Subgroups — #85921

Order 384.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#953	C₂	1	2	yes	maximal, complemented
3	#5806	C₂	1	2	yes	maximal, complemented
4	#5805	C₂	1	1	yes	maximal, characteristic, complemented
5	#5804	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×#67	C₂	1	2	yes	maximal, complemented
7	#5595	C₂	1	2	yes	maximal, complemented
8	#5595	C₂	1	1	yes	maximal, characteristic, complemented
9	#5594	C₂	1	1	yes	maximal, characteristic, complemented
10	#5593	C₂	1	2	yes	maximal, complemented
11	#5593	C₂	1	2	yes	maximal, complemented
12	#5592	C₂	1	2	yes	maximal, complemented
13	#5591	C₂	1	2	yes	maximal, complemented
14	#5590	C₂	1	1	yes	maximal, characteristic, complemented
15	#5589	C₂	1	2	yes	maximal, complemented
16	#5587	C₂	1	1	yes	maximal, characteristic, complemented
17	#5495	C₂	1	2	yes	maximal, complemented
18	#5494	C₂	1	2	yes	maximal, complemented
19	#5490	C₂	1	2	yes	maximal, complemented
20	#3532	—	3	1	no	maximal, Sylow
21	C₂⁵×C₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
23	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#67	C₂²	1	2	yes	complemented
25	C₂²×#67	C₂²	1	2	yes	complemented
26	C₂²×#67	C₂²	1	2	yes	complemented
27	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
28	C₂×#237	C₂²	1	2	yes	complemented
29	C₂×D₃×D₄	C₂²	1	2	yes	complemented
30	C₂×#235	C₂²	1	1	yes	characteristic, complemented
31	C₃×#120	C₂²	1	1	yes	characteristic
32	C₃×#120	C₂²	1	2	yes	complemented
33	C₃×#120	C₂²	1	1	yes	characteristic, complemented
34	C₃×#120	C₂²	1	2	yes	complemented
35	C₃×#120	C₂²	1	1	yes	characteristic, complemented
36	C₃×#120	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	#953	C₂²	1	2	yes	—
40	#953	C₂²	1	2	yes	complemented
41	#953	C₂²	1	2	yes	complemented
42	#953	C₂²	1	2	yes	complemented
43	#953	C₂²	1	2	yes	complemented
44	#953	C₂²	1	2	yes	complemented
45	#953	C₂²	1	2	yes	complemented
46	#953	C₂²	1	2	yes	complemented
47	#953	C₂²	1	2	yes	complemented
48	C₂×#217	C₂²	1	2	yes	complemented
49	C₂×#217	C₂²	1	2	yes	complemented
50	C₂×#217	C₂²	1	2	yes	complemented
51	C₂×#217	C₂²	1	1	yes	characteristic, complemented
52	#940	C₂²	1	2	yes	complemented
53	#940	C₂²	1	1	yes	characteristic, complemented
54	#940	C₂²	1	1	yes	characteristic, complemented
55	#939	C₂²	1	2	yes	complemented
56	#939	C₂²	1	2	yes	complemented
57	#939	C₂²	1	2	yes	complemented
58	#939	C₂²	1	2	yes	complemented
59	#939	C₂²	1	2	yes	complemented
60	#939	C₂²	1	2	yes	complemented
61	#938	C₂²	1	2	yes	complemented
62	#938	C₂²	1	2	yes	complemented
63	#938	C₂²	1	2	yes	complemented
64	#938	C₂²	1	2	yes	complemented
