Subgroups — #15876852

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123753	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123688	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115747	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115735	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115369	C₂	1	2	yes	maximal, complemented
6	#13115364	C₂	1	2	yes	maximal, complemented
7	#13115325	C₂	1	2	yes	maximal, complemented
8	#13115318	C₂	1	2	yes	maximal, complemented
9	#13114960	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#535	C₂²	1	2	yes	—
16	#11719524	C₂²	1	2	yes	—
17	#11719503	C₂²	1	2	yes	—
18	C₁₃×#496	C₄	1	4	yes	complemented
19	C₁₃×#495	C₄	1	2	yes	complemented
20	C₁₃×#493	C₄	1	2	yes	complemented
21	C₁₃×#405	C₂²	1	1	yes	characteristic
22	#11718901	C₂²	1	2	yes	—
23	#11718897	C₂²	1	2	yes	—
24	#11718897	C₂²	1	2	yes	—
25	C₂×#88073	C₂²	1	2	yes	—
26	#11718876	C₂²	1	2	yes	—
27	#11718876	C₂²	1	2	yes	—
28	#11718858	—	2	2	no	—
29	#11718857	—	2	2	no	—
30	#11718813	—	2	2	no	—
31	D₈×Dic₁₃	—	2	2	no	—
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718762	C₂²	1	1	yes	characteristic
35	#11718762	C₂²	1	1	yes	characteristic
36	#11718152	C₂²	1	1	yes	characteristic
37	#11718149	C₂²	1	1	yes	characteristic
38	#11718148	C₂²	1	2	yes	—
39	#11718123	C₂²	1	2	yes	—
40	#11718123	C₂²	1	1	yes	characteristic
41	#11718123	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
45	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
46	C₁₃×#135	—	2	1	no	—
47	C₁₃×#135	—	2	1	no	—
48	C₁₃×#135	—	2	1	no	—
49	C₁₃×#135	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
52	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
61	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#127	C₂×C₄	1	4	yes	complemented
64	C₁₃×#124	C₂×C₄	1	4	yes	complemented
65	C₁₃×#121	—	4	2	no	—
66	C₁₃×#120	—	4	2	no	—
67	C₁₃×#117	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊Dic₁₃	—	4	2	no	—
69	#88202	—	2	4	no	—
70	#88202	—	4	2	no	—
71	D₄×Dic₁₃	—	2	4	no	—
72	D₄×Dic₁₃	—	4	2	no	—
73	#88180	C₂³	1	2	yes	—
74	#88180	C₂³	1	1	yes	characteristic
75	#88180	C₂³	1	1	yes	characteristic
76	C₂×#6099	—	4	2	no	—
77	C₂×#6099	C₂³	1	2	yes	—
78	C₂×#6099	C₂³	1	1	yes	characteristic
79	C₂×#6099	C₂³	1	1	yes	characteristic
80	C₁₃×#97	C₂×C₄	1	2	yes	complemented
81	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
82	#88077	—	2	4	no	—
83	#88077	—	4	2	no	—
84	#88074	—	4	2	no	—
85	#88073	—	4	2	no	—
86	#88072	—	2	4	no	—
87	#88072	—	4	2	no	—
88	#88059	—	2	1	no	—
89	#88059	—	2	1	no	—
90	#88058	—	2	1	no	—
91	#88057	—	2	1	no	—
92	#88055	—	2	1	no	—
93	#88055	D₄	1	2	yes	complemented
94	C₈×Dic₁₃	—	2	1	no	—
95	C₈×Dic₁₃	D₄	1	2	yes	complemented
96	#22286	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
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	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
111	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₁₃	—	4	4	no	—
115	C₁₃×Q₁₆	—	2	1	no	—
116	C₁₃×Q₁₆	—	2	1	no	—
117	C₁₃×SD₁₆	—	2	2	no	—
118	C₁₃×SD₁₆	—	2	2	no	—
119	C₁₃×SD₁₆	—	4	4	no	—
120	C₁₃×D₈	—	2	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×D₈	—	2	2	no	—
123	C₁₃×D₈	—	2	2	no	—
124	C₁₃×D₈	—	2	1	no	—
125	C₁₃×D₈	—	2	1	no	—
126	C₁₃×D₈	—	4	4	no	—
127	C₁₃×M₁₆	—	2	1	no	—
128	C₁₃×M₁₆	—	2	1	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
135	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
140	C₂²⋊Dic₁₃	—	2	1	no	—
141	C₂²⋊Dic₁₃	—	2	1	no	—
142	C₂²⋊Dic₁₃	—	2	2	no	—
143	C₂²⋊Dic₁₃	—	4	4	no	—
144	C₄⋊Dic₁₃	—	2	1	no	—
145	C₄⋊Dic₁₃	—	2	2	no	—
146	C₄⋊Dic₁₃	—	2	1	no	—
147	C₄×Dic₁₃	—	2	1	no	—
148	C₄×Dic₁₃	—	2	2	no	—
149	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
150	#6099	—	2	1	no	—
151	#6099	—	2	1	no	—
152	#6099	—	2	2	no	—
153	#6099	—	2	1	no	—
154	#6099	—	2	2	no	—
155	#6099	—	2	1	no	—
156	#6099	—	4	4	no	—
