Subgroups — #86480

Order 384.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	#5716	C₂	1	1	yes	maximal, characteristic, complemented
3	#5715	C₂	1	1	yes	maximal, characteristic, complemented
4	#5698	C₂	1	1	yes	maximal, characteristic, complemented
5	#5691	C₂	1	1	yes	maximal, characteristic, complemented
6	#5667	C₂	1	2	yes	maximal, complemented
7	#5665	C₂	1	2	yes	maximal, complemented
8	#5658	C₂	1	2	yes	maximal, complemented
9	#5657	C₂	1	2	yes	maximal, complemented
10	#5620	C₂	1	2	yes	maximal, complemented
11	#5619	C₂	1	2	yes	maximal, complemented
12	#5618	C₂	1	2	yes	maximal, complemented
13	#5617	C₂	1	2	yes	maximal, complemented
14	#5612	C₂	1	1	yes	maximal, characteristic, complemented
15	#5599	C₂	1	1	yes	maximal, characteristic, complemented
16	#5598	C₂	1	1	yes	maximal, characteristic, complemented
17	#5598	C₂	1	1	yes	maximal, characteristic, complemented
18	#5559	C₂	1	1	yes	maximal, characteristic, complemented
19	#5555	C₂	1	1	yes	maximal, characteristic, complemented
20	#5554	C₂	1	1	yes	maximal, characteristic, complemented
21	#5542	C₂	1	1	yes	maximal, characteristic, complemented
22	#5528	C₂	1	1	yes	maximal, characteristic, complemented
23	#5526	C₂	1	1	yes	maximal, characteristic, complemented
24	#3562	—	3	1	no	maximal, Sylow
25	C₂×#237	C₂²	1	1	yes	characteristic
26	C₂×#237	C₂²	1	1	yes	characteristic
27	C₂×#237	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×#235	C₂²	1	1	yes	characteristic
30	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#127	C₂²	1	1	yes	characteristic
32	C₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₃×#123	C₂²	1	2	yes	complemented
34	C₃×#123	C₂²	1	2	yes	complemented
35	C₃×#121	C₂²	1	1	yes	characteristic
36	C₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₃×#121	C₂²	1	2	yes	complemented
38	C₃×#121	C₂²	1	2	yes	complemented
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#117	C₂²	1	1	yes	characteristic, complemented
42	#940	C₂²	1	1	yes	characteristic
43	#940	C₂²	1	2	yes	complemented
44	#939	C₂²	1	2	yes	—
45	#939	C₂²	1	2	yes	—
46	#939	C₂²	1	2	yes	—
47	#939	C₂²	1	2	yes	complemented
48	#939	C₂²	1	2	yes	complemented
49	#938	C₂²	1	2	yes	—
50	#938	C₂²	1	2	yes	complemented
51	#938	C₂²	1	2	yes	complemented
52	#937	C₂²	1	2	yes	—
53	#937	C₂²	1	2	yes	—
54	#937	C₂²	1	2	yes	—
55	#936	C₂²	1	1	yes	characteristic
56	#936	C₂²	1	1	yes	characteristic
57	#936	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₃	C₂²	1	2	yes	complemented
59	D₄×Dic₃	C₂²	1	2	yes	complemented
60	D₄×Dic₃	C₂²	1	2	yes	complemented
61	D₄×Dic₃	C₂²	1	2	yes	complemented
62	#930	C₂²	1	2	yes	—
63	#930	C₂²	1	2	yes	—
64	#929	C₂²	1	2	yes	complemented
65	C₄×#67	C₂²	1	1	yes	characteristic
66	C₄×#67	C₂²	1	2	yes	complemented
67	C₄×#67	C₂²	1	1	yes	characteristic, complemented
68	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
69	#926	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₃	C₂²	1	2	yes	complemented
71	#924	C₂²	1	2	yes	complemented
72	#898	C₂²	1	2	yes	—
73	#898	C₂²	1	1	yes	characteristic
74	#898	C₂²	1	2	yes	—
75	#898	C₂²	1	2	yes	complemented
76	#897	C₂²	1	1	yes	characteristic
77	#897	C₂²	1	1	yes	characteristic
78	#897	C₂²	1	2	yes	complemented
79	#897	C₂²	1	2	yes	complemented
80	#897	C₂²	1	1	yes	characteristic, complemented
81	#896	C₂²	1	1	yes	characteristic, complemented
82	#895	C₂²	1	1	yes	characteristic
83	#894	C₂²	1	1	yes	characteristic
84	#894	C₂²	1	2	yes	complemented
