Subgroups — #86918

Order 384.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#5711	C₂	1	2	yes	maximal, complemented
3	#5710	C₂	1	2	yes	maximal, complemented
4	#5695	C₂	1	1	yes	maximal, characteristic, complemented
5	#5691	C₂	1	1	yes	maximal, characteristic, complemented
6	#5657	C₂	1	2	yes	maximal, complemented
7	#5654	C₂	1	2	yes	maximal, complemented
8	#5620	C₂	1	2	yes	maximal, complemented
9	#5609	C₂	1	1	yes	maximal, characteristic, complemented
10	#5608	C₂	1	1	yes	maximal, characteristic, complemented
11	#5607	C₂	1	2	yes	maximal, complemented
12	#5607	C₂	1	1	yes	maximal, characteristic, complemented
13	#5599	C₂	1	1	yes	maximal, characteristic, complemented
14	#5560	C₂	1	2	yes	maximal, complemented
15	#5554	C₂	1	1	yes	maximal, characteristic, complemented
16	#5553	C₂	1	2	yes	maximal, complemented
17	#5550	C₂	1	1	yes	maximal, characteristic, complemented
18	#5548	C₂	1	1	yes	maximal, characteristic, complemented
19	#5548	C₂	1	1	yes	maximal, characteristic, complemented
20	#5533	C₂	1	1	yes	maximal, characteristic, complemented
21	#5525	C₂	1	1	yes	maximal, characteristic, complemented
22	#5510	C₂	1	1	yes	maximal, characteristic, complemented
23	#5507	C₂	1	1	yes	maximal, characteristic, complemented
24	#3546	—	3	1	no	maximal, Sylow
25	C₂×#237	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₃×D₄	C₂²	1	2	yes	—
27	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×#235	C₂²	1	2	yes	complemented
29	C₂×#235	C₂²	1	2	yes	complemented
30	C₂×#235	C₂²	1	1	yes	characteristic, complemented
31	C₂×#235	C₂²	1	1	yes	characteristic, complemented
32	C₂×#235	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₁₂	C₂²	1	1	yes	characteristic
34	C₃×#126	C₂²	1	2	yes	complemented
35	C₃×#125	C₂²	1	1	yes	characteristic, complemented
36	C₃×#123	C₂²	1	2	yes	complemented
37	C₃×#121	C₂²	1	1	yes	characteristic
38	C₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₃×#121	C₂²	1	2	yes	complemented
40	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄×D₄	C₂²	1	2	yes	complemented
43	C₃×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	#940	C₂²	1	1	yes	characteristic
46	#940	C₂²	1	1	yes	characteristic
47	#940	C₂²	1	2	yes	complemented
48	#940	C₂²	1	2	yes	complemented
49	#939	C₂²	1	2	yes	complemented
50	#939	C₂²	1	2	yes	complemented
51	#938	C₂²	1	2	yes	complemented
52	#938	C₂²	1	1	yes	characteristic, complemented
53	#938	C₂²	1	1	yes	characteristic, complemented
54	#937	C₂²	1	2	yes	—
55	#937	C₂²	1	2	yes	complemented
56	#937	C₂²	1	2	yes	complemented
57	#930	C₂²	1	1	yes	characteristic
58	#930	C₂²	1	2	yes	complemented
59	#930	C₂²	1	2	yes	complemented
60	#930	C₂²	1	2	yes	complemented
61	#929	C₂²	1	2	yes	complemented
62	C₄×#67	C₂²	1	1	yes	characteristic
63	C₄×#67	C₂²	1	2	yes	complemented
64	C₄×#67	C₂²	1	1	yes	characteristic, complemented
65	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
66	#924	C₂²	1	1	yes	characteristic, complemented
67	#898	C₂²	1	2	yes	complemented
68	#898	C₂²	1	2	yes	complemented
