Subgroups — C₃×#86330 #11904287

Order 1152.

3967 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5828	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5717	C₂	1	4	yes	maximal, complemented
7	C₃×#5676	C₂	1	4	yes	maximal, complemented
8	C₃×#5612	C₂	1	4	yes	maximal, complemented
9	C₃×#5609	C₂	1	4	yes	maximal, complemented
10	C₃×#5589	C₂	1	4	yes	maximal, complemented
11	C₃×D₃×#120	C₂	1	4	yes	maximal, complemented
12	C₃×#5524	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5521	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3484	—	3	1	no	maximal
15	#86330	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×#67	C₂²	1	2	yes	complemented
20	C₃×#1009	—	2	8	no	—
21	C₂×C₃×#239	C₂²	1	2	yes	complemented
22	C₂×C₃×D₃×D₄	—	2	8	no	—
23	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
24	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
25	C₂×C₃×D₃×D₄	C₂²	1	8	yes	complemented
26	C₂×C₃×D₃×D₄	C₂²	1	4	yes	complemented
27	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
28	C₂×C₃×#235	C₂²	1	2	yes	complemented
29	C₂×C₃×#235	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
31	C₂²×C₃×D₁₂	C₂²	1	2	yes	complemented
32	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#127	C₂²	1	2	yes	complemented
34	C₃²×#124	C₂²	1	2	yes	complemented
35	C₃²×#121	C₂²	1	4	yes	complemented
36	C₃²×#120	C₂²	1	4	yes	complemented
37	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
38	C₃×#953	C₂²	1	4	yes	complemented
39	C₃×#946	C₂²	1	2	yes	complemented
40	C₃×#940	C₂²	1	2	yes	complemented
41	C₃×#938	C₂²	1	2	yes	complemented
42	C₃×#938	C₂²	1	8	yes	complemented
43	C₃×#938	C₂²	1	4	yes	complemented
44	C₃×#937	C₂²	1	2	yes	complemented
45	C₃×#937	C₂²	1	8	yes	complemented
46	C₃×#937	C₂²	1	8	yes	complemented
47	C₃×#936	C₂²	1	2	yes	complemented
48	C₃×#935	C₂²	1	2	yes	complemented
49	C₃×C₄×#67	C₂²	1	4	yes	complemented
50	C₃×#926	C₂²	1	1	yes	characteristic, complemented
51	C₃×#897	C₂²	1	2	yes	complemented
52	C₃×#895	C₂²	1	2	yes	complemented
53	C₃×#893	C₂²	1	4	yes	complemented
54	C₃×#886	C₂²	1	2	yes	complemented
55	C₃×#884	C₂²	1	8	yes	complemented
56	C₃×#883	C₂²	1	8	yes	complemented
57	C₃×#882	C₂²	1	2	yes	complemented
58	C₃×#882	C₂²	1	8	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
60	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
61	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
62	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
63	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
64	C₂³×C₃×D₄	—	3	1	no	—
65	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
67	C₃×#546	—	3	4	no	—
68	C₃×#546	—	3	4	no	—
69	C₃×D₄²	—	3	4	no	—
70	C₃×D₄²	—	3	4	no	—
71	C₃×#535	—	2	1	no	—
72	C₃×#535	—	3	1	no	—
73	C₃×#535	D₃	1	1	yes	characteristic, complemented
74	C₃×#535	C₂×C₃	1	1	yes	characteristic, complemented
75	C₃×#534	—	3	4	no	—
76	C₃×#525	—	3	1	no	—
77	C₃×#525	—	3	1	no	—
78	C₂×C₃×#120	—	3	4	no	—
79	C₃×#518	—	3	1	no	—
80	#5828	C₂×C₃	1	1	yes	characteristic, complemented
81	#5805	C₂×C₃	1	1	yes	characteristic, complemented
82	#5717	C₂×C₃	1	4	yes	complemented
83	#5676	C₂×C₃	1	4	yes	complemented
84	#5612	C₂×C₃	1	4	yes	complemented
85	#5609	C₂×C₃	1	4	yes	complemented
86	#5589	C₂×C₃	1	4	yes	complemented
87	D₃×#120	C₂×C₃	1	4	yes	complemented
88	#5524	C₂×C₃	1	1	yes	characteristic, complemented
89	#5521	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂⁴×C₃²	C₂³	1	2	yes	—
91	C₂³×C₃×D₃	—	2	8	no	—
92	C₂³×C₃×D₃	—	4	8	no	—
93	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
94	C₂³×C₃×D₃	C₂³	1	8	yes	—
95	C₂³×C₃×D₃	C₂³	1	2	yes	—
96	C₂³×C₃×D₃	C₂³	1	4	yes	complemented
97	C₃²×#41	—	2	4	no	—
98	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic, complemented
99	C₂×C₃²×D₄	—	2	4	no	—
100	C₂×C₃²×D₄	C₂³	1	2	yes	—
101	C₂×C₃²×D₄	C₂³	1	2	yes	—
102	C₂×C₃²×D₄	C₂³	1	2	yes	—
103	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic, complemented
104	C₂×C₃²×D₄	C₂³	1	8	yes	complemented
105	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
106	C₂²×C₃²×C₄	C₂³	1	2	yes	complemented
107	C₂×C₃×#67	—	2	8	no	—
108	C₂×C₃×#67	C₂³	1	2	yes	—
109	C₂×C₃×#67	C₂³	1	8	yes	—
110	C₂×C₃×#67	C₂³	1	4	yes	—
111	C₂×C₃×#67	C₂³	1	4	yes	complemented
112	C₂×C₃×#67	C₂³	1	8	yes	complemented
113	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
114	C₃×#239	—	2	8	no	—
115	C₃×D₃×D₄	—	2	16	no	—
116	C₃×D₃×D₄	—	2	16	no	—
