Subgroups — #86485

Order 384.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 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	#5691	C₂	1	1	yes	maximal, characteristic, complemented
5	#5689	C₂	1	1	yes	maximal, characteristic, complemented
6	#5661	C₂	1	2	yes	maximal, complemented
7	#5659	C₂	1	2	yes	maximal, complemented
8	#5658	C₂	1	2	yes	maximal, complemented
9	#5655	C₂	1	2	yes	maximal, complemented
10	#5619	C₂	1	1	yes	maximal, characteristic, complemented
11	#5616	C₂	1	2	yes	maximal, complemented
12	#5612	C₂	1	2	yes	maximal, complemented
13	#5610	C₂	1	2	yes	maximal, complemented
14	#5606	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	#5603	C₂	1	1	yes	maximal, characteristic, complemented
17	#5601	C₂	1	2	yes	maximal, complemented
18	#5557	C₂	1	1	yes	maximal, characteristic, complemented
19	#5548	C₂	1	1	yes	maximal, characteristic, complemented
20	#5546	C₂	1	1	yes	maximal, characteristic, complemented
21	#5545	C₂	1	1	yes	maximal, characteristic, complemented
22	#5534	C₂	1	1	yes	maximal, characteristic, complemented
23	D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	#3494	—	3	1	no	maximal, Sylow
25	C₂×#237	C₂²	1	1	yes	characteristic
26	C₂×#237	C₂²	1	2	yes	complemented
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×D₃×D₄	C₂²	1	2	yes	—
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
31	C₃×#127	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
37	C₃×#121	C₂²	1	1	yes	characteristic, complemented
38	C₃×#121	C₂²	1	2	yes	complemented
39	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
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, complemented
43	#939	C₂²	1	2	yes	—
44	#939	C₂²	1	2	yes	complemented
45	#939	C₂²	1	2	yes	complemented
46	#939	C₂²	1	2	yes	complemented
47	#938	C₂²	1	1	yes	characteristic
48	#938	C₂²	1	2	yes	complemented
49	#938	C₂²	1	1	yes	characteristic, complemented
50	#938	C₂²	1	2	yes	complemented
51	#937	C₂²	1	2	yes	—
52	#937	C₂²	1	2	yes	—
53	#937	C₂²	1	2	yes	—
54	#936	C₂²	1	2	yes	complemented
55	#936	C₂²	1	1	yes	characteristic, complemented
56	#936	C₂²	1	2	yes	complemented
57	#935	C₂²	1	2	yes	complemented
58	D₄×Dic₃	C₂²	1	2	yes	complemented
59	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
61	D₄×Dic₃	C₂²	1	2	yes	complemented
62	#930	C₂²	1	1	yes	characteristic
63	C₄×#67	C₂²	1	2	yes	—
64	C₄×#67	C₂²	1	2	yes	complemented
65	C₄×#67	C₂²	1	2	yes	complemented
66	C₄×#67	C₂²	1	2	yes	complemented
67	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
68	#926	C₂²	1	2	yes	complemented
69	#926	C₂²	1	1	yes	characteristic, complemented
70	#924	C₂²	1	1	yes	characteristic, complemented
71	C₂×Dic₃⋊C₄	C₂²	1	2	yes	complemented
72	#898	C₂²	1	2	yes	complemented
73	#898	C₂²	1	2	yes	complemented
74	#897	C₂²	1	2	yes	—
75	#897	C₂²	1	1	yes	characteristic, complemented
76	#896	C₂²	1	2	yes	—
77	#896	C₂²	1	2	yes	complemented
78	#895	C₂²	1	1	yes	characteristic
79	#894	C₂²	1	2	yes	complemented
80	#893	C₂²	1	2	yes	complemented
81	#893	C₂²	1	1	yes	characteristic, complemented
82	#892	C₂²	1	1	yes	characteristic
83	#892	C₂²	1	1	yes	characteristic
84	#892	C₂²	1	1	yes	characteristic
85	#892	C₂²	1	2	yes	complemented
86	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
87	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	#890	C₂²	1	1	yes	characteristic, complemented
90	#889	C₂²	1	2	yes	complemented
91	#888	C₂²	1	2	yes	complemented
92	#888	C₂²	1	1	yes	characteristic, complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	2	yes	complemented
