Subgroups — #86658

Order 384.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#5831	C₂	1	1	yes	maximal, characteristic, complemented
3	#5825	C₂	1	1	yes	maximal, characteristic, complemented
4	#5806	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#936	C₂	1	1	yes	maximal, characteristic, complemented
6	#5675	C₂	1	1	yes	maximal, characteristic, complemented
7	#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	#5662	C₂	1	2	yes	maximal, complemented
9	#5651	C₂	1	2	yes	maximal, complemented
10	#5632	C₂	1	1	yes	maximal, characteristic, complemented
11	#5622	C₂	1	1	yes	maximal, characteristic, complemented
12	#5621	C₂	1	2	yes	maximal, complemented
13	#5603	C₂	1	1	yes	maximal, characteristic, complemented
14	#5603	C₂	1	2	yes	maximal, complemented
15	#5598	C₂	1	1	yes	maximal, characteristic, complemented
16	#5593	C₂	1	2	yes	maximal, complemented
17	#5587	C₂	1	2	yes	maximal, complemented
18	#5561	C₂	1	1	yes	maximal, characteristic, complemented
19	#5542	C₂	1	1	yes	maximal, characteristic, complemented
20	#5538	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#5495	C₂	1	2	yes	maximal, complemented
23	#5483	C₂	1	2	yes	maximal, complemented
24	#3561	—	3	1	no	maximal, Sylow
25	C₂×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×#237	C₂²	1	1	yes	characteristic
29	C₂²×Dic₆	C₂²	1	1	yes	characteristic
30	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×#124	C₂²	1	1	yes	characteristic
32	C₃×#123	C₂²	1	2	yes	—
33	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×#121	C₂²	1	1	yes	characteristic
35	C₃×#121	C₂²	1	2	yes	—
36	C₃×#120	C₂²	1	2	yes	—
37	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	#953	C₂²	1	2	yes	—
41	C₂×#217	C₂²	1	2	yes	—
42	C₂×#217	C₂²	1	2	yes	—
43	C₂×#217	C₂²	1	2	yes	—
44	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	#944	C₂²	1	1	yes	characteristic, complemented
46	#944	C₂²	1	1	yes	characteristic, complemented
47	#939	C₂²	1	2	yes	—
48	#939	C₂²	1	1	yes	characteristic
49	#939	C₂²	1	2	yes	complemented
50	#938	C₂²	1	1	yes	characteristic
51	#938	C₂²	1	2	yes	complemented
52	#936	C₂²	1	2	yes	—
53	#936	C₂²	1	2	yes	—
54	#936	C₂²	1	1	yes	characteristic
55	#936	C₂²	1	1	yes	characteristic
56	#936	C₂²	1	1	yes	characteristic
57	#936	C₂²	1	1	yes	characteristic
58	#936	C₂²	1	1	yes	characteristic
59	#936	C₂²	1	2	yes	complemented
60	#936	C₂²	1	2	yes	complemented
61	#935	C₂²	1	2	yes	—
62	#935	C₂²	1	1	yes	characteristic
63	#935	C₂²	1	2	yes	complemented
64	#935	C₂²	1	2	yes	complemented
65	#935	C₂²	1	2	yes	complemented
66	D₄×Dic₃	C₂²	1	1	yes	characteristic
67	D₄×Dic₃	C₂²	1	2	yes	—
68	D₄×Dic₃	C₂²	1	2	yes	complemented
69	#929	C₂²	1	2	yes	complemented
70	C₄×#67	C₂²	1	1	yes	characteristic
71	C₄×#67	C₂²	1	2	yes	complemented
72	C₄×#67	C₂²	1	1	yes	characteristic, complemented
73	#926	C₂²	1	2	yes	complemented
74	#926	C₂²	1	1	yes	characteristic, complemented
75	#924	C₂²	1	1	yes	characteristic
76	#924	C₂²	1	2	yes	complemented
77	#924	C₂²	1	2	yes	complemented
78	#924	C₂²	1	2	yes	complemented
79	#924	C₂²	1	2	yes	complemented
80	#924	C₂²	1	2	yes	complemented
81	#924	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
83	#898	C₂²	1	1	yes	characteristic, complemented
84	#897	C₂²	1	1	yes	characteristic, complemented
85	#896	C₂²	1	2	yes	complemented
86	#889	C₂²	1	1	yes	characteristic, complemented
87	#889	C₂²	1	2	yes	complemented
88	#888	C₂²	1	2	yes	complemented
89	#888	C₂²	1	2	yes	complemented