117	C₃×D₃×D₄	—	2	16	no	—
118	C₃×D₃×D₄	—	2	8	no	—
119	C₃×D₃×D₄	—	4	16	no	—
120	C₃×#235	—	2	4	no	—
121	C₃×#235	—	2	8	no	—
122	C₂×C₃×D₁₂	—	2	8	no	—
123	C₂×C₃×D₁₂	D₄	1	8	yes	complemented
124	C₂×C₃×D₁₂	C₂³	1	4	yes	—
125	C₂×C₃×D₁₂	C₂³	1	2	yes	—
126	C₂×C₃×D₁₂	C₂³	1	2	yes	—
127	C₂×C₃×D₁₂	C₂³	1	4	yes	complemented
128	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic, complemented
129	C₂×C₃×C₄×D₃	—	2	4	no	—
130	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
131	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	complemented
133	C₂×C₃×C₄×D₃	C₂³	1	2	yes	complemented
134	C₂×C₃×C₄×D₃	C₂³	1	8	yes	complemented
135	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic, complemented
136	C₃²×C₄⋊C₄	C₂³	1	2	yes	complemented
137	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃²×C₂²⋊C₄	C₂³	1	8	yes	complemented
139	C₃²×C₄²	C₂³	1	2	yes	complemented
140	C₃×#217	C₂³	1	2	yes	—
141	C₃×#217	C₂³	1	8	yes	complemented
142	C₃×#217	C₂³	1	4	yes	complemented
143	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
146	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
147	C₃×C₄⋊Dic₃	C₂³	1	4	yes	complemented
148	C₃×C₄⋊Dic₃	C₂³	1	2	yes	complemented
149	C₃×Dic₃⋊C₄	C₂³	1	4	yes	complemented
150	C₃×C₄×Dic₃	C₂³	1	2	yes	complemented
151	#3484	—	3	1	no	Sylow
152	C₂⁵×C₃	—	3	2	no	—
153	C₂⁴×D₃	C₂²×C₃	1	2	yes	complemented
154	C₃×H(5,𝔽₂)	—	6	8	no	—
155	C₂×C₃×#41	—	2	1	no	—
156	C₂×C₃×#41	—	3	2	no	—
157	C₂×C₃×#41	—	3	1	no	—
158	C₂×C₃×#41	—	3	2	no	—
159	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂²×C₃×D₄	—	2	1	no	—
162	C₂²×C₃×D₄	—	3	2	no	—
163	C₂²×C₃×D₄	—	3	4	no	—
164	C₂²×C₃×D₄	—	3	4	no	—
165	C₂²×C₃×D₄	—	3	4	no	—
166	C₂²×C₃×D₄	—	3	2	no	—
167	C₂²×C₃×D₄	—	3	8	no	—
168	C₂²×C₃×D₄	—	3	1	no	—
169	C₂²×C₃×D₄	—	3	2	no	—
170	C₂²×C₃×D₄	—	6	8	no	—
171	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂³×C₃×C₄	—	3	1	no	—
174	C₂²×#67	C₂²×C₃	1	2	yes	complemented
175	#1009	—	2	8	no	—
176	C₂×#239	C₂²×C₃	1	2	yes	complemented
177	C₂×D₃×D₄	—	2	8	no	—
178	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
179	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
180	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
181	C₂×D₃×D₄	C₂²×C₃	1	8	yes	complemented
182	C₂×D₃×D₄	C₂²×C₃	1	4	yes	complemented
183	C₂×#235	C₂²×C₃	1	2	yes	complemented
184	C₂×#235	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
186	C₂²×D₁₂	C₂²×C₃	1	2	yes	complemented
187	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₃×#127	—	2	2	no	—
189	C₃×#127	—	3	2	no	—
190	C₃×#127	C₂×D₃	1	2	yes	complemented
191	C₃×#127	C₂²×C₃	1	2	yes	complemented
192	C₃×#124	—	2	2	no	—
193	C₃×#124	—	3	2	no	—
194	C₃×#124	C₂×D₃	1	2	yes	complemented
195	C₃×#124	C₂²×C₃	1	2	yes	complemented
196	C₃×#123	—	3	2	no	—
197	C₃×#123	—	3	2	no	—
198	C₃×#123	—	3	8	no	—
199	C₃×C₂²⋊Q₈	—	3	2	no	—
200	C₃×C₂²⋊Q₈	—	3	2	no	—
201	C₃×#121	—	2	4	no	—
202	C₃×#121	—	3	4	no	—
203	C₃×#121	—	3	2	no	—
204	C₃×#121	—	3	8	no	—
205	C₃×#121	—	3	2	no	—
206	C₃×#121	—	3	8	no	—
207	C₃×#121	C₂×D₃	1	4	yes	complemented
208	C₃×#121	C₂²×C₃	1	4	yes	complemented
209	C₃×#120	—	2	4	no	—
210	C₃×#120	—	3	4	no	—
211	C₃×#120	—	3	2	no	—
212	C₃×#120	—	3	8	no	—
213	C₃×#120	—	3	8	no	—
214	C₃×#120	—	3	2	no	—
215	C₃×#120	—	3	8	no	—
216	C₃×#120	C₂×D₃	1	4	yes	complemented
217	C₃×#120	C₂²×C₃	1	4	yes	complemented
218	C₃×C₄×D₄	—	3	4	no	—
219	C₃×C₄×D₄	—	3	4	no	—
220	C₃×C₄×D₄	—	3	4	no	—
221	C₃×C₄×D₄	—	3	4	no	—
222	C₃×#117	—	2	1	no	—
223	C₃×#117	—	3	1	no	—
224	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
225	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
226	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
227	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
228	#953	C₂²×C₃	1	4	yes	complemented
229	#946	C₂²×C₃	1	2	yes	complemented
230	#940	C₂²×C₃	1	2	yes	complemented
231	#938	C₂²×C₃	1	2	yes	complemented
232	#938	C₂²×C₃	1	8	yes	complemented
233	#938	C₂²×C₃	1	4	yes	complemented
234	#937	C₂²×C₃	1	2	yes	complemented
235	#937	C₂²×C₃	1	8	yes	complemented
236	#937	C₂²×C₃	1	8	yes	complemented
237	#936	C₂²×C₃	1	2	yes	complemented
238	#935	C₂²×C₃	1	2	yes	complemented
239	C₄×#67	C₂²×C₃	1	4	yes	complemented
240	#926	C₂²×C₃	1	1	yes	characteristic, complemented
241	#897	C₂²×C₃	1	2	yes	complemented
242	#895	C₂²×C₃	1	2	yes	complemented
243	#893	C₂²×C₃	1	4	yes	complemented
244	#886	C₂²×C₃	1	2	yes	complemented