85	#893	C₂²	1	1	yes	characteristic
86	#893	C₂²	1	2	yes	complemented
87	#892	C₂²	1	2	yes	complemented
88	#890	C₂²	1	2	yes	complemented
89	#890	C₂²	1	2	yes	complemented
90	#889	C₂²	1	1	yes	characteristic, complemented
91	#887	C₂²	1	1	yes	characteristic, complemented
92	#887	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	—
95	#886	C₂²	1	2	yes	—
96	#886	C₂²	1	2	yes	complemented
97	#886	C₂²	1	2	yes	complemented
98	#886	C₂²	1	2	yes	complemented
99	#885	C₂²	1	2	yes	—
100	#885	C₂²	1	1	yes	characteristic
101	#885	C₂²	1	2	yes	complemented
102	#885	C₂²	1	2	yes	complemented
103	#884	C₂²	1	1	yes	characteristic
104	#884	C₂²	1	2	yes	complemented
105	#883	C₂²	1	2	yes	—
106	#883	C₂²	1	2	yes	complemented
107	#883	C₂²	1	1	yes	characteristic, complemented
108	#882	C₂²	1	2	yes	—
109	#67⋊C₄	C₂²	1	2	yes	complemented
110	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	#879	C₂²	1	2	yes	complemented
112	#879	C₂²	1	2	yes	complemented
113	#879	C₂²	1	1	yes	characteristic, complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#875	C₂²	1	1	yes	characteristic
117	#875	C₂²	1	1	yes	characteristic
118	C₄×D₁₂	C₂²	1	1	yes	characteristic
119	#872	C₂²	1	1	yes	characteristic
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	#869	C₂²	1	1	yes	characteristic, complemented
122	#869	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#562	—	3	2	no	—
125	#560	—	3	2	no	—
126	#559	—	3	1	no	—
127	#556	—	3	1	no	—
128	#553	—	3	2	no	—
129	#551	—	3	2	no	—
130	#550	—	3	1	no	—
131	#548	—	3	1	no	—
132	#548	—	3	1	no	—
133	#547	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	—	3	1	no	—
136	#541	—	3	1	no	—
137	#540	—	3	2	no	—
138	#540	D₃	1	1	yes	characteristic, complemented
139	#539	—	3	2	no	—
140	#538	—	3	2	no	—
141	#538	—	3	2	no	—
142	#536	—	3	1	no	—
143	#535	—	3	1	no	—
144	#532	—	3	1	no	—
145	#529	—	3	1	no	—
146	#529	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	2	yes	—
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂×C₃×D₄	C₂³	1	2	yes	—
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	2	yes	—
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂×#67	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	1	yes	characteristic
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	2	yes	—
166	C₂²×Dic₃	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	2	yes	—
170	#237	—	4	2	no	—
171	#237	—	4	2	no	—
172	#237	—	4	2	no	—
173	D₃×D₄	—	4	2	no	—
174	#235	—	4	2	no	—
175	C₂×D₁₂	C₂³	1	1	yes	characteristic
176	C₂×D₁₂	C₂³	1	1	yes	characteristic
177	C₂×D₁₂	C₂³	1	2	yes	—
178	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₄×D₃	C₂³	1	2	yes	—
184	C₂×Dic₆	—	4	2	no	—
185	C₂×Dic₆	C₂³	1	1	yes	characteristic
186	C₂×Dic₆	C₂³	1	1	yes	characteristic
187	C₂×Dic₆	C₂³	1	1	yes	characteristic
188	C₂×Dic₆	C₂³	1	1	yes	characteristic
189	C₂×Dic₆	C₂³	1	2	yes	—
190	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₄²	C₂³	1	1	yes	characteristic
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	2	yes	—
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	1	yes	characteristic
209	#217	C₂³	1	1	yes	characteristic
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
221	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₄⋊Dic₃	C₂³	1	2	yes	—
235	C₄⋊Dic₃	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	2	yes	—
245	C₄×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	1	no	—
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂²×D₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	#127	—	3	1	no	—