95	#885	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#884	C₂²	1	2	yes	—
98	#884	C₂²	1	2	yes	complemented
99	#883	C₂²	1	2	yes	—
100	#883	C₂²	1	2	yes	complemented
101	#883	C₂²	1	2	yes	complemented
102	#883	C₂²	1	2	yes	complemented
103	#67⋊C₄	C₂²	1	2	yes	—
104	#67⋊C₄	C₂²	1	2	yes	complemented
105	#67⋊C₄	C₂²	1	2	yes	complemented
106	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
108	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	#879	C₂²	1	2	yes	complemented
111	#879	C₂²	1	2	yes	complemented
112	#878	C₂²	1	2	yes	complemented
113	#877	C₂²	1	2	yes	complemented
114	#877	C₂²	1	1	yes	characteristic, complemented
115	#877	C₂²	1	1	yes	characteristic, complemented
116	#875	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
118	#872	C₂²	1	1	yes	characteristic
119	#872	C₂²	1	1	yes	characteristic
120	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
122	#869	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#555	—	3	2	no	—
125	#553	—	3	2	no	—
126	#553	—	3	2	no	—
127	#551	—	3	2	no	—
128	#551	—	3	2	no	—
129	#547	—	3	2	no	—
130	#546	—	3	2	no	—
131	#546	—	3	2	no	—
132	#544	—	3	1	no	—
133	#542	—	3	1	no	—
134	#542	—	3	1	no	—
135	#540	—	3	1	no	—
136	#540	D₃	1	1	yes	characteristic, complemented
137	#535	—	3	1	no	—
138	#532	—	3	1	no	—
139	#532	—	3	1	no	—
140	#529	—	3	1	no	—
141	#529	—	3	1	no	—
142	#525	—	3	1	no	—
143	C₂×#121	—	3	1	no	—
144	#520	—	3	1	no	—
145	#518	—	3	1	no	—
146	C₂×#117	—	3	1	no	—
147	C₂³×D₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
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	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂×#67	C₂³	1	2	yes	—
159	C₂×#67	C₂³	1	2	yes	—
160	C₂×#67	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	2	yes	—
162	C₂×#67	C₂³	1	2	yes	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	2	yes	—
165	C₂²×Dic₃	C₂³	1	1	yes	characteristic
166	C₂²×Dic₃	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	2	yes	—
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	#237	—	2	4	no	—
170	#237	—	4	4	no	—
171	D₃×D₄	—	2	4	no	—
172	D₃×D₄	—	4	4	no	—
173	#235	—	4	4	no	—
174	C₂×D₁₂	C₂³	1	1	yes	characteristic
175	C₂×D₁₂	C₂³	1	2	yes	—
176	C₂×C₄×D₃	—	2	4	no	—
177	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	2	yes	—
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×Dic₆	C₂³	1	1	yes	characteristic
189	C₂×Dic₆	C₂³	1	2	yes	—
190	C₂×Dic₆	C₂³	1	2	yes	—
191	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄²	C₂³	1	1	yes	characteristic
204	C₃×C₄²	C₂³	1	1	yes	characteristic
205	#217	C₂³	1	1	yes	characteristic
206	#217	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	2	yes	—
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	2	yes	—
211	#217	C₂³	1	2	yes	—
212	#217	C₂³	1	2	yes	—
213	#217	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₄⋊Dic₃	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	2	yes	—
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	2	yes	—
242	Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×Dic₃	C₂³	1	2	yes	—
244	C₄×Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₂×#41	—	3	1	no	—
253	C₂×#41	—	3	2	no	—
254	C₂×#41	—	3	2	no	—
255	C₂²×D₄	—	3	1	no	—
256	C₂²×D₄	—	3	2	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	2	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	#127	—	3	1	no	—
262	#127	C₂×D₃	1	1	yes	characteristic, complemented
263	#126	—	3	2	no	—
264	#126	—	3	2	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#125	—	3	1	no	—
268	#125	—	3	2	no	—