245	#884	C₂²×C₃	1	8	yes	complemented
246	#883	C₂²×C₃	1	8	yes	complemented
247	#882	C₂²×C₃	1	2	yes	complemented
248	#882	C₂²×C₃	1	8	yes	complemented
249	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
250	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
251	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
252	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
253	C₂³×C₃²	—	2	4	no	—
254	C₂³×C₃²	—	4	4	no	—
255	C₂³×C₃²	C₂⁴	1	4	yes	—
256	C₂³×C₃²	C₂⁴	1	2	yes	—
257	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
258	C₂²×C₃×D₃	—	2	2	no	—
259	C₂²×C₃×D₃	—	2	4	no	—
260	C₂²×C₃×D₃	—	2	16	no	—
261	C₂²×C₃×D₃	—	2	16	no	—
262	C₂²×C₃×D₃	—	2	8	no	—
263	C₂²×C₃×D₃	—	4	4	no	—
264	C₂²×C₃×D₃	—	4	8	no	—
265	C₂²×C₃×D₃	—	4	8	no	—
266	C₂²×C₃×D₃	—	4	32	no	—
267	C₂²×C₃×D₃	C₂×D₄	1	8	yes	complemented
268	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
269	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
270	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
271	C₃²×Q₈	—	2	2	no	—
272	C₃²×D₄	—	2	4	no	—
273	C₃²×D₄	—	2	4	no	—
274	C₃²×D₄	—	2	4	no	—
275	C₃²×D₄	—	2	2	no	—
276	C₃²×D₄	—	4	8	no	—
277	C₂×C₃²×C₄	—	2	4	no	—
278	C₂×C₃²×C₄	C₂×D₄	1	4	yes	complemented
279	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
280	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
281	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
283	C₃×#67	—	2	4	no	—
284	C₃×#67	—	2	8	no	—
285	C₃×#67	—	2	16	no	—
286	C₃×#67	—	2	8	no	—
287	C₃×#67	—	4	8	no	—
288	C₂×C₃×Dic₃	—	2	2	no	—
289	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
290	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
291	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
292	C₃×D₁₂	—	2	8	no	—
293	C₃×D₁₂	—	2	8	no	—
294	C₃×D₁₂	—	2	2	no	—
295	C₃×D₁₂	C₂×D₄	1	8	yes	complemented
296	C₃×D₁₂	C₂×D₄	1	8	yes	complemented
297	C₃×C₄×D₃	—	2	8	no	—
298	C₃×C₄×D₃	—	2	4	no	—
299	C₃×C₄×D₃	—	2	4	no	—
300	C₃×C₄×D₃	—	2	4	no	—
301	C₃×C₄×D₃	—	4	8	no	—
302	C₃×Dic₆	—	2	2	no	—
303	C₂×H(5,𝔽₂)	—	3	1	no	—
304	C₂³×D₄	—	3	1	no	—
305	#546	—	3	4	no	—
306	#546	—	3	4	no	—
307	D₄²	—	3	4	no	—
308	D₄²	—	3	4	no	—
309	#535	—	3	1	no	—
310	#535	C₃×D₃	1	1	yes	characteristic, complemented
311	#534	—	3	4	no	—
312	#525	—	3	1	no	—
313	#525	—	3	1	no	—
314	C₂×#120	—	3	4	no	—
315	#518	—	3	1	no	—
316	C₂⁴×C₃	—	2	2	no	—
317	C₂⁴×C₃	—	3	2	no	—
318	C₂⁴×C₃	—	3	1	no	—
319	C₂⁴×C₃	—	3	8	no	—
320	C₂⁴×C₃	—	3	4	no	—
321	C₂⁴×C₃	—	6	8	no	—
322	C₂⁴×C₃	—	12	8	no	—
323	C₂⁴×C₃	C₂²×D₃	1	2	yes	—
324	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
325	C₂³×D₃	—	2	8	no	—
326	C₂³×D₃	—	4	8	no	—
327	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
328	C₂³×D₃	C₂³×C₃	1	8	yes	—
329	C₂³×D₃	C₂³×C₃	1	2	yes	—
330	C₂³×D₃	C₂³×C₃	1	4	yes	complemented
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	4	no	—
333	C₃×#41	—	4	4	no	—
334	C₃×#41	—	6	8	no	—
335	C₃×#41	—	6	8	no	—
336	C₃×#41	—	6	4	no	—
337	C₂×C₃×Q₈	—	2	1	no	—
338	C₂×C₃×Q₈	—	3	1	no	—
339	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
340	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
341	C₂×C₃×D₄	—	2	4	no	—
342	C₂×C₃×D₄	—	2	4	no	—
343	C₂×C₃×D₄	—	2	2	no	—
344	C₂×C₃×D₄	—	2	2	no	—
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	2	1	no	—
347	C₂×C₃×D₄	—	2	8	no	—
348	C₂×C₃×D₄	—	3	4	no	—
349	C₂×C₃×D₄	—	3	2	no	—
350	C₂×C₃×D₄	—	3	4	no	—
351	C₂×C₃×D₄	—	3	8	no	—
352	C₂×C₃×D₄	—	3	8	no	—
353	C₂×C₃×D₄	—	3	8	no	—
354	C₂×C₃×D₄	—	3	2	no	—
355	C₂×C₃×D₄	—	3	2	no	—
356	C₂×C₃×D₄	—	3	4	no	—
357	C₂×C₃×D₄	—	3	4	no	—
358	C₂×C₃×D₄	—	3	1	no	—
359	C₂×C₃×D₄	—	4	4	no	—
360	C₂×C₃×D₄	—	6	8	no	—
361	C₂×C₃×D₄	—	6	16	no	—
362	C₂×C₃×D₄	—	6	16	no	—
363	C₂×C₃×D₄	—	6	8	no	—
364	C₂×C₃×D₄	—	6	16	no	—
365	C₂×C₃×D₄	—	6	8	no	—
366	C₂×C₃×D₄	—	12	16	no	—
367	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
368	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
369	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
370	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic, complemented
371	C₂×C₃×D₄	C₂²×D₃	1	8	yes	complemented
372	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
373	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
374	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
375	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
376	C₂×C₃×D₄	C₂³×C₃	1	8	yes	complemented
