Subgroups — #86143

Order 384.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5708	C₂	1	2	yes	maximal, complemented
3	#5702	C₂	1	2	yes	maximal, complemented
4	#5696	C₂	1	2	yes	maximal, complemented
5	#5669	C₂	1	2	yes	maximal, complemented
6	#5662	C₂	1	2	yes	maximal, complemented
7	#5660	C₂	1	2	yes	maximal, complemented
8	#5646	C₂	1	2	yes	maximal, complemented
9	#5621	C₂	1	2	yes	maximal, complemented
10	#5579	C₂	1	1	yes	maximal, characteristic, complemented
11	#5567	C₂	1	1	yes	maximal, characteristic, complemented
12	#5565	C₂	1	1	yes	maximal, characteristic, complemented
13	#5565	C₂	1	1	yes	maximal, characteristic, complemented
14	#5563	C₂	1	1	yes	maximal, characteristic, complemented
15	#5542	C₂	1	1	yes	maximal, characteristic, complemented
16	#5541	C₂	1	1	yes	maximal, characteristic, complemented
17	#5541	C₂	1	1	yes	maximal, characteristic, complemented
18	#5534	C₂	1	1	yes	maximal, characteristic, complemented
19	#5534	C₂	1	1	yes	maximal, characteristic, complemented
20	#5519	C₂	1	1	yes	maximal, characteristic, complemented
21	#5519	C₂	1	1	yes	maximal, characteristic, complemented
22	#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	#5470	C₂	1	1	yes	maximal, characteristic, complemented
24	#3565	—	3	1	no	maximal, Sylow
25	C₃×#126	C₂²	1	1	yes	characteristic
26	C₃×#126	C₂²	1	1	yes	characteristic
27	C₃×#125	C₂²	1	1	yes	characteristic
28	C₃×#124	C₂²	1	1	yes	characteristic
29	C₃×#123	C₂²	1	1	yes	characteristic
30	C₃×#123	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×#121	C₂²	1	1	yes	characteristic
33	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₃×#117	C₂²	1	1	yes	characteristic
38	C₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
40	#946	C₂²	1	2	yes	—
41	#944	C₂²	1	2	yes	—
42	#939	C₂²	1	2	yes	—
43	#939	C₂²	1	2	yes	—
44	#938	C₂²	1	2	yes	—
45	#936	C₂²	1	2	yes	—
46	#935	C₂²	1	2	yes	—
47	#935	C₂²	1	2	yes	—
48	#930	C₂²	1	1	yes	characteristic
49	#930	C₂²	1	1	yes	characteristic
50	#930	C₂²	1	1	yes	characteristic
51	#929	C₂²	1	2	yes	—
52	C₄×#67	C₂²	1	2	yes	—
53	#926	C₂²	1	1	yes	characteristic
54	#926	C₂²	1	1	yes	characteristic
55	#926	C₂²	1	1	yes	characteristic
56	#926	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
59	#924	C₂²	1	2	yes	—
60	#924	C₂²	1	2	yes	—
61	#924	C₂²	1	1	yes	characteristic
62	#924	C₂²	1	1	yes	characteristic
63	#924	C₂²	1	1	yes	characteristic
64	#898	C₂²	1	2	yes	—
65	#898	C₂²	1	2	yes	—
66	#898	C₂²	1	2	yes	—
67	#898	C₂²	1	2	yes	—
68	#896	C₂²	1	2	yes	—
69	#896	C₂²	1	2	yes	—
70	#896	C₂²	1	2	yes	—
71	#896	C₂²	1	2	yes	—
72	#892	C₂²	1	2	yes	—
73	D₃×C₄⋊C₄	C₂²	1	2	yes	—
74	#890	C₂²	1	2	yes	—
75	#890	C₂²	1	2	yes	—
76	#889	C₂²	1	2	yes	—
77	#889	C₂²	1	2	yes	—
78	#889	C₂²	1	2	yes	—
79	#889	C₂²	1	2	yes	—
80	#888	C₂²	1	2	yes	—
81	#888	C₂²	1	2	yes	—
82	#887	C₂²	1	2	yes	—
83	#887	C₂²	1	2	yes	—
84	#885	C₂²	1	2	yes	—
85	#885	C₂²	1	2	yes	—
86	#885	C₂²	1	2	yes	—
87	#885	C₂²	1	2	yes	—
