Subgroups — #16795087

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131531	C₂	1	2	yes	maximal
2	#13130408	C₂	1	2	yes	maximal, complemented
3	#13130407	C₂	1	2	yes	maximal, complemented
4	#13130405	C₂	1	2	yes	maximal, complemented
5	#13130397	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130396	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130390	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130384	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130383	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718253	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	#11719146	—	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	#11719077	—	2	2	no	—
19	#11719068	—	2	2	no	—
20	#11719062	—	2	2	no	—
21	#11719054	C₂²	1	2	yes	—
22	#11719051	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	2	yes	—
40	#11718254	C₂²	1	2	yes	—
41	#11718254	C₂²	1	2	yes	—
42	#11718253	C₂²	1	1	yes	characteristic
43	#11718253	C₂²	1	1	yes	characteristic
44	#11718253	C₂²	1	2	yes	—
45	#11718253	C₂²	1	1	yes	characteristic
46	#11718253	C₂²	1	1	yes	characteristic
47	C₂×#6129	D₄	1	1	yes	characteristic
48	C₂×#6122	—	2	2	no	—
49	C₂²×#1057	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₁₃	Q₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
59	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	#88146	D₄	1	1	yes	characteristic
63	#88141	Q₈	1	1	yes	characteristic
64	#88135	Q₈	1	1	yes	characteristic
65	#88135	Q₈	1	1	yes	characteristic
66	#88131	D₄	1	1	yes	characteristic
67	#88131	D₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	1	yes	characteristic
69	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
70	C₂²⋊#1057	—	2	2	no	—
71	C₂²⋊#1057	—	2	2	no	—
72	#88112	—	2	2	no	—
73	#88111	—	2	2	no	—
74	#88111	—	2	2	no	—
75	#88110	—	2	2	no	—
76	#88110	—	2	2	no	—
77	C₄⋊#1057	—	2	2	no	—
78	C₄⋊#1057	C₂³	1	2	yes	—
79	C₄⋊#1057	C₂³	1	2	yes	—
80	C₄⋊#1057	C₂³	1	2	yes	—
81	C₄⋊#1057	C₂³	1	2	yes	—
82	C₄×#1057	—	2	2	no	—
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	#17827	—	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	—	4	4	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	—	4	4	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
134	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
135	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
139	#6103	C₄⋊C₄	1	1	yes	characteristic
140	#6103	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
142	#6101	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	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂×D₄	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×Q₈	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	C₂⁴	1	1	yes	characteristic
155	C₂×#1055	—	4	1	no	—
156	C₂×#1055	—	4	1	no	—
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₁₃	—	2	2	no	—
162	C₈×D₁₃	—	4	1	no	—
163	C₈×#41	—	13	1	no	—
164	#2925	—	13	2	no	—
165	#1572	—	13	2	no	—
166	#1572	—	13	2	no	—
167	#1571	—	13	2	no	—
168	#1568	—	13	1	no	—
169	#1568	—	13	1	no	—
170	#1566	—	13	1	no	—
171	#1564	—	13	1	no	—
172	#1564	—	13	1	no	—
173	C₂×#334	—	13	1	no	—
174	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	D₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	1	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	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
187	C₂²⋊D₁₃	—	2	2	no	—