377	C₂²×C₃×C₄	—	2	1	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	3	1	no	—
380	C₂²×C₃×C₄	—	3	4	no	—
381	C₂²×C₃×C₄	—	3	2	no	—
382	C₂²×C₃×C₄	—	3	2	no	—
383	C₂²×C₃×C₄	—	3	2	no	—
384	C₂²×C₃×C₄	—	3	8	no	—
385	C₂²×C₃×C₄	—	6	4	no	—
386	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	complemented
388	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	complemented
390	C₂×#67	—	2	8	no	—
391	C₂×#67	C₂³×C₃	1	2	yes	—
392	C₂×#67	C₂³×C₃	1	8	yes	—
393	C₂×#67	C₂³×C₃	1	4	yes	—
394	C₂×#67	C₂³×C₃	1	4	yes	complemented
395	C₂×#67	C₂³×C₃	1	8	yes	complemented
396	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
397	#239	—	2	8	no	—
398	D₃×D₄	—	2	16	no	—
399	D₃×D₄	—	2	16	no	—
400	D₃×D₄	—	2	16	no	—
401	D₃×D₄	—	2	8	no	—
402	D₃×D₄	—	4	16	no	—
403	#235	—	2	4	no	—
404	#235	—	2	8	no	—
405	C₂×D₁₂	—	2	8	no	—
406	C₂×D₁₂	C₃×D₄	1	8	yes	complemented
407	C₂×D₁₂	C₂³×C₃	1	4	yes	—
408	C₂×D₁₂	C₂³×C₃	1	2	yes	—
409	C₂×D₁₂	C₂³×C₃	1	2	yes	—
410	C₂×D₁₂	C₂³×C₃	1	4	yes	complemented
411	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic, complemented
412	C₂×C₄×D₃	—	2	4	no	—
413	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
414	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
415	C₂×C₄×D₃	C₂³×C₃	1	2	yes	complemented
416	C₂×C₄×D₃	C₂³×C₃	1	4	yes	complemented
417	C₂×C₄×D₃	C₂³×C₃	1	8	yes	complemented
418	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic, complemented
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	3	4	no	—
421	C₃×C₄⋊C₄	—	3	2	no	—
422	C₃×C₄⋊C₄	—	3	4	no	—
423	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
424	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
425	C₃×C₂²⋊C₄	—	2	2	no	—
426	C₃×C₂²⋊C₄	—	2	8	no	—
427	C₃×C₂²⋊C₄	—	3	2	no	—
428	C₃×C₂²⋊C₄	—	3	8	no	—
429	C₃×C₂²⋊C₄	—	3	4	no	—
430	C₃×C₂²⋊C₄	—	3	4	no	—
431	C₃×C₂²⋊C₄	—	3	4	no	—
432	C₃×C₂²⋊C₄	—	3	8	no	—
433	C₃×C₂²⋊C₄	—	3	4	no	—
434	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
435	C₃×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
436	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
438	C₃×C₄²	—	2	2	no	—
439	C₃×C₄²	—	3	2	no	—
440	C₃×C₄²	C₂²×D₃	1	2	yes	complemented
441	C₃×C₄²	C₂³×C₃	1	2	yes	complemented
442	#217	C₂³×C₃	1	2	yes	—
443	#217	C₂³×C₃	1	8	yes	complemented
444	#217	C₂³×C₃	1	4	yes	complemented
445	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
446	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
447	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	complemented
448	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	complemented
449	C₄⋊Dic₃	C₂³×C₃	1	2	yes	complemented
450	C₄⋊Dic₃	C₂³×C₃	1	4	yes	complemented
451	Dic₃⋊C₄	C₂³×C₃	1	4	yes	complemented
452	C₄×Dic₃	C₂³×C₃	1	2	yes	complemented
453	C₂²×C₃²	—	2	2	no	—
454	C₂²×C₃²	—	2	2	no	—
455	C₂²×C₃²	—	2	4	no	—
456	C₂²×C₃²	—	2	4	no	—
457	C₂²×C₃²	—	2	8	no	—
458	C₂²×C₃²	—	4	8	no	—
459	C₂²×C₃²	C₂²×D₄	1	2	yes	—
460	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
461	C₂×C₃×D₃	—	2	8	no	—
462	C₂×C₃×D₃	—	2	2	no	—
463	C₂×C₃×D₃	—	2	8	no	—
464	C₂×C₃×D₃	—	2	2	no	—
465	C₂×C₃×D₃	—	2	2	no	—
466	C₂×C₃×D₃	—	2	4	no	—
467	C₂×C₃×D₃	—	4	8	no	—
468	C₂×C₃×D₃	—	4	32	no	—
469	C₂×C₃×D₃	—	8	8	no	—
470	C₂×C₃×D₃	C₂²×D₄	1	8	yes	—
471	C₂×C₃×D₃	H(5,𝔽₂)	1	4	yes	complemented
472	C₃²×C₄	—	2	2	no	—
473	C₃²×C₄	—	2	4	no	—
474	C₃²×C₄	C₂²×D₄	1	2	yes	—
475	C₃²×C₄	C₂²×D₄	1	2	yes	—
476	C₃×Dic₃	—	2	2	no	—
477	C₃×Dic₃	—	2	2	no	—
478	C₃×Dic₃	—	2	4	no	—
479	C₂⁵	—	3	2	no	—
480	H(5,𝔽₂)	—	6	8	no	—
481	C₂×#41	—	3	2	no	—
482	C₂×#41	—	3	1	no	—
483	C₂×#41	—	3	2	no	—
484	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
485	C₂²×D₄	—	3	2	no	—
486	C₂²×D₄	—	3	4	no	—
487	C₂²×D₄	—	3	4	no	—
488	C₂²×D₄	—	3	4	no	—
489	C₂²×D₄	—	3	2	no	—
490	C₂²×D₄	—	3	8	no	—
491	C₂²×D₄	—	3	1	no	—
492	C₂²×D₄	—	3	2	no	—
493	C₂²×D₄	—	6	8	no	—
494	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
495	C₂³×C₄	—	3	1	no	—
496	#127	—	3	2	no	—
497	#127	C₂×C₃×D₃	1	2	yes	complemented
498	#124	—	3	2	no	—
499	#124	C₂×C₃×D₃	1	2	yes	complemented
500	#123	—	3	2	no	—
501	#123	—	3	2	no	—
502	#123	—	3	8	no	—
503	C₂²⋊Q₈	—	3	2	no	—
504	C₂²⋊Q₈	—	3	2	no	—
505	#121	—	3	4	no	—
506	#121	—	3	2	no	—
507	#121	—	3	8	no	—
508	#121	—	3	2	no	—
509	#121	—	3	8	no	—
510	#121	C₂×C₃×D₃	1	4	yes	complemented
511	#120	—	3	4	no	—
512	#120	—	3	2	no	—
513	#120	—	3	8	no	—
514	#120	—	3	8	no	—
515	#120	—	3	2	no	—
516	#120	—	3	8	no	—
517	#120	C₂×C₃×D₃	1	4	yes	complemented