88	#883	C₂²	1	2	yes	—
89	#883	C₂²	1	2	yes	—
90	#883	C₂²	1	2	yes	—
91	#883	C₂²	1	2	yes	—
92	#67⋊C₄	C₂²	1	2	yes	—
93	#67⋊C₄	C₂²	1	2	yes	—
94	#879	C₂²	1	2	yes	—
95	#879	C₂²	1	2	yes	—
96	#879	C₂²	1	2	yes	—
97	#879	C₂²	1	2	yes	—
98	#878	C₂²	1	2	yes	—
99	#878	C₂²	1	2	yes	—
100	#878	C₂²	1	2	yes	—
101	#878	C₂²	1	2	yes	—
102	#877	C₂²	1	2	yes	—
103	#877	C₂²	1	2	yes	—
104	#876	C₂²	1	2	yes	—
105	#875	C₂²	1	1	yes	characteristic
106	C₄×D₁₂	C₂²	1	1	yes	characteristic
107	C₄×D₁₂	C₂²	1	1	yes	characteristic
108	C₄×D₁₂	C₂²	1	1	yes	characteristic
109	#872	C₂²	1	2	yes	—
110	#870	C₂²	1	1	yes	characteristic
111	#870	C₂²	1	1	yes	characteristic
112	#870	C₂²	1	1	yes	characteristic
113	#870	C₂²	1	1	yes	characteristic
114	#870	C₂²	1	1	yes	characteristic
115	#869	C₂²	1	1	yes	characteristic
116	#869	C₂²	1	1	yes	characteristic
117	#869	C₂²	1	1	yes	characteristic
118	#869	C₂²	1	1	yes	characteristic
119	C₄×Dic₆	C₂²	1	2	yes	—
120	C₄×Dic₆	C₂²	1	2	yes	—
121	C₄×Dic₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₆	C₂²	1	1	yes	characteristic
123	C₄×Dic₆	C₂²	1	1	yes	characteristic
124	#563	—	3	2	no	—
125	#562	—	3	2	no	—
126	#557	—	3	1	no	—
127	#556	—	3	2	no	—
128	#556	—	3	1	no	—
129	#555	—	3	1	no	—
130	#554	—	3	1	no	—
131	#553	—	3	1	no	—
132	#553	—	3	1	no	—
133	#552	—	3	2	no	—
134	#552	—	3	1	no	—
135	#552	—	3	1	no	—
136	#544	—	3	1	no	—
137	#544	—	3	1	no	—
138	#542	—	3	2	no	—
139	#542	—	3	2	no	—
140	#542	—	3	1	no	—
141	#542	—	3	1	no	—
142	#541	—	3	2	no	—
143	#539	—	3	2	no	—
144	#533	—	3	1	no	—
145	#529	—	3	1	no	—
146	#529	D₃	1	1	yes	characteristic, complemented
147	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂×#67	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂²×Dic₃	C₂³	1	2	yes	—
160	C₂²×Dic₃	C₂³	1	2	yes	—
161	C₂×D₁₂	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₃	C₂³	1	2	yes	—
163	C₂×C₄×D₃	C₂³	1	2	yes	—
164	C₂×C₄×D₃	C₂³	1	2	yes	—
165	C₂×Dic₆	C₂³	1	1	yes	characteristic
166	C₂×Dic₆	C₂³	1	2	yes	—
167	C₂×Dic₆	C₂³	1	2	yes	—
168	C₂×Dic₆	C₂³	1	2	yes	—
169	C₂×Dic₆	C₂³	1	2	yes	—
170	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₃×C₄²	C₂³	1	1	yes	characteristic
192	C₃×C₄²	C₂³	1	1	yes	characteristic
193	C₃×C₄²	C₂³	1	1	yes	characteristic
194	C₃×C₄²	C₂³	1	1	yes	characteristic
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	#217	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	2	yes	—
199	#217	C₂³	1	2	yes	—
200	#217	C₂³	1	2	yes	—
201	#217	C₂³	1	2	yes	—
202	#217	C₂³	1	2	yes	—
203	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₃	C₂³	1	2	yes	—
215	C₄⋊Dic₃	C₂³	1	2	yes	—
216	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₄⋊Dic₃	C₂³	1	2	yes	—
221	C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	Dic₃⋊C₄	C₂³	1	2	yes	—
224	Dic₃⋊C₄	C₂³	1	2	yes	—
225	Dic₃⋊C₄	C₂³	1	2	yes	—
226	Dic₃⋊C₄	C₂³	1	2	yes	—
227	Dic₃⋊C₄	C₂³	1	2	yes	—
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	2	yes	—
230	Dic₃⋊C₄	C₂³	1	2	yes	—
