Subgroups — #86639

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 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	#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	#5829	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	#5678	C₂	1	1	yes	maximal, characteristic, complemented
7	#5670	C₂	1	1	yes	maximal, characteristic, complemented
8	#5663	C₂	1	1	yes	maximal, characteristic, complemented
9	#5661	C₂	1	1	yes	maximal, characteristic, complemented
10	#5654	C₂	1	1	yes	maximal, characteristic, complemented
11	#5649	C₂	1	1	yes	maximal, characteristic, complemented
12	#5644	C₂	1	1	yes	maximal, characteristic, complemented
13	#5636	C₂	1	1	yes	maximal, characteristic, complemented
14	#5615	C₂	1	1	yes	maximal, characteristic, complemented
15	#5613	C₂	1	1	yes	maximal, characteristic, complemented
16	#5610	C₂	1	1	yes	maximal, characteristic, complemented
17	D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	#5601	C₂	1	1	yes	maximal, characteristic, complemented
19	#5599	C₂	1	1	yes	maximal, characteristic, complemented
20	#5593	C₂	1	1	yes	maximal, characteristic, complemented
21	#5590	C₂	1	1	yes	maximal, characteristic, complemented
22	#5590	C₂	1	1	yes	maximal, characteristic, complemented
23	#5586	C₂	1	1	yes	maximal, characteristic, complemented
24	#5547	C₂	1	1	yes	maximal, characteristic, complemented
25	#5545	C₂	1	1	yes	maximal, characteristic, complemented
26	#5540	C₂	1	1	yes	maximal, characteristic, complemented
27	#5540	C₂	1	1	yes	maximal, characteristic, complemented
28	#5490	C₂	1	1	yes	maximal, characteristic, complemented
29	#5490	C₂	1	1	yes	maximal, characteristic, complemented
30	#5486	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
32	#3519	—	3	1	no	maximal, Sylow
33	C₂×C₃×#41	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#67	C₂²	1	1	yes	characteristic
36	C₂²×#67	C₂²	1	1	yes	characteristic
37	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#67	C₂²	1	1	yes	characteristic, complemented
39	C₂³×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#237	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₃×D₄	C₂²	1	1	yes	characteristic
42	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×#235	C₂²	1	1	yes	characteristic, complemented
46	C₂×#235	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
48	C₃×#124	C₂²	1	1	yes	characteristic, complemented
49	C₃×#123	C₂²	1	1	yes	characteristic, complemented
50	C₃×#123	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×#121	C₂²	1	1	yes	characteristic, complemented
53	C₃×#121	C₂²	1	1	yes	characteristic, complemented
54	C₃×#121	C₂²	1	1	yes	characteristic, complemented
55	C₃×#120	C₂²	1	1	yes	characteristic, complemented
56	C₃×#120	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	#953	C₂²	1	1	yes	characteristic, complemented
62	#953	C₂²	1	1	yes	characteristic, complemented
63	C₂×#217	C₂²	1	1	yes	characteristic, complemented
64	#947	C₂²	1	1	yes	characteristic, complemented
65	#947	C₂²	1	1	yes	characteristic, complemented
66	#946	C₂²	1	1	yes	characteristic, complemented
67	#944	C₂²	1	1	yes	characteristic, complemented
68	#940	C₂²	1	1	yes	characteristic, complemented
69	#940	C₂²	1	1	yes	characteristic, complemented
70	#940	C₂²	1	1	yes	characteristic, complemented
71	#939	C₂²	1	1	yes	characteristic
72	#939	C₂²	1	1	yes	characteristic, complemented
73	#939	C₂²	1	1	yes	characteristic, complemented
74	#939	C₂²	1	1	yes	characteristic, complemented
75	#939	C₂²	1	1	yes	characteristic, complemented
76	#939	C₂²	1	1	yes	characteristic, complemented
77	#939	C₂²	1	1	yes	characteristic, complemented
78	#939	C₂²	1	1	yes	characteristic, complemented
79	#939	C₂²	1	1	yes	characteristic, complemented
80	#939	C₂²	1	1	yes	characteristic, complemented
81	#939	C₂²	1	1	yes	characteristic, complemented
82	#939	C₂²	1	1	yes	characteristic, complemented
83	#939	C₂²	1	1	yes	characteristic, complemented
84	#939	C₂²	1	1	yes	characteristic, complemented
85	#939	C₂²	1	1	yes	characteristic, complemented
86	#939	C₂²	1	1	yes	characteristic, complemented
87	#938	C₂²	1	1	yes	characteristic, complemented
88	#938	C₂²	1	1	yes	characteristic, complemented
89	#937	C₂²	1	1	yes	characteristic, complemented
90	#937	C₂²	1	1	yes	characteristic, complemented
91	#937	C₂²	1	1	yes	characteristic, complemented
92	#937	C₂²	1	1	yes	characteristic, complemented
93	#936	C₂²	1	1	yes	characteristic, complemented