65	#937	C₂²	1	2	yes	complemented
66	#937	C₂²	1	2	yes	complemented
67	#937	C₂²	1	1	yes	characteristic, complemented
68	#937	C₂²	1	1	yes	characteristic, complemented
69	#936	C₂²	1	1	yes	characteristic, complemented
70	#936	C₂²	1	1	yes	characteristic, complemented
71	#936	C₂²	1	2	yes	complemented
72	#935	C₂²	1	1	yes	characteristic, complemented
73	#935	C₂²	1	1	yes	characteristic, complemented
74	#935	C₂²	1	2	yes	complemented
75	#935	C₂²	1	2	yes	complemented
76	D₄×Dic₃	C₂²	1	2	yes	complemented
77	D₄×Dic₃	C₂²	1	2	yes	complemented
78	#930	C₂²	1	2	yes	complemented
79	#929	C₂²	1	2	yes	complemented
80	C₄×#67	C₂²	1	2	yes	complemented
81	C₄×#67	C₂²	1	2	yes	complemented
82	#926	C₂²	1	1	yes	characteristic, complemented
83	#924	C₂²	1	2	yes	complemented
84	#886	C₂²	1	2	yes	complemented
85	#885	C₂²	1	2	yes	complemented
86	#885	C₂²	1	2	yes	complemented
87	#885	C₂²	1	2	yes	complemented
88	#885	C₂²	1	2	yes	complemented
89	#884	C₂²	1	2	yes	complemented
90	#884	C₂²	1	2	yes	complemented
91	#884	C₂²	1	2	yes	complemented
92	#884	C₂²	1	2	yes	complemented
93	#883	C₂²	1	2	yes	complemented
94	#883	C₂²	1	2	yes	complemented
95	#883	C₂²	1	2	yes	complemented
96	#883	C₂²	1	2	yes	complemented
97	#882	C₂²	1	2	yes	complemented
98	#67⋊C₄	C₂²	1	2	yes	complemented
99	#67⋊C₄	C₂²	1	2	yes	complemented
100	D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
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	#878	C₂²	1	2	yes	complemented
106	#878	C₂²	1	2	yes	complemented
107	#877	C₂²	1	2	yes	complemented
108	H(3,𝔽₄)	—	3	1	no	—
109	#560	—	3	1	no	—
110	#560	—	3	2	no	—
111	#551	—	3	1	no	—
112	#551	—	3	2	no	—
113	#546	—	3	2	no	—
114	#546	—	3	2	no	—
115	#546	—	3	2	no	—
116	D₄²	—	3	2	no	—
117	D₄²	—	3	1	no	—
118	#538	—	3	2	no	—
119	#538	—	3	2	no	—
120	#538	—	3	2	no	—
121	#535	—	3	1	no	—
122	#535	—	3	2	no	—
123	#534	—	3	1	no	—
124	#534	—	3	2	no	—
125	C₂×#120	—	3	2	no	—
126	C₂×#120	D₃	1	1	yes	characteristic, complemented
127	C₂⁴×C₃	—	4	4	no	—
128	C₂⁴×C₃	—	4	2	no	—
129	C₂⁴×C₃	C₂³	1	1	yes	characteristic
130	C₂⁴×C₃	C₂³	1	2	yes	—
131	C₂⁴×C₃	C₂³	1	2	yes	—
132	C₂⁴×C₃	C₂³	1	1	yes	characteristic
133	C₂⁴×C₃	C₂³	1	1	yes	characteristic
134	C₂⁴×C₃	C₂³	1	1	yes	characteristic
135	C₂³×D₃	C₂³	1	2	yes	—
136	C₂³×D₃	C₂³	1	1	yes	characteristic, complemented
137	C₂×C₃×D₄	—	4	2	no	—
138	C₂×C₃×D₄	—	4	4	no	—
139	C₂×C₃×D₄	C₂³	1	2	yes	—
140	C₂×C₃×D₄	C₂³	1	2	yes	—
141	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
142	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×D₄	C₂³	1	2	yes	—
144	C₂×C₃×D₄	C₂³	1	2	yes	—
145	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³	1	2	yes	—
