Subgroups — #15832896

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124916	C₂	1	1	yes	maximal, characteristic
2	#13123805	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113711	C₂	1	2	yes	maximal, complemented
5	#13113704	C₂	1	2	yes	maximal, complemented
6	#13113640	C₂	1	2	yes	maximal, complemented
7	#13113633	C₂	1	2	yes	maximal, complemented
8	#13113622	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113250	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	#11719184	C₂²	1	1	yes	characteristic
14	C₁₃×#432	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	#11718889	C₄	1	1	yes	characteristic
17	#11718888	C₄	1	1	yes	characteristic
18	C₄×#6107	C₂²	1	2	yes	—
19	#11718689	C₄	1	2	yes	—
20	C₄×#6106	C₂²	1	2	yes	—
21	Q₈×#1055	—	2	1	no	—
22	Q₈×#1055	—	2	1	no	—
23	Q₈×#1055	C₂²	1	2	yes	—
24	Q₈×#1055	C₂²	1	2	yes	—
25	#11718683	C₄	1	2	yes	—
26	#11718632	C₄	1	1	yes	characteristic
27	#11718628	C₄	1	1	yes	characteristic
28	#11718586	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	—	2	1	no	—
30	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
31	C₂×C₄×#1055	—	2	1	no	—
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	#11718499	C₂²	1	1	yes	characteristic
34	#11718495	C₂²	1	1	yes	characteristic
35	#11718492	C₂²	1	1	yes	characteristic
36	#11718491	C₂²	1	1	yes	characteristic
37	#11718391	—	2	1	no	—
38	#11718386	—	2	1	no	—
39	#11718370	—	2	1	no	—
40	#11718369	—	2	1	no	—
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	#11718072	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718051	C₂²	1	2	yes	—
46	#11718048	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	C₈×#1055	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₄×Q₈×C₁₃	—	2	1	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6107	C₂×C₄	1	2	yes	—
60	C₂×#6106	C₂×C₄	1	2	yes	—
61	#88184	C₂×C₄	1	1	yes	characteristic
62	#88183	—	2	1	no	—
63	C₄×C₂²⋊D₁₃	—	2	1	no	—
64	#88178	C₂×C₄	1	1	yes	characteristic
65	C₂²×#1055	—	2	1	no	—
66	C₂²×#1055	D₄	1	1	yes	characteristic
67	C₂²×#1055	D₄	1	1	yes	characteristic
68	C₂×#6094	—	2	1	no	—
69	C₂×C₈×D₁₃	—	2	1	no	—
70	#88130	—	2	1	no	—
71	#88129	C₂×C₄	1	1	yes	characteristic
72	C₄×D₅₂	C₂³	1	1	yes	characteristic
73	#88126	—	2	1	no	—
74	#88124	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×#97	—	2	1	no	—
80	C₁₃×#97	—	2	1	no	—
81	C₄×C₈×C₁₃	C₂³	1	2	yes	—
82	#88075	C₂×C₄	1	2	yes	—
83	#88075	C₂×C₄	1	2	yes	—
84	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
86	#88060	—	2	1	no	—
87	#88060	—	2	1	no	—
88	#88055	—	2	1	no	—
89	#88054	—	2	1	no	—
90	#88054	—	2	1	no	—
91	C₈×Dic₁₃	—	2	1	no	—
92	#88050	C₂×C₄	1	2	yes	—
93	#88049	C₂×C₄	1	2	yes	—
94	#88048	C₂×C₄	1	2	yes	—
95	#88047	C₂×C₄	1	2	yes	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	—	2	2	no	—
98	C₄⋊#1055	—	2	2	no	—
99	C₄⋊#1055	C₂×C₄	1	2	yes	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	C₄×#1055	—	2	2	no	—
102	C₄×#1055	—	2	2	no	—
103	C₄×#1055	D₄	1	1	yes	characteristic
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	C₂³	1	2	yes	—
106	C₄×#1055	C₂³	1	1	yes	characteristic
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	#17911	—	13	1	no	maximal, Sylow
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₁₃	—	2	1	no	—
118	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	—	2	1	no	—
120	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
121	C₁₃×M₁₆	—	2	4	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₁₃	—	2	1	no	—
136	#6107	—	2	4	no	—
137	#6106	—	2	4	no	—
138	#6103	—	2	1	no	—
139	#6103	—	2	1	no	—
140	#6103	—	2	1	no	—
141	#6103	—	2	1	no	—
142	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	#6101	—	2	1	no	—
145	#6101	—	2	1	no	—
146	#6101	—	2	1	no	—
