Subgroups — #16795131

Order 3328.

616 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	#13131761	C₂	1	2	yes	maximal
2	#13130412	C₂	1	2	yes	maximal, complemented
3	#13130410	C₂	1	2	yes	maximal, complemented
4	#13130409	C₂	1	2	yes	maximal, complemented
5	#13130399	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130398	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130390	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130385	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718255	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃⋊#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#6129	C₂	1	1	yes	maximal, characteristic
12	C₄×#6129	C₂²	1	1	yes	characteristic
13	#11719144	—	2	2	no	—
14	#11719130	C₂²	1	2	yes	—
15	#11719129	C₂²	1	2	yes	—
16	#11719119	C₂²	1	2	yes	—
17	C₂×C₄⋊#1057	C₂²	1	2	yes	—
18	#11719078	—	2	2	no	—
19	#11719065	—	2	2	no	—
20	#11719063	—	2	2	no	—
21	#11719054	C₂²	1	2	yes	—
22	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
23	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
26	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	D₄×#1055	C₄	1	1	yes	characteristic
29	#11718494	C₂²	1	1	yes	characteristic
30	#11718491	C₄	1	1	yes	characteristic
31	#11718386	C₄	1	1	yes	characteristic
32	#11718386	C₄	1	1	yes	characteristic
33	#11718379	C₂²	1	1	yes	characteristic
34	#11718379	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₆	C₄	1	1	yes	characteristic
37	#11718256	C₂²	1	2	yes	—
38	#11718256	C₂²	1	2	yes	—
39	#11718255	C₂²	1	1	yes	characteristic
40	#11718255	C₂²	1	1	yes	characteristic
41	#11718255	C₂²	1	1	yes	characteristic
42	#11718255	C₂²	1	2	yes	—
43	#11718255	C₂²	1	1	yes	characteristic
44	#11718254	C₂²	1	2	yes	—
45	#11718253	C₂²	1	2	yes	—
46	#11718253	C₂²	1	2	yes	—
47	C₂×#6129	Q₈	1	1	yes	characteristic
48	C₂×#6122	—	2	2	no	—
49	C₂²×#1057	—	2	2	no	—
50	C₂×D₁₃⋊C₈	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	D₄×Dic₁₃	D₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
59	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
60	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	#88146	Q₈	1	1	yes	characteristic
64	#88141	D₄	1	1	yes	characteristic
65	#88135	D₄	1	1	yes	characteristic
66	#88135	D₄	1	1	yes	characteristic
67	#88131	Q₈	1	1	yes	characteristic
68	#88131	Q₈	1	1	yes	characteristic
69	C₄²×D₁₃	C₂³	1	1	yes	characteristic
70	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊#1057	—	2	2	no	—
72	C₂²⋊#1057	—	2	2	no	—
73	#88112	—	2	2	no	—
74	#88112	—	2	2	no	—
75	#88111	—	2	2	no	—
76	#88110	—	2	2	no	—
77	#88110	—	2	2	no	—
78	C₄⋊#1057	—	2	2	no	—
79	C₄⋊#1057	C₂³	1	2	yes	—
80	C₄⋊#1057	C₂³	1	2	yes	—
81	C₄⋊#1057	C₂³	1	2	yes	—
82	C₄⋊#1057	C₂³	1	2	yes	—
83	C₄×#1057	—	2	2	no	—
84	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
90	#88060	C₂×C₄	1	1	yes	characteristic
91	#88060	C₂×C₄	1	1	yes	characteristic
92	#88054	C₂×C₄	1	1	yes	characteristic
93	#88054	C₂×C₄	1	1	yes	characteristic
94	#88054	C₂×C₄	1	1	yes	characteristic
95	#88054	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₃	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	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
105	C₄×#1055	C₂×C₄	1	1	yes	characteristic
106	#17834	—	13	1	no	maximal, Sylow
107	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
116	#6129	—	2	4	no	—
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
121	#6122	—	8	2	no	—
122	C₂×#1057	—	2	2	no	—
123	C₂×#1057	—	2	2	no	—
124	C₂×#1057	—	2	2	no	—
125	C₂×#1057	—	2	2	no	—
126	C₂×#1057	—	8	2	no	—
127	D₁₃⋊C₈	—	8	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
135	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
140	#6103	C₄⋊C₄	1	1	yes	characteristic
141	#6103	C₄⋊C₄	1	1	yes	characteristic
