Subgroups — #16785706

Order 3328.

822 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719092	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718234	C₂	1	2	yes	maximal
4	#13130501	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#88237	C₂²	1	2	yes	—
7	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	D₁₃⋊#108	—	2	2	no	—
12	D₁₃⋊#108	—	2	2	no	—
13	C₂×#88104	C₄	1	2	yes	complemented
14	C₂×#88103	C₄	1	2	yes	complemented
15	#11719092	—	2	2	no	—
16	#11719092	—	2	2	no	—
17	C₂×#88102	C₄	1	2	yes	complemented
18	C₂×#88101	C₄	1	2	yes	complemented
19	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
20	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
21	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
23	C₄×C₈×D₁₃	—	2	2	no	—
24	C₄×C₈×D₁₃	—	2	2	no	—
25	(C₂×#261)⋊C₈	—	2	4	no	—
26	#11718234	—	2	4	no	—
27	C₂²×C₄×D₁₃	—	2	1	no	—
28	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊#261	—	2	2	no	—
30	C₂×#6122	—	2	2	no	—
31	#88237	—	2	2	no	—
32	#88237	—	2	2	no	—
33	#88237	—	2	2	no	—
34	#88237	—	2	2	no	—
35	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
36	C₂×C₄×#261	—	2	2	no	—
37	D₁₃⋊M₁₆	—	2	2	no	—
38	D₁₃⋊M₁₆	—	2	2	no	—
39	D₁₃⋊M₁₆	—	2	2	no	—
40	D₁₃⋊M₁₆	—	2	2	no	—
41	C₂×#6118	C₂×C₄	1	4	yes	—
42	C₂×D₁₃⋊C₈	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	—	2	1	no	—
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
49	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	—	2	1	no	—
51	C₂×C₈×D₁₃	—	2	1	no	—
52	C₂×C₈×D₁₃	—	2	1	no	—
53	C₂×C₈×D₁₃	—	2	1	no	—
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	D₄	1	2	yes	—
59	C₂×C₈×D₁₃	D₄	1	2	yes	—
60	C₂×C₈×D₁₃	D₄	1	2	yes	—
61	C₂×C₈×D₁₃	D₄	1	2	yes	—
62	C₂×C₈×D₁₃	Q₈	1	2	yes	—
63	C₂×C₈×D₁₃	Q₈	1	2	yes	—
64	C₄²×D₁₃	—	2	1	no	—
65	C₄²×D₁₃	—	2	1	no	—
66	C₄²×D₁₃	D₄	1	2	yes	—
67	C₄²×D₁₃	Q₈	1	2	yes	—
68	#88104	—	2	4	no	—
69	#88103	—	2	4	no	—
70	#88102	—	2	4	no	—
71	#88101	—	2	4	no	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	C₈×Dic₁₃	—	2	2	no	—
74	C₈×Dic₁₃	—	2	2	no	—
75	C₄×#1055	—	2	2	no	—
76	#10859	—	13	1	no	maximal, Sylow
77	C₂³×D₁₃	#41	1	1	yes	characteristic
78	C₂²×#261	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×Dic₁₃	—	2	1	no	—
82	C₂²×Dic₁₃	#41	1	1	yes	characteristic
83	C₂×C₄×D₁₃	—	2	8	no	—
84	C₂×C₄×D₁₃	—	2	2	no	—
85	C₂×C₄×D₁₃	—	2	2	no	—
86	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
97	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
98	C₂²⋊#261	—	4	2	no	—
99	C₂²⋊#261	—	4	2	no	—
100	#6122	—	4	2	no	—
101	#6122	—	4	2	no	—
102	C₂×#1057	—	2	4	no	—
103	C₄⋊#261	—	2	4	no	—
104	C₄⋊#261	—	2	4	no	—
105	C₄×#261	—	4	2	no	—
106	C₄×#261	—	4	2	no	—
107	#6118	—	2	4	no	—
108	#6118	—	2	4	no	—
109	D₁₃⋊C₈	—	4	2	no	—
110	D₁₃⋊C₈	—	4	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
118	C₄²×C₁₃	—	2	1	no	—
119	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
120	C₄×Dic₁₃	—	2	1	no	—
121	C₄×Dic₁₃	—	2	2	no	—
122	C₄×Dic₁₃	—	2	2	no	—
123	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
124	C₂×#1055	—	2	1	no	—
125	C₂×#1055	—	2	1	no	—
126	C₂×#1055	C₄²	1	1	yes	characteristic
127	C₂×#1055	C₄²	1	1	yes	characteristic
128	C₂×#1055	C₂²⋊C₄	1	2	yes	—
129	C₂×#1055	C₄⋊C₄	1	2	yes	—
130	C₂×#1055	C₄⋊C₄	1	2	yes	—
131	C₈×D₁₃	—	2	2	no	—
132	C₈×D₁₃	—	2	2	no	—
133	C₈×D₁₃	—	2	2	no	—
134	C₈×D₁₃	—	2	2	no	—
135	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
136	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
137	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
138	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
139	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
140	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
141	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
142	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
143	C₂²×#108	—	13	1	no	—
144	C₂×#427	—	13	1	no	—
