Subgroups — #15869774

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718858	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	#13115725	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115585	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115549	C₂	1	2	yes	maximal, complemented
7	#13115280	C₂	1	2	yes	maximal, complemented
8	#13114878	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114722	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114676	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	#11718858	—	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	4	yes	—
73	C₂×#6099	C₂³	1	2	yes	—
74	C₂×#6099	C₂³	1	2	yes	—
75	C₂²×#1055	—	2	2	no	—
76	C₂²×#1055	C₂³	1	1	yes	characteristic
77	C₂²×#1055	C₂³	1	1	yes	characteristic
78	C₁₃×#107	C₂×C₄	1	2	yes	complemented
79	C₁₃×#106	C₂×C₄	1	2	yes	complemented
80	C₁₃×#103	C₂×C₄	1	4	yes	complemented
81	C₁₃×#102	C₂×C₄	1	4	yes	complemented
82	#88077	—	2	4	no	—
83	#88077	—	2	4	no	—
84	C₂²⋊#1055	—	2	4	no	—
85	C₂²⋊#1055	—	2	4	no	—
86	#88059	—	2	2	no	—
87	#88059	—	2	2	no	—
88	#88055	—	2	2	no	—
89	#88055	D₄	1	4	yes	complemented
90	C₈×Dic₁₃	—	2	2	no	—
91	C₈×Dic₁₃	—	2	2	no	—
92	C₄⋊#1055	—	2	4	no	—
93	#88043	—	2	2	no	—
94	C₄×#1055	—	2	2	no	—
95	#21551	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	—	2	2	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
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	2	no	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₁₃	—	2	1	no	—
115	C₂²×Dic₁₃	—	2	4	no	—
116	C₂²×Dic₁₃	—	2	1	no	—
117	C₂²×Dic₁₃	—	4	4	no	—
118	C₁₃×Q₁₆	—	2	2	no	—
119	C₁₃×SD₁₆	—	2	4	no	—
120	C₁₃×D₈	—	2	2	no	—
121	C₁₃×M₁₆	—	2	4	no	—
122	C₁₃×M₁₆	—	2	4	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
132	C₁₃×C₂²⋊C₄	—	2	4	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄×Dic₁₃	—	2	4	no	—
137	C₄×Dic₁₃	—	2	1	no	—
138	C₄×Dic₁₃	—	2	1	no	—
139	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
140	C₄×Dic₁₃	#41	1	2	yes	—
141	#6099	—	2	8	no	—
142	#6099	—	2	2	no	—
143	#6099	—	2	2	no	—
144	#6099	—	2	2	no	—
145	#6099	—	2	2	no	—
146	#6099	—	4	4	no	—
147	C₂×#1055	—	2	1	no	—
148	C₂×#1055	—	2	1	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	4	4	no	—
152	C₂×#1055	C₂×D₄	1	2	yes	—
153	C₂×#1055	C₂×D₄	1	2	yes	—
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	C₂×#1055	#41	1	2	yes	—
156	#3054	D₁₃	1	1	yes	characteristic
157	C₂×#444	—	13	1	no	—
158	#2930	—	13	2	no	—
159	C₂×C₄×M₁₆	—	13	1	no	—
160	#1974	—	13	1	no	—
161	#1945	—	13	1	no	—
162	#1938	—	13	2	no	—
163	#1896	—	13	2	no	—
164	#1811	—	13	1	no	—
165	#1773	—	13	1	no	—
166	#1764	—	13	2	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	C₄×D₄	1	2	yes	—
172	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	8	4	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×Dic₁₃	—	2	4	no	—
198	C₂×Dic₁₃	—	2	2	no	—
199	C₂×Dic₁₃	—	2	2	no	—
200	C₂×Dic₁₃	—	4	8	no	—
201	C₂×Dic₁₃	—	4	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	C₄×D₄	1	2	yes	—
204	C₈×C₁₃	C₄×D₄	1	2	yes	—
205	#1055	—	2	2	no	—
206	#1055	—	4	2	no	—
207	#1055	—	4	2	no	—
208	#1055	#121	1	4	yes	—
209	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
210	C₂×#131	—	13	2	no	—
211	C₂²×M₁₆	—	13	1	no	—
212	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
213	#525	C₂×D₁₃	1	2	yes	—
214	C₂²×C₄²	—	13	1	no	—
215	#470	Dic₁₃	1	2	yes	complemented
216	#469	Dic₁₃	1	2	yes	complemented
217	#468	Dic₁₃	1	4	yes	complemented
218	#444	—	26	4	no	—
219	#436	—	26	4	no	—
220	#435	—	26	4	no	—
221	C₂×#108	—	13	1	no	—
222	C₂×#108	—	13	1	no	—
223	#427	C₂×D₁₃	1	1	yes	characteristic
224	#424	—	13	2	no	—
225	C₂×#104	—	13	2	no	—
226	C₂×#104	—	13	2	no	—
227	#416	C₂×D₁₃	1	2	yes	—
228	#408	—	13	2	no	—
229	#407	—	13	2	no	—
230	#405	—	13	2	no	—
231	C₄×M₁₆	—	26	4	no	—
232	C₂×#97	—	13	1	no	—
233	C₂×#97	—	13	1	no	—
234	C₂×C₄×C₈	—	13	1	no	—
235	C₂×C₄×C₈	—	13	1	no	—
236	#341	—	13	2	no	—
237	#339	—	13	2	no	—
238	#339	—	13	2	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	#525	1	1	yes	characteristic
248	C₂²×C₁₃	#529	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
255	C₄×C₁₃	#532	1	1	yes	characteristic
256	Dic₁₃	—	2	4	no	—
257	Dic₁₃	—	4	2	no	—
258	C₂×#41	C₂²×D₁₃	1	2	yes	—
259	C₂³×C₄	—	26	1	no	—
260	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic, complemented
264	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	complemented