188	C₂²⋊D₁₃	—	2	2	no	—
189	C₂×Dic₁₃	—	2	2	no	—
190	C₂×Dic₁₃	—	4	1	no	—
191	C₂×Dic₁₃	—	4	1	no	—
192	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	#135	1	4	yes	—
198	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
200	C₄×D₁₃	—	2	1	no	—
201	C₄×D₁₃	—	2	1	no	—
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	4	1	no	—
204	Dic₂₆	—	2	2	no	—
205	#1057	—	4	2	no	—
206	#1057	—	4	2	no	—
207	#1057	—	4	2	no	—
208	#1057	—	4	2	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	#131	1	2	yes	—
213	#1055	—	2	1	no	—
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	C₄×#41	—	13	1	no	—
218	C₈×Q₈	—	13	1	no	—
219	C₈×Q₈	—	13	1	no	—
220	C₈×D₄	—	13	1	no	—
221	C₈×D₄	—	13	1	no	—
222	C₈×D₄	—	13	1	no	—
223	C₈×D₄	—	13	1	no	—
224	C₈×D₄	—	13	1	no	—
225	C₈×D₄	#261	1	1	yes	characteristic
226	#433	—	26	2	no	—
227	#433	—	26	2	no	—
228	#432	—	13	2	no	—
229	#432	—	13	2	no	—
230	#431	—	13	1	no	—
231	#431	—	13	1	no	—
232	#431	—	13	1	no	—
233	#431	—	13	2	no	—
234	#431	—	13	2	no	—
235	#423	—	13	2	no	—
236	C₂×C₄⋊C₈	—	13	2	no	—
237	#408	—	26	2	no	—
238	#405	—	26	2	no	—
239	C₂×C₄×C₈	—	13	1	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	#335	—	13	2	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	2	no	—
249	#334	—	13	1	no	—
250	#334	—	13	1	no	—
251	#334	—	13	2	no	—
252	C₂²×C₁₃	—	2	1	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	#427	1	2	yes	—
258	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂×D₁₃	—	2	1	no	—
260	C₂×D₁₃	—	2	1	no	—
261	C₂×D₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₁₃	#568	1	1	yes	characteristic
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	1	no	—
270	Dic₁₃	—	2	1	no	—
271	Dic₁₃	—	2	1	no	—
272	Dic₁₃	—	2	1	no	—
273	Dic₁₃	#427	1	2	yes	—
274	Dic₁₃	C₂×#135	1	2	yes	—
275	C₂×#41	—	13	1	no	—
276	C₂×M₁₆	—	26	2	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	26	2	no	—
282	C₂²×C₈	C₂×#261	1	1	yes	characteristic
283	C₂²×C₈	C₂×#261	1	1	yes	characteristic
284	C₄×Q₈	—	13	1	no	—
285	C₄×Q₈	—	13	1	no	—
286	C₄×D₄	—	13	1	no	—
287	C₄×D₄	—	13	1	no	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	13	1	no	—
291	C₄×D₄	C₂×#261	1	1	yes	characteristic
292	#117	—	13	1	no	—
293	#117	—	13	1	no	—
294	#117	—	13	1	no	—
295	C₂×C₄²	—	13	1	no	—
296	C₂×C₄²	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₄⋊C₈	—	13	1	no	—
299	C₄⋊C₈	—	13	1	no	—
300	C₄⋊C₈	—	13	1	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	—	13	2	no	—
304	C₄⋊C₈	—	13	2	no	—
305	C₄⋊C₈	—	13	2	no	—
306	C₄⋊C₈	—	13	1	no	—
307	C₄⋊C₈	—	26	2	no	—
308	C₄⋊C₈	—	26	2	no	—
309	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
310	C₂²⋊C₈	—	13	1	no	—
311	C₂²⋊C₈	—	13	1	no	—
312	C₂²⋊C₈	—	13	1	no	—
313	C₂²⋊C₈	—	13	1	no	—
314	C₂²⋊C₈	—	26	2	no	—
315	C₂²⋊C₈	—	26	2	no	—
316	C₂²⋊C₈	—	26	2	no	—
317	C₂²⋊C₈	—	26	2	no	—
318	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
319	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
320	#97	—	26	2	no	—
321	#97	—	26	2	no	—
322	C₄×C₈	—	13	1	no	—
323	C₄×C₈	—	13	1	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	—	26	2	no	—
332	C₄×C₈	—	26	2	no	—
333	C₄×C₈	C₂×#261	1	1	yes	characteristic
334	C₂×C₁₃	—	2	2	no	—
335	C₂×C₁₃	—	4	1	no	—
336	C₂×C₁₃	#2906	1	1	yes	characteristic
337	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
338	C₂×C₁₃	#2916	1	1	yes	characteristic
339	D₁₃	—	4	1	no	—
340	#41	—	26	4	no	—
341	C₂×Q₈	—	13	1	no	—