69	#897	C₂²	1	2	yes	complemented
70	#897	C₂²	1	1	yes	characteristic, complemented
71	#897	C₂²	1	1	yes	characteristic, complemented
72	#896	C₂²	1	2	yes	complemented
73	#895	C₂²	1	1	yes	characteristic
74	#895	C₂²	1	1	yes	characteristic
75	#895	C₂²	1	1	yes	characteristic
76	#895	C₂²	1	2	yes	complemented
77	#895	C₂²	1	2	yes	complemented
78	#895	C₂²	1	1	yes	characteristic, complemented
79	#895	C₂²	1	1	yes	characteristic, complemented
80	#895	C₂²	1	1	yes	characteristic, complemented
81	#894	C₂²	1	2	yes	complemented
82	#894	C₂²	1	2	yes	complemented
83	#894	C₂²	1	2	yes	complemented
84	#894	C₂²	1	2	yes	complemented
85	#893	C₂²	1	1	yes	characteristic
86	#893	C₂²	1	2	yes	complemented
87	#893	C₂²	1	2	yes	complemented
88	#892	C₂²	1	2	yes	complemented
89	#892	C₂²	1	1	yes	characteristic, complemented
90	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	#888	C₂²	1	1	yes	characteristic, 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	—
96	#885	C₂²	1	1	yes	characteristic, complemented
97	#885	C₂²	1	2	yes	complemented
98	#885	C₂²	1	2	yes	complemented
99	#885	C₂²	1	1	yes	characteristic, complemented
100	#884	C₂²	1	1	yes	characteristic
101	#884	C₂²	1	2	yes	—
102	#884	C₂²	1	2	yes	complemented
103	#884	C₂²	1	2	yes	complemented
104	#884	C₂²	1	2	yes	complemented
105	#884	C₂²	1	1	yes	characteristic, complemented
106	#884	C₂²	1	2	yes	complemented
107	#882	C₂²	1	2	yes	—
108	#882	C₂²	1	2	yes	complemented
109	#882	C₂²	1	2	yes	complemented
110	#882	C₂²	1	2	yes	complemented
111	#882	C₂²	1	2	yes	complemented
112	#67⋊C₄	C₂²	1	2	yes	complemented
113	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	#879	C₂²	1	2	yes	complemented
115	#878	C₂²	1	2	yes	complemented
116	#876	C₂²	1	2	yes	complemented
117	#875	C₂²	1	1	yes	characteristic
118	#875	C₂²	1	2	yes	complemented
119	#874	C₂²	1	2	yes	complemented
120	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
122	C₄²×D₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Dic₆	C₂²	1	2	yes	complemented
124	#560	—	3	2	no	—
125	#560	—	3	2	no	—
126	#556	—	3	1	no	—
127	#553	—	3	1	no	—
128	#553	D₃	1	1	yes	characteristic, complemented
129	#550	—	3	1	no	—
130	#550	—	3	2	no	—
131	#547	—	3	1	no	—
132	#546	—	3	2	no	—
133	#546	—	3	1	no	—
134	#546	—	3	1	no	—
135	D₄²	—	3	1	no	—
136	#542	—	3	2	no	—
137	#538	—	3	2	no	—
138	#538	—	3	2	no	—
139	#537	—	3	1	no	—
140	#537	—	3	1	no	—
141	#535	—	3	2	no	—
142	#535	—	3	1	no	—
143	#535	—	3	1	no	—
144	#532	—	3	1	no	—
145	#532	—	3	1	no	—
146	#529	—	3	1	no	—
147	C₂³×D₃	C₂³	1	2	yes	—
148	C₂³×D₃	C₂³	1	2	yes	—
149	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂×C₃×D₄	C₂³	1	2	yes	—
151	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
159	C₂×#67	C₂³	1	1	yes	characteristic
160	C₂×#67	C₂³	1	2	yes	—
161	C₂×#67	C₂³	1	1	yes	characteristic
162	C₂×#67	C₂³	1	1	yes	characteristic
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	2	yes	—
165	C₂×#67	C₂³	1	2	yes	—
166	C₂×#67	C₂³	1	2	yes	—
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	1	yes	characteristic
