Subgroups — #16797471

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#13131295	C₂	1	1	yes	maximal, characteristic
3	#13130634	C₂	1	2	yes	maximal
4	#13130633	C₂	1	1	yes	maximal, characteristic
5	#13130633	C₂	1	2	yes	maximal
6	C₈×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
7	#13130625	C₂	1	2	yes	maximal
8	C₄⋊C₈×#261	C₂	1	1	yes	maximal, characteristic
9	#13130494	C₂	1	2	yes	maximal
10	C₄×#88100	C₂	1	1	yes	maximal, characteristic
11	D₁₃×#446	C₂	1	1	yes	maximal, characteristic
12	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
13	(C₂×#261)⋊Q₈	C₄	1	2	yes	—
14	Q₈×#1057	C₄	1	2	yes	complemented
15	C₂×#88100	C₂²	1	1	yes	characteristic
16	C₂×#88100	C₂²	1	1	yes	characteristic
17	C₂×#88100	C₂²	1	2	yes	—
18	C₂×#88100	C₂²	1	1	yes	characteristic
19	C₂×#88100	C₂²	1	1	yes	characteristic
20	C₂×C₈×#261	C₂²	1	2	yes	—
21	C₂×C₈×#261	C₂²	1	2	yes	—
22	#11719083	C₄	1	2	yes	—
23	#11719082	C₄	1	4	yes	—
24	#11719074	C₄	1	4	yes	complemented
25	#11719074	C₄	1	2	yes	complemented
26	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊#261	C₂²	1	2	yes	—
28	#11719057	C₂²	1	2	yes	—
29	C₄²×#261	C₂²	1	1	yes	characteristic
30	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
31	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
32	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
34	C₁₃×#446	C₄	1	1	yes	characteristic, complemented
35	#11718685	C₄	1	1	yes	characteristic, complemented
36	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
38	#11718492	C₄	1	1	yes	characteristic, complemented
39	#11718489	C₄	1	2	yes	complemented
40	D₁₃×#97	C₂²	1	2	yes	—
41	#11718362	C₄	1	2	yes	complemented
42	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
43	#11718340	C₄	1	1	yes	characteristic, complemented
44	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
45	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
46	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
47	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
50	C₂×C₄×#261	C₂×C₄	1	2	yes	—
51	C₂×C₄×#261	C₂×C₄	1	2	yes	—
52	C₂×C₄×#261	C₂³	1	1	yes	characteristic
53	C₂×C₄×#261	C₂³	1	2	yes	—
54	C₂×C₄×#261	C₂³	1	1	yes	characteristic
55	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
56	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂³	1	2	yes	—
61	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
63	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
64	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
65	#88141	C₂×C₄	1	2	yes	—
66	#88141	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	2	yes	—
69	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
70	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
71	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
72	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
73	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
74	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
75	#88112	C₂×C₄	1	2	yes	—
76	#88112	C₂×C₄	1	4	yes	—
77	C₄⋊#1057	C₂×C₄	1	2	yes	—
78	C₄⋊#1057	C₂×C₄	1	4	yes	—
79	C₄×#1057	C₂×C₄	1	2	yes	—
80	C₄×#1057	C₂×C₄	1	4	yes	—
81	C₄×#1057	C₂×C₄	1	2	yes	—
82	C₄×#1057	C₂×C₄	1	4	yes	—
83	#88100	—	2	2	no	—
84	#88100	—	2	2	no	—
85	#88100	—	2	4	no	—
86	#88100	—	2	2	no	—