342	C₂×D₄	—	13	1	no	—
343	C₂×D₄	—	13	1	no	—
344	C₂×D₄	C₄⋊#261	1	1	yes	characteristic
345	C₂²×C₄	—	13	1	no	—
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	C₂²×#261	1	1	yes	characteristic
353	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
354	M₁₆	—	52	4	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	13	1	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	26	2	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	—	52	1	no	—
367	C₂×C₈	—	52	1	no	—
368	C₂×C₈	—	52	1	no	—
369	C₂×C₈	—	52	4	no	—
370	C₂×C₈	C₂²×#261	1	1	yes	characteristic
371	C₂×C₈	C₂²×#261	1	1	yes	characteristic
372	C₂×C₈	C₂²×#261	1	1	yes	characteristic
373	C₂×C₈	C₂²×#261	1	1	yes	characteristic
374	C₄⋊C₄	—	13	1	no	—
375	C₄⋊C₄	—	13	1	no	—
376	C₄⋊C₄	—	13	1	no	—
377	C₄⋊C₄	—	13	1	no	—
378	C₄⋊C₄	—	13	1	no	—
379	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
380	C₂²⋊C₄	—	13	1	no	—
381	C₂²⋊C₄	—	13	1	no	—
382	C₂²⋊C₄	—	13	1	no	—
383	C₂²⋊C₄	—	13	1	no	—
384	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
385	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
386	C₄²	—	13	1	no	—
387	C₄²	—	13	1	no	—
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	C₂²×#261	1	1	yes	characteristic
396	C₁₃	#17827	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	13	1	no	—
398	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
399	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
400	Q₈	—	26	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	26	2	no	—
403	D₄	—	26	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	13	4	no	—
409	C₂×C₄	—	13	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	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	52	1	no	—
421	C₂×C₄	—	52	1	no	—
422	C₂×C₄	—	52	1	no	—
423	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
427	C₂×C₄	C₂³×#261	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	26	1	no	—
432	C₈	—	26	1	no	—
433	C₈	—	26	1	no	—
434	C₈	—	26	1	no	—
435	C₈	—	52	2	no	—
436	C₈	—	52	2	no	—
437	C₈	—	52	2	no	—
438	C₈	—	52	2	no	—
439	C₈	#88238	1	2	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	26	1	no	—
446	C₂²	—	26	1	no	—
447	C₂²	—	26	1	no	—
448	C₂²	#11719092	1	2	yes	—
449	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	13	2	no	—
455	C₄	—	13	2	no	—
456	C₄	—	26	1	no	—
457	C₄	—	26	1	no	—
458	C₄	—	26	1	no	—
459	C₄	—	26	1	no	—
460	C₄	—	26	1	no	—
461	C₄	C₂×#88238	1	1	yes	characteristic
462	C₄	#11719629	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	1	no	—
465	C₂	—	52	1	no	—
466	C₂	#13131481	1	1	yes	characteristic
467	C₂	C₂×#11719092	1	1	yes	characteristic
468	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	C₈×D₄×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6129	D₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	#17827
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. #13130408	C₂	semidirect
3. #13130407	C₂	semidirect
4. #13130405	C₂	semidirect
5. #13130397	C₂	semidirect
6. #13130396	C₂	semidirect
7. #13130390	C₂	semidirect
8. #13130384	C₂	semidirect
9. #13130383	C₂	semidirect
10. C₂×#11718253	C₂	semidirect
396. C₁₃	#17827	semidirect

Maximal subgroups

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

subgroup	index
#13131531	2
#13130408	2
#13130407	2
#13130405	2
#13130397	2
#13130396	2
#13130390	2
#13130384	2
#13130383	2
C₂×#11718253	2
C₈×#6129	2
#17827	13