169	C₂×#67	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	#237	—	4	2	no	—
172	D₃×D₄	—	4	2	no	—
173	D₃×D₄	—	4	4	no	—
174	#235	—	4	4	no	—
175	#235	—	4	4	no	—
176	#235	—	4	2	no	—
177	#235	—	4	2	no	—
178	#235	—	4	2	no	—
179	C₂×D₁₂	—	4	2	no	—
180	C₂×D₁₂	C₂³	1	1	yes	characteristic
181	C₂×D₁₂	C₂³	1	1	yes	characteristic
182	C₂×D₁₂	C₂³	1	1	yes	characteristic
183	C₂×D₁₂	C₂³	1	1	yes	characteristic
184	C₂×D₁₂	C₂³	1	2	yes	—
185	C₂×D₁₂	C₂³	1	2	yes	—
186	C₂×D₁₂	C₂³	1	2	yes	—
187	C₂×D₁₂	C₂³	1	2	yes	—
188	C₂×D₁₂	C₂³	1	2	yes	—
189	C₂×D₁₂	C₂³	1	2	yes	—
190	C₂×D₁₂	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
193	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
195	C₂×C₄×D₃	C₂³	1	2	yes	—
196	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂³	1	2	yes	—
198	C₂×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₄×D₃	C₂³	1	2	yes	—
200	C₂×Dic₆	C₂³	1	2	yes	—
201	C₂×Dic₆	C₂³	1	1	yes	characteristic
202	C₂×Dic₆	C₂³	1	1	yes	characteristic
203	C₂×Dic₆	C₂³	1	1	yes	characteristic
204	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₃×C₄²	C₂³	1	2	yes	—
218	C₃×C₄²	C₂³	1	1	yes	characteristic
219	#217	C₂³	1	2	yes	—
220	#217	C₂³	1	1	yes	characteristic
221	#217	C₂³	1	2	yes	—
222	#217	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
227	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
233	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
235	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
236	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
239	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₄⋊Dic₃	C₂³	1	2	yes	—
241	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₃	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₃⋊C₄	C₂³	1	2	yes	—
246	Dic₃⋊C₄	C₂³	1	2	yes	—
247	Dic₃⋊C₄	C₂³	1	2	yes	—
248	Dic₃⋊C₄	C₂³	1	2	yes	—
249	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	2	yes	—
252	C₄×Dic₃	C₂³	1	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	1	yes	characteristic
254	C₄×Dic₃	C₂³	1	1	yes	characteristic
255	C₂×#41	—	3	1	no	—
256	C₂×#41	—	3	1	no	—
257	C₂×#41	—	3	1	no	—
258	C₂×#41	—	3	2	no	—
259	C₂×#41	—	3	2	no	—
260	C₂×#41	—	3	1	no	—
261	C₂²×D₄	—	3	2	no	—
262	C₂²×D₄	—	3	1	no	—
263	C₂²×D₄	—	3	1	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	C₄⋊Q₈	—	3	1	no	—
266	#127	—	3	1	no	—
267	#127	—	3	1	no	—
268	#127	—	3	2	no	—
269	#127	—	3	2	no	—
270	#127	—	3	2	no	—
271	#126	—	3	2	no	—
272	#126	—	3	2	no	—
273	#126	—	3	2	no	—
274	#126	—	3	2	no	—
275	#126	C₂×D₃	1	2	yes	complemented
276	#125	C₂×D₃	1	1	yes	characteristic, complemented
277	#124	—	3	2	no	—
278	#124	—	3	1	no	—
279	#124	—	3	1	no	—
280	#124	—	3	2	no	—
281	#124	—	3	2	no	—
282	#124	—	3	1	no	—
283	#124	—	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	2	yes	complemented
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	#121	—	3	1	no	—
298	#121	—	3	1	no	—
299	#121	—	3	2	no	—
300	#121	—	3	2	no	—
301	#121	—	3	2	no	—
302	#121	—	3	2	no	—
303	#121	—	3	1	no	—
304	#121	—	3	2	no	—
305	#121	—	3	2	no	—
306	#121	—	3	1	no	—