87	#88100	Q₈	1	4	yes	complemented
88	C₈×#261	—	2	4	no	—
89	C₈×#261	—	2	4	no	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#97	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
94	#88055	C₂×C₄	1	2	yes	—
95	#88055	C₂×C₄	1	2	yes	—
96	#88054	C₂×C₄	1	2	yes	—
97	#88054	C₂×C₄	1	2	yes	—
98	#88054	C₂×C₄	1	2	yes	—
99	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#1055	C₂×C₄	1	2	yes	—
103	#88043	C₂×C₄	1	2	yes	—
104	C₄×#1055	C₂×C₄	1	1	yes	characteristic
105	#20521	—	13	1	no	maximal, Sylow
106	C₂²×#261	C₂²×C₄	1	4	yes	—
107	C₂²×#261	C₂²×C₄	1	2	yes	—
108	C₂²×#261	C₂²×C₄	1	2	yes	—
109	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
110	Q₈×D₁₃	—	2	4	no	—
111	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
117	C₂×Dic₂₆	C₄²	1	2	yes	—
118	C₂×#1057	C₂²×C₄	1	4	yes	—
119	C₂×#1057	C₂²×C₄	1	2	yes	—
120	C₂×#1057	C₂²×C₄	1	2	yes	—
121	C₄⋊#261	—	2	4	no	—
122	C₄⋊#261	—	4	4	no	—
123	C₄×#261	—	2	4	no	—
124	C₄×#261	—	2	2	no	—
125	C₄×#261	—	2	1	no	—
126	C₄×#261	—	2	2	no	—
127	C₄×#261	—	2	1	no	—
128	C₄×#261	—	4	2	no	—
129	C₄×#261	C₂×Q₈	1	2	yes	—
130	C₄×#261	#41	1	2	yes	—
131	D₁₃⋊C₈	—	2	2	no	—
132	D₁₃⋊C₈	—	2	2	no	—
133	D₁₃⋊C₈	—	2	1	no	—
134	D₁₃⋊C₈	—	2	1	no	—
135	D₁₃⋊C₈	C₂×Q₈	1	2	yes	—
136	D₁₃⋊C₈	#41	1	2	yes	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
144	C₄⋊Dic₁₃	C₄²	1	2	yes	—
145	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
146	#6101	C₄²	1	2	yes	—
147	#6101	C₄²	1	2	yes	—
148	#6101	C₄²	1	2	yes	—
149	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
151	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	2	yes	—
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	C₈×D₁₃	—	2	2	no	—
159	C₈×D₁₃	—	2	2	no	—
160	C₈×D₁₃	—	2	1	no	—
161	C₈×D₁₃	—	2	1	no	—
162	C₈×D₁₃	C₂×Q₈	1	2	yes	—
163	C₈×D₁₃	#41	1	2	yes	—
164	C₂×#446	—	13	1	no	—
165	C₂×C₈×Q₈	—	13	1	no	—
166	#2295	—	13	1	no	—
167	#1771	—	13	2	no	—
168	#1770	—	13	2	no	—
169	#1770	—	13	1	no	—
170	C₈×C₄⋊C₄	—	13	1	no	—
171	#1768	—	13	2	no	—
172	C₄×C₄⋊C₈	—	13	1	no	—
173	#1726	—	13	2	no	—
174	C₄×#97	—	13	1	no	—
175	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×#261	—	2	2	no	—
177	C₂×#261	—	2	2	no	—
178	C₂×#261	—	2	4	no	—
179	C₂×#261	—	2	2	no	—
180	C₂×#261	—	2	2	no	—
181	C₂×#261	—	2	4	no	—
182	C₂×#261	—	2	2	no	—
183	C₂×#261	—	2	4	no	—
184	C₂×#261	C₄×Q₈	1	4	yes	—
185	Q₈×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
193	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
194	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
196	C₄×D₁₃	—	2	4	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	4	no	—
199	C₄×D₁₃	#131	1	4	yes	—
200	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
201	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
202	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
203	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
204	Dic₂₆	—	2	2	no	—
205	Dic₂₆	—	2	4	no	—
206	#1057	—	2	4	no	—
207	#1057	—	2	2	no	—
208	#1057	C₄×Q₈	1	4	yes	—
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	C₄×Q₈	1	2	yes	—
212	#1055	—	2	2	no	—
213	#1055	—	2	1	no	—
214	#1055	C₄×Q₈	1	2	yes	—
215	C₂×C₄×Q₈	—	13	1	no	—
216	#446	—	13	1	no	—
217	#446	—	13	2	no	—
218	#446	—	13	1	no	—
219	#446	—	13	2	no	—
220	#446	—	13	1	no	—