261	#127	—	3	2	no	—
262	#127	C₂×D₃	1	1	yes	characteristic
263	#126	—	3	2	no	—
264	#126	—	3	1	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	1	no	—
268	#126	—	3	2	no	—
269	#126	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	—	3	2	no	—
272	#125	—	3	2	no	—
273	#125	C₂×D₃	1	1	yes	characteristic, complemented
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	1	no	—
277	#124	—	3	1	no	—
278	#124	—	3	2	no	—
279	#124	—	3	2	no	—
280	#124	—	3	2	no	—
281	#124	—	3	1	no	—
282	#124	—	3	1	no	—
283	#123	—	3	2	no	—
284	#123	—	3	1	no	—
285	#123	—	3	2	no	—
286	#123	—	3	1	no	—
287	#123	—	3	2	no	—
288	#123	—	3	2	no	—
289	#123	—	3	2	no	—
290	#123	—	3	2	no	—
291	#123	—	3	2	no	—
292	#123	—	3	2	no	—
293	#123	—	3	2	no	—
294	#123	C₂×D₃	1	2	yes	complemented
295	#123	C₂×D₃	1	2	yes	complemented
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	1	no	—
298	C₂²⋊Q₈	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	—	3	2	no	—
301	C₂²⋊Q₈	—	3	1	no	—
302	C₂²⋊Q₈	—	3	1	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	2	no	—
307	#121	—	3	2	no	—
308	#121	—	3	2	no	—
309	#121	—	3	2	no	—
310	#121	—	3	2	no	—
311	#121	—	3	2	no	—
312	#121	—	3	2	no	—
313	#121	—	3	2	no	—
314	#121	—	3	2	no	—
315	#121	—	3	1	no	—
316	#121	—	3	1	no	—
317	#121	—	3	2	no	—
318	#121	C₂×D₃	1	1	yes	characteristic
319	#121	C₂×D₃	1	2	yes	complemented
320	#121	C₂×D₃	1	1	yes	characteristic, complemented
321	#121	C₂×D₃	1	2	yes	complemented
322	#120	—	3	2	no	—
323	#120	—	3	2	no	—
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	C₄×Q₈	—	3	1	no	—
327	C₄×Q₈	—	3	1	no	—
328	C₄×Q₈	—	3	1	no	—
329	C₄×Q₈	—	3	1	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	2	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	1	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	—	3	1	no	—
341	C₄×D₄	C₂×D₃	1	1	yes	characteristic
342	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
343	#117	—	3	2	no	—
344	#117	—	3	2	no	—
345	#117	—	3	1	no	—
346	#117	C₂×D₃	1	1	yes	characteristic, complemented
347	C₂×C₄⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	2	yes	—
352	C₂³×C₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂²×D₃	—	4	2	no	—
355	C₂²×D₃	—	4	2	no	—
356	C₂²×D₃	—	4	2	no	—
357	C₂²×D₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	2	yes	—
359	C₂²×D₃	C₂⁴	1	1	yes	characteristic
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	4	2	no	—
363	C₃×D₄	—	4	2	no	—
364	C₃×D₄	—	4	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	C₂⁴	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	#67	—	4	2	no	—
378	#67	—	4	2	no	—
379	#67	—	4	2	no	—
380	#67	—	4	2	no	—
381	#67	—	4	2	no	—
382	#67	—	4	1	no	—
383	#67	—	4	2	no	—
384	#67	—	4	1	no	—
385	#67	—	4	2	no	—
386	C₂×Dic₃	—	4	2	no	—
387	C₂×Dic₃	—	4	2	no	—
388	C₂×Dic₃	—	4	2	no	—
389	C₂×Dic₃	—	4	2	no	—
390	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	2	yes	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	D₁₂	—	2	2	no	—
400	D₁₂	—	4	1	no	—
401	D₁₂	—	4	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	4	1	no	—
405	C₄×D₃	—	4	2	no	—
406	C₄×D₃	—	4	1	no	—
407	C₄×D₃	—	4	2	no	—
408	Dic₆	—	2	2	no	—
409	Dic₆	—	2	2	no	—
410	Dic₆	—	2	2	no	—
411	Dic₆	—	4	2	no	—
412	Dic₆	—	4	1	no	—
413	C₂⁴	—	3	2	no	—
414	#41	—	12	2	no	—
415	#41	—	12	2	no	—
416	#41	—	12	2	no	—
417	#41	—	12	2	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×Q₈	—	3	1	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×Q₈	—	3	2	no	—