94	#935	C₂²	1	1	yes	characteristic, complemented
95	#935	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
99	#930	C₂²	1	1	yes	characteristic, complemented
100	#930	C₂²	1	1	yes	characteristic, complemented
101	#930	C₂²	1	1	yes	characteristic, complemented
102	#929	C₂²	1	1	yes	characteristic, complemented
103	#929	C₂²	1	1	yes	characteristic, complemented
104	#929	C₂²	1	1	yes	characteristic, complemented
105	C₄×#67	C₂²	1	1	yes	characteristic
106	C₄×#67	C₂²	1	1	yes	characteristic, complemented
107	C₄×#67	C₂²	1	1	yes	characteristic, complemented
108	C₄×#67	C₂²	1	1	yes	characteristic, complemented
109	C₄×#67	C₂²	1	1	yes	characteristic, complemented
110	C₄×#67	C₂²	1	1	yes	characteristic, complemented
111	C₄×#67	C₂²	1	1	yes	characteristic, complemented
112	C₄×#67	C₂²	1	1	yes	characteristic, complemented
113	C₄×#67	C₂²	1	1	yes	characteristic, complemented
114	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
120	#898	C₂²	1	1	yes	characteristic, complemented
121	#898	C₂²	1	1	yes	characteristic, complemented
122	#896	C₂²	1	1	yes	characteristic, complemented
123	#896	C₂²	1	1	yes	characteristic, complemented
124	#895	C₂²	1	1	yes	characteristic, complemented
125	#895	C₂²	1	1	yes	characteristic, complemented
126	#894	C₂²	1	1	yes	characteristic, complemented
127	#894	C₂²	1	1	yes	characteristic, complemented
128	#894	C₂²	1	1	yes	characteristic, complemented
129	#893	C₂²	1	1	yes	characteristic, complemented
130	#892	C₂²	1	1	yes	characteristic, complemented
131	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
132	#889	C₂²	1	1	yes	characteristic, complemented
133	#889	C₂²	1	1	yes	characteristic, complemented
134	#889	C₂²	1	1	yes	characteristic, complemented
135	#887	C₂²	1	1	yes	characteristic, complemented
136	#886	C₂²	1	1	yes	characteristic, complemented
137	#885	C₂²	1	1	yes	characteristic, complemented
138	#885	C₂²	1	1	yes	characteristic, complemented
139	#885	C₂²	1	1	yes	characteristic, complemented
140	#884	C₂²	1	1	yes	characteristic, complemented
141	#884	C₂²	1	1	yes	characteristic, complemented
142	#884	C₂²	1	1	yes	characteristic, complemented
143	#884	C₂²	1	1	yes	characteristic, complemented
144	#884	C₂²	1	1	yes	characteristic, complemented
145	#884	C₂²	1	1	yes	characteristic, complemented
146	#884	C₂²	1	1	yes	characteristic, complemented
147	#884	C₂²	1	1	yes	characteristic, complemented
148	#884	C₂²	1	1	yes	characteristic, complemented
149	#883	C₂²	1	1	yes	characteristic, complemented
150	#883	C₂²	1	1	yes	characteristic, complemented
151	#883	C₂²	1	1	yes	characteristic, complemented
152	#882	C₂²	1	1	yes	characteristic, complemented
153	#882	C₂²	1	1	yes	characteristic, complemented
154	#882	C₂²	1	1	yes	characteristic, complemented
155	#882	C₂²	1	1	yes	characteristic, complemented
156	#67⋊C₄	C₂²	1	1	yes	characteristic
157	#67⋊C₄	C₂²	1	1	yes	characteristic
158	#67⋊C₄	C₂²	1	1	yes	characteristic
159	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
173	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
174	D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	#879	C₂²	1	1	yes	characteristic, complemented
176	#879	C₂²	1	1	yes	characteristic, complemented
177	#879	C₂²	1	1	yes	characteristic, complemented
178	#878	C₂²	1	1	yes	characteristic, complemented
179	#878	C₂²	1	1	yes	characteristic, complemented
180	#878	C₂²	1	1	yes	characteristic, complemented
181	#877	C₂²	1	1	yes	characteristic, complemented
182	#877	C₂²	1	1	yes	characteristic, complemented
183	#877	C₂²	1	1	yes	characteristic, complemented
184	#876	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
186	#872	C₂²	1	1	yes	characteristic, complemented
187	#872	C₂²	1	1	yes	characteristic, complemented
188	#555	—	3	1	no	—
189	#554	—	3	1	no	—
190	#553	—	3	1	no	—
191	#553	—	3	1	no	—
192	#553	—	3	1	no	—
193	#553	—	3	1	no	—
194	#550	—	3	1	no	—
195	#546	—	3	1	no	—
196	#546	—	3	1	no	—
197	#546	—	3	1	no	—
198	#546	—	3	1	no	—
199	#546	—	3	1	no	—
200	#546	D₃	1	1	yes	characteristic, complemented
201	D₄²	—	3	1	no	—
202	D₄²	—	3	1	no	—
203	D₄²	—	3	1	no	—
204	#540	—	3	1	no	—
205	#540	—	3	1	no	—
206	#538	—	3	1	no	—
207	#538	—	3	1	no	—
208	#538	—	3	1	no	—
209	#538	—	3	1	no	—
210	#532	—	3	1	no	—
211	#529	—	3	1	no	—
212	#525	—	3	1	no	—
213	#525	—	3	1	no	—
214	C₂×#121	—	3	1	no	—
215	C₂×#121	—	3	1	no	—
216	#518	—	3	1	no	—
217	#518	—	3	1	no	—
218	C₂×C₄×D₄	—	3	1	no	—
219	C₂⁴×C₃	C₂³	1	1	yes	characteristic
220	C₂⁴×C₃	C₂³	1	1	yes	characteristic