142	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
143	#6101	C₄⋊C₄	1	1	yes	characteristic
144	#6101	C₄⋊C₄	1	1	yes	characteristic
145	#6101	C₄⋊C₄	1	1	yes	characteristic
146	#6101	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
159	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
162	C₈×D₁₃	—	2	2	no	—
163	C₈×D₁₃	—	4	1	no	—
164	#2990	—	13	2	no	—
165	C₈×#41	—	13	1	no	—
166	#1574	—	13	2	no	—
167	#1573	—	13	2	no	—
168	#1573	—	13	2	no	—
169	#1568	—	13	1	no	—
170	#1568	—	13	1	no	—
171	#1566	—	13	1	no	—
172	#1564	—	13	1	no	—
173	C₂×#334	—	13	1	no	—
174	C₂×#334	—	13	1	no	—
175	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	D₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂²⋊D₁₃	—	2	2	no	—
189	C₂²⋊D₁₃	#108	1	4	yes	—
190	C₂×Dic₁₃	—	2	2	no	—
191	C₂×Dic₁₃	—	2	2	no	—
192	C₂×Dic₁₃	—	2	2	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	2	1	no	—
203	C₄×D₁₃	—	2	1	no	—
204	C₄×D₁₃	—	2	2	no	—
205	Dic₂₆	—	2	2	no	—
206	#1057	—	4	2	no	—
207	#1057	—	4	2	no	—
208	#1057	—	4	2	no	—
209	#1057	—	4	2	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	1	no	—
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	#1055	#131	1	2	yes	—
218	C₄×#41	—	13	1	no	—
219	#446	—	26	2	no	—
220	C₈×Q₈	—	13	1	no	—
221	C₈×Q₈	—	13	1	no	—
222	#435	—	26	2	no	—
223	#435	—	26	2	no	—
224	C₈×D₄	—	13	1	no	—
225	C₈×D₄	—	13	1	no	—
226	C₈×D₄	—	13	1	no	—
227	C₈×D₄	—	13	1	no	—
228	C₈×D₄	—	13	1	no	—
229	C₈×D₄	—	26	2	no	—
230	C₈×D₄	#261	1	1	yes	characteristic
231	#432	—	13	2	no	—
232	#432	—	13	2	no	—
233	#431	—	13	1	no	—
234	#431	—	13	1	no	—
235	#431	—	13	1	no	—
236	#431	—	13	2	no	—
237	#423	—	13	2	no	—
238	C₂×C₄⋊C₈	—	13	2	no	—
239	C₂×C₄⋊C₈	—	13	2	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	C₂×C₄×C₈	—	13	1	no	—
243	#335	—	13	2	no	—
244	#335	—	13	2	no	—
245	#335	—	13	2	no	—
246	#334	—	13	1	no	—
247	#334	—	13	1	no	—
248	#334	—	13	1	no	—
249	#334	—	13	2	no	—
250	#334	—	13	2	no	—
251	#334	—	13	1	no	—
252	#334	—	13	2	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	C₂×#108	1	2	yes	—
259	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
260	C₂×D₁₃	—	2	1	no	—
261	C₂×D₁₃	—	2	1	no	—
262	C₂×D₁₃	C₂×#108	1	2	yes	—
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	C₂×#131	1	1	yes	characteristic
268	C₄×C₁₃	#568	1	1	yes	characteristic
269	Dic₁₃	—	2	1	no	—
270	Dic₁₃	—	2	1	no	—
271	Dic₁₃	—	2	1	no	—
272	Dic₁₃	—	2	1	no	—
273	Dic₁₃	—	2	1	no	—
274	Dic₁₃	C₂×#108	1	2	yes	—
275	Dic₁₃	#577	1	2	yes	—
276	C₂×#41	—	13	1	no	—
277	C₂×M₁₆	—	26	2	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	13	1	no	—
282	C₂²×C₈	—	26	2	no	—
283	C₂²×C₈	—	26	2	no	—
284	C₂²×C₈	C₂×#261	1	1	yes	characteristic
285	C₂²×C₈	C₂×#261	1	1	yes	characteristic
286	C₄×Q₈	—	13	1	no	—
287	C₄×Q₈	—	13	1	no	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	13	1	no	—
291	C₄×D₄	—	13	1	no	—
292	C₄×D₄	—	13	1	no	—
293	C₄×D₄	C₂×#261	1	1	yes	characteristic
294	#117	—	13	1	no	—
295	#117	—	13	1	no	—
296	#117	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	—	13	1	no	—
300	C₄⋊C₈	—	13	1	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	1	no	—
303	C₄⋊C₈	—	13	1	no	—
304	C₄⋊C₈	—	13	2	no	—
305	C₄⋊C₈	—	13	2	no	—
306	C₄⋊C₈	—	13	2	no	—
307	C₄⋊C₈	—	13	2	no	—
308	C₄⋊C₈	—	13	1	no	—
309	C₄⋊C₈	—	26	2	no	—
310	C₄⋊C₈	—	26	2	no	—
311	C₄⋊C₈	—	26	2	no	—
312	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
313	C₂²⋊C₈	—	13	1	no	—
314	C₂²⋊C₈	—	13	1	no	—
315	C₂²⋊C₈	—	13	1	no	—
316	C₂²⋊C₈	—	13	1	no	—
317	C₂²⋊C₈	—	26	2	no	—
318	C₂²⋊C₈	—	26	2	no	—
319	C₂²⋊C₈	—	26	2	no	—
320	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
321	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
322	#97	—	26	2	no	—
323	#97	—	26	2	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	13	1	no	—