149	C₂×#67	—	4	4	no	—
150	C₂×#67	—	4	4	no	—
151	C₂×#67	—	4	4	no	—
152	C₂×#67	—	4	2	no	—
153	C₂×#67	C₂³	1	2	yes	—
154	C₂×#67	C₂³	1	2	yes	—
155	C₂×#67	C₂³	1	2	yes	—
156	C₂×#67	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	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	C₂×#67	C₂³	1	2	yes	complemented
166	C₂×#67	C₂³	1	2	yes	complemented
167	C₂×#67	C₂³	1	2	yes	complemented
168	C₂²×Dic₃	C₂³	1	2	yes	—
169	C₂²×Dic₃	C₂³	1	2	yes	—
170	C₂²×Dic₃	C₂³	1	2	yes	—
171	C₂²×Dic₃	C₂³	1	1	yes	characteristic, complemented
172	C₂²×Dic₃	C₂³	1	2	yes	complemented
173	#237	—	4	4	no	—
174	D₃×D₄	—	4	4	no	—
175	#235	—	4	2	no	—
176	C₂×D₁₂	C₂³	1	1	yes	characteristic, complemented
177	C₂×D₁₂	C₂³	1	2	yes	complemented
178	C₂×C₄×D₃	C₂³	1	2	yes	complemented
179	C₂×C₄×D₃	C₂³	1	2	yes	complemented
180	C₂×C₄×D₃	C₂³	1	2	yes	complemented
181	C₂×Dic₆	C₂³	1	1	yes	characteristic, complemented
182	C₂×Dic₆	C₂³	1	2	yes	complemented
183	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	#217	C₂³	1	2	yes	—
191	#217	C₂³	1	2	yes	—
192	#217	C₂³	1	2	yes	—
193	#217	C₂³	1	2	yes	—
194	#217	C₂³	1	2	yes	—
195	#217	C₂³	1	2	yes	—
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	complemented
203	#217	C₂³	1	2	yes	complemented
204	#217	C₂³	1	1	yes	characteristic, complemented
205	#217	C₂³	1	1	yes	characteristic, complemented
206	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
207	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
208	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
209	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
210	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
212	C₄⋊Dic₃	C₂³	1	2	yes	complemented
213	C₄⋊Dic₃	C₂³	1	2	yes	complemented
214	C₄⋊Dic₃	C₂³	1	2	yes	complemented
215	Dic₃⋊C₄	C₂³	1	2	yes	complemented
216	Dic₃⋊C₄	C₂³	1	2	yes	complemented
217	Dic₃⋊C₄	C₂³	1	2	yes	complemented
218	Dic₃⋊C₄	C₂³	1	2	yes	complemented
219	Dic₃⋊C₄	C₂³	1	2	yes	complemented
220	Dic₃⋊C₄	C₂³	1	2	yes	complemented
221	C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
222	C₄×Dic₃	C₂³	1	2	yes	complemented
223	C₄×Dic₃	C₂³	1	1	yes	characteristic, complemented
224	C₄×Dic₃	C₂³	1	2	yes	complemented
225	C₂⁵	C₂×D₃	1	1	yes	characteristic, complemented
226	C₂×#41	—	3	2	no	—
227	C₂×#41	—	3	1	no	—
228	C₂²×D₄	—	3	2	no	—
229	C₂²×D₄	—	3	2	no	—
230	C₂²×D₄	—	3	2	no	—
231	C₂²×D₄	—	3	1	no	—
232	C₂²×D₄	—	3	2	no	—
233	C₂²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
234	C₂²×D₄	C₂×D₃	1	2	yes	complemented
235	#127	—	3	1	no	—
236	#127	—	3	2	no	—
237	#127	—	3	1	no	—
238	#126	—	3	2	no	—
239	#126	—	3	2	no	—
240	#126	—	3	2	no	—