221	C₂³×D₃	C₂³	1	1	yes	characteristic
222	C₂³×D₃	C₂³	1	1	yes	characteristic
223	C₂³×D₃	C₂³	1	1	yes	characteristic
224	C₂³×D₃	C₂³	1	1	yes	characteristic
225	C₃×#41	—	4	2	no	—
226	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₃×D₄	—	4	2	no	—
228	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
243	C₂×#67	—	2	4	no	—
244	C₂×#67	—	2	4	no	—
245	C₂×#67	—	4	2	no	—
246	C₂×#67	—	4	2	no	—
247	C₂×#67	C₂³	1	1	yes	characteristic
248	C₂×#67	C₂³	1	1	yes	characteristic
249	C₂×#67	C₂³	1	1	yes	characteristic
250	C₂×#67	C₂³	1	1	yes	characteristic
251	C₂×#67	C₂³	1	1	yes	characteristic
252	C₂×#67	C₂³	1	1	yes	characteristic
253	C₂×#67	C₂³	1	1	yes	characteristic
254	C₂×#67	C₂³	1	1	yes	characteristic
255	C₂×#67	C₂³	1	1	yes	characteristic
256	C₂×#67	C₂³	1	1	yes	characteristic
257	C₂×#67	C₂³	1	1	yes	characteristic
258	C₂×#67	C₂³	1	1	yes	characteristic
259	C₂×#67	C₂³	1	1	yes	characteristic
260	C₂×#67	C₂³	1	1	yes	characteristic
261	C₂×#67	C₂³	1	1	yes	characteristic
262	C₂×#67	C₂³	1	1	yes	characteristic
263	C₂×#67	C₂³	1	1	yes	characteristic
264	C₂×#67	C₂³	1	1	yes	characteristic
265	C₂×#67	C₂³	1	1	yes	characteristic
266	C₂×#67	C₂³	1	1	yes	characteristic
267	C₂×#67	C₂³	1	1	yes	characteristic
268	C₂×#67	C₂³	1	1	yes	characteristic
269	C₂²×Dic₃	—	4	2	no	—
270	C₂²×Dic₃	C₂³	1	1	yes	characteristic
271	C₂²×Dic₃	C₂³	1	1	yes	characteristic
272	C₂²×Dic₃	C₂³	1	1	yes	characteristic
273	C₂²×Dic₃	C₂³	1	1	yes	characteristic
274	C₂²×Dic₃	C₂³	1	1	yes	characteristic
275	C₂²×Dic₃	C₂³	1	1	yes	characteristic
276	C₂²×Dic₃	C₂³	1	1	yes	characteristic
277	C₂²×Dic₃	C₂³	1	1	yes	characteristic
278	C₂²×Dic₃	C₂³	1	1	yes	characteristic
279	C₂²×Dic₃	C₂³	1	1	yes	characteristic
280	#237	—	4	2	no	—
281	D₃×D₄	—	2	4	no	—
282	D₃×D₄	—	4	2	no	—
283	D₃×D₄	—	4	2	no	—
284	D₃×D₄	—	4	2	no	—
285	#235	—	4	2	no	—
286	#235	—	4	2	no	—
287	C₂×D₁₂	C₂³	1	1	yes	characteristic
288	C₂×D₁₂	C₂³	1	1	yes	characteristic
289	C₂×D₁₂	C₂³	1	1	yes	characteristic
290	C₂×D₁₂	C₂³	1	1	yes	characteristic
291	C₂×D₁₂	C₂³	1	1	yes	characteristic
292	C₂×D₁₂	C₂³	1	1	yes	characteristic
293	C₂×C₄×D₃	—	4	2	no	—
294	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
305	C₂×Dic₆	C₂³	1	1	yes	characteristic
306	C₂×Dic₆	C₂³	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
309	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
310	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
321	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₃×C₄²	C₂³	1	1	yes	characteristic
324	#217	C₂³	1	1	yes	characteristic
325	#217	C₂³	1	1	yes	characteristic
326	#217	C₂³	1	1	yes	characteristic
327	#217	C₂³	1	1	yes	characteristic
328	#217	C₂³	1	1	yes	characteristic
329	#217	C₂³	1	1	yes	characteristic
330	#217	C₂³	1	1	yes	characteristic
331	#217	C₂³	1	1	yes	characteristic
332	#217	C₂³	1	1	yes	characteristic
333	#217	C₂³	1	1	yes	characteristic
334	#217	C₂³	1	1	yes	characteristic
335	#217	C₂³	1	1	yes	characteristic
336	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
337	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
338	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
339	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
340	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
341	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
342	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
343	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
344	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
345	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
346	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
347	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
349	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
350	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
351	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
353	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
354	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
355	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
356	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
357	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
358	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
359	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
360	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
361	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
362	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
