Subgroups — #15869718

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124417	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718378	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123530	C₂	1	2	yes	maximal, complemented
4	#13115729	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115589	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115547	C₂	1	2	yes	maximal, complemented
7	#13115279	C₂	1	2	yes	maximal, complemented
8	#13114874	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114720	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114680	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	#11719496	C₂²	1	2	yes	—
16	C₂×#88158	C₂²	1	1	yes	characteristic
17	C₂×#88155	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	—	2	4	no	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	#11718868	C₂²	1	2	yes	—
24	#11718777	C₄	1	2	yes	complemented
25	#11718776	C₄	1	2	yes	complemented
26	#11718775	C₄	1	4	yes	complemented
27	#11718774	C₂²	1	2	yes	—
28	#11718772	—	2	4	no	—
29	#11718771	C₂²	1	2	yes	—
30	C₈×C₂²⋊D₁₃	—	2	4	no	—
31	C₂×#88059	C₂²	1	1	yes	characteristic
32	C₂×#88059	C₂²	1	1	yes	characteristic
33	#11718767	C₂²	1	1	yes	characteristic
34	#11718763	C₂²	1	2	yes	—
35	#11718762	C₂²	1	2	yes	—
36	C₂×#88045	C₂²	1	2	yes	—
37	C₂×#88045	C₂²	1	2	yes	—
38	#11718378	—	2	4	no	—
39	#11718144	C₂²	1	2	yes	—
40	#11718115	C₂²	1	2	yes	—
41	#11718115	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×#6127	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	4	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	—	2	1	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	#88207	—	2	2	no	—
62	#88184	C₂×C₄	1	4	yes	—
63	#88183	—	2	2	no	—
64	C₄×C₂²⋊D₁₃	—	2	4	no	—
65	#88180	C₂³	1	2	yes	—
66	#88178	C₂×C₄	1	4	yes	—
67	C₂×#6099	C₂³	1	2	yes	—
68	C₂×#6099	C₂³	1	2	yes	—
69	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
70	#88158	—	2	2	no	—
71	#88158	—	2	2	no	—
72	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×#6095	C₂×C₄	1	2	yes	complemented
74	#88155	—	2	4	no	—
75	#88155	—	2	4	no	—
76	C₂×#6094	—	2	2	no	—
77	C₂×C₈×D₁₃	—	2	2	no	—
78	C₁₃×#97	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₁₃×#97	—	2	2	no	—
81	C₁₃×#97	D₄	1	4	yes	complemented
82	C₂²⋊#1055	—	2	4	no	—
83	#88061	C₂×C₄	1	4	yes	complemented
84	#88060	—	2	4	no	—
85	#88059	—	2	2	no	—
86	#88059	—	2	2	no	—
87	#88058	C₂×C₄	1	2	yes	complemented
88	#88057	C₂×C₄	1	2	yes	complemented
89	#88056	C₂×C₄	1	4	yes	complemented
90	#88055	—	2	2	no	—
91	#88054	—	2	4	no	—
92	C₈×Dic₁₃	—	2	2	no	—
93	#88045	—	2	4	no	—
94	#88045	—	2	4	no	—
95	#21546	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₃	—	2	4	no	—
110	C₂×C₂²⋊D₁₃	—	2	2	no	—
111	#6127	—	2	2	no	—
112	#6127	—	2	2	no	—
113	#6127	—	2	2	no	—
114	#6127	—	2	2	no	—
115	C₂×D₅₂	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₁₃	—	2	2	no	—
117	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	4	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	8	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	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₃	#41	1	2	yes	—
133	C₂×C₈×C₁₃	#41	1	2	yes	—
134	C₄²×C₁₃	—	2	4	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	C₂²⋊Dic₁₃	—	2	4	no	—
140	C₂²⋊Dic₁₃	—	2	2	no	—
141	#6103	—	2	4	no	—
142	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
143	#6101	—	2	4	no	—
144	C₄×Dic₁₃	—	2	2	no	—
145	#6099	—	2	2	no	—
146	#6099	—	2	2	no	—
147	#6099	—	2	2	no	—
148	#6099	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	Dic₅₂	—	2	2	no	—
152	D₁₀₄	—	2	2	no	—
153	#6095	—	2	4	no	—
154	#6094	—	4	4	no	—
155	C₈×D₁₃	—	4	4	no	—
156	#3050	—	13	1	no	—
157	C₂×#444	—	13	1	no	—