307	#121	—	3	1	no	—
308	#121	—	3	1	no	—
309	#121	—	3	1	no	—
310	#121	—	3	1	no	—
311	#121	—	3	2	no	—
312	#121	—	3	1	no	—
313	#121	—	3	2	no	—
314	#121	—	3	1	no	—
315	#121	—	3	1	no	—
316	#121	—	3	2	no	—
317	#121	—	3	2	no	—
318	#121	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	2	no	—
321	#121	C₂×D₃	1	1	yes	characteristic
322	#121	C₂×D₃	1	1	yes	characteristic, complemented
323	#121	C₂×D₃	1	2	yes	complemented
324	#120	—	3	2	no	—
325	#120	—	3	2	no	—
326	#120	—	3	2	no	—
327	#120	—	3	2	no	—
328	#120	—	3	2	no	—
329	#120	—	3	2	no	—
330	#120	—	3	2	no	—
331	#120	—	3	2	no	—
332	C₄×Q₈	—	3	1	no	—
333	C₄×Q₈	—	3	2	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	1	no	—
336	C₄×D₄	—	3	1	no	—
337	C₄×D₄	—	3	1	no	—
338	C₄×D₄	—	3	2	no	—
339	C₄×D₄	—	3	2	no	—
340	C₄×D₄	—	3	2	no	—
341	C₄×D₄	—	3	1	no	—
342	C₄×D₄	—	3	1	no	—
343	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
344	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
345	C₄×D₄	C₂×D₃	1	2	yes	complemented
346	#117	—	3	2	no	—
347	#117	—	3	1	no	—
348	#117	C₂×D₃	1	1	yes	characteristic, complemented
349	C₂×C₄⋊C₄	—	3	1	no	—
350	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₄²	—	3	1	no	—
354	C₂³×C₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴	1	2	yes	—
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₃	—	4	2	no	—
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	—	4	2	no	—
360	C₂²×D₃	—	4	2	no	—
361	C₂²×D₃	—	4	2	no	—
362	C₂²×D₃	—	4	2	no	—
363	C₂²×D₃	C₂⁴	1	2	yes	—
364	C₂²×D₃	C₂⁴	1	1	yes	characteristic
365	C₂²×D₃	C₂⁴	1	2	yes	—
366	C₂²×D₃	C₂⁴	1	1	yes	characteristic
367	C₂²×D₃	C₂⁴	1	1	yes	characteristic
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	4	2	no	—
370	C₃×D₄	—	4	1	no	—
371	C₃×D₄	—	4	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	#67	—	2	2	no	—
385	#67	—	2	4	no	—
386	#67	—	2	2	no	—
387	#67	—	4	2	no	—
388	#67	—	4	2	no	—
389	#67	—	4	2	no	—
390	#67	—	4	1	no	—
391	#67	—	4	1	no	—
392	#67	—	4	1	no	—
393	#67	—	4	1	no	—
394	#67	—	4	2	no	—
395	#67	—	4	2	no	—
396	#67	—	4	2	no	—
397	C₂×Dic₃	—	4	2	no	—
398	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃	C₂⁴	1	2	yes	—
402	C₂×Dic₃	C₂⁴	1	2	yes	—
403	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
405	D₁₂	—	2	2	no	—
406	D₁₂	—	2	2	no	—
407	D₁₂	—	4	2	no	—
408	D₁₂	—	4	1	no	—
409	D₁₂	—	4	2	no	—
410	D₁₂	—	4	2	no	—
411	D₁₂	—	4	2	no	—
412	D₁₂	—	4	2	no	—
413	D₁₂	—	4	1	no	—
414	D₁₂	—	4	1	no	—
415	D₁₂	—	4	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	2	2	no	—
418	C₄×D₃	—	2	2	no	—
419	C₄×D₃	—	2	2	no	—
420	C₄×D₃	—	2	4	no	—
421	C₄×D₃	—	4	1	no	—
422	C₄×D₃	—	4	2	no	—
423	C₄×D₃	—	4	2	no	—
424	C₄×D₃	—	4	2	no	—
425	Dic₆	—	2	2	no	—
426	Dic₆	—	2	4	no	—
427	Dic₆	—	4	1	no	—
428	Dic₆	—	4	1	no	—
429	C₂⁴	—	3	2	no	—
430	C₂⁴	—	3	2	no	—
431	#41	—	12	2	no	—
432	#41	—	12	2	no	—
433	#41	—	12	2	no	—
434	#41	—	12	4	no	—
435	#41	—	12	4	no	—
436	#41	—	12	2	no	—
437	C₂×Q₈	—	3	1	no	—
438	C₂×Q₈	—	3	2	no	—
439	C₂×Q₈	—	3	1	no	—
440	C₂×Q₈	—	3	1	no	—
441	C₂×D₄	—	3	1	no	—
442	C₂×D₄	—	3	2	no	—