241	#126	—	3	2	no	—
242	#124	—	3	1	no	—
243	#124	—	3	1	no	—
244	#124	—	3	2	no	—
245	#124	—	3	2	no	—
246	#124	—	3	2	no	—
247	#124	—	3	2	no	—
248	#124	—	3	2	no	—
249	#123	—	3	1	no	—
250	#123	—	3	2	no	—
251	#123	—	3	1	no	—
252	#123	—	3	2	no	—
253	#123	—	3	2	no	—
254	#123	—	3	2	no	—
255	#123	—	3	2	no	—
256	#123	—	3	2	no	—
257	#123	—	3	2	no	—
258	#123	—	3	2	no	—
259	C₂²⋊Q₈	—	3	2	no	—
260	C₂²⋊Q₈	—	3	2	no	—
261	C₂²⋊Q₈	—	3	2	no	—
262	#121	—	3	2	no	—
263	#121	—	3	2	no	—
264	#121	—	3	2	no	—
265	#121	—	3	2	no	—
266	#121	—	3	2	no	—
267	#121	—	3	2	no	—
268	#121	—	3	2	no	—
269	#121	—	3	2	no	—
270	#121	—	3	2	no	—
271	#121	—	3	2	no	—
272	#121	—	3	2	no	—
273	#121	—	3	2	no	—
274	#121	—	3	2	no	—
275	#121	—	3	2	no	—
276	#121	—	3	2	no	—
277	#120	—	3	2	no	—
278	#120	—	3	2	no	—
279	#120	—	3	2	no	—
280	#120	—	3	2	no	—
281	#120	—	3	2	no	—
282	#120	—	3	2	no	—
283	#120	—	3	2	no	—
284	#120	—	3	2	no	—
285	#120	—	3	2	no	—
286	#120	—	3	1	no	—
287	#120	—	3	1	no	—
288	#120	—	3	2	no	—
289	#120	—	3	2	no	—
290	#120	—	3	2	no	—
291	#120	C₂×D₃	1	1	yes	characteristic
292	#120	C₂×D₃	1	2	yes	complemented
293	#120	C₂×D₃	1	2	yes	complemented
294	#120	C₂×D₃	1	1	yes	characteristic, complemented
295	#120	C₂×D₃	1	1	yes	characteristic, complemented
296	#120	C₂×D₃	1	1	yes	characteristic, complemented
297	C₄×D₄	—	3	2	no	—
298	C₄×D₄	—	3	2	no	—
299	C₄×D₄	—	3	2	no	—
300	C₄×D₄	—	3	2	no	—
301	C₄×D₄	—	3	2	no	—
302	C₄×D₄	—	3	2	no	—
303	#117	—	3	1	no	—
304	#117	—	3	2	no	—
305	C₂×C₂²⋊C₄	—	3	2	no	—
306	C₂×C₂²⋊C₄	—	3	2	no	—
307	C₂×C₂²⋊C₄	—	3	2	no	—
308	C₂×C₂²⋊C₄	—	3	1	no	—
309	C₂×C₂²⋊C₄	—	3	2	no	—
310	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
311	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
312	C₂³×C₃	—	2	4	no	—
313	C₂³×C₃	—	2	4	no	—
314	C₂³×C₃	—	2	4	no	—
315	C₂³×C₃	—	2	4	no	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	4	1	no	—
319	C₂³×C₃	—	4	2	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	—	4	2	no	—
322	C₂³×C₃	—	4	2	no	—
323	C₂³×C₃	—	4	1	no	—
324	C₂³×C₃	—	4	2	no	—
325	C₂³×C₃	—	4	2	no	—
326	C₂³×C₃	—	4	16	no	—
327	C₂³×C₃	C₂⁴	1	2	yes	—
328	C₂³×C₃	C₂⁴	1	1	yes	characteristic
329	C₂³×C₃	C₂⁴	1	1	yes	characteristic
330	C₂³×C₃	C₂⁴	1	1	yes	characteristic
331	C₂³×C₃	C₂⁴	1	1	yes	characteristic
332	C₂³×C₃	C₂⁴	1	1	yes	characteristic
333	C₂³×C₃	C₂⁴	1	2	yes	—
334	C₂²×D₃	—	2	4	no	—
335	C₂²×D₃	—	4	2	no	—
336	C₂²×D₃	—	4	2	no	—
337	C₂²×D₃	—	4	2	no	—
338	C₂²×D₃	—	4	1	no	—
339	C₂²×D₃	C₂⁴	1	2	yes	—
340	C₂²×D₃	C₂⁴	1	2	yes	—
341	C₃×D₄	—	2	4	no	—
342	C₃×D₄	—	2	4	no	—
343	C₃×D₄	—	4	2	no	—
344	C₃×D₄	—	4	1	no	—
345	C₃×D₄	—	4	1	no	—
346	C₃×D₄	—	4	1	no	—
