈	C₂²×#261	1	1	yes	characteristic
395	C₂×C₈	C₂²×#261	1	1	yes	characteristic
396	C₂×C₈	C₂²×#261	1	1	yes	characteristic
397	C₂×C₈	C₂²×#261	1	1	yes	characteristic
398	C₄⋊C₄	—	13	1	no	—
399	C₄⋊C₄	—	13	1	no	—
400	C₄⋊C₄	—	13	1	no	—
401	C₄⋊C₄	—	13	1	no	—
402	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
403	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
404	C₂²⋊C₄	—	13	1	no	—
405	C₂²⋊C₄	—	13	1	no	—
406	C₂²⋊C₄	—	13	1	no	—
407	C₂²⋊C₄	—	13	1	no	—
408	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
409	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
410	C₄²	—	13	1	no	—
411	C₄²	—	13	1	no	—
412	C₄²	—	13	1	no	—
413	C₄²	—	13	1	no	—
414	C₄²	—	13	1	no	—
415	C₄²	—	13	1	no	—
416	C₄²	—	13	1	no	—
417	C₄²	—	13	1	no	—
418	C₄²	C₂²×#261	1	1	yes	characteristic
419	C₄²	C₂²×#261	1	1	yes	characteristic
420	C₁₃	#17799	1	1	yes	characteristic, complemented, Sylow
421	C₂³	—	13	1	no	—
422	C₂³	—	13	1	no	—
423	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
424	Q₈	—	26	2	no	—
425	D₄	—	26	2	no	—
426	D₄	—	26	2	no	—
427	D₄	—	26	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	2	no	—
433	C₂×C₄	—	13	2	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	26	1	no	—
439	C₂×C₄	—	26	1	no	—
440	C₂×C₄	—	26	1	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	1	no	—
445	C₂×C₄	—	26	1	no	—
446	C₂×C₄	—	52	1	no	—
447	C₂×C₄	—	52	1	no	—
448	C₂×C₄	—	52	1	no	—
449	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
454	C₂×C₄	C₂³×#261	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	13	2	no	—
458	C₈	—	13	2	no	—
459	C₈	—	26	1	no	—
460	C₈	—	26	1	no	—
461	C₈	—	52	2	no	—
462	C₈	—	52	2	no	—
463	C₈	—	52	2	no	—
464	C₈	—	52	2	no	—
465	C₈	D₁₃⋊M₁₆	1	2	yes	—
466	C₈	D₁₃⋊M₁₆	1	2	yes	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	13	2	no	—
471	C₂²	—	26	1	no	—
472	C₂²	—	26	1	no	—
473	C₂²	—	26	1	no	—
474	C₂²	—	26	1	no	—
475	C₂²	—	26	1	no	—
476	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	13	2	no	—
483	C₄	—	13	1	no	—
484	C₄	—	13	1	no	—
485	C₄	—	26	1	no	—
486	C₄	—	26	1	no	—
487	C₄	—	26	1	no	—
488	C₄	—	26	1	no	—
489	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
490	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	26	2	no	—
493	C₂	—	52	1	no	—
494	C₂	D₁₃⋊#423	1	1	yes	characteristic
495	C₂	#13131491	1	1	yes	characteristic
496	C₂	#13131497	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#17799
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13130401	C₂	semidirect
3. #13130400	C₂	semidirect
4. #13130399	C₂	semidirect
5. #13130396	C₂	semidirect
6. #13130395	C₂	semidirect
7. #13130393	C₂	semidirect
8. #13130388	C₂	semidirect
9. #13130384	C₂	semidirect
10. D₁₃⋊#335	C₂	semidirect
168. #6094	M₁₆	semidirect
172. C₈×D₁₃	M₁₆	semidirect
420. C₁₃	#17799	semidirect

Maximal subgroups

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

subgroup	index
#13131758	2
#13130401	2
#13130400	2
#13130399	2
#13130396	2
#13130395	2
#13130393	2
#13130388	2
#13130384	2
D₁₃⋊#335	2
#13123258	2
#17799	13