221	#446	#261	1	1	yes	characteristic, complemented
222	C₈×Q₈	—	13	4	no	—
223	C₈×Q₈	—	13	2	no	—
224	C₈×Q₈	—	13	2	no	—
225	C₂×C₄⋊C₈	—	13	1	no	—
226	C₂×C₄⋊C₈	—	13	2	no	—
227	C₂×C₄⋊C₈	—	13	1	no	—
228	C₂×C₄⋊C₈	—	13	2	no	—
229	C₂×#97	—	13	1	no	—
230	C₂×#97	—	13	2	no	—
231	C₂×#97	—	13	1	no	—
232	C₂×#97	—	13	1	no	—
233	C₂×#97	—	13	1	no	—
234	C₂×#97	—	13	2	no	—
235	C₂×C₄×C₈	—	13	1	no	—
236	C₂×C₄×C₈	—	13	2	no	—
237	C₂×C₄×C₈	—	13	1	no	—
238	C₂×C₄×C₈	—	13	2	no	—
239	C₂×C₄×C₈	—	13	2	no	—
240	#391	—	13	2	no	—
241	#389	—	13	2	no	—
242	#387	—	13	4	no	—
243	C₄×C₄⋊C₄	—	13	1	no	—
244	C₄×C₄⋊C₄	—	13	2	no	—
245	#376	—	13	2	no	—
246	C₄³	—	13	1	no	—
247	#336	—	13	2	no	—
248	#336	—	13	2	no	—
249	#336	—	13	2	no	—
250	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
251	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
252	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
253	C₂×D₁₃	C₂×#131	1	2	yes	—
254	C₂×D₁₃	#568	1	2	yes	—
255	#261	—	2	4	no	—
256	#261	—	4	2	no	—
257	#261	—	4	4	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	#405	1	2	yes	—
262	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
264	Dic₁₃	—	2	2	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	2	no	—
267	Dic₁₃	#405	1	2	yes	—
268	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
269	Dic₁₃	C₄×#41	1	1	yes	characteristic
270	C₂²×Q₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	2	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	2	no	—
277	C₄×Q₈	—	13	1	no	—
278	C₄×Q₈	—	13	2	no	—
279	C₄×Q₈	—	13	1	no	—
280	C₄×Q₈	—	13	2	no	—
281	C₄×Q₈	—	13	1	no	—
282	C₄×Q₈	C₂×#261	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	13	2	no	—
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	2	no	—
286	C₂×C₄⋊C₄	—	13	4	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	2	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	2	no	—
292	C₂×C₄²	—	13	2	no	—
293	C₂×C₄²	—	13	2	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	13	4	no	—
296	C₄⋊C₈	—	13	2	no	—
297	C₄⋊C₈	—	13	4	no	—
298	C₄⋊C₈	—	13	2	no	—
299	C₄⋊C₈	—	13	2	no	—
300	C₄⋊C₈	—	13	2	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
304	C₄⋊C₈	C₂×#261	1	2	yes	—
305	#97	—	13	4	no	—
306	#97	—	13	2	no	—
307	#97	—	13	2	no	—
308	#97	—	13	2	no	—
309	#97	—	26	2	no	—
310	#97	—	26	2	no	—
311	#97	—	26	4	no	—
312	#97	—	26	2	no	—
313	#97	C₂×#261	1	2	yes	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	4	no	—
316	C₄×C₈	—	13	2	no	—
317	C₄×C₈	—	13	4	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	—	13	1	no	—
320	C₄×C₈	—	13	1	no	—
321	C₄×C₈	—	26	4	no	—
322	C₄×C₈	—	26	4	no	—
323	C₄×C₈	C₂×#261	1	1	yes	characteristic
324	#95	—	13	4	no	—
325	#95	—	13	4	no	—
326	#95	—	13	2	no	—
327	#95	—	13	4	no	—
328	C₂×C₁₃	C₄²×Q₈	1	1	yes	characteristic
329	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
330	C₂×C₁₃	#2875	1	1	yes	characteristic
331	D₁₃	#2962	1	2	yes	—
332	D₁₃	#2969	1	2	yes	—
333	C₂×Q₈	—	13	2	no	—
334	C₂×Q₈	—	13	1	no	—
335	C₂×Q₈	—	26	4	no	—
336	C₂×Q₈	C₄×#261	1	1	yes	characteristic
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	2	no	—
340	C₂²×C₄	—	13	2	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	2	no	—
343	C₂²×C₄	—	13	4	no	—
344	C₂²×C₄	—	13	2	no	—