157	C₂×#1055	—	2	1	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	4	4	no	—
160	C₂×#1055	C₂×D₄	1	2	yes	—
161	#3155	D₁₃	1	1	yes	characteristic
162	#2957	—	13	1	no	—
163	#2948	—	13	1	no	—
164	#1978	—	13	1	no	—
165	#1976	—	13	1	no	—
166	#1911	—	13	2	no	—
167	#1910	—	13	2	no	—
168	#1904	—	13	2	no	—
169	#1903	—	13	2	no	—
170	#1833	—	13	1	no	—
171	#1747	—	13	1	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	16	2	no	—
177	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	4	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	16	4	no	—
189	C₂×C₄×C₁₃	—	2	2	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	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×Dic₁₃	—	2	2	no	—
200	C₂×Dic₁₃	—	4	2	no	—
201	C₂×Dic₁₃	—	4	1	no	—
202	C₂×Dic₁₃	—	16	4	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
208	#1055	—	2	2	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	1	no	—
211	C₂×AGL(1,ℤ/8)	C₂×D₁₃	1	2	yes	—
212	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
213	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
214	#568	—	13	2	no	—
215	#535	C₂×D₁₃	1	2	yes	—
216	#518	—	13	2	no	—
217	#496	Dic₁₃	1	4	yes	complemented
218	#495	Dic₁₃	1	2	yes	complemented
219	#493	Dic₁₃	1	2	yes	complemented
220	#444	—	26	2	no	—
221	#443	—	26	2	no	—
222	#442	—	26	2	no	—
223	C₄×D₈	—	26	2	no	—
224	C₂×#108	—	13	1	no	—
225	#427	—	13	1	no	—
226	#421	—	13	2	no	—
227	#421	—	13	2	no	—
228	#418	—	13	2	no	—
229	#418	—	13	2	no	—
230	C₂×#100	—	13	2	no	—
231	#410	—	13	2	no	—
232	#405	—	13	1	no	—
233	#405	—	13	1	no	—
234	#405	C₂×D₁₃	1	1	yes	characteristic
235	#344	—	13	2	no	—
236	#338	—	13	1	no	—
237	H(3,ℤ/4)	—	13	1	no	—
238	H(3,ℤ/4)	—	13	2	no	—
239	H(3,ℤ/4)	—	13	1	no	—
240	H(3,ℤ/4)	—	13	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	4	no	—
246	C₂²×C₁₃	—	8	4	no	—
247	C₂²×C₁₃	—	16	2	no	—
248	C₂²×C₁₃	#518	1	1	yes	characteristic
249	C₂²×C₁₃	#535	1	1	yes	characteristic
250	C₂²×C₁₃	#540	1	1	yes	characteristic
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₁₃	#518	1	1	yes	characteristic
255	C₄×C₁₃	#535	1	1	yes	characteristic
256	C₄×C₁₃	#540	1	1	yes	characteristic
257	Dic₁₃	—	4	2	no	—
258	Dic₁₃	—	8	1	no	—
259	Dic₁₃	—	8	2	no	—
260	C₂×#41	C₂²×D₁₃	1	2	yes	—
261	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
262	AGL(1,ℤ/8)	—	4	2	no	—
263	AGL(1,ℤ/8)	—	4	2	no	—
264	#135	—	2	1	no	—
265	#135	—	2	1	no	—
266	#135	—	2	1	no	—
267	#135	—	2	1	no	—
268	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	complemented
270	C₂×SD₁₆	C₂×Dic₁₃	1	4	yes	complemented
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
276	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
277	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
278	C₂×D₈	C₂×Dic₁₃	1	4	yes	complemented
279	#131	—	26	4	no	—
280	#131	—	52	2	no	—
281	C₂×M₁₆	—	13	1	no	—
282	C₂×M₁₆	—	13	2	no	—
283	C₂×M₁₆	—	13	1	no	—
284	C₂×M₁₆	—	52	2	no	—
285	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
287	#127	C₂×Dic₁₃	1	4	yes	complemented
288	#124	C₂×Dic₁₃	1	4	yes	complemented
289	#121	—	4	2	no	—
290	#120	—	4	2	no	—
291	C₄×D₄	—	26	4	no	—
292	C₄×D₄	—	52	2	no	—
293	#117	—	13	1	no	—
294	#117	—	13	2	no	—
295	#117	—	13	1	no	—
296	#117	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	52	2	no	—
298	#108	—	26	1	no	—
299	#108	—	26	1	no	—
300	#107	—	26	1	no	—
301	#106	—	26	1	no	—
302	#104	—	26	4	no	—
303	#104	—	52	2	no	—
304	#102	—	26	4	no	—
305	#102	—	52	2	no	—
306	#100	—	52	2	no	—
307	#99	—	52	2	no	—
308	#97	—	13	2	no	—
309	#97	—	26	1	no	—
310	#97	C₂×Dic₁₃	1	2	yes	complemented
311	C₄×C₈	—	13	2	no	—
312	C₄×C₈	—	26	1	no	—
313	C₄×C₈	C₂×Dic₁₃	1	2	yes	complemented
314	C₂×C₁₃	—	2	1	no	—
315	C₂×C₁₃	—	2	1	no	—
316	C₂×C₁₃	—	2	1	no	—
317	C₂×C₁₃	—	8	2	no	—
318	C₂×C₁₃	—	8	4	no	—
319	C₂×C₁₃	#2328	1	1	yes	characteristic
320	C₂⁴	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
334	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	52	4	no	—