269	#125	C₂×D₃	1	1	yes	characteristic, complemented
270	#124	—	3	1	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	3	2	no	—
274	#124	—	3	2	no	—
275	#124	—	3	1	no	—
276	#123	—	3	2	no	—
277	#123	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	C₂×D₃	1	2	yes	complemented
284	#123	C₂×D₃	1	2	yes	complemented
285	C₂²⋊Q₈	—	3	1	no	—
286	C₂²⋊Q₈	—	3	1	no	—
287	C₂²⋊Q₈	—	3	2	no	—
288	C₂²⋊Q₈	—	3	2	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	#121	—	3	1	no	—
292	#121	—	3	2	no	—
293	#121	—	3	1	no	—
294	#121	—	3	2	no	—
295	#121	—	3	2	no	—
296	#121	—	3	2	no	—
297	#121	—	3	2	no	—
298	#121	—	3	2	no	—
299	#121	—	3	1	no	—
300	#121	—	3	1	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	C₂×D₃	1	1	yes	characteristic
304	#121	C₂×D₃	1	1	yes	characteristic, complemented
305	#121	C₂×D₃	1	2	yes	complemented
306	#121	C₂×D₃	1	2	yes	complemented
307	#120	—	3	2	no	—
308	#120	—	3	2	no	—
309	#120	—	3	2	no	—
310	C₄×Q₈	—	3	1	no	—
311	C₄×Q₈	—	3	1	no	—
312	C₄×D₄	—	3	1	no	—
313	C₄×D₄	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	2	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
327	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
328	#117	—	3	1	no	—
329	#117	—	3	2	no	—
330	#117	—	3	1	no	—
331	#117	—	3	1	no	—
332	#117	—	3	1	no	—
333	#117	—	3	2	no	—
334	#117	—	3	1	no	—
335	#117	—	3	1	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	1	no	—
339	#117	C₂×D₃	1	1	yes	characteristic, complemented
340	C₂×C₄⋊C₄	—	3	2	no	—
341	C₂×C₄⋊C₄	—	3	1	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₂²⋊C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	3	1	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₄²	—	3	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	C₂⁴	1	1	yes	characteristic
352	C₂³×C₃	C₂⁴	1	2	yes	—
353	C₂³×C₃	C₂⁴	1	2	yes	—
354	C₂²×D₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	2	4	no	—
357	C₂²×D₃	—	4	1	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	C₂⁴	1	2	yes	—
361	C₂²×D₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	4	2	no	—
367	C₃×D₄	—	4	2	no	—
368	C₃×D₄	—	4	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	4	2	no	—
371	C₂×C₃×C₄	—	4	2	no	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	#67	—	2	4	no	—
381	#67	—	2	4	no	—
382	#67	—	2	4	no	—
383	#67	—	2	4	no	—
384	#67	—	4	2	no	—
385	#67	—	4	2	no	—
386	#67	—	4	2	no	—
387	C₂×Dic₃	—	2	2	no	—
388	C₂×Dic₃	—	2	4	no	—
389	C₂×Dic₃	—	4	2	no	—
390	C₂×Dic₃	—	4	2	no	—
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	2	yes	—
395	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃	C₂⁴	1	2	yes	—
398	C₂×Dic₃	C₂⁴	1	2	yes	—
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	D₁₂	—	2	4	no	—
401	D₁₂	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	2	2	no	—
407	C₄×D₃	—	4	2	no	—
408	C₄×D₃	—	4	1	no	—
409	C₄×D₃	—	4	1	no	—
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	#41	1	4	yes	complemented
413	Dic₆	—	2	2	no	—
414	Dic₆	—	4	2	no	—
415	Dic₆	—	4	2	no	—
416	C₂⁴	—	3	1	no	—
417	C₂⁴	—	3	2	no	—
418	#41	—	6	4	no	—
419	#41	—	12	4	no	—
420	#41	—	12	4	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×Q₈	—	3	2	no	—
423	C₂×Q₈	—	3	2	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	2	no	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	6	4	no	—
434	C₂×D₄	—	12	4	no	—
435	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
436	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
437	C₂×D₄	C₂²×D₃	1	2	yes	—
438	C₂×D₄	C₂²×D₃	1	2	yes	—
439	C₂×D₄	C₂²×D₃	1	2	yes	—