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₄×Dic₃	C₂³	1	2	yes	—
240	C₄×Dic₃	C₂³	1	2	yes	—
241	C₄×Dic₃	C₂³	1	2	yes	—
242	C₄×Dic₃	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	2	yes	—
244	C₄×Dic₃	C₂³	1	2	yes	—
245	C₄×Dic₃	C₂³	1	2	yes	—
246	C₄⋊Q₈	—	3	2	no	—
247	C₄⋊Q₈	—	3	2	no	—
248	C₄⋊Q₈	—	3	2	no	—
249	C₄⋊Q₈	—	3	1	no	—
250	C₄⋊Q₈	—	3	1	no	—
251	C₄⋊Q₈	—	3	1	no	—
252	C₄⋊Q₈	—	3	1	no	—
253	#126	—	3	2	no	—
254	#126	—	3	2	no	—
255	#126	—	3	2	no	—
256	#126	—	3	2	no	—
257	#126	—	3	2	no	—
258	#126	—	3	2	no	—
259	#126	—	3	2	no	—
260	#126	—	3	2	no	—
261	#126	—	3	2	no	—
262	#126	C₂×D₃	1	1	yes	characteristic
263	#126	C₂×D₃	1	1	yes	characteristic
264	#125	—	3	2	no	—
265	#125	—	3	2	no	—
266	#125	—	3	2	no	—
267	#125	—	3	2	no	—
268	#125	—	3	2	no	—
269	#125	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	—	3	1	no	—
272	#125	—	3	1	no	—
273	#125	—	3	1	no	—
274	#125	—	3	1	no	—
275	#125	C₂×D₃	1	1	yes	characteristic
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	1	no	—
282	#124	C₂×D₃	1	1	yes	characteristic
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	C₂×D₃	1	1	yes	characteristic
291	#123	C₂×D₃	1	1	yes	characteristic
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	1	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	1	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	2	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	1	no	—
311	#121	—	3	1	no	—
312	#121	—	3	1	no	—
313	#121	C₂×D₃	1	1	yes	characteristic
314	C₄×Q₈	—	3	2	no	—
315	C₄×Q₈	—	3	2	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×Q₈	—	3	2	no	—
318	C₄×Q₈	—	3	2	no	—
319	C₄×Q₈	—	3	1	no	—
320	C₄×Q₈	—	3	1	no	—
321	C₄×Q₈	C₂×D₃	1	1	yes	characteristic
322	C₄×D₄	—	3	2	no	—
323	C₄×D₄	—	3	2	no	—
324	C₄×D₄	—	3	2	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	1	no	—
328	C₄×D₄	C₂×D₃	1	1	yes	characteristic
329	C₄×D₄	C₂×D₃	1	1	yes	characteristic
330	C₄×D₄	C₂×D₃	1	1	yes	characteristic
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	1	no	—
334	#117	—	3	1	no	—
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	3	2	no	—
338	#117	—	3	2	no	—
339	#117	C₂×D₃	1	1	yes	characteristic
340	#117	C₂×D₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
345	C₂³×C₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₃	C₂⁴	1	1	yes	characteristic
347	C₂³×C₃	C₂⁴	1	1	yes	characteristic
348	C₂²×D₃	C₂⁴	1	2	yes	—
349	C₃×Q₈	—	4	1	no	—
350	C₃×D₄	—	4	1	no	—
351	C₃×D₄	—	4	1	no	—
352	C₃×D₄	—	4	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	4	1	no	—
357	C₂×C₃×C₄	—	4	1	no	—
358	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
361	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
370	#67	—	4	2	no	—
371	#67	—	4	2	no	—
372	#67	—	4	2	no	—
373	C₂×Dic₃	—	4	2	no	—
374	C₂×Dic₃	—	4	2	no	—
375	C₂×Dic₃	C₂⁴	1	2	yes	—
376	C₂×Dic₃	C₂⁴	1	2	yes	—
377	C₂×Dic₃	C₂⁴	1	2	yes	—
378	C₂×Dic₃	C₂⁴	1	2	yes	—
379	C₂×Dic₃	C₂⁴	1	2	yes	—
380	C₂×Dic₃	C₂⁴	1	2	yes	—