337	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	2	1	no	—
340	SD₁₆	—	2	2	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	4	4	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	1	no	—
349	D₈	—	4	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	26	1	no	—
353	M₁₆	—	26	1	no	—
354	M₁₆	—	26	2	no	—
355	M₁₆	—	26	1	no	—
356	M₁₆	—	26	2	no	—
357	M₁₆	—	26	1	no	—
358	M₁₆	—	52	4	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	52	4	no	—
363	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
364	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
365	C₂×C₈	#6129	1	1	yes	characteristic
366	C₂×C₈	#6129	1	1	yes	characteristic
367	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
368	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	26	1	no	—
372	C₄⋊C₄	—	26	2	no	—
373	C₄⋊C₄	—	26	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	26	1	no	—
377	C₂²⋊C₄	—	26	1	no	—
378	C₂²⋊C₄	—	26	2	no	—
379	C₂²⋊C₄	—	52	4	no	—
380	C₄²	—	13	2	no	—
381	C₄²	—	26	1	no	—
382	C₄²	—	26	2	no	—
383	C₄²	C₂²×Dic₁₃	1	2	yes	—
384	C₁₃	#22286	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	#88251	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	52	1	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	—	208	4	no	—
410	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂×#6129	1	1	yes	characteristic
412	C₂×C₄	#88251	1	1	yes	characteristic
413	C₂×C₄	#88251	1	1	yes	characteristic
414	C₂×C₄	#88251	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	26	2	no	—
418	C₈	—	52	1	no	—
419	C₈	—	52	2	no	—
420	C₈	D₄×Dic₁₃	1	1	yes	characteristic
421	C₈	D₄×Dic₁₃	1	1	yes	characteristic
422	C₈	D₄×Dic₁₃	1	1	yes	characteristic
423	C₈	D₄×Dic₁₃	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	#11719420	1	1	yes	characteristic
432	C₂²	#11719424	1	1	yes	characteristic
433	C₂²	#11719503	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	52	2	no	—
437	C₄	—	104	1	no	—
438	C₄	—	104	2	no	—
439	C₄	#11719420	1	1	yes	characteristic
440	C₄	#11719424	1	1	yes	characteristic
441	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
442	C₄	#11719503	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	#13117562	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13117562
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3155	C₂
socle	C₂×C₁₃	#2328
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3155	D₁₃
hypocenter	C₁₃	#22286
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #13123753	C₂	semidirect
2. #13123688	C₂	semidirect
3. #13115747	C₂	semidirect
4. #13115735	C₂	semidirect
5. #13115369	C₂	semidirect
6. #13115364	C₂	semidirect
7. #13115325	C₂	semidirect
8. #13115318	C₂	semidirect
9. #13114960	C₂	semidirect
10. #13114591	C₂	semidirect
18. C₁₃×#496	C₄	semidirect
19. C₁₃×#495	C₄	semidirect
20. C₁₃×#493	C₄	semidirect
50. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
51. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
52. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
59. C₂×C₁₃×D₈	C₂×C₄	semidirect
60. C₂×C₁₃×D₈	C₂×C₄	semidirect
63. C₁₃×#127	C₂×C₄	semidirect
64. C₁₃×#124	C₂×C₄	semidirect
80. C₁₃×#97	C₂×C₄	semidirect
81. C₄×C₈×C₁₃	C₂×C₄	semidirect
93. #88055	D₄	semidirect
95. C₈×Dic₁₃	D₄	semidirect
217. #496	Dic₁₃	semidirect
218. #495	Dic₁₃	semidirect
219. #493	Dic₁₃	semidirect
268. C₂×Q₁₆	C₂×Dic₁₃	semidirect
269. C₂×SD₁₆	C₂×Dic₁₃	semidirect
270. C₂×SD₁₆	C₂×Dic₁₃	semidirect
277. C₂×D₈	C₂×Dic₁₃	semidirect
278. C₂×D₈	C₂×Dic₁₃	semidirect
287. #127	C₂×Dic₁₃	semidirect
288. #124	C₂×Dic₁₃	semidirect
310. #97	C₂×Dic₁₃	semidirect
313. C₄×C₈	C₂×Dic₁₃	semidirect
384. C₁₃	#22286	semidirect

Maximal subgroups

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

subgroup	index
#13123753	2
#13123688	2
#13115747	2
#13115735	2
#13115369	2
#13115364	2
#13115325	2
#13115318	2
#13114960	2
#13114591	2
C₁₃×#3155	2
#22286	13