158	#2929	—	13	2	no	—
159	C₂²×#97	D₁₃	1	1	yes	characteristic, complemented
160	#1975	—	13	1	no	—
161	#1946	—	13	1	no	—
162	#1938	—	13	2	no	—
163	#1896	—	13	2	no	—
164	#1810	—	13	1	no	—
165	#1773	—	13	1	no	—
166	#1765	—	13	2	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	C₄×D₄	1	2	yes	—
171	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂²⋊D₁₃	—	4	2	no	—
192	C₂²⋊D₁₃	—	4	2	no	—
193	C₂²⋊D₁₃	—	4	8	no	—
194	C₂×Dic₁₃	—	2	4	no	—
195	C₂×Dic₁₃	—	2	2	no	—
196	D₅₂	—	2	2	no	—
197	D₅₂	—	2	2	no	—
198	C₄×D₁₃	—	4	2	no	—
199	C₄×D₁₃	—	4	2	no	—
200	Dic₂₆	—	2	2	no	—
201	Dic₂₆	—	2	2	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	C₄×D₄	1	2	yes	—
205	C₈×C₁₃	C₄×D₄	1	2	yes	—
206	C₈×C₁₃	#121	1	4	yes	—
207	#1055	—	4	2	no	—
208	#1055	—	4	2	no	—
209	C₂×#135	—	13	1	no	—
210	C₂×#131	—	13	2	no	—
211	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
212	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
213	#525	—	13	2	no	—
214	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
215	#467	—	13	2	no	—
216	#466	—	13	2	no	—
217	#465	—	13	4	no	—
218	#444	—	26	4	no	—
219	#435	—	26	4	no	—
220	C₈×D₄	—	26	4	no	—
221	C₂×#108	—	13	1	no	—
222	C₂×#108	—	13	1	no	—
223	#427	—	13	1	no	—
224	#424	—	13	2	no	—
225	C₂×#104	—	13	2	no	—
226	C₂×#104	—	13	2	no	—
227	#416	—	13	2	no	—
228	#408	—	13	2	no	—
229	#407	—	13	2	no	—
230	#405	—	13	2	no	—
231	C₂×#97	—	2	4	no	—
232	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
233	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
234	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
235	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
236	#341	—	13	2	no	—
237	#339	—	13	2	no	—
238	#339	—	13	2	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	#444	1	4	yes	complemented
245	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₃	#525	1	1	yes	characteristic
247	C₂²×C₁₃	#529	1	1	yes	characteristic
248	C₂×D₁₃	—	4	4	no	—
249	C₂×D₁₃	—	4	2	no	—
250	C₄×C₁₃	—	2	2	no	—
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	C₄×#41	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
256	C₄×C₁₃	#532	1	1	yes	characteristic
257	Dic₁₃	—	4	4	no	—
258	Dic₁₃	—	4	2	no	—
259	C₂×#41	—	13	2	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
262	#135	—	26	2	no	—
263	#135	—	26	2	no	—
264	C₂×Q₁₆	—	13	1	no	—
265	C₂×SD₁₆	—	13	2	no	—
266	C₂×D₈	—	13	1	no	—
267	#131	—	26	4	no	—
268	#131	—	26	4	no	—
269	C₂×M₁₆	—	13	2	no	—
270	C₂×M₁₆	—	13	2	no	—
271	C₂×M₁₆	—	26	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	26	2	no	—
277	C₂²×C₈	C₄×D₁₃	1	2	yes	—
278	C₂²×C₈	C₄×D₁₃	1	2	yes	—
279	C₂²×C₈	D₅₂	1	4	yes	—
280	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
284	#123	—	26	2	no	—
285	C₂²⋊Q₈	—	13	4	no	—
286	#121	—	13	4	no	—
287	#120	—	26	2	no	—
288	C₄×D₄	—	26	4	no	—
289	#117	—	13	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
295	#108	—	26	2	no	—
296	#108	—	26	2	no	—
297	#107	—	13	2	no	—
298	#106	—	13	2	no	—
299	C₄⋊C₈	—	26	4	no	—
300	#104	—	26	4	no	—
301	#104	—	26	4	no	—
302	#103	—	13	4	no	—
303	#102	—	13	4	no	—
304	C₂²⋊C₈	—	26	4	no	—
305	C₂²⋊C₈	—	26	4	no	—
306	#97	—	2	2	no	—
307	#97	—	2	2	no	—
308	#97	—	2	2	no	—
309	#97	—	26	2	no	—
310	#97	C₂²⋊D₁₃	1	4	yes	complemented
311	C₄×C₈	—	26	2	no	—
312	C₂×C₁₃	—	2	1	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	—	2	4	no	—
315	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#444	1	2	yes	—
317	D₁₃	—	8	2	no	—
318	C₂⁴	#6127	1	1	yes	characteristic
319	#41	—	26	2	no	—
320	#41	—	26	2	no	—
321	#41	—	26	2	no	—
322	#41	—	26	2	no	—
323	C₂×Q₈	—	13	2	no	—
324	C₂×D₄	—	13	2	no	—
325	C₂×D₄	—	26	4	no	—
326	C₂×D₄	—	26	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	26	2	no	—