265	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
266	#131	—	26	4	no	—
267	#131	—	26	4	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	13	4	no	—
271	C₂×M₁₆	—	13	2	no	—
272	C₂×M₁₆	—	13	2	no	—
273	C₂×M₁₆	—	26	2	no	—
274	C₂×M₁₆	—	26	2	no	—
275	C₂×M₁₆	—	26	2	no	—
276	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
277	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
283	#123	—	2	2	no	—
284	C₂²⋊Q₈	C₂×Dic₁₃	1	4	yes	—
285	#121	C₂×Dic₁₃	1	4	yes	—
286	#120	—	2	2	no	—
287	C₄×D₄	—	2	4	no	—
288	#117	C₂²×D₁₃	1	2	yes	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	26	2	no	—
292	C₂×C₄²	—	26	2	no	—
293	C₂×C₄²	—	26	1	no	—
294	#108	—	26	2	no	—
295	#108	—	26	2	no	—
296	#107	C₂×Dic₁₃	1	2	yes	complemented
297	#106	C₂×Dic₁₃	1	2	yes	complemented
298	C₄⋊C₈	—	26	4	no	—
299	#104	—	26	4	no	—
300	#104	—	26	4	no	—
301	#103	C₂×Dic₁₃	1	4	yes	complemented
302	#102	C₂×Dic₁₃	1	4	yes	complemented
303	C₂²⋊C₈	—	26	4	no	—
304	C₂²⋊C₈	—	26	4	no	—
305	#97	—	13	4	no	—
306	#97	—	26	2	no	—
307	#97	—	26	2	no	—
308	C₄×C₈	—	26	2	no	—
309	C₄×C₈	—	26	2	no	—
310	C₄×C₈	—	26	2	no	—
311	C₂×C₁₃	—	2	1	no	—
312	C₂×C₁₃	—	2	1	no	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
316	C₂×C₁₃	#2956	1	2	yes	—
317	C₂⁴	#6129	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	26	1	no	—
332	C₂²×C₄	—	26	4	no	—
333	C₂²×C₄	—	26	1	no	—
334	C₂²×C₄	—	52	4	no	—
335	C₂²×C₄	D₄×D₁₃	1	2	yes	—
336	C₂²×C₄	#6129	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
338	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
339	Q₁₆	—	2	2	no	—
340	SD₁₆	—	2	4	no	—
341	D₈	—	2	2	no	—
342	M₁₆	—	2	4	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	26	8	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	—	26	2	no	—
347	M₁₆	—	26	2	no	—
348	M₁₆	—	26	2	no	—
349	M₁₆	—	52	4	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	26	1	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	52	4	no	—
361	C₂×C₈	D₄×D₁₃	1	2	yes	—
362	C₂×C₈	#6129	1	2	yes	—
363	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
364	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	13	2	no	—
373	C₄²	—	13	2	no	—
374	C₄²	—	26	4	no	—
375	C₄²	—	26	1	no	—
376	C₄²	—	26	1	no	—
377	C₁₃	#21551	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	D₄×Dic₁₃	1	2	yes	—
383	C₂³	C₂×#6129	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	26	4	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	52	8	no	—
405	C₂×C₄	—	52	2	no	—
406	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂×#6129	1	1	yes	characteristic
410	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
411	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	13	4	no	—
415	C₈	—	26	2	no	—
416	C₈	—	52	2	no	—
417	C₈	—	52	2	no	—
418	C₈	D₄×Dic₁₃	1	2	yes	—
419	C₈	D₄×Dic₁₃	1	2	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	#11719305	1	1	yes	characteristic
428	C₂²	#11719311	1	1	yes	characteristic
429	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	26	4	no	—
434	C₄	—	52	2	no	—
435	C₄	#11719301	1	1	yes	characteristic
436	C₄	D₁₃×#121	1	1	yes	characteristic
437	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
438	C₄	#41×Dic₁₃	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	2	no	—
443	C₂	#121×Dic₁₃	1	1	yes	characteristic
444	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	#21551
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×#11718858	C₂	semidirect
2. #13123540	C₂	semidirect
3. C₂×M₁₆×Dic₁₃	C₂	semidirect
4. #13115725	C₂	semidirect
5. #13115585	C₂	semidirect
6. #13115549	C₂	semidirect
7. #13115280	C₂	semidirect
8. #13114878	C₂	semidirect
9. #13114722	C₂	semidirect
10. #13114676	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
78. C₁₃×#107	C₂×C₄	semidirect
79. C₁₃×#106	C₂×C₄	semidirect
80. C₁₃×#103	C₂×C₄	semidirect
81. C₁₃×#102	C₂×C₄	semidirect
89. #88055	D₄	semidirect
215. #470	Dic₁₃	semidirect
216. #469	Dic₁₃	semidirect
217. #468	Dic₁₃	semidirect
263. C₂×Q₁₆	C₂×Dic₁₃	semidirect
264. C₂×SD₁₆	C₂×Dic₁₃	semidirect
265. C₂×D₈	C₂×Dic₁₃	semidirect
296. #107	C₂×Dic₁₃	semidirect
297. #106	C₂×Dic₁₃	semidirect
301. #103	C₂×Dic₁₃	semidirect
302. #102	C₂×Dic₁₃	semidirect
377. C₁₃	#21551	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718858	2
#13123540	2
C₂×M₁₆×Dic₁₃	2
#13115725	2
#13115585	2
#13115549	2
#13115280	2
#13114878	2
#13114722	2
#13114676	2
C₁₃×#3054	2
#21551	13