367	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
368	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
369	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
370	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
371	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
378	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
379	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
380	C₄×Dic₃	C₂³	1	1	yes	characteristic
381	C₄×Dic₃	C₂³	1	1	yes	characteristic
382	C₄×Dic₃	C₂³	1	1	yes	characteristic
383	C₄×Dic₃	C₂³	1	1	yes	characteristic
384	C₄×Dic₃	C₂³	1	1	yes	characteristic
385	C₄×Dic₃	C₂³	1	1	yes	characteristic
386	C₄×Dic₃	C₂³	1	1	yes	characteristic
387	C₄×Dic₃	C₂³	1	1	yes	characteristic
388	C₄×Dic₃	C₂³	1	1	yes	characteristic
389	C₂×#41	—	3	1	no	—
390	C₂×#41	—	3	1	no	—
391	C₂×#41	—	3	1	no	—
392	C₂×#41	C₂×D₃	1	1	yes	characteristic, complemented
393	C₂²×D₄	—	3	1	no	—
394	C₂²×D₄	—	3	1	no	—
395	C₂²×D₄	—	3	1	no	—
396	C₂²×D₄	—	3	1	no	—
397	C₂²×D₄	—	3	1	no	—
398	C₂²×D₄	—	3	1	no	—
399	C₂²×D₄	—	3	1	no	—
400	C₂²×D₄	—	3	1	no	—
401	C₂²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
402	C₂³×C₄	—	3	1	no	—
403	C₂³×C₄	—	3	1	no	—
404	C₄⋊Q₈	—	3	1	no	—
405	#127	—	3	1	no	—
406	#127	—	3	1	no	—
407	#127	—	3	1	no	—
408	#126	—	3	1	no	—
409	#126	—	3	1	no	—
410	#126	—	3	1	no	—
411	#126	—	3	1	no	—
412	#126	—	3	1	no	—
413	#126	—	3	1	no	—
414	#125	—	3	1	no	—
415	#125	—	3	1	no	—
416	#125	—	3	1	no	—
417	#124	—	3	1	no	—
418	#124	—	3	1	no	—
419	#124	—	3	1	no	—
420	#124	—	3	1	no	—
421	#124	—	3	1	no	—
422	#124	—	3	1	no	—
423	#124	C₂×D₃	1	1	yes	characteristic, complemented
424	#123	—	3	1	no	—
425	#123	—	3	1	no	—
426	#123	—	3	1	no	—
427	#123	—	3	1	no	—
428	#123	—	3	1	no	—
429	#123	—	3	1	no	—
430	#123	—	3	1	no	—
431	#123	—	3	1	no	—
432	#123	—	3	1	no	—
433	#123	—	3	1	no	—
434	#123	—	3	1	no	—
435	#123	—	3	1	no	—
436	#123	C₂×D₃	1	1	yes	characteristic, complemented
437	#123	C₂×D₃	1	1	yes	characteristic, complemented
438	C₂²⋊Q₈	—	3	1	no	—
439	C₂²⋊Q₈	—	3	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
445	#121	—	3	1	no	—
446	#121	—	3	1	no	—
447	#121	—	3	1	no	—
448	#121	—	3	1	no	—
449	#121	—	3	1	no	—
450	#121	—	3	1	no	—
451	#121	—	3	1	no	—
452	#121	—	3	1	no	—
453	#121	—	3	1	no	—
454	#121	—	3	1	no	—
455	#121	—	3	1	no	—
456	#121	—	3	1	no	—
457	#121	—	3	1	no	—
458	#121	—	3	1	no	—
459	#121	—	3	1	no	—
460	#121	—	3	1	no	—
461	#121	—	3	1	no	—
462	#121	—	3	1	no	—
463	#121	—	3	1	no	—
464	#121	—	3	1	no	—
465	#121	—	3	1	no	—
466	#121	—	3	1	no	—
467	#121	—	3	1	no	—
468	#121	—	3	1	no	—
469	#121	—	3	1	no	—
470	#121	—	3	1	no	—
471	#121	—	3	1	no	—
472	#121	—	3	1	no	—
473	#121	—	3	1	no	—
474	#121	—	3	1	no	—
475	#121	—	3	1	no	—
476	#121	—	3	1	no	—
477	#121	C₂×D₃	1	1	yes	characteristic, complemented
478	#121	C₂×D₃	1	1	yes	characteristic, complemented
479	#121	C₂×D₃	1	1	yes	characteristic, complemented
480	#120	—	3	1	no	—
481	#120	—	3	1	no	—
482	#120	—	3	1	no	—
483	#120	—	3	1	no	—
484	#120	—	3	1	no	—
485	#120	—	3	1	no	—
486	#120	—	3	1	no	—
487	#120	—	3	1	no	—
488	#120	—	3	1	no	—
489	#120	—	3	1	no	—
490	#120	C₂×D₃	1	1	yes	characteristic, complemented
491	#120	C₂×D₃	1	1	yes	characteristic, complemented
492	C₄×Q₈	—	3	1	no	—
493	C₄×D₄	—	3	1	no	—
494	C₄×D₄	—	3	1	no	—
495	C₄×D₄	—	3	1	no	—
496	C₄×D₄	—	3	1	no	—
497	C₄×D₄	—	3	1	no	—
498	C₄×D₄	—	3	1	no	—
499	C₄×D₄	—	3	1	no	—
500	C₄×D₄	—	3	1	no	—
501	C₄×D₄	—	3	1	no	—
502	C₄×D₄	—	3	1	no	—
503	C₄×D₄	—	3	1	no	—
504	C₄×D₄	—	3	1	no	—
505	C₄×D₄	—	3	1	no	—
506	C₄×D₄	—	3	1	no	—
507	C₄×D₄	—	3	1	no	—
508	C₄×D₄	—	3	1	no	—
509	C₄×D₄	—	3	1	no	—
510	C₄×D₄	—	3	1	no	—
511	C₄×D₄	—	3	1	no	—
512	C₄×D₄	—	3	1	no	—
513	C₄×D₄	—	3	1	no	—
514	C₄×D₄	—	3	1	no	—
515	C₄×D₄	—	3	1	no	—
516	C₄×D₄	—	3	1	no	—
517	C₄×D₄	—	3	1	no	—
518	C₄×D₄	—	3	1	no	—
519	C₄×D₄	—	3	1	no	—
520	C₄×D₄	—	3	1	no	—
521	C₄×D₄	—	3	1	no	—
522	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
523	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
524	#117	—	3	1	no	—
525	#117	—	3	1	no	—
526	#117	—	3	1	no	—
527	#117	—	3	1	no	—
528	#117	—	3	1	no	—
529	#117	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	—	3	1	no	—
540	C₂×C₂²⋊C₄	—	3	1	no	—
541	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
542	C₂×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
543	C₂×C₄²	—	3	1	no	—
544	C₂³×C₃	—	2	2	no	—
545	C₂³×C₃	—	2	2	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	4	1	no	—
548	C₂³×C₃	—	4	1	no	—
549	C₂³×C₃	—	4	1	no	—