90	#888	C₂²	1	1	yes	characteristic, complemented
91	#887	C₂²	1	1	yes	characteristic, complemented
92	#887	C₂²	1	2	yes	complemented
93	#887	C₂²	1	1	yes	characteristic, complemented
94	#886	C₂²	1	1	yes	characteristic
95	#885	C₂²	1	2	yes	complemented
96	#885	C₂²	1	2	yes	complemented
97	#885	C₂²	1	1	yes	characteristic, complemented
98	#883	C₂²	1	2	yes	complemented
99	#883	C₂²	1	2	yes	complemented
100	#67⋊C₄	C₂²	1	2	yes	—
101	#879	C₂²	1	2	yes	complemented
102	#879	C₂²	1	2	yes	complemented
103	#879	C₂²	1	2	yes	complemented
104	#879	C₂²	1	2	yes	complemented
105	#879	C₂²	1	2	yes	complemented
106	#879	C₂²	1	2	yes	complemented
107	#879	C₂²	1	1	yes	characteristic, complemented
108	#878	C₂²	1	2	yes	—
109	#878	C₂²	1	1	yes	characteristic
110	#878	C₂²	1	2	yes	—
111	#878	C₂²	1	2	yes	—
112	#878	C₂²	1	2	yes	complemented
113	#878	C₂²	1	2	yes	complemented
114	#878	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#878	C₂²	1	2	yes	complemented
117	#878	C₂²	1	2	yes	complemented
118	#877	C₂²	1	2	yes	—
119	#877	C₂²	1	2	yes	complemented
120	#872	C₂²	1	1	yes	characteristic, complemented
121	#869	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#563	—	3	2	no	—
125	#562	—	3	2	no	—
126	#556	—	3	1	no	—
127	#556	—	3	1	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	D₄×Q₈	—	3	1	no	—
132	#548	—	3	1	no	—
133	#548	—	3	1	no	—
134	#546	—	3	1	no	—
135	#546	D₃	1	1	yes	characteristic, complemented
136	#543	—	3	2	no	—
137	#542	—	3	2	no	—
138	#542	—	3	1	no	—
139	#542	—	3	2	no	—
140	#542	—	3	1	no	—
141	#538	—	3	2	no	—
142	#536	—	3	1	no	—
143	#536	—	3	1	no	—
144	#533	—	3	1	no	—
145	#529	—	3	1	no	—
146	C₂×#124	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	2	yes	—
148	C₃×#41	—	4	2	no	—
149	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	—	4	2	no	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂³	1	2	yes	—
155	C₂×C₃×D₄	C₂³	1	2	yes	—
156	C₂×C₃×D₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	2	yes	—
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
165	C₂²×Dic₃	C₂³	1	1	yes	characteristic
166	C₂²×Dic₃	C₂³	1	2	yes	—
167	C₂²×Dic₃	C₂³	1	1	yes	characteristic
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	D₃×Q₈	—	4	2	no	—
172	#237	—	4	2	no	—
173	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₃	C₂³	1	2	yes	—
175	C₂×Dic₆	—	4	2	no	—
176	C₂×Dic₆	—	4	2	no	—
177	C₂×Dic₆	C₂³	1	1	yes	characteristic
178	C₂×Dic₆	C₂³	1	1	yes	characteristic
179	C₂×Dic₆	C₂³	1	1	yes	characteristic
180	C₂×Dic₆	C₂³	1	1	yes	characteristic
181	C₂×Dic₆	C₂³	1	2	yes	—
182	C₂×Dic₆	C₂³	1	2	yes	—
183	C₂×Dic₆	C₂³	1	2	yes	—
184	C₂×Dic₆	C₂³	1	2	yes	—
185	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄²	C₂³	1	1	yes	characteristic
196	#217	C₂³	1	2	yes	—
197	#217	C₂³	1	2	yes	—
198	#217	C₂³	1	1	yes	characteristic
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	#217	C₂³	1	2	yes	—
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	2	yes	—
209	#217	C₂³	1	2	yes	—
210	#217	C₂³	1	1	yes	characteristic
211	#217	C₂³	1	1	yes	characteristic
212	#217	C₂³	1	2	yes	—
213	#217	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	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₄⋊Dic₃	C₂³	1	2	yes	—
223	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
227	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	Dic₃⋊C₄	C₂³	1	2	yes	—
229	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	2	yes	—
