Subgroups — #15869752

Order 3328.

938 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×#11718857	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123540	C₂	1	2	yes	maximal, complemented
3	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115730	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115590	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115542	C₂	1	2	yes	maximal, complemented
7	#13115280	C₂	1	2	yes	maximal, complemented
8	#13114878	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114717	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114683	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₁₃×#525	C₂²	1	2	yes	—
15	C₂×#88202	C₂²	1	2	yes	—
16	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂²×#6099	C₂²	1	1	yes	characteristic
18	C₁₃×#470	C₄	1	2	yes	complemented
19	C₁₃×#469	C₄	1	2	yes	complemented
20	C₁₃×#468	C₄	1	4	yes	complemented
21	C₁₃×#427	C₂²	1	1	yes	characteristic
22	C₁₃×#416	C₂²	1	2	yes	—
23	C₂×#88077	C₂²	1	2	yes	—
24	C₂×#88077	C₂²	1	2	yes	—
25	#11718895	C₂²	1	2	yes	—
26	#11718868	C₂²	1	2	yes	—
27	#11718857	—	2	4	no	—
28	M₁₆×Dic₁₃	—	2	4	no	—
29	C₂×#88059	C₂²	1	1	yes	characteristic
30	C₂×#88059	C₂²	1	1	yes	characteristic
31	C₂×#88055	C₂²	1	1	yes	characteristic
32	C₂×#88055	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
35	#11718673	—	2	4	no	—
36	#11718672	—	2	4	no	—
37	#11718660	C₂²	1	2	yes	—
38	#11718658	C₂²	1	2	yes	—
39	#11718144	C₂²	1	2	yes	—
40	#11718124	C₂²	1	2	yes	—
41	#11718124	C₂²	1	2	yes	—
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×Dic₁₃	—	2	1	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#123	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
58	C₁₃×#121	C₂×C₄	1	4	yes	—
59	C₁₃×#120	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₁₃×#117	C₂³	1	2	yes	—
62	#88202	—	2	4	no	—
63	#88202	—	2	4	no	—
64	C₂×C₄×Dic₁₃	—	2	1	no	—
65	C₂×C₄×Dic₁₃	—	2	2	no	—
66	C₂×C₄×Dic₁₃	—	2	2	no	—
67	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
69	C₂×#6099	—	2	2	no	—
70	C₂×#6099	—	2	2	no	—
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	D₄	1	2	yes	—
73	C₂×#6099	D₄	1	2	yes	—
74	C₂×#6099	C₂³	1	2	yes	—
75	C₂×#6099	C₂³	1	2	yes	—
76	C₂²×#1055	—	2	2	no	—
77	C₂²×#1055	C₂³	1	1	yes	characteristic
78	C₂²×#1055	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	complemented
80	C₁₃×#106	C₂×C₄	1	2	yes	complemented
81	C₁₃×#103	C₂×C₄	1	4	yes	complemented
82	C₁₃×#102	C₂×C₄	1	4	yes	complemented
83	#88077	—	2	4	no	—
84	#88077	—	2	4	no	—
85	C₂²⋊#1055	—	2	4	no	—
86	C₂²⋊#1055	—	2	4	no	—
87	#88059	—	2	2	no	—
88	#88059	—	2	2	no	—
89	#88055	—	2	2	no	—
90	#88055	—	2	2	no	—
91	C₈×Dic₁₃	—	2	2	no	—
92	C₈×Dic₁₃	D₄	1	4	yes	complemented
93	C₄⋊#1055	—	2	4	no	—
94	#88043	—	2	2	no	—
95	C₄×#1055	—	2	2	no	—
96	#21549	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	#41	1	1	yes	characteristic
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₁₃	—	2	1	no	—
116	C₂²×Dic₁₃	—	2	4	no	—
117	C₂²×Dic₁₃	—	2	1	no	—
118	C₂²×Dic₁₃	—	4	4	no	—
119	C₁₃×Q₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	2	4	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×M₁₆	—	2	4	no	—
123	C₁₃×M₁₆	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	#41	1	2	yes	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
133	C₁₃×C₂²⋊C₄	—	2	4	no	—
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄×Dic₁₃	—	2	4	no	—
138	C₄×Dic₁₃	—	2	1	no	—
139	C₄×Dic₁₃	—	2	1	no	—
140	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
141	C₄×Dic₁₃	#41	1	2	yes	—
142	#6099	—	2	4	no	—
143	#6099	—	2	4	no	—
144	#6099	—	2	2	no	—
145	#6099	—	2	2	no	—
146	#6099	—	2	2	no	—
147	#6099	—	2	2	no	—
148	#6099	—	4	4	no	—
149	C₂×#1055	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	4	4	no	—