347	C₃×D₄	—	4	1	no	—
348	C₃×D₄	—	4	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	4	2	no	—
351	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂×C₃×C₄	C₂⁴	1	2	yes	—
354	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
355	#67	—	2	4	no	—
356	#67	—	2	4	no	—
357	#67	—	2	4	no	—
358	#67	—	2	4	no	—
359	#67	—	4	2	no	—
360	#67	—	4	2	no	—
361	#67	—	4	2	no	—
362	#67	—	4	2	no	—
363	#67	—	4	2	no	—
364	#67	—	4	2	no	—
365	#67	—	4	2	no	—
366	#67	—	4	2	no	—
367	#67	—	4	2	no	—
368	#67	—	4	2	no	—
369	#67	—	4	2	no	—
370	C₂×Dic₃	—	2	4	no	—
371	C₂×Dic₃	—	4	2	no	—
372	C₂×Dic₃	—	4	2	no	—
373	C₂×Dic₃	—	4	2	no	—
374	C₂×Dic₃	—	4	1	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	D₁₂	—	4	1	no	—
382	D₁₂	—	4	2	no	—
383	C₄×D₃	—	4	2	no	—
384	C₄×D₃	—	4	2	no	—
385	C₄×D₃	—	4	2	no	—
386	Dic₆	—	4	1	no	—
387	Dic₆	—	4	2	no	—
388	C₂⁴	—	3	2	no	—
389	C₂⁴	—	3	1	no	—
390	C₂⁴	—	4	4	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	C₂²×D₃	1	1	yes	characteristic
393	C₂⁴	C₂²×D₃	1	2	yes	—
394	C₂⁴	C₂²×D₃	1	2	yes	—
395	C₂⁴	C₂²×D₃	1	1	yes	characteristic
396	C₂⁴	C₂²×D₃	1	1	yes	characteristic
397	C₂⁴	C₂²×D₃	1	1	yes	characteristic
398	#41	—	12	2	no	—
399	#41	—	12	4	no	—
400	C₂×Q₈	—	3	2	no	—
401	C₂×Q₈	—	3	1	no	—
402	C₂×D₄	—	3	2	no	—
403	C₂×D₄	—	3	2	no	—
404	C₂×D₄	—	3	2	no	—
405	C₂×D₄	—	3	2	no	—
406	C₂×D₄	—	3	2	no	—
407	C₂×D₄	—	3	2	no	—
408	C₂×D₄	—	3	2	no	—
409	C₂×D₄	—	3	2	no	—
410	C₂×D₄	—	3	2	no	—
411	C₂×D₄	—	3	2	no	—
412	C₂×D₄	—	3	2	no	—
413	C₂×D₄	—	3	2	no	—
414	C₂×D₄	—	3	2	no	—
415	C₂×D₄	—	3	2	no	—
416	C₂×D₄	—	3	2	no	—
417	C₂×D₄	—	3	1	no	—
418	C₂×D₄	—	3	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	12	4	no	—
422	C₂×D₄	—	12	4	no	—
423	C₂×D₄	—	12	2	no	—
424	C₂×D₄	—	12	4	no	—
425	C₂×D₄	—	12	4	no	—
426	C₂×D₄	C₂²×D₃	1	2	yes	—
427	C₂×D₄	C₂²×D₃	1	2	yes	—
428	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₃	1	2	yes	—
431	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
432	C₂×D₄	C₂²×D₃	1	2	yes	—
433	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₃	1	2	yes	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	3	2	no	—
446	C₄⋊C₄	—	3	2	no	—
447	C₄⋊C₄	—	3	2	no	—
448	C₄⋊C₄	—	3	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊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	1	no	—
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	2	no	—
475	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
476	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
477	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
478	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
479	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