443	C₂×D₄	—	3	1	no	—
444	C₂×D₄	—	3	2	no	—
445	C₂×D₄	—	3	1	no	—
446	C₂×D₄	—	3	2	no	—
447	C₂×D₄	—	3	1	no	—
448	C₂×D₄	—	3	1	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	2	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	3	1	no	—
454	C₂×D₄	—	3	1	no	—
455	C₂×D₄	—	3	1	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂×D₄	—	3	2	no	—
458	C₂×D₄	—	3	2	no	—
459	C₂×D₄	—	3	1	no	—
460	C₂×D₄	—	3	2	no	—
461	C₂×D₄	—	3	2	no	—
462	C₂×D₄	—	3	2	no	—
463	C₂×D₄	—	3	2	no	—
464	C₂×D₄	—	3	1	no	—
465	C₂×D₄	—	12	2	no	—
466	C₂×D₄	—	12	2	no	—
467	C₂×D₄	—	12	4	no	—
468	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₃	1	2	yes	—
471	C₂×D₄	C₂²×D₃	1	2	yes	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	—	3	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	—	3	1	no	—
476	C₂²×C₄	—	3	2	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	2	no	—
480	C₂²×C₄	—	3	2	no	—
481	C₂²×C₄	—	3	2	no	—
482	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₃	1	2	yes	—
485	C₂²×C₄	C₂²×D₃	1	2	yes	—
486	C₄⋊C₄	—	3	1	no	—
487	C₄⋊C₄	—	3	2	no	—
488	C₄⋊C₄	—	3	2	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	3	2	no	—
492	C₄⋊C₄	—	3	1	no	—
493	C₄⋊C₄	—	3	2	no	—
494	C₄⋊C₄	—	3	2	no	—
495	C₄⋊C₄	—	3	2	no	—
496	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	1	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	1	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	1	no	—
509	C₂²⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	2	no	—
512	C₂²⋊C₄	—	3	2	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	2	no	—
515	C₂²⋊C₄	—	3	1	no	—
516	C₂²⋊C₄	—	3	1	no	—
517	C₂²⋊C₄	—	3	2	no	—
518	C₂²⋊C₄	—	3	2	no	—
519	C₂²⋊C₄	—	3	2	no	—
520	C₂²⋊C₄	—	3	2	no	—
521	C₂²⋊C₄	—	3	2	no	—
522	C₂²⋊C₄	—	3	2	no	—
523	C₂²⋊C₄	—	3	1	no	—
524	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
528	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
530	C₄²	—	3	1	no	—
531	C₄²	—	3	1	no	—
532	C₄²	—	3	1	no	—
533	C₄²	—	3	2	no	—
534	C₄²	—	3	2	no	—
535	C₄²	C₂²×D₃	1	1	yes	characteristic
536	C₄²	C₂²×D₃	1	2	yes	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	2	no	—
540	C₂²×C₃	—	2	1	no	—
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	2	1	no	—
546	C₂²×C₃	C₂⁵	1	1	yes	characteristic
547	C₂×D₃	—	2	1	no	—
548	C₂×D₃	—	2	1	no	—
549	C₂×D₃	—	2	1	no	—
550	C₂×D₃	—	2	1	no	—
551	C₂×D₃	—	2	2	no	—
552	C₂×D₃	—	2	1	no	—
553	C₂×D₃	—	2	2	no	—
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	1	no	—
557	C₂×D₃	—	2	1	no	—
558	C₂×D₃	—	2	1	no	—
559	C₂×D₃	—	2	2	no	—
560	C₂×D₃	—	2	2	no	—
561	C₂×D₃	—	2	1	no	—
562	C₂×D₃	—	8	4	no	—
563	C₂×D₃	—	8	4	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	2	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	—	2	2	no	—
571	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
572	Dic₃	—	2	2	no	—
573	Dic₃	—	2	2	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	—	2	1	no	—
576	Dic₃	—	2	1	no	—
577	Dic₃	—	2	1	no	—
578	Dic₃	H(5,𝔽₂)	1	2	yes	—
579	C₂³	—	3	1	no	—
580	C₂³	—	3	2	no	—
581	C₂³	—	3	2	no	—
582	C₂³	—	3	1	no	—