336	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
337	C₂²×C₄	C₂×D₅₂	1	2	yes	—
338	C₂²×C₄	#6127	1	1	yes	characteristic
339	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
340	Q₁₆	—	26	2	no	—
341	SD₁₆	—	26	4	no	—
342	D₈	—	26	2	no	—
343	M₁₆	—	26	2	no	—
344	M₁₆	—	26	2	no	—
345	M₁₆	—	26	2	no	—
346	M₁₆	—	26	2	no	—
347	M₁₆	—	52	4	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	52	4	no	—
358	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
359	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂×C₈	C₂×D₅₂	1	2	yes	—
362	C₂×C₈	C₂×D₅₂	1	2	yes	—
363	C₂×C₈	#6127	1	2	yes	—
364	C₂×C₈	#6127	1	2	yes	—
365	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
366	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
367	C₄⋊C₄	—	13	4	no	—
368	C₄⋊C₄	—	26	4	no	—
369	C₂²⋊C₄	—	26	4	no	—
370	C₂²⋊C₄	—	26	2	no	—
371	C₂²⋊C₄	—	26	4	no	—
372	C₄²	—	2	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	26	2	no	—
376	C₄²	#6127	1	2	yes	—
377	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
378	C₁₃	#21546	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	26	2	no	—
383	C₂³	C₄×D₅₂	1	2	yes	—
384	C₂³	C₂×#6127	1	1	yes	characteristic
385	Q₈	—	26	2	no	—
386	Q₈	—	26	2	no	—
387	D₄	—	26	2	no	—
388	D₄	—	26	2	no	—
389	D₄	—	52	2	no	—
390	D₄	—	52	2	no	—
391	D₄	—	52	8	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	26	4	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	52	2	no	—
406	C₂×C₄	—	52	2	no	—
407	C₂×C₄	C₄×D₅₂	1	2	yes	—
408	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
410	C₂×C₄	C₂×#6127	1	1	yes	characteristic
411	C₂×C₄	C₂×#6127	1	1	yes	characteristic
412	C₂×C₄	C₂×#6127	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	52	2	no	—
417	C₈	—	52	2	no	—
418	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
419	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
420	C₈	#88184	1	4	yes	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	52	4	no	—
427	C₂²	—	52	2	no	—
428	C₂²	#11718378	1	4	yes	complemented
429	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
430	C₂²	#11719184	1	1	yes	characteristic
431	C₂²	#11719496	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	52	4	no	—
436	C₄	—	52	2	no	—
437	C₄	C₄×#6127	1	1	yes	characteristic
438	C₄	#11719182	1	1	yes	characteristic
439	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
440	C₄	C₂×#88184	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	4	no	—
444	C₂	—	104	2	no	—
445	C₂	C₄×#88184	1	1	yes	characteristic
446	C₂	C₂×#11718378	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124417	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#21546
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
2. C₂×#11718378	C₂	semidirect
3. #13123530	C₂	semidirect
4. #13115729	C₂	semidirect
5. #13115589	C₂	semidirect
6. #13115547	C₂	semidirect
7. #13115279	C₂	semidirect
8. #13114874	C₂	semidirect
9. #13114720	C₂	semidirect
10. #13114680	C₂	semidirect
11. C₂²×C₁₃×#97	C₂	semidirect
24. #11718777	C₄	semidirect
25. #11718776	C₄	semidirect
26. #11718775	C₄	semidirect
69. C₂×Dic₅₂	C₂×C₄	semidirect
72. C₂×D₁₀₄	C₂×C₄	semidirect
73. C₂×#6095	C₂×C₄	semidirect
81. C₁₃×#97	D₄	semidirect
83. #88061	C₂×C₄	semidirect
87. #88058	C₂×C₄	semidirect
88. #88057	C₂×C₄	semidirect
89. #88056	C₂×C₄	semidirect
159. C₂²×#97	D₁₃	semidirect
244. C₂²×C₁₃	#444	semidirect
310. #97	C₂²⋊D₁₃	semidirect
378. C₁₃	#21546	semidirect
428. C₂²	#11718378	semidirect

Maximal subgroups

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

subgroup	index
#13124417	2
C₂×#11718378	2
#13123530	2
#13115729	2
#13115589	2
#13115547	2
#13115279	2
#13114874	2
#13114720	2
#13114680	2
C₂²×C₁₃×#97	2
#21546	13