145	C₂²×C₄×C₈	—	13	1	no	—
146	C₂×#339	—	13	2	no	—
147	#1729	—	13	2	no	—
148	C₂³×C₁₃	#117	1	1	yes	characteristic
149	C₂²×D₁₃	—	2	4	no	—
150	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
152	C₂²×D₁₃	#121	1	1	yes	characteristic
153	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂²×D₁₃	#124	1	1	yes	characteristic
155	C₂²×D₁₃	#125	1	1	yes	characteristic
156	C₂×#261	—	4	4	no	—
157	C₂×#261	—	4	8	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
166	C₂×Dic₁₃	—	2	4	no	—
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
169	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
170	C₂×Dic₁₃	#121	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×Dic₁₃	#124	1	1	yes	characteristic
173	C₂×Dic₁₃	#125	1	1	yes	characteristic
174	C₄×D₁₃	—	2	8	no	—
175	C₄×D₁₃	—	2	8	no	—
176	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
181	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
182	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
183	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
184	C₄×D₁₃	#121	1	1	yes	characteristic
185	C₄×D₁₃	#121	1	1	yes	characteristic
186	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
188	C₄×D₁₃	#127	1	1	yes	characteristic
189	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
190	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
191	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
192	#1057	—	4	4	no	—
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	#95	1	2	yes	—
195	C₈×C₁₃	#95	1	2	yes	—
196	#1055	—	2	2	no	—
197	#1055	#95	1	2	yes	—
198	#1055	#95	1	2	yes	—
199	C₂²×M₁₆	—	13	2	no	—
200	C₂³×C₈	—	13	1	no	—
201	C₂³×C₈	—	13	1	no	—
202	C₂×#117	—	13	2	no	—
203	C₂²×C₄²	—	13	1	no	—
204	C₂×#108	—	13	2	no	—
205	C₂×#108	—	13	2	no	—
206	C₂×#108	—	26	2	no	—
207	C₂×#108	—	26	2	no	—
208	#427	—	26	2	no	—
209	#427	—	26	2	no	—
210	C₂×#107	—	13	2	no	—
211	C₂×#106	—	13	2	no	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	—	13	1	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	C₂×C₄×C₈	—	26	2	no	—
216	C₂×C₄×C₈	—	26	2	no	—
217	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
218	#339	—	26	4	no	—
219	#336	—	26	4	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
222	C₂²×C₁₃	#380	1	1	yes	characteristic
223	C₂²×C₁₃	#382	1	1	yes	characteristic
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	—	2	2	no	—
226	C₂×D₁₃	—	2	2	no	—
227	C₂×D₁₃	—	2	2	no	—
228	C₂×D₁₃	—	2	2	no	—
229	C₂×D₁₃	#389	1	1	yes	characteristic
230	C₂×D₁₃	#389	1	1	yes	characteristic
231	C₂×D₁₃	#390	1	1	yes	characteristic
232	C₂×D₁₃	#391	1	1	yes	characteristic
233	C₂×D₁₃	#443	1	4	yes	—
234	#261	—	8	4	no	—
235	C₄×C₁₃	—	2	4	no	—
236	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
237	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₁₃	#380	1	1	yes	characteristic
239	C₄×C₁₃	#384	1	1	yes	characteristic
240	Dic₁₃	—	2	4	no	—
241	Dic₁₃	#389	1	1	yes	characteristic
242	Dic₁₃	#389	1	1	yes	characteristic
243	Dic₁₃	#390	1	1	yes	characteristic
244	Dic₁₃	#391	1	1	yes	characteristic
245	C₂³×C₄	—	13	1	no	—
246	C₂³×C₄	—	26	1	no	—
247	C₂×M₁₆	—	13	4	no	—
248	C₂×M₁₆	—	26	2	no	—
249	C₂×M₁₆	—	26	2	no	—
250	C₂×M₁₆	—	26	2	no	—
251	C₂×M₁₆	—	26	2	no	—
252	C₂×M₁₆	—	26	2	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	2	no	—
259	C₂²×C₈	—	13	2	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	26	1	no	—
266	C₂²×C₈	—	26	1	no	—
267	C₂²×C₈	—	26	1	no	—
268	C₂²×C₈	—	26	1	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	C₂×#261	1	1	yes	characteristic
271	C₂²×C₈	C₂×#261	1	1	yes	characteristic
272	#117	—	26	2	no	—
273	#117	—	26	2	no	—
274	#117	—	26	2	no	—
275	#117	—	26	2	no	—
276	C₂×C₄⋊C₄	—	13	4	no	—
277	C₂×C₂²⋊C₄	—	26	2	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	2	no	—
280	C₂×C₄²	—	13	2	no	—
281	C₂×C₄²	—	26	1	no	—
282	C₂×C₄²	—	26	1	no	—