250	C₄×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×#41	C₂×D₃	1	1	yes	characteristic
254	C₂²×Q₈	—	3	1	no	—
255	C₂²×Q₈	—	3	1	no	—
256	C₂²×Q₈	—	3	1	no	—
257	C₂²×D₄	C₂×D₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	3	1	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	—	3	1	no	—
261	C₄⋊Q₈	—	3	2	no	—
262	C₄⋊Q₈	—	3	2	no	—
263	C₄⋊Q₈	—	3	1	no	—
264	#126	—	3	1	no	—
265	#126	—	3	1	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	3	2	no	—
269	#126	—	3	2	no	—
270	#126	—	3	2	no	—
271	#126	—	3	2	no	—
272	#125	—	3	1	no	—
273	#125	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	1	no	—
276	#124	—	3	2	no	—
277	#124	—	3	1	no	—
278	#124	—	3	1	no	—
279	#124	—	3	2	no	—
280	#124	—	3	1	no	—
281	#124	—	3	2	no	—
282	#124	—	3	2	no	—
283	#124	—	3	1	no	—
284	#124	—	3	2	no	—
285	#124	—	3	2	no	—
286	#124	C₂×D₃	1	1	yes	characteristic
287	#123	—	3	1	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	1	no	—
294	#123	—	3	2	no	—
295	#123	—	3	2	no	—
296	#123	C₂×D₃	1	2	yes	—
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	1	no	—
302	C₂²⋊Q₈	—	3	2	no	—
303	C₂²⋊Q₈	—	3	2	no	—
304	C₂²⋊Q₈	—	3	1	no	—
305	C₂²⋊Q₈	—	3	2	no	—
306	C₂²⋊Q₈	—	3	1	no	—
307	C₂²⋊Q₈	—	3	2	no	—
308	C₂²⋊Q₈	—	3	2	no	—
309	C₂²⋊Q₈	—	3	2	no	—
310	C₂²⋊Q₈	—	3	2	no	—
311	C₂²⋊Q₈	—	3	2	no	—
312	C₂²⋊Q₈	—	3	2	no	—
313	C₂²⋊Q₈	—	3	2	no	—
314	C₂²⋊Q₈	—	3	2	no	—
315	C₂²⋊Q₈	—	3	2	no	—
316	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
317	#121	—	3	1	no	—
318	#121	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	1	no	—
321	#121	—	3	2	no	—
322	#121	C₂×D₃	1	1	yes	characteristic
323	#121	C₂×D₃	1	2	yes	—
324	#120	—	3	2	no	—
325	#120	C₂×D₃	1	2	yes	—
326	C₄×Q₈	—	3	1	no	—
327	C₄×Q₈	—	3	2	no	—
328	C₄×Q₈	—	3	1	no	—
329	C₄×Q₈	—	3	1	no	—
330	C₄×Q₈	—	3	1	no	—
331	C₄×Q₈	—	3	1	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	2	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	C₂×D₃	1	1	yes	characteristic
340	C₄×D₄	C₂×D₃	1	1	yes	characteristic
341	#117	—	3	1	no	—
342	#117	—	3	2	no	—
343	#117	—	3	2	no	—
344	#117	—	3	2	no	—
345	#117	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	3	2	no	—
347	C₂×C₂²⋊C₄	—	3	2	no	—
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	—
350	C₂×C₄²	—	3	1	no	—
351	C₂³×C₃	—	2	4	no	—
352	C₂³×C₃	—	4	2	no	—
353	C₂³×C₃	—	4	2	no	—
354	C₂³×C₃	C₂⁴	1	2	yes	—
355	C₂³×C₃	C₂⁴	1	2	yes	—
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃	C₂⁴	1	1	yes	characteristic
359	C₃×Q₈	—	2	2	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	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	—	2	2	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	—	4	2	no	—
370	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴	1	2	yes	—
372	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴	1	2	yes	—
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	—	2	2	no	—
378	#67	—	4	2	no	—
379	#67	—	4	2	no	—
380	#67	—	4	1	no	—
381	C₂×Dic₃	—	2	2	no	—
382	C₂×Dic₃	—	4	2	no	—
383	C₂×Dic₃	—	4	2	no	—
384	C₂×Dic₃	—	4	2	no	—
385	C₂×Dic₃	—	4	1	no	—
386	C₂×Dic₃	—	4	2	no	—
387	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃	C₂⁴	1	2	yes	—
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	2	yes	—
396	C₂×Dic₃	C₂⁴	1	2	yes	—
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₄×D₃	—	2	2	no	—
399	C₄×D₃	—	4	2	no	—
400	Dic₆	—	2	2	no	—
401	Dic₆	—	2	2	no	—
402	Dic₆	—	2	2	no	—
403	Dic₆	—	4	2	no	—
404	Dic₆	—	4	2	no	—
405	Dic₆	—	4	2	no	—
406	Dic₆	—	4	1	no	—
407	Dic₆	—	4	2	no	—