518	C₄×D₄	—	3	4	no	—
519	C₄×D₄	—	3	4	no	—
520	C₄×D₄	—	3	4	no	—
521	C₄×D₄	—	3	4	no	—
522	#117	—	3	1	no	—
523	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
524	C₂×C₂²⋊C₄	—	3	4	no	—
525	C₂×C₂²⋊C₄	—	3	8	no	—
526	C₂³×C₃	—	2	4	no	—
527	C₂³×C₃	—	2	4	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	—	2	4	no	—
530	C₂³×C₃	—	2	2	no	—
531	C₂³×C₃	—	3	2	no	—
532	C₂³×C₃	—	3	4	no	—
533	C₂³×C₃	—	3	8	no	—
534	C₂³×C₃	—	3	2	no	—
535	C₂³×C₃	—	4	4	no	—
536	C₂³×C₃	—	4	4	no	—
537	C₂³×C₃	—	4	4	no	—
538	C₂³×C₃	—	6	4	no	—
539	C₂³×C₃	—	6	16	no	—
540	C₂³×C₃	—	6	16	no	—
541	C₂³×C₃	—	6	8	no	—
542	C₂³×C₃	—	6	2	no	—
543	C₂³×C₃	—	8	4	no	—
544	C₂³×C₃	—	12	4	no	—
545	C₂³×C₃	—	12	8	no	—
546	C₂³×C₃	—	12	8	no	—
547	C₂³×C₃	—	12	32	no	—
548	C₂³×C₃	C₂³×D₃	1	4	yes	—
549	C₂³×C₃	C₂³×D₃	1	2	yes	—
550	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
551	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
552	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
553	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
554	C₂²×D₃	—	2	2	no	—
555	C₂²×D₃	—	2	4	no	—
556	C₂²×D₃	—	2	16	no	—
557	C₂²×D₃	—	2	16	no	—
558	C₂²×D₃	—	2	8	no	—
559	C₂²×D₃	—	4	4	no	—
560	C₂²×D₃	—	4	8	no	—
561	C₂²×D₃	—	4	8	no	—
562	C₂²×D₃	—	4	32	no	—
563	C₂²×D₃	C₂×C₃×D₄	1	8	yes	complemented
564	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
565	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
566	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
567	C₃×Q₈	—	2	2	no	—
568	C₃×Q₈	—	2	2	no	—
569	C₃×Q₈	—	4	2	no	—
570	C₃×Q₈	—	6	2	no	—
571	C₃×D₄	—	2	4	no	—
572	C₃×D₄	—	2	4	no	—
573	C₃×D₄	—	2	4	no	—
574	C₃×D₄	—	2	4	no	—
575	C₃×D₄	—	2	2	no	—
576	C₃×D₄	—	2	4	no	—
577	C₃×D₄	—	2	4	no	—
578	C₃×D₄	—	2	2	no	—
579	C₃×D₄	—	3	8	no	—
580	C₃×D₄	—	3	8	no	—
581	C₃×D₄	—	4	4	no	—
582	C₃×D₄	—	4	4	no	—
583	C₃×D₄	—	4	2	no	—
584	C₃×D₄	—	4	4	no	—
585	C₃×D₄	—	4	8	no	—
586	C₃×D₄	—	4	8	no	—
587	C₃×D₄	—	6	8	no	—
588	C₃×D₄	—	6	8	no	—
589	C₃×D₄	—	6	16	no	—
590	C₃×D₄	—	6	8	no	—
591	C₃×D₄	—	6	8	no	—
592	C₃×D₄	—	6	4	no	—
593	C₃×D₄	—	6	2	no	—
594	C₃×D₄	—	8	8	no	—
595	C₃×D₄	—	12	8	no	—
596	C₂×C₃×C₄	—	2	4	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	4	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	4	no	—
603	C₂×C₃×C₄	—	3	4	no	—
604	C₂×C₃×C₄	—	3	2	no	—
605	C₂×C₃×C₄	—	3	2	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	—	6	8	no	—
608	C₂×C₃×C₄	—	6	2	no	—
609	C₂×C₃×C₄	—	6	4	no	—
610	C₂×C₃×C₄	—	6	4	no	—
611	C₂×C₃×C₄	—	6	4	no	—
612	C₂×C₃×C₄	—	12	8	no	—
613	C₂×C₃×C₄	D₃×D₄	1	4	yes	complemented
614	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	complemented
615	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
616	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
617	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
618	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
619	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
620	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
621	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
622	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
623	#67	—	2	4	no	—
624	#67	—	2	8	no	—
625	#67	—	2	16	no	—
626	#67	—	2	8	no	—
627	#67	—	4	8	no	—
628	C₂×Dic₃	—	2	2	no	—
629	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
630	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
631	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
632	D₁₂	—	2	8	no	—
633	D₁₂	—	2	8	no	—
634	D₁₂	—	2	2	no	—
635	D₁₂	C₂×C₃×D₄	1	8	yes	complemented
636	D₁₂	C₂×C₃×D₄	1	8	yes	complemented
637	C₄×D₃	—	2	8	no	—
638	C₄×D₃	—	2	4	no	—
639	C₄×D₃	—	2	4	no	—
640	C₄×D₃	—	2	4	no	—
641	C₄×D₃	—	4	8	no	—
642	Dic₆	—	2	2	no	—
643	C₂×C₃²	—	2	2	no	—
644	C₂×C₃²	—	4	4	no	—
645	C₂×C₃²	—	4	2	no	—
646	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
647	C₂×C₃²	C₂×H(5,𝔽₂)	1	2	yes	—
648	C₃×D₃	—	2	4	no	—
649	C₃×D₃	—	2	8	no	—
650	C₃×D₃	—	4	2	no	—
651	C₂⁴	—	3	2	no	—
652	C₂⁴	—	3	1	no	—
653	C₂⁴	—	3	8	no	—
654	C₂⁴	—	3	4	no	—
655	C₂⁴	—	6	8	no	—
656	C₂⁴	—	12	8	no	—
657	C₂⁴	C₂²×C₃×D₃	1	2	yes	—
658	#41	—	2	4	no	—
659	#41	—	6	8	no	—
660	#41	—	6	8	no	—
661	#41	—	6	4	no	—
662	C₂×Q₈	—	3	1	no	—
663	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	3	4	no	—
666	C₂×D₄	—	3	2	no	—
667	C₂×D₄	—	3	4	no	—
668	C₂×D₄	—	3	8	no	—
669	C₂×D₄	—	3	8	no	—
670	C₂×D₄	—	3	2	no	—
671	C₂×D₄	—	3	2	no	—
672	C₂×D₄	—	3	4	no	—