381	C₂×Dic₃	C₂⁴	1	2	yes	—
382	D₁₂	—	2	2	no	—
383	C₄×D₃	—	4	2	no	—
384	C₄×D₃	—	4	2	no	—
385	C₄×D₃	—	4	2	no	—
386	Dic₆	—	2	2	no	—
387	Dic₆	—	4	2	no	—
388	Dic₆	—	4	2	no	—
389	Dic₆	—	4	2	no	—
390	Dic₆	—	4	2	no	—
391	C₂×Q₈	—	3	1	no	—
392	C₂×Q₈	—	3	2	no	—
393	C₂×Q₈	—	3	2	no	—
394	C₂×Q₈	—	3	2	no	—
395	C₂×Q₈	—	3	2	no	—
396	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
397	C₂×D₄	—	3	2	no	—
398	C₂×D₄	—	3	2	no	—
399	C₂×D₄	—	3	2	no	—
400	C₂×D₄	—	3	1	no	—
401	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
402	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
403	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
404	C₂²×C₄	—	3	2	no	—
405	C₂²×C₄	—	3	2	no	—
406	C₂²×C₄	—	3	2	no	—
407	C₂²×C₄	—	3	2	no	—
408	C₂²×C₄	—	3	2	no	—
409	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
411	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
412	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
413	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
414	C₄⋊C₄	—	3	1	no	—
415	C₄⋊C₄	—	3	1	no	—
416	C₄⋊C₄	—	3	1	no	—
417	C₄⋊C₄	—	3	1	no	—
418	C₄⋊C₄	—	3	2	no	—
419	C₄⋊C₄	—	3	2	no	—
420	C₄⋊C₄	—	3	2	no	—
421	C₄⋊C₄	—	3	2	no	—
422	C₄⋊C₄	—	3	2	no	—
423	C₄⋊C₄	—	3	1	no	—
424	C₄⋊C₄	—	3	1	no	—
425	C₄⋊C₄	—	3	2	no	—
426	C₄⋊C₄	—	3	2	no	—
427	C₄⋊C₄	—	3	2	no	—
428	C₄⋊C₄	—	3	2	no	—
429	C₄⋊C₄	—	3	2	no	—
430	C₄⋊C₄	—	3	2	no	—
431	C₄⋊C₄	—	3	2	no	—
432	C₄⋊C₄	—	3	2	no	—
433	C₄⋊C₄	—	3	2	no	—
434	C₄⋊C₄	—	3	2	no	—
435	C₄⋊C₄	—	3	2	no	—
436	C₄⋊C₄	—	3	2	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	—	3	2	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	2	no	—
442	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
443	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
444	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
446	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
447	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
448	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
449	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
450	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
451	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
452	C₂²⋊C₄	—	3	2	no	—
453	C₂²⋊C₄	—	3	2	no	—
454	C₂²⋊C₄	—	3	2	no	—
455	C₂²⋊C₄	—	3	2	no	—
456	C₂²⋊C₄	—	3	2	no	—
457	C₂²⋊C₄	—	3	2	no	—
458	C₂²⋊C₄	—	3	2	no	—
459	C₂²⋊C₄	—	3	2	no	—
460	C₂²⋊C₄	—	3	2	no	—
461	C₂²⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	—	3	2	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
468	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
469	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
470	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
473	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄²	—	3	2	no	—
478	C₄²	—	3	2	no	—
479	C₄²	—	3	2	no	—
480	C₄²	—	3	2	no	—
481	C₄²	—	3	2	no	—
482	C₄²	—	3	2	no	—
483	C₄²	—	3	2	no	—
484	C₄²	C₂²×D₃	1	1	yes	characteristic
485	C₄²	C₂²×D₃	1	1	yes	characteristic