423	C₂×Q₈	—	12	2	no	—
424	C₂×D₄	—	3	1	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	2	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	1	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	2	no	—
436	C₂×D₄	—	12	2	no	—
437	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
438	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
439	C₂×D₄	C₂²×D₃	1	2	yes	—
440	C₂×D₄	C₂²×D₃	1	2	yes	—
441	C₂×D₄	C₂²×D₃	1	2	yes	—
442	C₂×D₄	C₂²×D₃	1	2	yes	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₃	1	2	yes	—
455	C₂²×C₄	C₂²×D₃	1	2	yes	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	2	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	1	no	—
474	C₄⋊C₄	C₂²×D₃	1	2	yes	—
475	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	1	no	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	1	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	2	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	1	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	1	no	—
503	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
505	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	2	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	2	no	—
515	C₄²	—	3	2	no	—
516	C₄²	C₂²×D₃	1	1	yes	characteristic
517	C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	2	2	no	—
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	C₂⁵	1	1	yes	characteristic
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	—	2	1	no	—
530	C₂×D₃	—	2	2	no	—
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	2	no	—
535	C₂×D₃	—	2	1	no	—
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	8	4	no	—
538	C₃×C₄	—	2	1	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	1	no	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
546	Dic₃	—	2	2	no	—
547	Dic₃	—	2	2	no	—
548	Dic₃	—	2	2	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	2	1	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	1	no	—
554	Dic₃	—	2	1	no	—
555	C₂³	—	3	1	no	—
556	C₂³	—	3	2	no	—
557	C₂³	—	3	1	no	—
558	C₂³	—	12	2	no	—
559	C₂³	—	12	2	no	—
560	C₂³	—	12	2	no	—
561	C₂³	C₂³×D₃	1	2	yes	—
562	C₂³	C₂³×D₃	1	1	yes	characteristic
563	C₂³	C₂³×D₃	1	2	yes	—
564	Q₈	—	6	2	no	—
565	Q₈	—	6	2	no	—
566	Q₈	—	6	2	no	—
567	Q₈	—	12	2	no	—
568	Q₈	—	12	1	no	—
569	D₄	—	2	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	6	2	no	—
576	D₄	—	12	1	no	—
577	D₄	—	12	2	no	—
578	D₄	—	12	2	no	—
579	D₄	—	12	2	no	—
580	D₄	—	12	2	no	—
581	D₄	—	12	2	no	—
582	D₄	—	12	2	no	—
583	D₄	—	12	1	no	—
584	D₄	—	12	2	no	—
585	D₄	—	12	1	no	—
586	D₄	—	12	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	3	1	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	2	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	2	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	6	2	no	—
600	C₂×C₄	—	6	2	no	—
601	C₂×C₄	—	12	2	no	—
602	C₂×C₄	—	12	2	no	—
603	C₂×C₄	—	12	1	no	—
604	C₂×C₄	—	12	1	no	—
605	C₂×C₄	—	12	2	no	—
606	C₂×C₄	—	12	2	no	—
607	C₂×C₄	—	12	2	no	—
608	C₂×C₄	—	12	2	no	—
609	C₂×C₄	C₂³×D₃	1	2	yes	—
610	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₃	1	2	yes	—
613	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
615	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₃	—	4	2	no	—
618	C₂×C₃	—	4	1	no	—
619	C₂×C₃	—	4	2	no	—
620	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂×C₃	#585	1	1	yes	characteristic
622	C₂×C₃	#585	1	1	yes	characteristic