673	C₂×D₄	—	3	4	no	—
674	C₂×D₄	—	3	1	no	—
675	C₂×D₄	—	3	8	no	—
676	C₂×D₄	—	6	8	no	—
677	C₂×D₄	—	6	16	no	—
678	C₂×D₄	—	6	16	no	—
679	C₂×D₄	—	6	8	no	—
680	C₂×D₄	—	6	16	no	—
681	C₂×D₄	—	6	8	no	—
682	C₂×D₄	—	12	16	no	—
683	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
684	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
685	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
686	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic, complemented
687	C₂×D₄	C₂²×C₃×D₃	1	8	yes	complemented
688	C₂²×C₄	—	3	1	no	—
689	C₂²×C₄	—	3	4	no	—
690	C₂²×C₄	—	3	2	no	—
691	C₂²×C₄	—	3	2	no	—
692	C₂²×C₄	—	3	2	no	—
693	C₂²×C₄	—	3	8	no	—
694	C₂²×C₄	—	6	4	no	—
695	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
696	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	complemented
697	C₄⋊C₄	—	3	2	no	—
698	C₄⋊C₄	—	3	4	no	—
699	C₄⋊C₄	—	3	4	no	—
700	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	complemented
701	C₂²⋊C₄	—	3	2	no	—
702	C₂²⋊C₄	—	3	8	no	—
703	C₂²⋊C₄	—	3	4	no	—
704	C₂²⋊C₄	—	3	4	no	—
705	C₂²⋊C₄	—	3	4	no	—
706	C₂²⋊C₄	—	3	8	no	—
707	C₂²⋊C₄	—	3	4	no	—
708	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
709	C₂²⋊C₄	C₂²×C₃×D₃	1	8	yes	complemented
710	C₄²	—	3	2	no	—
711	C₄²	C₂²×C₃×D₃	1	2	yes	complemented
712	C₂²×C₃	—	2	2	no	—
713	C₂²×C₃	—	2	2	no	—
714	C₂²×C₃	—	2	2	no	—
715	C₂²×C₃	—	2	4	no	—
716	C₂²×C₃	—	2	4	no	—
717	C₂²×C₃	—	2	8	no	—
718	C₂²×C₃	—	2	2	no	—
719	C₂²×C₃	—	2	4	no	—
720	C₂²×C₃	—	2	4	no	—
721	C₂²×C₃	—	2	8	no	—
722	C₂²×C₃	—	2	2	no	—
723	C₂²×C₃	—	2	1	no	—
724	C₂²×C₃	—	3	8	no	—
725	C₂²×C₃	—	3	4	no	—
726	C₂²×C₃	—	4	2	no	—
727	C₂²×C₃	—	4	2	no	—
728	C₂²×C₃	—	4	4	no	—
729	C₂²×C₃	—	4	4	no	—
730	C₂²×C₃	—	4	8	no	—
731	C₂²×C₃	—	4	8	no	—
732	C₂²×C₃	—	4	8	no	—
733	C₂²×C₃	—	6	8	no	—
734	C₂²×C₃	—	6	2	no	—
735	C₂²×C₃	—	6	8	no	—
736	C₂²×C₃	—	6	2	no	—
737	C₂²×C₃	—	6	2	no	—
738	C₂²×C₃	—	6	4	no	—
739	C₂²×C₃	—	8	8	no	—
740	C₂²×C₃	—	12	8	no	—
741	C₂²×C₃	—	12	32	no	—
742	C₂²×C₃	—	24	8	no	—
743	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
744	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
745	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
746	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
747	C₂×D₃	—	2	8	no	—
748	C₂×D₃	—	2	2	no	—
749	C₂×D₃	—	2	8	no	—
750	C₂×D₃	—	2	2	no	—
751	C₂×D₃	—	2	2	no	—
752	C₂×D₃	—	2	4	no	—
753	C₂×D₃	—	4	8	no	—
754	C₂×D₃	—	4	32	no	—
755	C₂×D₃	—	8	8	no	—
756	C₂×D₃	C₂²×C₃×D₄	1	8	yes	—
757	C₂×D₃	C₃×H(5,𝔽₂)	1	4	yes	complemented
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	4	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	2	4	no	—
762	C₃×C₄	—	2	2	no	—
763	C₃×C₄	—	2	2	no	—
764	C₃×C₄	—	4	2	no	—
765	C₃×C₄	—	4	4	no	—
766	C₃×C₄	—	6	2	no	—
767	C₃×C₄	—	6	2	no	—
768	C₃×C₄	—	6	4	no	—
769	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
770	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
771	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
772	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
773	Dic₃	—	2	2	no	—
774	Dic₃	—	2	2	no	—
775	Dic₃	—	2	4	no	—
776	C₃²	#3484	1	1	yes	characteristic, complemented, Sylow
777	C₂³	—	2	4	no	—
778	C₂³	—	3	2	no	—
779	C₂³	—	3	4	no	—
780	C₂³	—	3	8	no	—
781	C₂³	—	3	2	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	6	4	no	—
784	C₂³	—	6	16	no	—
785	C₂³	—	6	16	no	—
786	C₂³	—	6	8	no	—
787	C₂³	—	6	2	no	—
788	C₂³	—	12	4	no	—
789	C₂³	—	12	8	no	—
790	C₂³	—	12	8	no	—
791	C₂³	—	12	32	no	—
792	C₂³	C₂³×C₃×D₃	1	4	yes	—
793	C₂³	C₂³×C₃×D₃	1	2	yes	—
794	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	6	2	no	—
797	D₄	—	2	4	no	—
798	D₄	—	2	4	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	3	8	no	—
802	D₄	—	3	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	6	8	no	—
805	D₄	—	6	8	no	—
806	D₄	—	6	16	no	—
807	D₄	—	6	8	no	—
808	D₄	—	6	8	no	—
809	D₄	—	6	4	no	—
810	D₄	—	6	2	no	—
811	D₄	—	12	8	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	3	4	no	—
814	C₂×C₄	—	3	2	no	—
815	C₂×C₄	—	3	2	no	—
816	C₂×C₄	—	6	8	no	—
817	C₂×C₄	—	6	2	no	—
818	C₂×C₄	—	6	4	no	—
819	C₂×C₄	—	6	4	no	—
820	C₂×C₄	—	6	4	no	—
821	C₂×C₄	—	12	8	no	—
822	C₂×C₄	C₃×D₃×D₄	1	4	yes	complemented
823	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
824	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
825	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
826	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