283	C₂×C₄²	—	26	1	no	—
284	C₂×C₄²	—	26	2	no	—
285	C₂×C₄²	C₂×#261	1	1	yes	characteristic
286	#108	—	26	4	no	—
287	#108	—	26	4	no	—
288	#107	—	26	4	no	—
289	#106	—	26	4	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	26	2	no	—
292	C₄×C₈	—	26	2	no	—
293	C₄×C₈	—	26	2	no	—
294	C₂×C₁₃	—	2	1	no	—
295	C₂×C₁₃	—	2	1	no	—
296	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
297	C₂×C₁₃	#1772	1	2	yes	—
298	D₁₃	—	2	1	no	—
299	D₁₃	—	2	1	no	—
300	D₁₃	#1945	1	2	yes	—
301	D₁₃	#1974	1	2	yes	—
302	C₂⁴	—	13	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	26	2	no	—
318	C₂²×C₄	—	26	2	no	—
319	C₂²×C₄	—	26	8	no	—
320	C₂²×C₄	—	26	1	no	—
321	C₂²×C₄	—	26	4	no	—
322	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
323	M₁₆	—	26	4	no	—
324	M₁₆	—	26	4	no	—
325	M₁₆	—	52	2	no	—
326	M₁₆	—	52	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	2	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	13	2	no	—
338	C₂×C₈	—	13	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	26	2	no	—
343	C₂×C₈	—	26	2	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	1	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	26	4	no	—
349	C₂×C₈	—	52	2	no	—
350	C₂×C₈	—	52	2	no	—
351	C₂×C₈	C₄×#261	1	1	yes	characteristic
352	C₂×C₈	C₄×#261	1	1	yes	characteristic
353	C₂×C₈	C₄⋊#261	1	2	yes	—
354	C₂×C₈	C₄⋊#261	1	2	yes	—
355	C₂×C₈	C₂²⋊#261	1	2	yes	—
356	C₄⋊C₄	—	26	4	no	—
357	C₄⋊C₄	—	26	4	no	—
358	C₂²⋊C₄	—	52	2	no	—
359	C₂²⋊C₄	—	52	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	13	2	no	—
362	C₄²	—	26	2	no	—
363	C₄²	—	26	2	no	—
364	C₄²	—	26	1	no	—
365	C₄²	—	52	2	no	—
366	C₄²	—	52	2	no	—
367	C₄²	C₄⋊#261	1	2	yes	—
368	C₁₃	#10859	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	13	1	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	—	13	1	no	—
373	C₂³	—	13	1	no	—
374	C₂³	—	13	1	no	—
375	C₂³	—	26	4	no	—
376	C₂³	#88237	1	1	yes	characteristic
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	26	8	no	—
402	C₂×C₄	—	26	8	no	—
403	C₂×C₄	—	26	4	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	52	4	no	—
406	C₂×C₄	—	52	8	no	—
407	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
411	C₂×C₄	#88237	1	1	yes	characteristic
412	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	13	2	no	—
415	C₈	—	13	2	no	—
416	C₈	—	26	2	no	—
417	C₈	—	52	4	no	—
418	C₈	(C₂×#261)⋊C₄	1	2	yes	—
419	C₈	(C₂×#261)⋊C₄	1	2	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	13	1	no	—
422	C₂²	—	13	1	no	—
423	C₂²	—	13	4	no	—
424	C₂²	—	13	1	no	—
425	C₂²	—	13	1	no	—
426	C₂²	—	26	2	no	—
427	C₂²	—	26	2	no	—
428	C₂²	—	26	2	no	—
429	C₂²	—	26	2	no	—
430	C₂²	—	26	2	no	—
431	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
432	C₂²	#11719060	1	1	yes	characteristic
433	C₂²	#11719136	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	13	1	no	—
436	C₄	—	13	1	no	—
437	C₄	—	13	1	no	—
438	C₄	—	13	1	no	—
439	C₄	—	26	4	no	—
440	C₄	—	104	4	no	—
441	C₄	C₄×C₄⋊#261	1	1	yes	characteristic
442	C₄	#11719059	1	1	yes	characteristic
443	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
444	C₄	#11719136	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	13	2	no	—
448	C₂	—	13	2	no	—
449	C₂	—	26	1	no	—
450	C₂	—	26	1	no	—
451	C₂	#13130014	1	1	yes	characteristic
452	C₂	#13130638	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×D₁₃	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#10859
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. C₂×#88104	C₄	semidirect
14. C₂×#88103	C₄	semidirect
17. C₂×#88102	C₄	semidirect
18. C₂×#88101	C₄	semidirect
19. C₂×C₄×C₈×C₁₃	C₄	semidirect
20. C₂×C₈×Dic₁₃	C₄	semidirect
21. C₂×C₈×Dic₁₃	C₄	semidirect
22. C₂×C₄×#1055	C₄	semidirect
217. C₂×C₄×C₈	#261	semidirect
368. C₁₃	#10859	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊#108	2
C₂×#11719092	2
C₂×#11718234	2
#13130501	2
C₂×C₄×C₈×D₁₃	2
#10859	13