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	C₂×#1055	C₂×D₄	1	1	yes	characteristic
156	C₂×#1055	C₂×D₄	1	1	yes	characteristic
157	C₂×#1055	C₂×D₄	1	2	yes	—
158	C₂×#1055	#41	1	2	yes	—
159	#3054	D₁₃	1	1	yes	characteristic
160	C₂×#443	—	13	1	no	—
161	#2930	—	13	2	no	—
162	C₂×C₄×M₁₆	—	13	1	no	—
163	#1975	—	13	1	no	—
164	#1946	—	13	1	no	—
165	#1937	—	13	2	no	—
166	#1896	—	13	2	no	—
167	#1811	—	13	1	no	—
168	#1772	—	13	1	no	—
169	#1765	—	13	2	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	C₄×D₄	1	2	yes	—
175	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	8	4	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₁₃	—	2	4	no	—
201	C₂×Dic₁₃	—	2	2	no	—
202	C₂×Dic₁₃	—	2	2	no	—
203	C₂×Dic₁₃	—	4	8	no	—
204	C₂×Dic₁₃	—	4	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	C₄×D₄	1	2	yes	—
207	C₈×C₁₃	C₄×D₄	1	2	yes	—
208	#1055	—	2	2	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	2	no	—
211	#1055	#121	1	2	yes	—
212	#1055	#121	1	2	yes	—
213	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
214	C₂×#131	—	13	2	no	—
215	C₂²×M₁₆	—	13	1	no	—
216	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
217	#525	C₂×D₁₃	1	2	yes	—
218	C₂²×C₄²	—	13	1	no	—
219	#470	Dic₁₃	1	2	yes	complemented
220	#469	Dic₁₃	1	2	yes	complemented
221	#468	Dic₁₃	1	4	yes	complemented
222	#443	—	26	4	no	—
223	#436	—	26	4	no	—
224	#435	—	26	4	no	—
225	C₂×#108	—	13	1	no	—
226	C₂×#108	—	13	1	no	—
227	#427	C₂×D₁₃	1	1	yes	characteristic
228	#424	—	13	2	no	—
229	C₂×#104	—	13	2	no	—
230	C₂×#104	—	13	2	no	—
231	#416	C₂×D₁₃	1	2	yes	—
232	#408	—	13	2	no	—
233	#407	—	13	2	no	—
234	#405	—	13	2	no	—
235	C₄×M₁₆	—	26	4	no	—
236	C₂×#97	—	13	1	no	—
237	C₂×#97	—	13	1	no	—
238	C₂×C₄×C₈	—	13	1	no	—
239	C₂×C₄×C₈	—	13	1	no	—
240	#341	—	13	2	no	—
241	#339	—	13	2	no	—
242	#339	—	13	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₁₃	#525	1	1	yes	characteristic
252	C₂²×C₁₃	#529	1	1	yes	characteristic
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
258	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
259	C₄×C₁₃	#532	1	1	yes	characteristic
260	Dic₁₃	—	2	4	no	—
261	Dic₁₃	—	4	2	no	—
262	C₂×#41	C₂²×D₁₃	1	2	yes	—
263	C₂³×C₄	—	26	1	no	—
264	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
265	#135	—	2	2	no	—
266	#135	—	2	2	no	—
267	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic, complemented
268	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	complemented
269	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
270	#131	—	26	4	no	—
271	#131	—	26	4	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	13	2	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	26	2	no	—
279	C₂×M₁₆	—	26	2	no	—
280	C₂×M₁₆	—	26	2	no	—
281	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
282	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	26	2	no	—
286	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
288	#123	—	2	2	no	—
289	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
290	#121	C₂×Dic₁₃	1	4	yes	—
291	#120	—	2	2	no	—
292	C₄×D₄	—	2	4	no	—
293	#117	C₂²×D₁₃	1	2	yes	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	13	1	no	—
296	C₂×C₄²	—	26	2	no	—
297	C₂×C₄²	—	26	2	no	—
298	C₂×C₄²	—	26	1	no	—
299	#108	—	26	2	no	—
300	#108	—	26	2	no	—
301	#107	C₂×Dic₁₃	1	2	yes	complemented
302	#106	C₂×Dic₁₃	1	2	yes	complemented
303	C₄⋊C₈	—	26	4	no	—
304	#104	—	26	4	no	—
305	#104	—	26	4	no	—
306	#103	C₂×Dic₁₃	1	4	yes	complemented
307	#102	C₂×Dic₁₃	1	4	yes	complemented
308	C₂²⋊C₈	—	26	4	no	—
309	C₂²⋊C₈	—	26	4	no	—
310	#97	—	26	2	no	—
311	#97	—	26	2	no	—
312	#97	—	26	2	no	—
313	C₄×C₈	—	13	4	no	—
314	C₄×C₈	—	26	2	no	—
315	C₄×C₈	—	26	2	no	—
316	C₂×C₁₃	—	2	1	no	—
317	C₂×C₁₃	—	2	1	no	—
318	C₂×C₁₃	—	4	2	no	—
319	C₂×C₁₃	—	8	2	no	—