440	C₂×D₄	C₂²×D₃	1	2	yes	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	1	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	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	2	no	—
454	C₂²×C₄	—	3	2	no	—
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	6	4	no	—
457	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₃	1	2	yes	—
459	C₂²×C₄	C₂²×D₃	1	2	yes	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₃	1	2	yes	—
483	C₂²⋊C₄	—	3	1	no	—
484	C₂²⋊C₄	—	3	1	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	2	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	2	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	1	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	2	no	—
499	C₂²⋊C₄	—	3	2	no	—
500	C₂²⋊C₄	—	3	2	no	—
501	C₂²⋊C₄	—	3	2	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
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	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
510	C₄²	—	3	1	no	—
511	C₄²	—	3	1	no	—
512	C₄²	—	3	1	no	—
513	C₄²	—	3	1	no	—
514	C₄²	—	3	1	no	—
515	C₄²	—	3	1	no	—
516	C₄²	—	3	2	no	—
517	C₄²	—	3	2	no	—
518	C₄²	—	3	2	no	—
519	C₄²	C₂²×D₃	1	1	yes	characteristic
520	C₄²	C₂²×D₃	1	1	yes	characteristic
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	1	no	—
530	C₂²×C₃	C₂⁵	1	1	yes	characteristic
531	C₂×D₃	—	2	1	no	—
532	C₂×D₃	—	2	1	no	—
533	C₂×D₃	—	2	1	no	—
534	C₂×D₃	—	2	1	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	2	2	no	—
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	4	4	no	—
539	C₂×D₃	—	8	4	no	—
540	C₂×D₃	C₂×#41	1	2	yes	—
541	C₂×D₃	H(5,𝔽₂)	1	2	yes	—
542	C₃×C₄	—	2	1	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	C₂×#41	1	2	yes	—
550	Dic₃	—	2	2	no	—
551	Dic₃	—	2	1	no	—
552	Dic₃	—	2	1	no	—
553	Dic₃	—	2	2	no	—
554	Dic₃	—	2	2	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	1	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	C₂×#41	1	2	yes	—
559	C₂³	—	3	1	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	3	2	no	—
562	C₂³	—	6	2	no	—
563	C₂³	—	6	2	no	—
564	C₂³	—	6	4	no	—
565	C₂³	—	12	1	no	—
566	C₂³	—	12	2	no	—
567	C₂³	—	12	2	no	—
568	C₂³	C₂³×D₃	1	1	yes	characteristic
569	C₂³	C₂³×D₃	1	2	yes	—
570	C₂³	C₂³×D₃	1	2	yes	—
571	Q₈	—	6	2	no	—
572	Q₈	—	12	2	no	—
573	Q₈	—	12	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	6	4	no	—
581	D₄	—	6	4	no	—
582	D₄	—	6	4	no	—
583	D₄	—	6	4	no	—
584	D₄	—	6	4	no	—
585	D₄	—	6	2	no	—
586	D₄	—	12	2	no	—
587	D₄	—	12	2	no	—
588	D₄	—	12	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	3	1	no	—
591	C₂×C₄	—	3	4	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	1	no	—
598	C₂×C₄	—	3	2	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	2	no	—
604	C₂×C₄	—	6	2	no	—
605	C₂×C₄	—	6	2	no	—
606	C₂×C₄	—	6	2	no	—
607	C₂×C₄	—	6	4	no	—
608	C₂×C₄	—	6	2	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	—	12	1	no	—
612	C₂×C₄	—	12	2	no	—
613	C₂×C₄	—	12	1	no	—
614	C₂×C₄	—	12	2	no	—
615	C₂×C₄	—	12	2	no	—
616	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₃	1	2	yes	—
621	C₂×C₄	C₂³×D₃	1	2	yes	—
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
624	C₂×C₃	—	4	1	no	—
625	C₂×C₃	—	4	2	no	—
626	C₂×C₃	—	4	2	no	—
627	C₂×C₃	C₂²×#41	1	1	yes	characteristic
628	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂×C₃	#585	1	1	yes	characteristic
630	D₃	—	2	2	no	—
631	D₃	—	2	2	no	—
632	D₃	—	4	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	3	2	no	—
643	C₂²	—	3	2	no	—
644	C₂²	—	6	1	no	—
645	C₂²	—	6	1	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	1	no	—
648	C₂²	—	6	2	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	6	2	no	—