623	D₃	—	4	1	no	—
624	D₃	—	4	2	no	—
625	D₃	—	4	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	6	1	no	—
636	C₂²	—	6	1	no	—
637	C₂²	—	6	2	no	—
638	C₂²	—	6	1	no	—
639	C₂²	—	6	1	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	2	no	—
642	C₂²	—	6	1	no	—
643	C₂²	—	6	1	no	—
644	C₂²	—	24	4	no	—
645	C₂²	C₂⁴×D₃	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	6	1	no	—
654	C₄	—	6	1	no	—
655	C₄	—	6	2	no	—
656	C₄	—	6	2	no	—
657	C₄	—	6	2	no	—
658	C₄	—	6	1	no	—
659	C₄	—	6	1	no	—
660	C₄	—	6	1	no	—
661	C₄	—	6	1	no	—
662	C₄	#1009	1	2	yes	—
663	C₃	#3562	1	1	yes	characteristic, complemented, Sylow
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	12	1	no	—
668	C₂	—	12	2	no	—
669	C₂	—	12	1	no	—
670	C₂	C₂×#1009	1	1	yes	characteristic
671	C₂	#5966	1	1	yes	characteristic
672	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#540	C₂
hypercenter	#540	D₃
hypocenter	C₃	#3562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. C₃×#540	C₂	semidirect
2. #5716	C₂	semidirect
3. #5715	C₂	semidirect
4. #5698	C₂	semidirect
5. #5691	C₂	semidirect
6. #5667	C₂	semidirect
7. #5665	C₂	semidirect
8. #5658	C₂	semidirect
9. #5657	C₂	semidirect
10. #5620	C₂	semidirect
11. #5619	C₂	semidirect
12. #5618	C₂	semidirect
13. #5617	C₂	semidirect
14. #5612	C₂	semidirect
15. #5599	C₂	semidirect
16. #5598	C₂	semidirect
17. #5598	C₂	semidirect
18. #5559	C₂	semidirect
19. #5555	C₂	semidirect
20. #5554	C₂	semidirect
21. #5542	C₂	semidirect
22. #5528	C₂	semidirect
23. #5526	C₂	semidirect
27. C₂×#237	C₂²	semidirect
30. C₂²×Dic₆	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
33. C₃×#123	C₂²	semidirect
34. C₃×#123	C₂²	semidirect
36. C₃×#121	C₂²	semidirect
37. C₃×#121	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
43. #940	C₂²	semidirect
47. #939	C₂²	semidirect
48. #939	C₂²	semidirect
50. #938	C₂²	semidirect
51. #938	C₂²	semidirect
57. #936	C₂²	semidirect
58. D₄×Dic₃	C₂²	semidirect
59. D₄×Dic₃	C₂²	semidirect
60. D₄×Dic₃	C₂²	semidirect
61. D₄×Dic₃	C₂²	semidirect
64. #929	C₂²	semidirect
66. C₄×#67	C₂²	semidirect
67. C₄×#67	C₂²	semidirect
69. #926	C₂²	semidirect
70. C₂×C₄⋊Dic₃	C₂²	semidirect
71. #924	C₂²	semidirect
75. #898	C₂²	semidirect
78. #897	C₂²	semidirect
79. #897	C₂²	semidirect
80. #897	C₂²	semidirect
81. #896	C₂²	semidirect
84. #894	C₂²	semidirect
86. #893	C₂²	semidirect
87. #892	C₂²	semidirect
88. #890	C₂²	semidirect
89. #890	C₂²	semidirect
90. #889	C₂²	semidirect
91. #887	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
96. #886	C₂²	semidirect
97. #886	C₂²	semidirect
98. #886	C₂²	semidirect
101. #885	C₂²	semidirect
102. #885	C₂²	semidirect
104. #884	C₂²	semidirect
106. #883	C₂²	semidirect
107. #883	C₂²	semidirect
109. #67⋊C₄	C₂²	semidirect
111. #879	C₂²	semidirect
112. #879	C₂²	semidirect
113. #879	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. #869	C₂²	semidirect
122. #869	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
138. #540	D₃	semidirect
273. #125	C₂×D₃	semidirect
294. #123	C₂×D₃	semidirect
295. #123	C₂×D₃	semidirect
319. #121	C₂×D₃	semidirect
320. #121	C₂×D₃	semidirect
321. #121	C₂×D₃	semidirect
342. C₄×D₄	C₂×D₃	semidirect
346. #117	C₂×D₃	semidirect
663. C₃	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₃×#540	2
#5716	2
#5715	2
#5698	2
#5691	2
#5667	2
#5665	2
#5658	2
#5657	2
#5620	2
#5619	2
#5618	2
#5617	2
#5612	2
#5599	2
#5598	2
#5559	2
#5555	2
#5554	2
#5542	2
#5528	2
#5526	2
#3562	3