583	C₂³	—	3	1	no	—
584	C₂³	—	12	2	no	—
585	C₂³	—	12	2	no	—
586	C₂³	—	12	2	no	—
587	C₂³	—	12	2	no	—
588	C₂³	—	12	2	no	—
589	C₂³	—	12	2	no	—
590	C₂³	C₂³×D₃	1	1	yes	characteristic
591	C₂³	C₂³×D₃	1	2	yes	—
592	C₂³	C₂³×D₃	1	1	yes	characteristic
593	Q₈	—	6	4	no	—
594	Q₈	—	6	2	no	—
595	Q₈	—	12	1	no	—
596	Q₈	—	12	1	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	2	no	—
601	D₄	—	6	2	no	—
602	D₄	—	6	4	no	—
603	D₄	—	6	2	no	—
604	D₄	—	6	2	no	—
605	D₄	—	6	2	no	—
606	D₄	—	12	2	no	—
607	D₄	—	12	2	no	—
608	D₄	—	12	1	no	—
609	D₄	—	12	1	no	—
610	D₄	—	12	2	no	—
611	D₄	—	12	2	no	—
612	D₄	—	12	1	no	—
613	D₄	—	12	2	no	—
614	D₄	—	12	2	no	—
615	D₄	—	12	2	no	—
616	D₄	—	12	1	no	—
617	D₄	—	12	1	no	—
618	D₄	—	12	1	no	—
619	D₄	—	12	1	no	—
620	D₄	—	12	2	no	—
621	D₄	—	12	2	no	—
622	D₄	—	12	2	no	—
623	D₄	—	12	2	no	—
624	D₄	—	12	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	3	1	no	—
628	C₂×C₄	—	3	1	no	—
629	C₂×C₄	—	3	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	2	no	—
632	C₂×C₄	—	3	2	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	6	4	no	—
637	C₂×C₄	—	6	2	no	—
638	C₂×C₄	—	6	2	no	—
639	C₂×C₄	—	6	2	no	—
640	C₂×C₄	—	6	2	no	—
641	C₂×C₄	—	12	2	no	—
642	C₂×C₄	—	12	2	no	—
643	C₂×C₄	—	12	2	no	—
644	C₂×C₄	—	12	1	no	—
645	C₂×C₄	—	12	2	no	—
646	C₂×C₄	C₂³×D₃	1	2	yes	—
647	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₃	1	2	yes	—
651	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₃	1	2	yes	—
653	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
654	C₂×C₃	—	4	1	no	—
655	C₂×C₃	—	4	2	no	—
656	C₂×C₃	—	4	1	no	—
657	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₃	#585	1	1	yes	characteristic
660	D₃	—	4	1	no	—
661	D₃	—	4	1	no	—
662	D₃	—	4	2	no	—
663	D₃	—	4	2	no	—
664	D₃	—	4	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	6	1	no	—
675	C₂²	—	6	1	no	—
676	C₂²	—	6	1	no	—
677	C₂²	—	6	2	no	—
678	C₂²	—	6	2	no	—
679	C₂²	—	6	1	no	—
680	C₂²	—	6	1	no	—
681	C₂²	—	6	2	no	—
682	C₂²	—	6	1	no	—
683	C₂²	—	6	2	no	—
684	C₂²	—	6	1	no	—
685	C₂²	—	6	2	no	—
686	C₂²	—	6	1	no	—
687	C₂²	—	6	2	no	—
688	C₂²	—	6	1	no	—
689	C₂²	—	24	4	no	—
690	C₂²	—	24	4	no	—
691	C₂²	C₂⁴×D₃	1	1	yes	characteristic
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	3	2	no	—
700	C₄	—	6	1	no	—
701	C₄	—	6	1	no	—
702	C₄	—	6	1	no	—
703	C₄	—	6	2	no	—
704	C₄	—	6	1	no	—
705	C₄	—	6	2	no	—
706	C₄	#1009	1	2	yes	—
707	C₃	#3546	1	1	yes	characteristic, complemented, Sylow
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	12	1	no	—
712	C₂	—	12	2	no	—
713	C₂	—	12	2	no	—
714	C₂	—	12	1	no	—
715	C₂	—	12	1	no	—
716	C₂	C₂×#1009	1	1	yes	characteristic
717	C₂	#5964	1	1	yes	characteristic
718	C₂	D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#553	C₂
hypercenter	#553	D₃
hypocenter	C₃	#3546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₃×#553	C₂	semidirect
2. #5711	C₂	semidirect
3. #5710	C₂	semidirect
4. #5695	C₂	semidirect
5. #5691	C₂	semidirect
6. #5657	C₂	semidirect
7. #5654	C₂	semidirect
8. #5620	C₂	semidirect
9. #5609	C₂	semidirect
10. #5608	C₂	semidirect