147	#6101	—	2	1	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	4	1	no	—
152	C₂×#1055	—	4	2	no	—
153	C₂×#1055	C₂²×C₄	1	2	yes	—
154	C₂×#1055	C₂²×C₄	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	1	yes	characteristic
158	C₂×#1055	C₂×D₄	1	1	yes	characteristic
159	#6094	—	4	2	no	—
160	C₈×D₁₃	—	4	2	no	—
161	#3108	—	13	1	no	—
162	#2966	—	13	1	no	—
163	C₂×C₈×Q₈	—	13	1	no	—
164	#1588	—	13	2	no	—
165	#1587	—	13	2	no	—
166	C₈×Q₁₆	—	13	2	no	—
167	C₈×SD₁₆	—	13	2	no	—
168	#1573	—	13	1	no	—
169	#1491	D₁₃	1	1	yes	characteristic, complemented
170	#1483	—	13	1	no	—
171	C₈×M₁₆	—	13	1	no	—
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂²×D₁₃	—	2	1	no	—
174	Q₈×C₁₃	—	2	4	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	#131	1	4	yes	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂²⋊D₁₃	—	4	2	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	2	1	no	—
194	C₂×Dic₁₃	—	2	1	no	—
195	D₅₂	—	2	2	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	—	4	1	no	—
198	Dic₂₆	—	2	2	no	—
199	C₈×C₁₃	—	2	4	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	—	4	1	no	—
202	#1055	—	2	2	no	—
203	#1055	—	2	2	no	—
204	#1055	—	2	1	no	—
205	#1055	—	2	1	no	—
206	#1055	—	2	1	no	—
207	#1055	—	4	2	no	—
208	#1055	#137	1	2	yes	—
209	#529	—	13	1	no	—
210	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
211	#483	—	13	1	no	—
212	#480	—	13	1	no	—
213	#479	—	13	2	no	—
214	#464	—	13	2	no	—
215	#451	—	13	1	no	—
216	#448	—	13	1	no	—
217	#446	—	13	1	no	—
218	C₈×Q₈	—	13	2	no	—
219	C₈×Q₈	—	13	2	no	—
220	C₈×Q₈	—	13	1	no	—
221	C₈×Q₈	—	26	1	no	—
222	C₈×Q₈	—	26	1	no	—
223	C₄×Q₁₆	—	13	2	no	—
224	C₄×SD₁₆	—	13	2	no	—
225	#436	—	13	1	no	—
226	#435	—	26	1	no	—
227	C₈×D₄	—	13	1	no	—
228	C₈×D₄	—	26	1	no	—
229	#433	—	26	1	no	—
230	#432	C₂×D₁₃	1	1	yes	characteristic
231	#431	—	13	1	no	—
232	C₂×C₄⋊C₈	—	13	1	no	—
233	C₂×C₄⋊C₈	—	26	1	no	—
234	#405	—	26	1	no	—
235	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
236	C₂×C₄×C₈	—	13	1	no	—
237	C₂×C₄×C₈	—	26	1	no	—
238	#335	—	13	2	no	—
239	#334	—	13	2	no	—
240	Q₈⋊C₈	—	13	2	no	—
241	Q₈⋊C₈	C₂×D₁₃	1	2	yes	—
242	Q₈⋊C₈	C₂×D₁₃	1	2	yes	—
243	D₄⋊C₈	—	13	2	no	—
244	#322	—	13	2	no	—
245	C₈²	—	13	2	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	#443	1	2	yes	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₁₃	—	4	1	no	—
251	C₂×D₁₃	—	4	1	no	—
252	C₂×D₁₃	—	4	1	no	—
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	C₂×#131	1	2	yes	—
260	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
261	C₄×C₁₃	#575	1	1	yes	characteristic
262	Dic₁₃	—	4	1	no	—
263	Dic₁₃	—	4	1	no	—
264	Dic₁₃	—	4	1	no	—
265	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
266	C₂×Q₁₆	—	13	2	no	—
267	C₂×SD₁₆	—	13	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	26	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	26	1	no	—
273	C₂²×C₈	—	26	1	no	—
274	#126	—	26	1	no	—
275	#125	—	13	1	no	—
276	#124	—	13	1	no	—
277	#123	—	26	1	no	—
278	C₂²⋊Q₈	—	13	1	no	—
279	#121	—	13	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×Q₈	C₄×D₁₃	1	2	yes	—
284	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	—	26	1	no	—
287	#117	—	26	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
292	#107	—	13	2	no	—
293	#106	—	13	2	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	13	2	no	—
296	C₄⋊C₈	—	26	2	no	—
297	C₄⋊C₈	—	26	2	no	—
298	C₄⋊C₈	—	26	1	no	—
299	C₄⋊C₈	—	26	1	no	—
300	C₄⋊C₈	—	26	1	no	—
301	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
303	#103	—	13	2	no	—
304	#103	—	13	2	no	—
305	#103	—	13	2	no	—
306	#102	—	13	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	13	1	no	—
309	C₂²⋊C₈	—	13	1	no	—
310	C₂²⋊C₈	—	26	1	no	—
311	C₂²⋊C₈	—	26	1	no	—
312	#97	—	2	1	no	—