550	C₂³×C₃	C₂⁴	1	1	yes	characteristic
551	C₂³×C₃	C₂⁴	1	1	yes	characteristic
552	C₂³×C₃	C₂⁴	1	1	yes	characteristic
553	C₂³×C₃	C₂⁴	1	1	yes	characteristic
554	C₂³×C₃	C₂⁴	1	1	yes	characteristic
555	C₂³×C₃	C₂⁴	1	1	yes	characteristic
556	C₂²×D₃	—	2	2	no	—
557	C₂²×D₃	—	2	2	no	—
558	C₂²×D₃	—	2	2	no	—
559	C₂²×D₃	—	2	2	no	—
560	C₂²×D₃	—	2	2	no	—
561	C₂²×D₃	—	4	1	no	—
562	C₂²×D₃	—	4	1	no	—
563	C₂²×D₃	—	4	1	no	—
564	C₂²×D₃	—	4	1	no	—
565	C₂²×D₃	—	4	1	no	—
566	C₂²×D₃	—	4	1	no	—
567	C₂²×D₃	—	4	1	no	—
568	C₂²×D₃	C₂⁴	1	1	yes	characteristic
569	C₂²×D₃	C₂⁴	1	1	yes	characteristic
570	C₂²×D₃	C₂⁴	1	1	yes	characteristic
571	C₂²×D₃	C₂⁴	1	1	yes	characteristic
572	C₂²×D₃	C₂⁴	1	1	yes	characteristic
573	C₃×Q₈	—	4	1	no	—
574	C₃×D₄	—	2	2	no	—
575	C₃×D₄	—	2	2	no	—
576	C₃×D₄	—	2	2	no	—
577	C₃×D₄	—	2	2	no	—
578	C₃×D₄	—	4	1	no	—
579	C₃×D₄	—	4	1	no	—
580	C₃×D₄	—	4	1	no	—
581	C₃×D₄	—	4	1	no	—
582	C₃×D₄	—	4	1	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	4	1	no	—
585	C₂×C₃×C₄	—	4	1	no	—
586	C₂×C₃×C₄	—	4	1	no	—
587	C₂×C₃×C₄	—	4	1	no	—
588	C₂×C₃×C₄	—	4	1	no	—
589	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
590	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
591	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
598	#67	—	2	2	no	—
599	#67	—	2	2	no	—
600	#67	—	2	2	no	—
601	#67	—	2	2	no	—
602	#67	—	2	2	no	—
603	#67	—	2	2	no	—
604	#67	—	2	2	no	—
605	#67	—	2	2	no	—
606	#67	—	2	2	no	—
607	#67	—	2	2	no	—
608	#67	—	2	2	no	—
609	#67	—	2	2	no	—
610	#67	—	2	2	no	—
611	#67	—	4	1	no	—
612	#67	—	4	1	no	—
613	#67	—	4	1	no	—
614	#67	—	4	1	no	—
615	#67	—	4	1	no	—
616	#67	—	4	1	no	—
617	#67	—	4	1	no	—
618	#67	—	4	1	no	—
619	#67	#41	1	4	yes	complemented
620	C₂×Dic₃	—	2	2	no	—
621	C₂×Dic₃	—	2	2	no	—
622	C₂×Dic₃	—	2	2	no	—
623	C₂×Dic₃	—	2	2	no	—
624	C₂×Dic₃	—	2	2	no	—
625	C₂×Dic₃	—	4	1	no	—
626	C₂×Dic₃	—	4	1	no	—
627	C₂×Dic₃	—	4	1	no	—
628	C₂×Dic₃	—	4	1	no	—
629	C₂×Dic₃	—	4	1	no	—
630	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
631	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
632	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
633	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
634	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
635	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
636	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
637	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
638	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
639	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
640	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
641	D₁₂	—	2	2	no	—
642	D₁₂	—	4	1	no	—
643	D₁₂	—	4	1	no	—
644	D₁₂	—	4	1	no	—
645	D₁₂	—	4	1	no	—
646	D₁₂	—	4	1	no	—
647	C₄×D₃	—	2	2	no	—
648	C₄×D₃	—	2	2	no	—
649	C₄×D₃	—	2	2	no	—
650	C₄×D₃	—	4	1	no	—
651	C₄×D₃	—	4	1	no	—
652	C₄×D₃	—	4	1	no	—
653	C₄×D₃	—	4	1	no	—
654	C₄×D₃	—	4	1	no	—
655	C₄×D₃	—	4	1	no	—
656	C₄×D₃	—	4	1	no	—
657	C₄×D₃	—	4	1	no	—
658	Dic₆	—	2	2	no	—
659	Dic₆	—	4	1	no	—
660	C₂⁴	—	3	1	no	—
661	C₂⁴	—	3	1	no	—
662	C₂⁴	—	3	1	no	—
663	C₂⁴	—	3	1	no	—
664	C₂⁴	C₂²×D₃	1	1	yes	characteristic
665	C₂⁴	C₂²×D₃	1	1	yes	characteristic
666	#41	—	4	2	no	—
667	#41	—	12	2	no	—
668	#41	—	12	2	no	—
669	#41	—	12	2	no	—
670	C₂×Q₈	—	3	1	no	—
671	C₂×Q₈	—	3	1	no	—
672	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
673	C₂×D₄	—	3	1	no	—
674	C₂×D₄	—	3	1	no	—
675	C₂×D₄	—	3	1	no	—
676	C₂×D₄	—	3	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	3	1	no	—
681	C₂×D₄	—	3	1	no	—
682	C₂×D₄	—	3	1	no	—
683	C₂×D₄	—	3	1	no	—
684	C₂×D₄	—	3	1	no	—
685	C₂×D₄	—	3	1	no	—
686	C₂×D₄	—	3	1	no	—
687	C₂×D₄	—	3	1	no	—
688	C₂×D₄	—	3	1	no	—
689	C₂×D₄	—	3	1	no	—
690	C₂×D₄	—	3	1	no	—
691	C₂×D₄	—	3	1	no	—
692	C₂×D₄	—	3	1	no	—
693	C₂×D₄	—	3	1	no	—
694	C₂×D₄	—	3	1	no	—
695	C₂×D₄	—	3	1	no	—
696	C₂×D₄	—	3	1	no	—
697	C₂×D₄	—	3	1	no	—
698	C₂×D₄	—	3	1	no	—
699	C₂×D₄	—	3	1	no	—
700	C₂×D₄	—	3	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	6	4	no	—
703	C₂×D₄	—	6	4	no	—
704	C₂×D₄	—	6	4	no	—
705	C₂×D₄	—	12	2	no	—
706	C₂×D₄	—	12	2	no	—
707	C₂×D₄	—	12	2	no	—
708	C₂×D₄	—	12	2	no	—
709	C₂×D₄	—	12	2	no	—
710	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
711	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
712	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
713	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
714	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
715	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