11. #5607	C₂	semidirect
12. #5607	C₂	semidirect
13. #5599	C₂	semidirect
14. #5560	C₂	semidirect
15. #5554	C₂	semidirect
16. #5553	C₂	semidirect
17. #5550	C₂	semidirect
18. #5548	C₂	semidirect
19. #5548	C₂	semidirect
20. #5533	C₂	semidirect
21. #5525	C₂	semidirect
22. #5510	C₂	semidirect
23. #5507	C₂	semidirect
25. C₂×#237	C₂²	semidirect
28. C₂×#235	C₂²	semidirect
29. C₂×#235	C₂²	semidirect
30. C₂×#235	C₂²	semidirect
31. C₂×#235	C₂²	semidirect
32. C₂×#235	C₂²	semidirect
34. C₃×#126	C₂²	semidirect
35. C₃×#125	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
38. C₃×#121	C₂²	semidirect
39. C₃×#121	C₂²	semidirect
40. C₃×C₄×D₄	C₂²	semidirect
41. C₃×C₄×D₄	C₂²	semidirect
42. C₃×C₄×D₄	C₂²	semidirect
43. C₃×#117	C₂²	semidirect
44. C₂×C₃×C₄⋊C₄	C₂²	semidirect
47. #940	C₂²	semidirect
48. #940	C₂²	semidirect
49. #939	C₂²	semidirect
50. #939	C₂²	semidirect
51. #938	C₂²	semidirect
52. #938	C₂²	semidirect
53. #938	C₂²	semidirect
55. #937	C₂²	semidirect
56. #937	C₂²	semidirect
58. #930	C₂²	semidirect
59. #930	C₂²	semidirect
60. #930	C₂²	semidirect
61. #929	C₂²	semidirect
63. C₄×#67	C₂²	semidirect
64. C₄×#67	C₂²	semidirect
65. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
66. #924	C₂²	semidirect
67. #898	C₂²	semidirect
68. #898	C₂²	semidirect
69. #897	C₂²	semidirect
70. #897	C₂²	semidirect
71. #897	C₂²	semidirect
72. #896	C₂²	semidirect
76. #895	C₂²	semidirect
77. #895	C₂²	semidirect
78. #895	C₂²	semidirect
79. #895	C₂²	semidirect
80. #895	C₂²	semidirect
81. #894	C₂²	semidirect
82. #894	C₂²	semidirect
83. #894	C₂²	semidirect
84. #894	C₂²	semidirect
86. #893	C₂²	semidirect
87. #893	C₂²	semidirect
88. #892	C₂²	semidirect
89. #892	C₂²	semidirect
90. D₃×C₄⋊C₄	C₂²	semidirect
91. #888	C₂²	semidirect
92. #888	C₂²	semidirect
93. #887	C₂²	semidirect
94. #886	C₂²	semidirect
96. #885	C₂²	semidirect
97. #885	C₂²	semidirect
98. #885	C₂²	semidirect
99. #885	C₂²	semidirect
102. #884	C₂²	semidirect
103. #884	C₂²	semidirect
104. #884	C₂²	semidirect
105. #884	C₂²	semidirect
106. #884	C₂²	semidirect
108. #882	C₂²	semidirect
109. #882	C₂²	semidirect
110. #882	C₂²	semidirect
111. #882	C₂²	semidirect
112. #67⋊C₄	C₂²	semidirect
113. D₃×C₂²⋊C₄	C₂²	semidirect
114. #879	C₂²	semidirect
115. #878	C₂²	semidirect
116. #876	C₂²	semidirect
118. #875	C₂²	semidirect
119. #874	C₂²	semidirect
120. C₄×D₁₂	C₂²	semidirect
121. C₄×D₁₂	C₂²	semidirect
122. C₄²×D₃	C₂²	semidirect
123. C₄×Dic₆	C₂²	semidirect
128. #553	D₃	semidirect
275. #126	C₂×D₃	semidirect
276. #125	C₂×D₃	semidirect
290. #123	C₂×D₃	semidirect
322. #121	C₂×D₃	semidirect
323. #121	C₂×D₃	semidirect
343. C₄×D₄	C₂×D₃	semidirect
344. C₄×D₄	C₂×D₃	semidirect
345. C₄×D₄	C₂×D₃	semidirect
348. #117	C₂×D₃	semidirect
350. C₂×C₄⋊C₄	C₂×D₃	semidirect
707. C₃	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₃×#553	2
#5711	2
#5710	2
#5695	2
#5691	2
#5657	2
#5654	2
#5620	2
#5609	2
#5608	2
#5607	2
#5599	2
#5560	2
#5554	2
#5553	2
#5550	2
#5548	2
#5533	2
#5525	2
#5510	2
#5507	2
#3546	3