482	C₄²	—	3	1	no	—
483	C₄²	—	3	2	no	—
484	C₄²	—	3	1	no	—
485	C₄²	—	3	2	no	—
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	2	2	no	—
488	C₂²×C₃	—	2	2	no	—
489	C₂²×C₃	—	2	2	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	2	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	4	4	no	—
501	C₂²×C₃	—	4	8	no	—
502	C₂²×C₃	—	4	8	no	—
503	C₂²×C₃	—	4	4	no	—
504	C₂²×C₃	—	4	4	no	—
505	C₂²×C₃	—	8	2	no	—
506	C₂²×C₃	H(5,𝔽₂)	1	4	yes	—
507	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
508	C₂²×C₃	C₂⁵	1	1	yes	characteristic
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	2	2	no	—
511	C₂×D₃	—	2	2	no	—
512	C₂×D₃	—	2	2	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	2	2	no	—
515	C₂×D₃	—	8	4	no	—
516	C₂×D₃	—	8	2	no	—
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	2	2	no	—
521	Dic₃	—	2	2	no	—
522	Dic₃	—	2	2	no	—
523	Dic₃	—	2	2	no	—
524	Dic₃	—	2	2	no	—
525	Dic₃	—	2	2	no	—
526	Dic₃	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	3	2	no	—
534	C₂³	—	3	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	16	no	—
544	C₂³	—	6	4	no	—
545	C₂³	—	12	2	no	—
546	C₂³	—	12	2	no	—
547	C₂³	—	12	1	no	—
548	C₂³	—	12	2	no	—
549	C₂³	C₂³×D₃	1	2	yes	—
550	C₂³	C₂³×D₃	1	1	yes	characteristic
551	C₂³	C₂³×D₃	1	1	yes	characteristic
552	C₂³	C₂³×D₃	1	1	yes	characteristic
553	C₂³	C₂³×D₃	1	1	yes	characteristic
554	C₂³	C₂³×D₃	1	1	yes	characteristic
555	C₂³	C₂³×D₃	1	2	yes	—
556	Q₈	—	12	1	no	—
557	Q₈	—	12	2	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	4	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	6	4	no	—
567	D₄	—	6	4	no	—
568	D₄	—	6	4	no	—
569	D₄	—	6	4	no	—
570	D₄	—	12	2	no	—
571	D₄	—	12	1	no	—
572	D₄	—	12	2	no	—
573	D₄	—	12	2	no	—
574	D₄	—	12	2	no	—
575	D₄	—	12	2	no	—
576	D₄	—	12	2	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	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	3	2	no	—
585	C₂×C₄	—	3	2	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	3	2	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	12	2	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	—	12	2	no	—
595	C₂×C₄	—	12	1	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	2	no	—
598	C₂×C₄	—	12	2	no	—
599	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₃	1	2	yes	—
601	C₂×C₄	C₂³×D₃	1	2	yes	—
602	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
603	C₂×C₃	—	2	4	no	—
604	C₂×C₃	—	2	2	no	—
605	C₂×C₃	—	4	1	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	—	4	2	no	—
608	C₂×C₃	—	4	1	no	—
609	C₂×C₃	—	4	1	no	—
610	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
612	D₃	—	4	2	no	—
