Subgroups — #16017186

Order 3328.

718 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	C₂×#11718855	C₂	1	2	yes	maximal, complemented
2	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116898	C₂	1	2	yes	maximal, complemented
4	#13116891	C₂	1	2	yes	maximal, complemented
5	#13116886	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116881	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116876	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊#6090	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116541	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	—	2	1	no	—
14	C₂×#88158	—	2	1	no	—
15	C₂×#88158	C₂²	1	2	yes	—
16	#11719182	—	2	1	no	—
17	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×SD₁₆	—	2	1	no	—
20	C₄×C₁₃×SD₁₆	—	2	1	no	—
21	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₂²	1	1	yes	characteristic
24	C₁₃×#416	—	2	1	no	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	#11718855	—	2	8	no	—
27	C₂×#88069	C₂²	1	2	yes	—
28	C₂×#88068	C₂²	1	2	yes	—
29	C₂×#88067	C₂²	1	2	yes	—
30	C₂×#88066	C₂²	1	2	yes	—
31	C₂²×#6090	C₂²	1	2	yes	—
32	#11718360	C₂²	1	1	yes	characteristic
33	#11718357	—	2	1	no	—
34	#11718357	C₂²	1	2	yes	—
35	#11718356	C₂²	1	1	yes	characteristic
36	#11718354	—	2	1	no	—
37	#11718084	C₂²	1	2	yes	—
38	#11718084	C₂²	1	2	yes	—
39	#11718083	C₂²	1	2	yes	—
40	#11718083	C₂²	1	2	yes	—
41	C₄⋊#6090	C₂²	1	1	yes	characteristic
42	C₄⋊#6090	C₂²	1	1	yes	characteristic
43	C₄⋊#6090	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×#6127	—	2	2	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₁₃×#135	D₄	1	4	yes	complemented
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	4	1	no	—
58	C₄×D₄×C₁₃	—	4	1	no	—
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	—	4	1	no	—
61	C₂×C₄²×C₁₃	—	4	1	no	—
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	#88184	—	4	1	no	—
64	#88184	—	4	1	no	—
65	C₂×Dic₅₂	—	2	1	no	—
66	C₂×Dic₅₂	C₂³	1	2	yes	—
67	#88158	—	2	4	no	—
68	#88158	—	2	4	no	—
69	#88158	—	4	4	no	—
70	C₂×D₁₀₄	—	2	1	no	—
71	C₂×D₁₀₄	C₂³	1	2	yes	—
72	C₂×#6095	—	2	2	no	—
73	C₂×#6095	—	2	2	no	—
74	#88129	—	2	2	no	—
75	#88128	—	2	1	no	—
76	C₄×D₅₂	—	4	1	no	—
77	C₄×D₅₂	—	4	1	no	—
78	#88123	—	2	1	no	—
79	C₁₃×#107	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂³	1	1	yes	characteristic
81	C₁₃×#106	—	2	1	no	—
82	C₁₃×#103	—	2	1	no	—
83	C₁₃×#103	—	2	1	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₁₃×#102	—	2	1	no	—
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	#88069	—	2	4	no	—
91	#88068	—	2	4	no	—
92	#88067	—	2	4	no	—
93	#88066	—	2	4	no	—
94	C₂×#6090	—	2	4	no	—
95	C₂×#6090	C₂³	1	2	yes	—
96	C₂×#6090	C₂³	1	2	yes	—
97	#33579	—	13	1	no	maximal, Sylow
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₃	—	4	2	no	—
110	#6127	—	4	4	no	—
111	#6127	—	4	4	no	—
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	4	1	no	—
114	C₂×D₅₂	—	4	1	no	—
115	C₂×C₄×D₁₃	—	4	2	no	—
116	C₂×Dic₂₆	—	2	2	no	—
117	C₁₃×Q₁₆	—	2	1	no	—
118	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
119	C₁₃×SD₁₆	—	2	4	no	—
120	C₁₃×D₈	—	2	1	no	—
121	C₁₃×D₈	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	#41	1	2	yes	—
128	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	1	no	—
136	C₄²×C₁₃	—	4	1	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₄²×C₁₃	D₈	1	1	yes	characteristic
140	C₄²×C₁₃	D₈	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
143	#6103	—	4	2	no	—
144	#6103	—	4	2	no	—
145	C₄⋊Dic₁₃	—	4	1	no	—
146	C₄⋊Dic₁₃	—	4	1	no	—
147	Dic₅₂	—	2	2	no	—
148	Dic₅₂	—	2	2	no	—