408	C₂⁴	C₂²×D₃	1	2	yes	—
409	#41	—	4	2	no	—
410	#41	—	12	2	no	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	—	3	1	no	—
413	C₂×Q₈	—	3	1	no	—
414	C₂×Q₈	—	3	1	no	—
415	C₂×Q₈	—	3	2	no	—
416	C₂×Q₈	—	3	2	no	—
417	C₂×Q₈	—	3	2	no	—
418	C₂×Q₈	—	3	2	no	—
419	C₂×Q₈	—	12	2	no	—
420	C₂×Q₈	—	12	2	no	—
421	C₂×Q₈	—	12	2	no	—
422	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
423	C₂×D₄	—	3	1	no	—
424	C₂×D₄	—	3	2	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
431	C₂×D₄	C₂²×D₃	1	2	yes	—
432	C₂×D₄	C₂²×D₃	1	2	yes	—
433	C₂×D₄	C₂²×D₃	1	2	yes	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²×D₃	1	2	yes	—
445	C₂²×C₄	C₂²×D₃	1	2	yes	—
446	C₄⋊C₄	—	3	1	no	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	1	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	3	2	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	2	no	—
460	C₄⋊C₄	—	3	2	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	2	no	—
468	C₄⋊C₄	—	3	2	no	—
469	C₄⋊C₄	—	3	2	no	—
470	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₃	1	2	yes	—
473	C₂²⋊C₄	—	3	1	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	—	3	2	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	—	3	2	no	—
483	C₂²⋊C₄	—	3	2	no	—
484	C₂²⋊C₄	—	3	2	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	1	no	—
487	C₂²⋊C₄	—	3	1	no	—
488	C₂²⋊C₄	—	3	1	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	2	no	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	1	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	2	no	—
496	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
497	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	2	no	—
508	C₄²	—	3	2	no	—
509	C₄²	—	3	1	no	—
510	C₄²	—	3	2	no	—
511	C₄²	—	3	2	no	—
512	C₄²	C₂²×D₃	1	1	yes	characteristic
513	C₂²×C₃	—	2	1	no	—
514	C₂²×C₃	—	2	1	no	—
515	C₂²×C₃	—	2	1	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	2	2	no	—
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	2	no	—
523	C₂²×C₃	—	2	1	no	—
524	C₂²×C₃	—	8	4	no	—
525	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
526	C₂²×C₃	C₂⁵	1	1	yes	characteristic
527	C₂×D₃	—	2	1	no	—
528	C₂×D₃	—	2	1	no	—
529	C₂×D₃	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
537	Dic₃	—	2	2	no	—
538	Dic₃	—	2	2	no	—
539	Dic₃	—	2	2	no	—
540	Dic₃	—	2	1	no	—
541	Dic₃	—	2	1	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	—	2	1	no	—
545	Dic₃	—	2	1	no	—
546	Dic₃	—	2	2	no	—
547	Dic₃	—	2	1	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	3	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	C₂³×D₃	1	2	yes	—
553	C₂³	C₂³×D₃	1	2	yes	—
554	C₂³	C₂³×D₃	1	1	yes	characteristic
555	C₂³	C₂³×D₃	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	6	2	no	—
559	Q₈	—	6	2	no	—
560	Q₈	—	12	2	no	—
561	Q₈	—	12	2	no	—
562	Q₈	—	12	2	no	—
563	Q₈	—	12	1	no	—
564	Q₈	—	12	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	6	2	no	—
572	D₄	—	12	2	no	—
573	D₄	—	12	2	no	—
574	D₄	—	12	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	2	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	2	no	—
585	C₂×C₄	—	3	2	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	3	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	6	2	no	—
591	C₂×C₄	—	6	2	no	—
592	C₂×C₄	—	12	2	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	—	12	2	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	1	no	—
598	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₃	1	2	yes	—