613	D₃	—	4	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	4	8	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	8	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	6	2	no	—
634	C₂²	—	6	2	no	—
635	C₂²	—	6	2	no	—
636	C₂²	—	6	2	no	—
637	C₂²	—	6	2	no	—
638	C₂²	—	6	2	no	—
639	C₂²	—	8	2	no	—
640	C₂²	—	24	4	no	—
641	C₂²	—	24	2	no	—
642	C₂²	#1004	1	2	yes	—
643	C₂²	#1004	1	4	yes	—
644	C₂²	C₂⁴×D₃	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	6	2	no	—
650	C₄	—	6	2	no	—
651	C₄	—	6	2	no	—
652	C₄	—	6	2	no	—
653	C₄	—	6	2	no	—
654	C₄	—	6	2	no	—
655	C₃	#3532	1	1	yes	characteristic, complemented, Sylow
656	C₂	—	2	2	no	—
657	C₂	—	2	4	no	—
658	C₂	—	4	2	no	—
659	C₂	—	4	1	no	—
660	C₂	—	4	1	no	—
661	C₂	—	4	1	no	—
662	C₂	—	4	1	no	—
663	C₂	—	12	2	no	—
664	C₂	—	12	2	no	—
665	C₂	C₂×#1004	1	1	yes	characteristic
666	C₂	C₂×#1004	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₂×C₃×#120	C₂
hypercenter	C₂×#120	D₃
hypocenter	C₃	#3532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#120	C₂	semidirect
2. C₂×#953	C₂	semidirect
3. #5806	C₂	semidirect
4. #5805	C₂	semidirect
5. #5804	C₂	semidirect
6. D₄×#67	C₂	semidirect
7. #5595	C₂	semidirect
8. #5595	C₂	semidirect
9. #5594	C₂	semidirect
10. #5593	C₂	semidirect
11. #5593	C₂	semidirect
12. #5592	C₂	semidirect
13. #5591	C₂	semidirect
14. #5590	C₂	semidirect
15. #5589	C₂	semidirect
16. #5587	C₂	semidirect
17. #5495	C₂	semidirect
18. #5494	C₂	semidirect
19. #5490	C₂	semidirect
21. C₂⁵×C₃	C₂²	semidirect
22. C₂²×C₃×D₄	C₂²	semidirect
23. C₂²×C₃×D₄	C₂²	semidirect
24. C₂²×#67	C₂²	semidirect
25. C₂²×#67	C₂²	semidirect
26. C₂²×#67	C₂²	semidirect
27. C₂²×#67	C₂²	semidirect
28. C₂×#237	C₂²	semidirect
29. C₂×D₃×D₄	C₂²	semidirect
30. C₂×#235	C₂²	semidirect
32. C₃×#120	C₂²	semidirect
33. C₃×#120	C₂²	semidirect
34. C₃×#120	C₂²	semidirect
35. C₃×#120	C₂²	semidirect
36. C₃×#120	C₂²	semidirect
37. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
40. #953	C₂²	semidirect
41. #953	C₂²	semidirect
42. #953	C₂²	semidirect
43. #953	C₂²	semidirect
44. #953	C₂²	semidirect
45. #953	C₂²	semidirect
46. #953	C₂²	semidirect
47. #953	C₂²	semidirect
48. C₂×#217	C₂²	semidirect
49. C₂×#217	C₂²	semidirect
50. C₂×#217	C₂²	semidirect
51. C₂×#217	C₂²	semidirect
52. #940	C₂²	semidirect
53. #940	C₂²	semidirect
54. #940	C₂²	semidirect
55. #939	C₂²	semidirect
56. #939	C₂²	semidirect
57. #939	C₂²	semidirect
58. #939	C₂²	semidirect
59. #939	C₂²	semidirect
60. #939	C₂²	semidirect
61. #938	C₂²	semidirect
62. #938	C₂²	semidirect
63. #938	C₂²	semidirect
64. #938	C₂²	semidirect
65. #937	C₂²	semidirect
66. #937	C₂²	semidirect