716	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
717	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
718	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
719	C₂²×C₄	—	3	1	no	—
720	C₂²×C₄	—	3	1	no	—
721	C₂²×C₄	—	3	1	no	—
722	C₂²×C₄	—	3	1	no	—
723	C₂²×C₄	—	3	1	no	—
724	C₂²×C₄	—	3	1	no	—
725	C₂²×C₄	—	3	1	no	—
726	C₂²×C₄	—	3	1	no	—
727	C₂²×C₄	—	3	1	no	—
728	C₂²×C₄	—	3	1	no	—
729	C₂²×C₄	—	3	1	no	—
730	C₂²×C₄	—	3	1	no	—
731	C₂²×C₄	—	3	1	no	—
732	C₂²×C₄	—	3	1	no	—
733	C₂²×C₄	—	3	1	no	—
734	C₂²×C₄	—	3	1	no	—
735	C₂²×C₄	—	3	1	no	—
736	C₂²×C₄	—	3	1	no	—
737	C₂²×C₄	—	3	1	no	—
738	C₂²×C₄	—	3	1	no	—
739	C₂²×C₄	—	3	1	no	—
740	C₂²×C₄	—	12	2	no	—
741	C₂²×C₄	—	12	2	no	—
742	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
747	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
748	C₄⋊C₄	—	3	1	no	—
749	C₄⋊C₄	—	3	1	no	—
750	C₄⋊C₄	—	3	1	no	—
751	C₄⋊C₄	—	3	1	no	—
752	C₄⋊C₄	—	3	1	no	—
753	C₄⋊C₄	—	3	1	no	—
754	C₄⋊C₄	—	3	1	no	—
755	C₄⋊C₄	—	3	1	no	—
756	C₄⋊C₄	—	3	1	no	—
757	C₄⋊C₄	—	3	1	no	—
758	C₄⋊C₄	—	3	1	no	—
759	C₄⋊C₄	—	3	1	no	—
760	C₄⋊C₄	—	3	1	no	—
761	C₄⋊C₄	—	3	1	no	—
762	C₄⋊C₄	—	3	1	no	—
763	C₄⋊C₄	—	3	1	no	—
764	C₄⋊C₄	—	3	1	no	—
765	C₄⋊C₄	—	3	1	no	—
766	C₄⋊C₄	—	3	1	no	—
767	C₄⋊C₄	—	3	1	no	—
768	C₄⋊C₄	—	3	1	no	—
769	C₄⋊C₄	—	3	1	no	—
770	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
774	C₂²⋊C₄	—	3	1	no	—
775	C₂²⋊C₄	—	3	1	no	—
776	C₂²⋊C₄	—	3	1	no	—
777	C₂²⋊C₄	—	3	1	no	—
778	C₂²⋊C₄	—	3	1	no	—
779	C₂²⋊C₄	—	3	1	no	—
780	C₂²⋊C₄	—	3	1	no	—
781	C₂²⋊C₄	—	3	1	no	—
782	C₂²⋊C₄	—	3	1	no	—
783	C₂²⋊C₄	—	3	1	no	—
784	C₂²⋊C₄	—	3	1	no	—
785	C₂²⋊C₄	—	3	1	no	—
786	C₂²⋊C₄	—	3	1	no	—
787	C₂²⋊C₄	—	3	1	no	—
788	C₂²⋊C₄	—	3	1	no	—
789	C₂²⋊C₄	—	3	1	no	—
790	C₂²⋊C₄	—	3	1	no	—
791	C₂²⋊C₄	—	3	1	no	—
792	C₂²⋊C₄	—	3	1	no	—
793	C₂²⋊C₄	—	3	1	no	—
794	C₂²⋊C₄	—	3	1	no	—
795	C₂²⋊C₄	—	3	1	no	—
796	C₂²⋊C₄	—	3	1	no	—
797	C₂²⋊C₄	—	3	1	no	—
798	C₂²⋊C₄	—	3	1	no	—
799	C₂²⋊C₄	—	3	1	no	—
800	C₂²⋊C₄	—	3	1	no	—
801	C₂²⋊C₄	—	3	1	no	—
802	C₂²⋊C₄	—	3	1	no	—
803	C₂²⋊C₄	—	3	1	no	—
804	C₂²⋊C₄	—	3	1	no	—
805	C₂²⋊C₄	—	3	1	no	—
806	C₂²⋊C₄	—	3	1	no	—
807	C₂²⋊C₄	—	3	1	no	—
808	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
820	C₄²	—	3	1	no	—
821	C₄²	—	3	1	no	—
822	C₄²	—	3	1	no	—
823	C₄²	—	3	1	no	—
824	C₄²	—	3	1	no	—
825	C₄²	—	3	1	no	—
826	C₄²	—	3	1	no	—
827	C₄²	—	3	1	no	—
828	C₄²	—	3	1	no	—
829	C₄²	C₂²×D₃	1	1	yes	characteristic
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	2	1	no	—
832	C₂²×C₃	—	2	1	no	—
833	C₂²×C₃	—	2	1	no	—
834	C₂²×C₃	—	2	1	no	—
835	C₂²×C₃	—	2	1	no	—
836	C₂²×C₃	—	2	1	no	—
837	C₂²×C₃	—	2	1	no	—
838	C₂²×C₃	—	2	1	no	—
839	C₂²×C₃	—	2	1	no	—
840	C₂²×C₃	—	2	1	no	—
841	C₂²×C₃	—	2	1	no	—
842	C₂²×C₃	—	2	1	no	—
843	C₂²×C₃	—	2	1	no	—
844	C₂²×C₃	—	2	1	no	—
845	C₂²×C₃	—	2	1	no	—
846	C₂²×C₃	—	4	4	no	—
847	C₂²×C₃	—	8	2	no	—
848	C₂²×C₃	C₂×#41	1	2	yes	—
849	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
850	C₂²×C₃	C₂⁵	1	1	yes	characteristic
851	C₂×D₃	—	2	1	no	—
852	C₂×D₃	—	2	1	no	—
853	C₂×D₃	—	2	1	no	—
854	C₂×D₃	—	2	1	no	—
855	C₂×D₃	—	2	1	no	—
856	C₂×D₃	—	2	1	no	—
857	C₂×D₃	—	2	1	no	—
858	C₂×D₃	—	2	1	no	—
859	C₂×D₃	—	2	1	no	—
860	C₂×D₃	—	2	1	no	—
861	C₂×D₃	—	2	1	no	—
862	C₂×D₃	—	2	1	no	—
863	C₂×D₃	—	2	1	no	—
864	C₂×D₃	—	2	1	no	—
865	C₂×D₃	—	4	4	no	—
866	C₂×D₃	—	8	2	no	—
867	C₂×D₃	—	8	2	no	—
868	C₂×D₃	—	8	2	no	—
869	C₂×D₃	C₂×#41	1	2	yes	—
870	C₃×C₄	—	2	1	no	—
871	C₃×C₄	—	2	1	no	—
872	C₃×C₄	—	2	1	no	—
873	C₃×C₄	—	2	1	no	—
874	C₃×C₄	—	2	1	no	—
875	C₃×C₄	—	2	1	no	—
876	C₃×C₄	—	2	1	no	—
877	C₃×C₄	—	2	1	no	—
878	C₃×C₄	—	2	1	no	—
879	Dic₃	—	2	1	no	—
880	Dic₃	—	2	1	no	—
881	Dic₃	—	2	1	no	—
882	Dic₃	—	2	1	no	—
883	Dic₃	—	2	1	no	—
884	Dic₃	—	2	1	no	—
885	Dic₃	—	2	1	no	—
886	Dic₃	—	2	1	no	—
887	Dic₃	—	2	1	no	—
888	Dic₃	C₂×#41	1	2	yes	—
889	Dic₃	H(5,𝔽₂)	1	2	yes	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	3	1	no	—
894	C₂³	—	3	1	no	—
895	C₂³	—	3	1	no	—
896	C₂³	—	3	1	no	—
897	C₂³	—	3	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	6	2	no	—
902	C₂³	—	6	2	no	—
903	C₂³	—	6	2	no	—
904	C₂³	—	6	2	no	—
905	C₂³	—	6	2	no	—
906	C₂³	—	12	1	no	—
907	C₂³	—	12	1	no	—
908	C₂³	—	12	1	no	—
909	C₂³	—	12	1	no	—
910	C₂³	—	12	1	no	—
911	C₂³	—	12	1	no	—
912	C₂³	—	12	1	no	—
913	C₂³	C₂³×D₃	1	1	yes	characteristic
914	C₂³	C₂³×D₃	1	1	yes	characteristic
915	C₂³	C₂³×D₃	1	1	yes	characteristic
916	C₂³	C₂³×D₃	1	1	yes	characteristic
917	C₂³	C₂³×D₃	1	1	yes	characteristic