486	C₄²	C₂²×D₃	1	1	yes	characteristic
487	C₄²	C₂²×D₃	1	1	yes	characteristic
488	C₄²	C₂²×D₃	1	1	yes	characteristic
489	C₄²	C₂²×D₃	1	1	yes	characteristic
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	C₂⁵	1	1	yes	characteristic
500	C₂×D₃	—	2	2	no	—
501	C₂×D₃	—	2	2	no	—
502	C₂×D₃	—	2	2	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
515	Dic₃	—	2	2	no	—
516	Dic₃	—	2	2	no	—
517	Dic₃	—	2	2	no	—
518	Dic₃	—	2	2	no	—
519	Dic₃	—	2	2	no	—
520	Dic₃	—	2	2	no	—
521	Dic₃	—	2	2	no	—
522	C₂³	—	3	2	no	—
523	C₂³	C₂³×D₃	1	1	yes	characteristic
524	C₂³	C₂³×D₃	1	1	yes	characteristic
525	C₂³	C₂³×D₃	1	1	yes	characteristic
526	Q₈	—	4	1	no	—
527	Q₈	—	6	2	no	—
528	Q₈	—	12	2	no	—
529	Q₈	—	12	2	no	—
530	Q₈	—	12	2	no	—
531	Q₈	—	12	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	6	2	no	—
536	D₄	—	12	2	no	—
537	D₄	—	12	2	no	—
538	D₄	—	12	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	3	2	no	—
543	C₂×C₄	—	3	2	no	—
544	C₂×C₄	—	3	2	no	—
545	C₂×C₄	—	3	2	no	—
546	C₂×C₄	—	3	2	no	—
547	C₂×C₄	—	3	2	no	—
548	C₂×C₄	—	3	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	12	2	no	—
552	C₂×C₄	—	12	2	no	—
553	C₂×C₄	—	12	2	no	—
554	C₂×C₄	—	12	2	no	—
555	C₂×C₄	—	12	2	no	—
556	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
560	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
568	C₂×C₃	—	4	1	no	—
569	C₂×C₃	—	4	1	no	—
570	C₂×C₃	—	4	1	no	—
571	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
572	C₂×C₃	#585	1	1	yes	characteristic
573	C₂×C₃	#585	1	1	yes	characteristic
574	D₃	—	4	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	6	2	no	—
585	C₂²	—	6	2	no	—
586	C₂²	—	6	2	no	—
587	C₂²	C₂⁴×D₃	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	6	2	no	—
600	C₄	—	6	2	no	—
601	C₄	—	6	2	no	—
602	C₄	—	6	2	no	—
603	C₄	—	6	2	no	—
604	C₄	—	6	2	no	—
605	C₄	—	6	2	no	—
606	C₄	#1010	1	2	yes	—
607	C₃	#3565	1	1	yes	characteristic, complemented, Sylow
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	12	2	no	—
612	C₂	C₂×#1010	1	1	yes	characteristic
613	C₂	#5964	1	1	yes	characteristic
614	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3565
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5708	C₂	semidirect
3. #5702	C₂	semidirect
4. #5696	C₂	semidirect
5. #5669	C₂	semidirect
6. #5662	C₂	semidirect
7. #5660	C₂	semidirect
8. #5646	C₂	semidirect
9. #5621	C₂	semidirect
10. #5579	C₂	semidirect
11. #5567	C₂	semidirect
12. #5565	C₂	semidirect
13. #5565	C₂	semidirect
14. #5563	C₂	semidirect
15. #5542	C₂	semidirect
16. #5541	C₂	semidirect
17. #5541	C₂	semidirect
18. #5534	C₂	semidirect
19. #5534	C₂	semidirect
20. #5519	C₂	semidirect
21. #5519	C₂	semidirect
22. #5479	C₂	semidirect
23. #5470	C₂	semidirect
146. #529	D₃	semidirect
607. C₃	#3565	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5708	2
#5702	2
#5696	2
#5669	2
#5662	2
#5660	2
#5646	2
#5621	2
#5579	2
#5567	2
#5565	2
#5563	2
#5542	2
#5541	2
#5534	2
#5519	2
#5479	2
#5470	2
#3565	3