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	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	26	2	no	—
334	C₄×C₈	C₂×#261	1	1	yes	characteristic
335	C₂×C₁₃	—	2	2	no	—
336	C₂×C₁₃	—	4	1	no	—
337	C₂×C₁₃	#2906	1	1	yes	characteristic
338	C₂×C₁₃	#2912	1	1	yes	characteristic
339	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
340	D₁₃	—	2	2	no	—
341	#41	—	26	4	no	—
342	C₂×Q₈	—	13	1	no	—
343	C₂×D₄	—	13	1	no	—
344	C₂×D₄	—	13	1	no	—
345	C₂×D₄	C₄⋊#261	1	1	yes	characteristic
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
355	M₁₆	—	104	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	26	2	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	—	26	2	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	26	2	no	—
368	C₂×C₈	—	26	2	no	—
369	C₂×C₈	—	52	1	no	—
370	C₂×C₈	—	104	2	no	—
371	C₂×C₈	—	104	2	no	—
372	C₂×C₈	C₂²×#261	1	1	yes	characteristic
373	C₂×C₈	C₂²×#261	1	1	yes	characteristic
374	C₂×C₈	C₂²×#261	1	1	yes	characteristic
375	C₂×C₈	C₂²×#261	1	1	yes	characteristic
376	C₄⋊C₄	—	13	1	no	—
377	C₄⋊C₄	—	13	1	no	—
378	C₄⋊C₄	—	13	1	no	—
379	C₄⋊C₄	—	13	1	no	—
380	C₄⋊C₄	—	13	1	no	—
381	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
382	C₂²⋊C₄	—	13	1	no	—
383	C₂²⋊C₄	—	13	1	no	—
384	C₂²⋊C₄	—	13	1	no	—
385	C₂²⋊C₄	—	13	1	no	—
386	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
387	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
388	C₄²	—	13	1	no	—
389	C₄²	—	13	1	no	—
390	C₄²	—	13	1	no	—
391	C₄²	—	13	1	no	—
392	C₄²	—	13	1	no	—
393	C₄²	—	13	1	no	—
394	C₄²	—	13	1	no	—
395	C₄²	—	13	1	no	—
396	C₄²	—	13	1	no	—
397	C₄²	C₂²×#261	1	1	yes	characteristic
398	C₁₃	#17834	1	1	yes	characteristic, complemented, Sylow
399	C₂³	—	13	1	no	—
400	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
401	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
402	Q₈	—	26	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	13	4	no	—
405	D₄	—	26	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	1	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	2	no	—
420	C₂×C₄	—	26	2	no	—
421	C₂×C₄	—	26	2	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	1	no	—
424	C₂×C₄	—	26	1	no	—
425	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
428	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
429	C₂×C₄	C₂³×#261	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	2	1	no	—
434	C₈	—	13	2	no	—
435	C₈	—	26	1	no	—
436	C₈	—	26	1	no	—
437	C₈	—	26	1	no	—
438	C₈	—	52	2	no	—
439	C₈	—	52	2	no	—
440	C₈	—	52	2	no	—
441	C₈	—	52	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	13	2	no	—
448	C₂²	—	26	1	no	—
449	C₂²	—	26	1	no	—
450	C₂²	D₁₃⋊#108	1	2	yes	—
451	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	13	2	no	—
457	C₄	—	13	2	no	—
458	C₄	—	26	1	no	—
459	C₄	—	26	1	no	—
460	C₄	—	26	1	no	—
461	C₄	—	26	1	no	—
462	C₄	—	26	1	no	—
463	C₄	#11719621	1	1	yes	characteristic
464	C₄	D₁₃⋊#131	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	1	no	—
467	C₂	—	26	2	no	—
468	C₂	#13131483	1	1	yes	characteristic
469	C₂	#13131490	1	1	yes	characteristic
470	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₈×D₄×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6129	Q₈
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	#17834
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #13130412	C₂	semidirect
3. #13130410	C₂	semidirect
4. #13130409	C₂	semidirect
5. #13130399	C₂	semidirect
6. #13130398	C₂	semidirect
7. #13130390	C₂	semidirect
8. #13130385	C₂	semidirect
9. C₂×#11718255	C₂	semidirect
10. D₁₃⋊#334	C₂	semidirect
398. C₁₃	#17834	semidirect

Maximal subgroups

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

subgroup	index
#13131761	2
#13130412	2
#13130410	2
#13130409	2
#13130399	2
#13130398	2
#13130390	2
#13130385	2
C₂×#11718255	2
D₁₃⋊#334	2
C₈×#6129	2
#17834	13