313	#97	—	2	1	no	—
314	#97	—	26	1	no	—
315	C₄×C₈	—	13	1	no	—
316	C₄×C₈	—	13	1	no	—
317	C₄×C₈	—	13	1	no	—
318	C₄×C₈	—	13	2	no	—
319	C₄×C₈	—	13	1	no	—
320	C₄×C₈	—	26	2	no	—
321	C₄×C₈	—	26	2	no	—
322	C₄×C₈	—	26	1	no	—
323	C₄×C₈	C₂²×D₁₃	1	2	yes	—
324	C₂×C₁₃	—	2	2	no	—
325	C₂×C₁₃	#2929	1	1	yes	characteristic
326	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
327	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
328	D₁₃	—	8	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	13	1	no	—
332	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
333	C₂×D₄	—	13	1	no	—
334	C₂×D₄	—	26	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	26	1	no	—
338	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
340	C₂²×C₄	#6129	1	1	yes	characteristic
341	Q₁₆	—	26	4	no	—
342	SD₁₆	—	26	4	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	52	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	1	no	—
352	C₂×C₈	—	13	1	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	52	2	no	—
357	C₂×C₈	—	52	1	no	—
358	C₂×C₈	—	52	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	13	1	no	—
363	C₄⋊C₄	—	13	1	no	—
364	C₄⋊C₄	—	26	1	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	—	26	1	no	—
367	C₄⋊C₄	—	26	1	no	—
368	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
369	C₂²⋊C₄	—	26	1	no	—
370	C₂²⋊C₄	—	26	1	no	—
371	C₂²⋊C₄	—	26	1	no	—
372	C₂²⋊C₄	—	26	1	no	—
373	C₂²⋊C₄	—	26	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	26	1	no	—
377	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₄²	D₄×D₁₃	1	1	yes	characteristic
379	C₄²	#6129	1	1	yes	characteristic
380	C₄²	C₂³×D₁₃	1	1	yes	characteristic
381	C₁₃	#17911	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	26	1	no	—
383	C₂³	#88135	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	26	2	no	—
387	Q₈	#88161	1	4	yes	—
388	D₄	—	26	2	no	—
389	D₄	—	52	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	26	1	no	—
399	C₂×C₄	—	26	1	no	—
400	C₂×C₄	—	26	1	no	—
401	C₂×C₄	—	52	1	no	—
402	C₂×C₄	—	52	1	no	—
403	C₂×C₄	#88135	1	1	yes	characteristic
404	C₂×C₄	#88135	1	1	yes	characteristic
405	C₂×C₄	#88135	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#6129	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	13	2	no	—
413	C₈	—	26	2	no	—
414	C₈	—	26	2	no	—
415	C₈	—	26	1	no	—
416	C₈	—	26	1	no	—
417	C₈	—	26	1	no	—
418	C₈	—	52	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	52	1	no	—
422	C₂²	—	52	1	no	—
423	C₂²	—	52	1	no	—
424	C₂²	#11718485	1	2	yes	—
425	C₂²	C₂×#88135	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	52	1	no	—
433	C₄	—	52	1	no	—
434	C₄	—	52	1	no	—
435	C₄	C₂×#88161	1	2	yes	—
436	C₄	D₁₃×#137	1	1	yes	characteristic
437	C₄	#11719482	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	104	1	no	—
440	C₂	#13123526	1	1	yes	characteristic
441	C₂	#13123651	1	1	yes	characteristic
442	C₂	C₂×#11718485	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1491	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#88184	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1491	D₁₃
hypocenter	C₁₃	#17911
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1491

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×#1055	C₂	semidirect
4. #13113711	C₂	semidirect
5. #13113704	C₂	semidirect
6. #13113640	C₂	semidirect
7. #13113633	C₂	semidirect
8. #13113622	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
11. C₁₃×#1491	C₂	semidirect
169. #1491	D₁₃	semidirect
381. C₁₃	#17911	semidirect

Maximal subgroups

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

subgroup	index
#13124916	2
#13123805	2
C₂×Q₈×#1055	2
#13113711	2
#13113704	2
#13113640	2
#13113633	2
#13113622	2
#13113250	2
M₁₆×#1055	2
C₁₃×#1491	2
#17911	13