827	C₂×C₃	—	2	2	no	—
828	C₂×C₃	—	2	2	no	—
829	C₂×C₃	—	2	1	no	—
830	C₂×C₃	—	2	2	no	—
831	C₂×C₃	—	4	2	no	—
832	C₂×C₃	—	4	4	no	—
833	C₂×C₃	—	4	2	no	—
834	C₂×C₃	—	4	4	no	—
835	C₂×C₃	—	4	2	no	—
836	C₂×C₃	—	6	4	no	—
837	C₂×C₃	—	6	8	no	—
838	C₂×C₃	—	8	4	no	—
839	C₂×C₃	—	8	2	no	—
840	C₂×C₃	—	12	2	no	—
841	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
842	C₂×C₃	D₃×H(5,𝔽₂)	1	2	yes	—
843	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
844	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
845	D₃	—	2	4	no	—
846	D₃	—	2	8	no	—
847	D₃	—	4	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	8	no	—
853	C₂²	—	3	8	no	—
854	C₂²	—	3	4	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	6	8	no	—
857	C₂²	—	6	2	no	—
858	C₂²	—	6	8	no	—
859	C₂²	—	6	2	no	—
860	C₂²	—	6	2	no	—
861	C₂²	—	6	4	no	—
862	C₂²	—	12	8	no	—
863	C₂²	—	12	32	no	—
864	C₂²	—	24	8	no	—
865	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
866	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	6	2	no	—
870	C₄	—	6	2	no	—
871	C₄	—	6	4	no	—
872	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
873	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
874	C₃	—	2	1	no	—
875	C₃	#86330	1	1	yes	characteristic, direct product factor
876	C₃	C₃×#3484	1	1	yes	characteristic, complemented
877	C₂	—	2	2	no	—
878	C₂	—	4	4	no	—
879	C₂	—	4	2	no	—
880	C₂	—	6	4	no	—
881	C₂	—	6	8	no	—
882	C₂	—	12	2	no	—
883	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
884	C₂	C₃×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#535	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#535	D₃
hypocenter	C₃	C₃×#3484
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1009	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₃²×#535	C₂	semidirect
4. C₃×#5828	C₂	semidirect
5. C₃×#5805	C₂	semidirect
6. C₃×#5717	C₂	semidirect
7. C₃×#5676	C₂	semidirect
8. C₃×#5612	C₂	semidirect
9. C₃×#5609	C₂	semidirect
10. C₃×#5589	C₂	semidirect
11. C₃×D₃×#120	C₂	semidirect
12. C₃×#5524	C₂	semidirect
13. C₃×#5521	C₂	semidirect
15. #86330	C₃	direct (N × H)
16. C₂⁴×C₃×D₃	C₂²	semidirect
17. C₂×C₃²×#41	C₂²	semidirect
18. C₂²×C₃²×D₄	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
21. C₂×C₃×#239	C₂²	semidirect
23. C₂×C₃×D₃×D₄	C₂²	semidirect
24. C₂×C₃×D₃×D₄	C₂²	semidirect
25. C₂×C₃×D₃×D₄	C₂²	semidirect
26. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂×C₃×D₃×D₄	C₂²	semidirect
28. C₂×C₃×#235	C₂²	semidirect
29. C₂×C₃×#235	C₂²	semidirect
31. C₂²×C₃×D₁₂	C₂²	semidirect
32. C₂²×C₃×C₄×D₃	C₂²	semidirect
33. C₃²×#127	C₂²	semidirect
34. C₃²×#124	C₂²	semidirect
35. C₃²×#121	C₂²	semidirect
36. C₃²×#120	C₂²	semidirect
37. C₃²×#117	C₂²	semidirect
38. C₃×#953	C₂²	semidirect
39. C₃×#946	C₂²	semidirect
40. C₃×#940	C₂²	semidirect
41. C₃×#938	C₂²	semidirect
42. C₃×#938	C₂²	semidirect
43. C₃×#938	C₂²	semidirect
44. C₃×#937	C₂²	semidirect
45. C₃×#937	C₂²	semidirect
46. C₃×#937	C₂²	semidirect
47. C₃×#936	C₂²	semidirect
48. C₃×#935	C₂²	semidirect
49. C₃×C₄×#67	C₂²	semidirect
50. C₃×#926	C₂²	semidirect
51. C₃×#897	C₂²	semidirect
52. C₃×#895	C₂²	semidirect
53. C₃×#893	C₂²	semidirect
54. C₃×#886	C₂²	semidirect
55. C₃×#884	C₂²	semidirect
56. C₃×#883	C₂²	semidirect
57. C₃×#882	C₂²	semidirect
58. C₃×#882	C₂²	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
60. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
61. C₃×C₄×D₁₂	C₂²	semidirect
62. C₃×C₄×D₁₂	C₂²	semidirect
65. C₂×#1009	C₂×C₃	semidirect
66. C₂²×D₃×D₄	C₂×C₃	semidirect
73. C₃×#535	D₃	semidirect
74. C₃×#535	C₂×C₃	semidirect
80. #5828	C₂×C₃	semidirect
81. #5805	C₂×C₃	semidirect
82. #5717	C₂×C₃	semidirect
83. #5676	C₂×C₃	semidirect
84. #5612	C₂×C₃	semidirect
85. #5609	C₂×C₃	semidirect
86. #5589	C₂×C₃	semidirect
87. D₃×#120	C₂×C₃	semidirect
88. #5524	C₂×C₃	semidirect
89. #5521	C₂×C₃	semidirect
96. C₂³×C₃×D₃	C₂³	semidirect
98. C₂×C₃²×Q₈	C₂³	semidirect
103. C₂×C₃²×D₄	C₂³	semidirect
104. C₂×C₃²×D₄	C₂³	semidirect
106. C₂²×C₃²×C₄	C₂³	semidirect
111. C₂×C₃×#67	C₂³	semidirect
112. C₂×C₃×#67	C₂³	semidirect
123. C₂×C₃×D₁₂	D₄	semidirect
127. C₂×C₃×D₁₂	C₂³	semidirect
128. C₂×C₃×D₁₂	C₂³	semidirect
132. C₂×C₃×C₄×D₃	C₂³	semidirect
133. C₂×C₃×C₄×D₃	C₂³	semidirect
134. C₂×C₃×C₄×D₃	C₂³	semidirect
135. C₂×C₃×Dic₆	C₂³	semidirect
136. C₃²×C₄⋊C₄	C₂³	semidirect
138. C₃²×C₂²⋊C₄	C₂³	semidirect
139. C₃²×C₄²	C₂³	semidirect