320	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
321	C₂×C₁₃	#2956	1	2	yes	—
322	C₂⁴	#6129	1	1	yes	characteristic
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	26	1	no	—
337	C₂²×C₄	—	26	4	no	—
338	C₂²×C₄	—	26	1	no	—
339	C₂²×C₄	—	52	4	no	—
340	C₂²×C₄	D₄×D₁₃	1	2	yes	—
341	C₂²×C₄	#6129	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
343	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
344	Q₁₆	—	2	2	no	—
345	SD₁₆	—	2	4	no	—
346	D₈	—	2	2	no	—
347	M₁₆	—	2	4	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	26	4	no	—
350	M₁₆	—	26	4	no	—
351	M₁₆	—	26	2	no	—
352	M₁₆	—	26	2	no	—
353	M₁₆	—	26	2	no	—
354	M₁₆	—	26	2	no	—
355	M₁₆	—	52	4	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	2	no	—
362	C₂×C₈	—	13	2	no	—
363	C₂×C₈	—	26	1	no	—
364	C₂×C₈	—	26	1	no	—
365	C₂×C₈	—	26	2	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	52	4	no	—
368	C₂×C₈	D₄×D₁₃	1	2	yes	—
369	C₂×C₈	#6129	1	2	yes	—
370	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
371	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
372	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	13	2	no	—
380	C₄²	—	13	2	no	—
381	C₄²	—	26	4	no	—
382	C₄²	—	26	1	no	—
383	C₄²	—	26	1	no	—
384	C₁₃	#21549	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	D₄×Dic₁₃	1	2	yes	—
390	C₂³	C₂×#6129	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	26	4	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	52	8	no	—
412	C₂×C₄	—	52	2	no	—
413	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
414	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×#6129	1	1	yes	characteristic
417	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
418	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	13	2	no	—
422	C₈	—	13	2	no	—
423	C₈	—	26	2	no	—
424	C₈	—	52	2	no	—
425	C₈	—	52	2	no	—
426	C₈	D₄×Dic₁₃	1	2	yes	—
427	C₈	D₄×Dic₁₃	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	#11719305	1	1	yes	characteristic
436	C₂²	#11719311	1	1	yes	characteristic
437	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	26	4	no	—
442	C₄	—	52	2	no	—
443	C₄	#11719301	1	1	yes	characteristic
444	C₄	D₁₃×#121	1	1	yes	characteristic
445	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
446	C₄	#41×Dic₁₃	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	2	no	—
450	C₂	—	8	2	no	—
451	C₂	#121×Dic₁₃	1	1	yes	characteristic
452	C₂	#13123746	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3054	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3054	D₁₃
hypocenter	C₁₃	#21549
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. C₂×#11718857	C₂	semidirect
2. #13123540	C₂	semidirect
3. C₂×M₁₆×Dic₁₃	C₂	semidirect
4. #13115730	C₂	semidirect
5. #13115590	C₂	semidirect
6. #13115542	C₂	semidirect
7. #13115280	C₂	semidirect
8. #13114878	C₂	semidirect
9. #13114717	C₂	semidirect
10. #13114683	C₂	semidirect
18. C₁₃×#470	C₄	semidirect
19. C₁₃×#469	C₄	semidirect
20. C₁₃×#468	C₄	semidirect
47. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
48. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
49. C₂×C₁₃×D₈	C₂×C₄	semidirect
79. C₁₃×#107	C₂×C₄	semidirect
80. C₁₃×#106	C₂×C₄	semidirect
81. C₁₃×#103	C₂×C₄	semidirect
82. C₁₃×#102	C₂×C₄	semidirect
92. C₈×Dic₁₃	D₄	semidirect
219. #470	Dic₁₃	semidirect
220. #469	Dic₁₃	semidirect
221. #468	Dic₁₃	semidirect
267. C₂×Q₁₆	C₂×Dic₁₃	semidirect
268. C₂×SD₁₆	C₂×Dic₁₃	semidirect
269. C₂×D₈	C₂×Dic₁₃	semidirect
301. #107	C₂×Dic₁₃	semidirect
302. #106	C₂×Dic₁₃	semidirect
306. #103	C₂×Dic₁₃	semidirect
307. #102	C₂×Dic₁₃	semidirect
384. C₁₃	#21549	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718857	2
#13123540	2
C₂×M₁₆×Dic₁₃	2
#13115730	2
#13115590	2
#13115542	2
#13115280	2
#13114878	2
#13114717	2
#13114683	2
C₁₃×#3054	2
#21549	13