149	Dic₅₂	—	4	2	no	—
150	D₁₀₄	—	2	2	no	—
151	D₁₀₄	—	2	2	no	—
152	D₁₀₄	—	4	2	no	—
153	#6095	—	4	4	no	—
154	#6095	—	4	4	no	—
155	#6090	—	2	2	no	—
156	#6090	—	2	2	no	—
157	C₂×#508	—	13	2	no	—
158	#3147	—	13	1	no	—
159	C₄×#135	D₁₃	1	1	yes	characteristic, complemented
160	#2211	—	13	2	no	—
161	#2210	—	13	2	no	—
162	#2209	—	13	1	no	—
163	#2208	—	13	1	no	—
164	#2207	—	13	1	no	—
165	#2206	—	13	1	no	—
166	C₂×C₄⋊C₁₆	—	13	1	no	—
167	#2138	—	13	2	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂²×D₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	—	8	2	no	—
184	C₂×C₄×C₁₃	#121	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂²⋊D₁₃	—	8	4	no	—
193	C₂×Dic₁₃	—	4	2	no	—
194	D₅₂	—	4	2	no	—
195	D₅₂	—	4	2	no	—
196	D₅₂	—	8	2	no	—
197	D₅₂	—	8	2	no	—
198	C₄×D₁₃	—	8	4	no	—
199	Dic₂₆	—	4	2	no	—
200	Dic₂₆	—	4	2	no	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	#121	1	2	yes	—
204	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×#135	—	13	2	no	—
207	C₂×#135	—	26	1	no	—
208	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
209	#532	—	26	1	no	—
210	C₄×#41	—	2	1	no	—
211	#508	—	26	8	no	—
212	C₂×Q₃₂	—	13	2	no	—
213	C₂×SD₃₂	—	13	2	no	—
214	C₂×SD₃₂	—	13	2	no	—
215	C₂×D₁₆	—	13	2	no	—
216	C₂²×C₁₆	—	13	2	no	—
217	#495	—	13	2	no	—
218	#495	—	26	1	no	—
219	#494	—	13	1	no	—
220	#493	—	13	1	no	—
221	#492	—	26	1	no	—
222	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
223	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
224	C₄×SD₁₆	—	2	1	no	—
225	C₄×SD₁₆	—	2	1	no	—
226	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
227	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
228	#427	C₂×D₁₃	1	1	yes	characteristic
229	#416	—	2	1	no	—
230	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
231	C₄⋊C₁₆	—	13	1	no	—
232	C₄⋊C₁₆	—	13	1	no	—
233	C₄⋊C₁₆	—	13	2	no	—
234	#358	—	13	2	no	—
235	#358	—	13	2	no	—
236	#357	—	13	2	no	—
237	#357	—	13	2	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	#459	1	2	yes	—
244	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
245	C₂×D₁₃	—	8	2	no	—
246	C₂×D₁₃	—	8	2	no	—
247	C₂×D₁₃	—	8	2	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	—	8	1	no	—
254	C₄×C₁₃	#459	1	2	yes	—
255	C₄×C₁₃	#508	1	2	yes	complemented
256	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	Dic₁₃	—	8	2	no	—
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	26	2	no	—
261	#135	—	2	2	no	—
262	#135	—	26	4	no	—
263	#135	—	26	4	no	—
264	#135	—	52	4	no	—
265	#135	D₅₂	1	4	yes	complemented
266	C₂×Q₁₆	—	13	2	no	—
267	C₂×Q₁₆	—	26	1	no	—
268	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
269	C₂×SD₁₆	—	2	1	no	—
270	C₂×SD₁₆	—	26	2	no	—
271	C₂×SD₁₆	—	26	2	no	—
272	C₂×D₈	—	13	2	no	—
273	C₂×D₈	—	26	1	no	—
274	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	26	1	no	—
278	#127	—	26	1	no	—
279	#124	—	26	2	no	—
280	#121	—	52	1	no	—
281	#121	—	52	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	4	1	no	—
287	C₄×D₄	—	4	1	no	—
288	C₄×D₄	—	52	1	no	—
289	C₄×D₄	—	52	1	no	—
290	#117	—	2	1	no	—
291	#117	—	4	1	no	—
292	C₂×C₄²	—	4	1	no	—
293	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
294	Q₃₂	—	26	4	no	—
295	SD₃₂	—	26	4	no	—
296	SD₃₂	—	26	4	no	—
297	D₁₆	—	26	4	no	—
298	C₂×C₁₆	—	13	2	no	—
299	C₂×C₁₆	—	13	2	no	—
300	C₂×C₁₆	—	26	4	no	—
301	#107	C₂²×D₁₃	1	1	yes	characteristic
302	#107	C₂²×D₁₃	1	1	yes	characteristic
303	#106	—	2	1	no	—
304	#103	—	2	1	no	—
305	#103	—	2	1	no	—
306	#102	—	2	1	no	—
307	#102	—	2	1	no	—
308	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	8	2	no	—