345	C₂×C₈	—	13	2	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	4	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	—	26	1	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	26	1	no	—
362	C₂×C₈	—	26	1	no	—
363	C₂×C₈	C₂²×#261	1	1	yes	characteristic
364	C₂×C₈	C₂²×#261	1	2	yes	—
365	C₂×C₈	C₂²×#261	1	1	yes	characteristic
366	C₄⋊C₄	—	13	2	no	—
367	C₄⋊C₄	—	13	2	no	—
368	C₄⋊C₄	—	13	2	no	—
369	C₄⋊C₄	—	13	2	no	—
370	C₄⋊C₄	—	13	1	no	—
371	C₄⋊C₄	—	26	4	no	—
372	C₄⋊C₄	—	52	4	no	—
373	C₄⋊C₄	C₄×#261	1	2	yes	—
374	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
375	C₄²	—	13	2	no	—
376	C₄²	—	13	2	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	2	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	2	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	13	2	no	—
383	C₄²	—	26	2	no	—
384	C₄²	—	26	1	no	—
385	C₄²	—	26	1	no	—
386	C₄²	—	26	2	no	—
387	C₄²	—	26	4	no	—
388	C₄²	—	52	2	no	—
389	C₄²	C₂²×#261	1	1	yes	characteristic
390	C₄²	C₂²×#261	1	2	yes	—
391	C₁₃	#20521	1	1	yes	characteristic, complemented, Sylow
392	C₂³	—	13	1	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	26	4	no	—
395	Q₈	—	26	2	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	4	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	4	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	2	no	—
406	C₂×C₄	—	13	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	4	no	—
409	C₂×C₄	—	26	4	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	4	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	26	4	no	—
417	C₂×C₄	—	26	4	no	—
418	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
419	C₂×C₄	C₂×C₄×#261	1	2	yes	—
420	C₂×C₄	C₂×C₄×#261	1	2	yes	—
421	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
422	C₂×C₄	C₂³×#261	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	1	no	—
425	C₈	—	13	4	no	—
426	C₈	—	13	2	no	—
427	C₈	—	26	4	no	—
428	C₈	—	26	2	no	—
429	C₈	—	26	1	no	—
430	C₈	—	26	2	no	—
431	C₈	Q₈×#261	1	2	yes	—
432	C₂²	—	13	1	no	—
433	C₂²	—	13	1	no	—
434	C₂²	—	13	2	no	—
435	C₂²	—	13	2	no	—
436	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	2	no	—
440	C₄	—	13	1	no	—
441	C₄	—	13	1	no	—
442	C₄	—	13	2	no	—
443	C₄	—	26	4	no	—
444	C₄	—	26	2	no	—
445	C₄	—	26	1	no	—
446	C₄	—	26	2	no	—
447	C₄	—	52	2	no	—
448	C₄	—	52	4	no	—
449	C₄	#11719099	1	2	yes	—
450	C₄	C₂×Q₈×#261	1	1	yes	characteristic
451	C₄	#41×#261	1	1	yes	characteristic
452	C₂	—	13	2	no	—
453	C₂	—	13	2	no	—
454	C₂	C₄×Q₈×#261	1	1	yes	characteristic
455	C₂	C₂×#11719099	1	1	yes	characteristic
456	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#446	C₄
prime radical	C₂²×D₁₃	C₂³×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#446	#261
hypocenter	C₁₃	#20521
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
14. Q₈×#1057	C₄	semidirect
24. #11719074	C₄	semidirect
25. #11719074	C₄	semidirect
34. C₁₃×#446	C₄	semidirect
35. #11718685	C₄	semidirect
38. #11718492	C₄	semidirect
39. #11718489	C₄	semidirect
41. #11718362	C₄	semidirect
43. #11718340	C₄	semidirect
87. #88100	Q₈	semidirect
221. #446	#261	semidirect
391. C₁₃	#20521	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₁₃⋊C₈	2
#13131295	2
#13130634	2
#13130633	2
C₈×C₄⋊#261	2
#13130625	2
C₄⋊C₈×#261	2
#13130494	2
C₄×#88100	2
D₁₃×#446	2
#20521	13