67. #937	C₂²	semidirect
68. #937	C₂²	semidirect
69. #936	C₂²	semidirect
70. #936	C₂²	semidirect
71. #936	C₂²	semidirect
72. #935	C₂²	semidirect
73. #935	C₂²	semidirect
74. #935	C₂²	semidirect
75. #935	C₂²	semidirect
76. D₄×Dic₃	C₂²	semidirect
77. D₄×Dic₃	C₂²	semidirect
78. #930	C₂²	semidirect
79. #929	C₂²	semidirect
80. C₄×#67	C₂²	semidirect
81. C₄×#67	C₂²	semidirect
82. #926	C₂²	semidirect
83. #924	C₂²	semidirect
84. #886	C₂²	semidirect
85. #885	C₂²	semidirect
86. #885	C₂²	semidirect
87. #885	C₂²	semidirect
88. #885	C₂²	semidirect
89. #884	C₂²	semidirect
90. #884	C₂²	semidirect
91. #884	C₂²	semidirect
92. #884	C₂²	semidirect
93. #883	C₂²	semidirect
94. #883	C₂²	semidirect
95. #883	C₂²	semidirect
96. #883	C₂²	semidirect
97. #882	C₂²	semidirect
98. #67⋊C₄	C₂²	semidirect
99. #67⋊C₄	C₂²	semidirect
100. D₃×C₂²⋊C₄	C₂²	semidirect
101. #879	C₂²	semidirect
102. #879	C₂²	semidirect
103. #879	C₂²	semidirect
104. #879	C₂²	semidirect
105. #878	C₂²	semidirect
106. #878	C₂²	semidirect
107. #877	C₂²	semidirect
126. C₂×#120	D₃	semidirect
136. C₂³×D₃	C₂³	semidirect
165. C₂×#67	C₂³	semidirect
166. C₂×#67	C₂³	semidirect
167. C₂×#67	C₂³	semidirect
171. C₂²×Dic₃	C₂³	semidirect
172. C₂²×Dic₃	C₂³	semidirect
176. C₂×D₁₂	C₂³	semidirect
177. C₂×D₁₂	C₂³	semidirect
178. C₂×C₄×D₃	C₂³	semidirect
179. C₂×C₄×D₃	C₂³	semidirect
180. C₂×C₄×D₃	C₂³	semidirect
181. C₂×Dic₆	C₂³	semidirect
182. C₂×Dic₆	C₂³	semidirect
202. #217	C₂³	semidirect
203. #217	C₂³	semidirect
204. #217	C₂³	semidirect
205. #217	C₂³	semidirect
206. (C₂×D₃)⋊C₄	C₂³	semidirect
207. (C₂×D₃)⋊C₄	C₂³	semidirect
208. (C₂×D₃)⋊C₄	C₂³	semidirect
209. (C₂×D₃)⋊C₄	C₂³	semidirect
210. (C₂×D₃)⋊C₄	C₂³	semidirect
211. (C₂×D₃)⋊C₄	C₂³	semidirect
212. C₄⋊Dic₃	C₂³	semidirect
213. C₄⋊Dic₃	C₂³	semidirect
214. C₄⋊Dic₃	C₂³	semidirect
215. Dic₃⋊C₄	C₂³	semidirect
216. Dic₃⋊C₄	C₂³	semidirect
217. Dic₃⋊C₄	C₂³	semidirect
218. Dic₃⋊C₄	C₂³	semidirect
219. Dic₃⋊C₄	C₂³	semidirect
220. Dic₃⋊C₄	C₂³	semidirect
221. C₄×Dic₃	C₂³	semidirect
222. C₄×Dic₃	C₂³	semidirect
223. C₄×Dic₃	C₂³	semidirect
224. C₄×Dic₃	C₂³	semidirect
225. C₂⁵	C₂×D₃	semidirect
233. C₂²×D₄	C₂×D₃	semidirect
234. C₂²×D₄	C₂×D₃	semidirect
292. #120	C₂×D₃	semidirect
293. #120	C₂×D₃	semidirect
294. #120	C₂×D₃	semidirect
295. #120	C₂×D₃	semidirect
296. #120	C₂×D₃	semidirect
310. C₂×C₂²⋊C₄	C₂×D₃	semidirect
311. C₂×C₂²⋊C₄	C₂×D₃	semidirect
655. C₃	#3532	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#120	2
C₂×#953	2
#5806	2
#5805	2
#5804	2
D₄×#67	2
#5595	2
#5594	2
#5593	2
#5592	2
#5591	2
#5590	2
#5589	2
#5587	2
#5495	2
#5494	2
#5490	2
#3532	3