314	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
316	C₂×C₁₃	#3414	1	1	yes	characteristic
317	D₁₃	—	16	2	no	—
318	#41	—	2	4	no	—
319	#41	—	4	2	no	—
320	#41	—	52	4	no	—
321	#41	—	52	4	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	26	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	26	2	no	—
327	C₂×D₄	—	52	2	no	—
328	C₂×D₄	—	52	1	no	—
329	C₂×D₄	—	52	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	52	2	no	—
334	C₂²×C₄	#6104	1	1	yes	characteristic
335	C₂²×C₄	#6104	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
337	Q₁₆	—	2	1	no	—
338	Q₁₆	—	26	2	no	—
339	Q₁₆	—	26	2	no	—
340	Q₁₆	—	52	2	no	—
341	Q₁₆	C₂×D₅₂	1	2	yes	—
342	SD₁₆	—	2	4	no	—
343	SD₁₆	—	52	4	no	—
344	SD₁₆	—	52	4	no	—
345	D₈	—	2	1	no	—
346	D₈	—	26	2	no	—
347	D₈	—	26	2	no	—
348	D₈	—	52	2	no	—
349	D₈	C₂×D₅₂	1	2	yes	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₅₂	1	2	yes	—
352	C₂×C₈	#6127	1	2	yes	—
353	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
356	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	52	1	no	—
362	C₄⋊C₄	—	52	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	52	2	no	—
367	C₂²⋊C₄	—	52	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	#6104	1	1	yes	characteristic
372	C₄²	#6104	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
375	C₁₆	—	26	2	no	—
376	C₁₆	—	26	2	no	—
377	C₁₃	#33579	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	4	1	no	—
379	C₂³	—	52	2	no	—
380	C₂³	C₂×#6104	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	52	2	no	—
384	Q₈	—	52	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	1	no	—
388	D₄	—	52	2	no	—
389	D₄	—	52	2	no	—
390	D₄	—	104	2	no	—
391	D₄	—	104	4	no	—
392	D₄	—	104	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	52	2	no	—
402	C₂×C₄	—	104	4	no	—
403	C₂×C₄	#88184	1	2	yes	—
404	C₂×C₄	C₂×#6104	1	1	yes	characteristic
405	C₂×C₄	C₂×#6104	1	1	yes	characteristic
406	C₂×C₄	C₂×#6104	1	1	yes	characteristic
407	C₂×C₄	C₂×#6104	1	1	yes	characteristic
408	C₂×C₄	C₂×#6104	1	1	yes	characteristic
409	C₂×C₄	#88203	1	2	yes	—
410	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	#88184	1	2	yes	—
414	C₈	C₂²×D₅₂	1	1	yes	characteristic
415	C₈	C₂×#6127	1	1	yes	characteristic
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	104	2	no	—
422	C₂²	—	104	2	no	—
423	C₂²	—	104	2	no	—
424	C₂²	#11718676	1	2	yes	—
425	C₂²	C₂²×#6104	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	104	2	no	—
433	C₄	#11718676	1	2	yes	—
434	C₄	#11718855	1	2	yes	complemented
435	C₄	C₂×#88184	1	1	yes	characteristic
436	C₄	C₂×#88203	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	208	2	no	—
440	C₂	C₂×#11718676	1	1	yes	characteristic
441	C₂	C₂×#11718855	1	1	yes	characteristic
442	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂²×D₈
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#33579
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#11718855	C₂	semidirect
2. #13125264	C₂	semidirect
3. #13116898	C₂	semidirect
4. #13116891	C₂	semidirect
5. #13116886	C₂	semidirect
6. #13116881	C₂	semidirect
7. #13116876	C₂	semidirect
8. #13116871	C₂	semidirect
9. C₂×C₄⋊#6090	C₂	semidirect
10. #13116541	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
47. C₁₃×#135	D₄	semidirect
159. C₄×#135	D₁₃	semidirect
255. C₄×C₁₃	#508	semidirect
265. #135	D₅₂	semidirect
377. C₁₃	#33579	semidirect
434. C₄	#11718855	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718855	2
#13125264	2
#13116898	2
#13116891	2
#13116886	2
#13116881	2
#13116876	2
#13116871	2
C₂×C₄⋊#6090	2
#13116541	2
C₄×C₁₃×#135	2
#33579	13