918	C₂³	C₂³×D₃	1	1	yes	characteristic
919	Q₈	—	4	1	no	—
920	Q₈	—	6	2	no	—
921	Q₈	—	12	1	no	—
922	D₄	—	2	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	2	2	no	—
926	D₄	—	3	4	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	6	2	no	—
933	D₄	—	6	2	no	—
934	D₄	—	6	2	no	—
935	D₄	—	6	2	no	—
936	D₄	—	6	2	no	—
937	D₄	—	6	2	no	—
938	D₄	—	6	2	no	—
939	D₄	—	6	2	no	—
940	D₄	—	6	2	no	—
941	D₄	—	6	2	no	—
942	D₄	—	6	2	no	—
943	D₄	—	6	2	no	—
944	D₄	—	6	2	no	—
945	D₄	—	6	2	no	—
946	D₄	—	12	1	no	—
947	D₄	—	12	1	no	—
948	D₄	—	12	1	no	—
949	D₄	—	12	1	no	—
950	D₄	—	12	1	no	—
951	D₄	—	12	1	no	—
952	D₄	—	12	1	no	—
953	D₄	—	12	1	no	—
954	D₄	—	12	1	no	—
955	D₄	—	12	1	no	—
956	D₄	—	12	1	no	—
957	D₄	—	12	1	no	—
958	D₄	—	12	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	3	1	no	—
961	C₂×C₄	—	3	1	no	—
962	C₂×C₄	—	3	1	no	—
963	C₂×C₄	—	3	1	no	—
964	C₂×C₄	—	3	1	no	—
965	C₂×C₄	—	3	1	no	—
966	C₂×C₄	—	3	1	no	—
967	C₂×C₄	—	3	1	no	—
968	C₂×C₄	—	3	1	no	—
969	C₂×C₄	—	3	1	no	—
970	C₂×C₄	—	3	1	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	6	2	no	—
977	C₂×C₄	—	6	2	no	—
978	C₂×C₄	—	6	2	no	—
979	C₂×C₄	—	6	2	no	—
980	C₂×C₄	—	6	2	no	—
981	C₂×C₄	—	6	2	no	—
982	C₂×C₄	—	6	2	no	—
983	C₂×C₄	—	6	2	no	—
984	C₂×C₄	—	12	1	no	—
985	C₂×C₄	—	12	1	no	—
986	C₂×C₄	—	12	1	no	—
987	C₂×C₄	—	12	1	no	—
988	C₂×C₄	—	12	1	no	—
989	C₂×C₄	—	12	1	no	—
990	C₂×C₄	—	12	1	no	—
991	C₂×C₄	—	12	1	no	—
992	C₂×C₄	—	12	1	no	—
993	C₂×C₄	—	12	1	no	—
994	C₂×C₄	—	12	1	no	—
995	C₂×C₄	—	12	1	no	—
996	C₂×C₄	—	12	1	no	—
997	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
1006	C₂×C₃	—	2	2	no	—
1007	C₂×C₃	—	2	2	no	—
1008	C₂×C₃	—	4	1	no	—
1009	C₂×C₃	—	4	1	no	—
1010	C₂×C₃	—	4	1	no	—
1011	C₂×C₃	—	4	1	no	—
1012	C₂×C₃	C₂²×#41	1	1	yes	characteristic
1013	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1014	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1015	D₃	—	2	2	no	—
1016	D₃	—	4	1	no	—
1017	D₃	—	4	1	no	—
1018	D₃	—	4	1	no	—
1019	D₃	—	4	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	3	2	no	—
1037	C₂²	—	4	4	no	—
1038	C₂²	—	6	1	no	—
1039	C₂²	—	6	1	no	—
1040	C₂²	—	6	1	no	—
1041	C₂²	—	6	1	no	—
1042	C₂²	—	6	1	no	—
1043	C₂²	—	6	1	no	—
1044	C₂²	—	6	1	no	—
1045	C₂²	—	6	1	no	—
1046	C₂²	—	6	1	no	—
1047	C₂²	—	6	1	no	—
1048	C₂²	—	6	1	no	—
1049	C₂²	—	6	1	no	—
1050	C₂²	—	6	1	no	—
1051	C₂²	—	6	1	no	—
1052	C₂²	—	8	2	no	—
1053	C₂²	—	12	4	no	—
1054	C₂²	—	24	2	no	—
1055	C₂²	—	24	2	no	—
1056	C₂²	—	24	2	no	—
1057	C₂²	#1004	1	2	yes	—
1058	C₂²	D₃×#41	1	2	yes	—
1059	C₂²	C₂⁴×D₃	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	3	2	no	—
1070	C₄	—	3	2	no	—
1071	C₄	—	6	1	no	—
1072	C₄	—	6	1	no	—
1073	C₄	—	6	1	no	—
1074	C₄	—	6	1	no	—
1075	C₄	—	6	1	no	—
1076	C₄	—	6	1	no	—
1077	C₄	—	6	1	no	—
1078	C₄	—	6	1	no	—
1079	C₄	—	6	1	no	—
1080	C₃	#3519	1	1	yes	characteristic, complemented, Sylow
1081	C₂	—	2	2	no	—
1082	C₂	—	2	2	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	4	1	no	—
1086	C₂	—	4	1	no	—
1087	C₂	—	6	2	no	—
1088	C₂	—	12	1	no	—
1089	C₂	—	12	1	no	—
1090	C₂	—	12	1	no	—
1091	C₂	—	12	1	no	—
1092	C₂	C₂×#1004	1	1	yes	characteristic
1093	C₂	C₂×D₃×#41	1	1	yes	characteristic
1094	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×#546	C₂
hypercenter	#546	D₃
hypocenter	C₃	#3519
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. #5832	C₂	semidirect
3. #5829	C₂	semidirect
4. C₂×#939	C₂	semidirect
5. D₄×#67	C₂	semidirect
6. #5678	C₂	semidirect
7. #5670	C₂	semidirect
8. #5663	C₂	semidirect
9. #5661	C₂	semidirect
10. #5654	C₂	semidirect
11. #5649	C₂	semidirect
12. #5644	C₂	semidirect
13. #5636	C₂	semidirect
14. #5615	C₂	semidirect
15. #5613	C₂	semidirect
16. #5610	C₂	semidirect
17. D₃×#121	C₂	semidirect
18. #5601	C₂	semidirect
19. #5599	C₂	semidirect
20. #5593	C₂	semidirect
21. #5590	C₂	semidirect
22. #5590	C₂	semidirect
23. #5586	C₂	semidirect
24. #5547	C₂	semidirect
25. #5545	C₂	semidirect
26. #5540	C₂	semidirect
27. #5540	C₂	semidirect
28. #5490	C₂	semidirect
29. #5490	C₂	semidirect
30. #5486	C₂	semidirect
31. C₂×#67⋊C₄	C₂	semidirect
33. C₂×C₃×#41	C₂²	semidirect
34. C₂²×C₃×D₄	C₂²	semidirect
37. C₂²×#67	C₂²	semidirect
38. C₂²×#67	C₂²	semidirect
39. C₂³×Dic₃	C₂²	semidirect
40. C₂×#237	C₂²	semidirect
42. C₂×D₃×D₄	C₂²	semidirect
43. C₂×D₃×D₄	C₂²	semidirect
44. C₂×D₃×D₄	C₂²	semidirect
45. C₂×#235	C₂²	semidirect
46. C₂×#235	C₂²	semidirect
47. C₂²×C₄×D₃	C₂²	semidirect
48. C₃×#124	C₂²	semidirect
49. C₃×#123	C₂²	semidirect
50. C₃×#123	C₂²	semidirect