651	C₂²	—	12	4	no	—
652	C₂²	—	24	4	no	—
653	C₂²	C₂⁴×D₃	1	1	yes	characteristic
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	3	2	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	2	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	—	6	2	no	—
667	C₄	—	6	2	no	—
668	C₄	—	6	1	no	—
669	C₄	—	6	1	no	—
670	C₄	D₃×#41	1	2	yes	—
671	C₃	#3494	1	1	yes	characteristic, complemented, Sylow
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	6	2	no	—
676	C₂	—	6	2	no	—
677	C₂	—	12	2	no	—
678	C₂	C₂×D₃×#41	1	1	yes	characteristic
679	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic
680	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	#3494
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. #5691	C₂	semidirect
5. #5689	C₂	semidirect
6. #5661	C₂	semidirect
7. #5659	C₂	semidirect
8. #5658	C₂	semidirect
9. #5655	C₂	semidirect
10. #5619	C₂	semidirect
11. #5616	C₂	semidirect
12. #5612	C₂	semidirect
13. #5610	C₂	semidirect
14. #5606	C₂	semidirect
15. D₃×#121	C₂	semidirect
16. #5603	C₂	semidirect
17. #5601	C₂	semidirect
18. #5557	C₂	semidirect
19. #5548	C₂	semidirect
20. #5546	C₂	semidirect
21. #5545	C₂	semidirect
22. #5534	C₂	semidirect
23. D₃×#117	C₂	semidirect
26. C₂×#237	C₂²	semidirect
29. C₂×#235	C₂²	semidirect
31. C₃×#127	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
39. C₃×C₄×D₄	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×#117	C₂²	semidirect
42. #940	C₂²	semidirect
44. #939	C₂²	semidirect
45. #939	C₂²	semidirect
46. #939	C₂²	semidirect
48. #938	C₂²	semidirect
49. #938	C₂²	semidirect
50. #938	C₂²	semidirect
54. #936	C₂²	semidirect
55. #936	C₂²	semidirect
56. #936	C₂²	semidirect
57. #935	C₂²	semidirect
58. D₄×Dic₃	C₂²	semidirect
59. D₄×Dic₃	C₂²	semidirect
60. D₄×Dic₃	C₂²	semidirect
61. D₄×Dic₃	C₂²	semidirect
64. C₄×#67	C₂²	semidirect
65. C₄×#67	C₂²	semidirect
66. C₄×#67	C₂²	semidirect
68. #926	C₂²	semidirect
69. #926	C₂²	semidirect
70. #924	C₂²	semidirect
71. C₂×Dic₃⋊C₄	C₂²	semidirect
72. #898	C₂²	semidirect
73. #898	C₂²	semidirect
75. #897	C₂²	semidirect
77. #896	C₂²	semidirect
79. #894	C₂²	semidirect
80. #893	C₂²	semidirect
81. #893	C₂²	semidirect
85. #892	C₂²	semidirect
87. D₃×C₄⋊C₄	C₂²	semidirect
88. D₃×C₄⋊C₄	C₂²	semidirect
89. #890	C₂²	semidirect
90. #889	C₂²	semidirect
91. #888	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
94. #886	C₂²	semidirect
95. #885	C₂²	semidirect
96. #885	C₂²	semidirect
98. #884	C₂²	semidirect
100. #883	C₂²	semidirect
101. #883	C₂²	semidirect
102. #883	C₂²	semidirect
104. #67⋊C₄	C₂²	semidirect
105. #67⋊C₄	C₂²	semidirect
110. #879	C₂²	semidirect
111. #879	C₂²	semidirect
112. #878	C₂²	semidirect
113. #877	C₂²	semidirect
114. #877	C₂²	semidirect
115. #877	C₂²	semidirect
116. #875	C₂²	semidirect
117. C₄×D₁₂	C₂²	semidirect
120. C₄²×D₃	C₂²	semidirect
121. C₄²×D₃	C₂²	semidirect
122. #869	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
136. #540	D₃	semidirect
262. #127	C₂×D₃	semidirect
269. #125	C₂×D₃	semidirect
283. #123	C₂×D₃	semidirect
284. #123	C₂×D₃	semidirect
304. #121	C₂×D₃	semidirect
305. #121	C₂×D₃	semidirect
306. #121	C₂×D₃	semidirect
326. C₄×D₄	C₂×D₃	semidirect
327. C₄×D₄	C₂×D₃	semidirect
339. #117	C₂×D₃	semidirect
412. C₄×D₃	#41	semidirect
671. C₃	#3494	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
#5691	2
#5689	2
#5661	2
#5659	2
#5658	2
#5655	2
#5619	2
#5616	2
#5612	2
#5610	2
#5606	2
D₃×#121	2
#5603	2
#5601	2
#5557	2
#5548	2
#5546	2
#5545	2
#5534	2
D₃×#117	2
#3494	3