141. C₃×#217	C₂³	semidirect
142. C₃×#217	C₂³	semidirect
145. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
146. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
147. C₃×C₄⋊Dic₃	C₂³	semidirect
148. C₃×C₄⋊Dic₃	C₂³	semidirect
149. C₃×Dic₃⋊C₄	C₂³	semidirect
150. C₃×C₄×Dic₃	C₂³	semidirect
153. C₂⁴×D₃	C₂²×C₃	semidirect
159. C₂×C₃×#41	C₂×D₃	semidirect
160. C₂×C₃×#41	C₂²×C₃	semidirect
171. C₂²×C₃×D₄	C₂×D₃	semidirect
172. C₂²×C₃×D₄	C₂²×C₃	semidirect
174. C₂²×#67	C₂²×C₃	semidirect
176. C₂×#239	C₂²×C₃	semidirect
178. C₂×D₃×D₄	C₂²×C₃	semidirect
179. C₂×D₃×D₄	C₂²×C₃	semidirect
180. C₂×D₃×D₄	C₂²×C₃	semidirect
181. C₂×D₃×D₄	C₂²×C₃	semidirect
182. C₂×D₃×D₄	C₂²×C₃	semidirect
183. C₂×#235	C₂²×C₃	semidirect
184. C₂×#235	C₂²×C₃	semidirect
186. C₂²×D₁₂	C₂²×C₃	semidirect
187. C₂²×C₄×D₃	C₂²×C₃	semidirect
190. C₃×#127	C₂×D₃	semidirect
191. C₃×#127	C₂²×C₃	semidirect
194. C₃×#124	C₂×D₃	semidirect
195. C₃×#124	C₂²×C₃	semidirect
207. C₃×#121	C₂×D₃	semidirect
208. C₃×#121	C₂²×C₃	semidirect
216. C₃×#120	C₂×D₃	semidirect
217. C₃×#120	C₂²×C₃	semidirect
224. C₃×#117	C₂×D₃	semidirect
225. C₃×#117	C₂²×C₃	semidirect
228. #953	C₂²×C₃	semidirect
229. #946	C₂²×C₃	semidirect
230. #940	C₂²×C₃	semidirect
231. #938	C₂²×C₃	semidirect
232. #938	C₂²×C₃	semidirect
233. #938	C₂²×C₃	semidirect
234. #937	C₂²×C₃	semidirect
235. #937	C₂²×C₃	semidirect
236. #937	C₂²×C₃	semidirect
237. #936	C₂²×C₃	semidirect
238. #935	C₂²×C₃	semidirect
239. C₄×#67	C₂²×C₃	semidirect
240. #926	C₂²×C₃	semidirect
241. #897	C₂²×C₃	semidirect
242. #895	C₂²×C₃	semidirect
243. #893	C₂²×C₃	semidirect
244. #886	C₂²×C₃	semidirect
245. #884	C₂²×C₃	semidirect
246. #883	C₂²×C₃	semidirect
247. #882	C₂²×C₃	semidirect
248. #882	C₂²×C₃	semidirect
249. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
250. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
251. C₄×D₁₂	C₂²×C₃	semidirect
252. C₄×D₁₂	C₂²×C₃	semidirect
267. C₂²×C₃×D₃	C₂×D₄	semidirect
278. C₂×C₃²×C₄	C₂×D₄	semidirect
295. C₃×D₁₂	C₂×D₄	semidirect
296. C₃×D₁₂	C₂×D₄	semidirect
310. #535	C₃×D₃	semidirect
330. C₂³×D₃	C₂³×C₃	semidirect
339. C₂×C₃×Q₈	C₂²×D₃	semidirect
340. C₂×C₃×Q₈	C₂³×C₃	semidirect
370. C₂×C₃×D₄	C₂²×D₃	semidirect
371. C₂×C₃×D₄	C₂²×D₃	semidirect
375. C₂×C₃×D₄	C₂³×C₃	semidirect
376. C₂×C₃×D₄	C₂³×C₃	semidirect
387. C₂²×C₃×C₄	C₂²×D₃	semidirect
389. C₂²×C₃×C₄	C₂³×C₃	semidirect
394. C₂×#67	C₂³×C₃	semidirect
395. C₂×#67	C₂³×C₃	semidirect
406. C₂×D₁₂	C₃×D₄	semidirect
410. C₂×D₁₂	C₂³×C₃	semidirect
411. C₂×D₁₂	C₂³×C₃	semidirect
415. C₂×C₄×D₃	C₂³×C₃	semidirect
416. C₂×C₄×D₃	C₂³×C₃	semidirect
417. C₂×C₄×D₃	C₂³×C₃	semidirect
418. C₂×Dic₆	C₂³×C₃	semidirect
423. C₃×C₄⋊C₄	C₂²×D₃	semidirect
424. C₃×C₄⋊C₄	C₂³×C₃	semidirect
435. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
437. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
440. C₃×C₄²	C₂²×D₃	semidirect
441. C₃×C₄²	C₂³×C₃	semidirect
443. #217	C₂³×C₃	semidirect
444. #217	C₂³×C₃	semidirect
447. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
448. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
449. C₄⋊Dic₃	C₂³×C₃	semidirect
450. C₄⋊Dic₃	C₂³×C₃	semidirect
451. Dic₃⋊C₄	C₂³×C₃	semidirect
452. C₄×Dic₃	C₂³×C₃	semidirect
471. C₂×C₃×D₃	H(5,𝔽₂)	semidirect
484. C₂×#41	C₂×C₃×D₃	semidirect
494. C₂²×D₄	C₂×C₃×D₃	semidirect
497. #127	C₂×C₃×D₃	semidirect
499. #124	C₂×C₃×D₃	semidirect
510. #121	C₂×C₃×D₃	semidirect
517. #120	C₂×C₃×D₃	semidirect
523. #117	C₂×C₃×D₃	semidirect
563. C₂²×D₃	C₂×C₃×D₄	semidirect
613. C₂×C₃×C₄	D₃×D₄	semidirect
614. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
635. D₁₂	C₂×C₃×D₄	semidirect
636. D₁₂	C₂×C₃×D₄	semidirect
663. C₂×Q₈	C₂²×C₃×D₃	semidirect
686. C₂×D₄	C₂²×C₃×D₃	semidirect
687. C₂×D₄	C₂²×C₃×D₃	semidirect
696. C₂²×C₄	C₂²×C₃×D₃	semidirect
700. C₄⋊C₄	C₂²×C₃×D₃	semidirect
709. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
711. C₄²	C₂²×C₃×D₃	semidirect
757. C₂×D₃	C₃×H(5,𝔽₂)	semidirect
776. C₃²	#3484	semidirect
822. C₂×C₄	C₃×D₃×D₄	semidirect
875. C₃	#86330	direct (N × H)
876. C₃	C₃×#3484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1009	2
C₂²×C₃×D₃×D₄	2
C₃²×#535	2
C₃×#5828	2
C₃×#5805	2
C₃×#5717	2
C₃×#5676	2
C₃×#5612	2
C₃×#5609	2
C₃×#5589	2
C₃×D₃×#120	2
C₃×#5524	2
C₃×#5521	2
C₃×#3484	3
#86330	3

Subgroups — C3×#86330 #11904287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86330 #11904287