51. C₃×C₂²⋊Q₈	C₂²	semidirect
52. C₃×#121	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
54. C₃×#121	C₂²	semidirect
55. C₃×#120	C₂²	semidirect
56. C₃×#120	C₂²	semidirect
57. C₃×C₄×D₄	C₂²	semidirect
58. C₃×C₄×D₄	C₂²	semidirect
59. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
60. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
61. #953	C₂²	semidirect
62. #953	C₂²	semidirect
63. C₂×#217	C₂²	semidirect
64. #947	C₂²	semidirect
65. #947	C₂²	semidirect
66. #946	C₂²	semidirect
67. #944	C₂²	semidirect
68. #940	C₂²	semidirect
69. #940	C₂²	semidirect
70. #940	C₂²	semidirect
72. #939	C₂²	semidirect
73. #939	C₂²	semidirect
74. #939	C₂²	semidirect
75. #939	C₂²	semidirect
76. #939	C₂²	semidirect
77. #939	C₂²	semidirect
78. #939	C₂²	semidirect
79. #939	C₂²	semidirect
80. #939	C₂²	semidirect
81. #939	C₂²	semidirect
82. #939	C₂²	semidirect
83. #939	C₂²	semidirect
84. #939	C₂²	semidirect
85. #939	C₂²	semidirect
86. #939	C₂²	semidirect
87. #938	C₂²	semidirect
88. #938	C₂²	semidirect
89. #937	C₂²	semidirect
90. #937	C₂²	semidirect
91. #937	C₂²	semidirect
92. #937	C₂²	semidirect
93. #936	C₂²	semidirect
94. #935	C₂²	semidirect
95. #935	C₂²	semidirect
96. D₄×Dic₃	C₂²	semidirect
97. D₄×Dic₃	C₂²	semidirect
98. D₄×Dic₃	C₂²	semidirect
99. #930	C₂²	semidirect
100. #930	C₂²	semidirect
101. #930	C₂²	semidirect
102. #929	C₂²	semidirect
103. #929	C₂²	semidirect
104. #929	C₂²	semidirect
106. C₄×#67	C₂²	semidirect
107. C₄×#67	C₂²	semidirect
108. C₄×#67	C₂²	semidirect
109. C₄×#67	C₂²	semidirect
110. C₄×#67	C₂²	semidirect
111. C₄×#67	C₂²	semidirect
112. C₄×#67	C₂²	semidirect
113. C₄×#67	C₂²	semidirect
114. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
115. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
116. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
117. C₂×Dic₃⋊C₄	C₂²	semidirect
118. C₂×Dic₃⋊C₄	C₂²	semidirect
119. C₂×C₄×Dic₃	C₂²	semidirect
120. #898	C₂²	semidirect
121. #898	C₂²	semidirect
122. #896	C₂²	semidirect
123. #896	C₂²	semidirect
124. #895	C₂²	semidirect
125. #895	C₂²	semidirect
126. #894	C₂²	semidirect
127. #894	C₂²	semidirect
128. #894	C₂²	semidirect
129. #893	C₂²	semidirect
130. #892	C₂²	semidirect
131. D₃×C₄⋊C₄	C₂²	semidirect
132. #889	C₂²	semidirect
133. #889	C₂²	semidirect
134. #889	C₂²	semidirect
135. #887	C₂²	semidirect
136. #886	C₂²	semidirect
137. #885	C₂²	semidirect
138. #885	C₂²	semidirect
139. #885	C₂²	semidirect
140. #884	C₂²	semidirect
141. #884	C₂²	semidirect
142. #884	C₂²	semidirect
143. #884	C₂²	semidirect
144. #884	C₂²	semidirect
145. #884	C₂²	semidirect
146. #884	C₂²	semidirect
147. #884	C₂²	semidirect
148. #884	C₂²	semidirect
149. #883	C₂²	semidirect
150. #883	C₂²	semidirect
151. #883	C₂²	semidirect
152. #882	C₂²	semidirect
153. #882	C₂²	semidirect
154. #882	C₂²	semidirect
155. #882	C₂²	semidirect
159. #67⋊C₄	C₂²	semidirect
160. #67⋊C₄	C₂²	semidirect
161. #67⋊C₄	C₂²	semidirect
162. #67⋊C₄	C₂²	semidirect
163. #67⋊C₄	C₂²	semidirect
164. #67⋊C₄	C₂²	semidirect
165. #67⋊C₄	C₂²	semidirect
166. #67⋊C₄	C₂²	semidirect
167. #67⋊C₄	C₂²	semidirect
168. #67⋊C₄	C₂²	semidirect
169. #67⋊C₄	C₂²	semidirect
170. #67⋊C₄	C₂²	semidirect
171. D₃×C₂²⋊C₄	C₂²	semidirect
172. D₃×C₂²⋊C₄	C₂²	semidirect
173. D₃×C₂²⋊C₄	C₂²	semidirect
174. D₃×C₂²⋊C₄	C₂²	semidirect
175. #879	C₂²	semidirect
176. #879	C₂²	semidirect
177. #879	C₂²	semidirect
178. #878	C₂²	semidirect
179. #878	C₂²	semidirect
180. #878	C₂²	semidirect
181. #877	C₂²	semidirect
182. #877	C₂²	semidirect
183. #877	C₂²	semidirect
184. #876	C₂²	semidirect
185. C₄×D₁₂	C₂²	semidirect
186. #872	C₂²	semidirect
187. #872	C₂²	semidirect
200. #546	D₃	semidirect
392. C₂×#41	C₂×D₃	semidirect
401. C₂²×D₄	C₂×D₃	semidirect
423. #124	C₂×D₃	semidirect
436. #123	C₂×D₃	semidirect
437. #123	C₂×D₃	semidirect
444. C₂²⋊Q₈	C₂×D₃	semidirect
477. #121	C₂×D₃	semidirect
478. #121	C₂×D₃	semidirect
479. #121	C₂×D₃	semidirect
490. #120	C₂×D₃	semidirect
491. #120	C₂×D₃	semidirect
522. C₄×D₄	C₂×D₃	semidirect
523. C₄×D₄	C₂×D₃	semidirect
541. C₂×C₂²⋊C₄	C₂×D₃	semidirect
542. C₂×C₂²⋊C₄	C₂×D₃	semidirect
619. #67	#41	semidirect
1080. C₃	#3519	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
#5832	2
#5829	2
C₂×#939	2
D₄×#67	2
#5678	2
#5670	2
#5663	2
#5661	2
#5654	2
#5649	2
#5644	2
#5636	2
#5615	2
#5613	2
#5610	2
D₃×#121	2
#5601	2
#5599	2
#5593	2
#5590	2
#5586	2
#5547	2
#5545	2
#5540	2
#5490	2
#5486	2
C₂×#67⋊C₄	2
#3519	3