600	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₃	1	2	yes	—
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
605	C₂×C₃	—	2	2	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	—	4	2	no	—
608	C₂×C₃	—	4	2	no	—
609	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
611	C₂×C₃	#585	1	1	yes	characteristic
612	D₃	—	4	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	6	1	no	—
625	C₂²	—	6	1	no	—
626	C₂²	—	6	1	no	—
627	C₂²	—	8	4	no	—
628	C₂²	#1010	1	2	yes	—
629	C₂²	C₂⁴×D₃	1	1	yes	characteristic
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	6	1	no	—
637	C₄	—	6	2	no	—
638	C₄	—	6	2	no	—
639	C₄	—	6	2	no	—
640	C₄	—	6	1	no	—
641	C₄	—	6	1	no	—
642	C₄	—	6	1	no	—
643	C₄	—	6	1	no	—
644	C₄	—	6	1	no	—
645	C₄	—	6	2	no	—
646	C₄	—	6	1	no	—
647	C₄	#1004	1	2	yes	—
648	C₃	#3561	1	1	yes	characteristic, complemented, Sylow
649	C₂	—	2	2	no	—
650	C₂	—	4	2	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	12	1	no	—
654	C₂	C₂×#1004	1	1	yes	characteristic
655	C₂	C₂×#1010	1	1	yes	characteristic
656	C₂	#5966	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3561
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₃×#546	C₂	semidirect
2. #5831	C₂	semidirect
3. #5825	C₂	semidirect
4. #5806	C₂	semidirect
5. C₂×#936	C₂	semidirect
6. #5675	C₂	semidirect
7. #5671	C₂	semidirect
8. #5662	C₂	semidirect
9. #5651	C₂	semidirect
10. #5632	C₂	semidirect
11. #5622	C₂	semidirect
12. #5621	C₂	semidirect
13. #5603	C₂	semidirect
14. #5603	C₂	semidirect
15. #5598	C₂	semidirect
16. #5593	C₂	semidirect
17. #5587	C₂	semidirect
18. #5561	C₂	semidirect
19. #5542	C₂	semidirect
20. #5538	C₂	semidirect
21. D₄×Dic₆	C₂	semidirect
22. #5495	C₂	semidirect
23. #5483	C₂	semidirect
27. C₂×D₃×Q₈	C₂²	semidirect
30. C₂²×Dic₆	C₂²	semidirect
44. Q₈×Dic₃	C₂²	semidirect
45. #944	C₂²	semidirect
46. #944	C₂²	semidirect
49. #939	C₂²	semidirect
51. #938	C₂²	semidirect
59. #936	C₂²	semidirect
60. #936	C₂²	semidirect
63. #935	C₂²	semidirect
64. #935	C₂²	semidirect
65. #935	C₂²	semidirect
68. D₄×Dic₃	C₂²	semidirect
69. #929	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
72. C₄×#67	C₂²	semidirect
73. #926	C₂²	semidirect
74. #926	C₂²	semidirect
76. #924	C₂²	semidirect
77. #924	C₂²	semidirect
78. #924	C₂²	semidirect
79. #924	C₂²	semidirect
80. #924	C₂²	semidirect
81. #924	C₂²	semidirect
83. #898	C₂²	semidirect
84. #897	C₂²	semidirect
85. #896	C₂²	semidirect
86. #889	C₂²	semidirect
87. #889	C₂²	semidirect
88. #888	C₂²	semidirect
89. #888	C₂²	semidirect
90. #888	C₂²	semidirect
91. #887	C₂²	semidirect
92. #887	C₂²	semidirect
93. #887	C₂²	semidirect
95. #885	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
98. #883	C₂²	semidirect
99. #883	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #879	C₂²	semidirect
104. #879	C₂²	semidirect
105. #879	C₂²	semidirect
106. #879	C₂²	semidirect
107. #879	C₂²	semidirect
112. #878	C₂²	semidirect
113. #878	C₂²	semidirect
114. #878	C₂²	semidirect
115. #878	C₂²	semidirect
116. #878	C₂²	semidirect
117. #878	C₂²	semidirect
119. #877	C₂²	semidirect
120. #872	C₂²	semidirect
121. #869	C₂²	semidirect
122. C₄×Dic₆	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
135. #546	D₃	semidirect
648. C₃	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₃×#546	2
#5831	2
#5825	2
#5806	2
C₂×#936	2
#5675	2
#5671	2
#5662	2
#5651	2
#5632	2
#5622	2
#5621	2
#5603	2
#5598	2
#5593	2
#5587	2
#5561	2
#5542	2
#5538	2
D₄×Dic₆	2
#5495	2
#5483	2
#3561	3