Subgroups — C₂×C₃×#3225 #10679403

Order 768.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3225	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#449	C₂	1	1	yes	maximal, characteristic
14	C₂×C₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#3225	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₃×D₈	C₂²	1	1	yes	characteristic
28	C₃×#542	—	2	4	no	—
29	C₃×#542	C₂²	1	8	yes	complemented
30	C₃×#536	—	2	4	no	—
31	C₃×#536	C₂²	1	8	yes	complemented
32	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×#126	—	2	1	no	—
36	C₂×C₃×#124	—	2	1	no	—
37	C₂×C₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₃×#124	C₂²	1	1	yes	characteristic
40	C₂×C₃×#123	—	2	1	no	—
41	C₂×C₃×#123	—	2	1	no	—
42	C₂×C₃×#123	—	2	1	no	—
43	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
46	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×#117	C₂²	1	1	yes	characteristic
51	C₃×#497	C₂²	1	8	yes	complemented
52	C₃×#495	C₂²	1	8	yes	complemented
53	C₃×#489	C₂²	1	8	yes	complemented
54	C₃×#487	C₂²	1	8	yes	complemented
55	C₃×#464	C₂²	1	8	yes	complemented
56	C₃×#463	C₂²	1	8	yes	complemented
57	C₃×#462	C₂²	1	8	yes	complemented
58	C₃×#461	C₂²	1	8	yes	complemented
59	C₃×#452	C₂²	1	8	yes	complemented
60	C₃×#451	C₂²	1	8	yes	complemented
61	C₃×#449	C₂²	1	8	yes	—
62	C₃×#448	C₂²	1	8	yes	complemented
63	C₃×#433	C₂²	1	8	yes	complemented
64	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₃×#97	C₂²	1	1	yes	characteristic
77	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
78	C₂×#542	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×#536	C₂×C₃	1	1	yes	characteristic, complemented
80	#3225	C₂×C₃	1	16	yes	direct product factor
81	C₂×#497	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#495	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#489	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#487	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#464	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂×#462	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×#463	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂×#461	C₂×C₃	1	1	yes	characteristic, complemented
89	C₂×#452	C₂×C₃	1	1	yes	characteristic, complemented
90	C₂×#449	C₂×C₃	1	1	yes	characteristic
91	C₂×#451	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×#448	C₂×C₃	1	1	yes	characteristic, complemented
93	C₂×#433	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂×C₃×#41	—	2	2	no	—
95	C₂×C₃×#41	—	4	2	no	—
96	C₂×C₃×#41	—	4	2	no	—
97	C₂×C₃×#41	C₂³	1	4	yes	—
98	C₂²×C₃×Q₈	—	2	1	no	—
99	C₂²×C₃×Q₈	—	2	2	no	—
100	C₂²×C₃×Q₈	—	2	1	no	—
101	C₂²×C₃×Q₈	—	4	2	no	—
102	C₂²×C₃×Q₈	—	4	2	no	—
103	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
107	C₂²×C₃×Q₈	C₂³	1	4	yes	—
108	C₂²×C₃×D₄	—	2	1	no	—
109	C₂²×C₃×D₄	—	2	1	no	—
110	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
111	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
112	C₂³×C₃×C₄	—	2	1	no	—
113	C₂³×C₃×C₄	—	2	1	no	—
114	C₂³×C₃×C₄	—	2	1	no	—
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂×C₃×Q₁₆	—	4	2	no	—
117	C₂×C₃×Q₁₆	—	4	2	no	—
118	C₂×C₃×Q₁₆	—	4	2	no	—
119	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
120	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
122	C₂×C₃×SD₁₆	—	4	2	no	—
123	C₂×C₃×SD₁₆	—	4	2	no	—
124	C₂×C₃×SD₁₆	—	4	2	no	—
125	C₂×C₃×SD₁₆	—	4	2	no	—
126	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
128	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₃×D₈	—	4	2	no	—
131	C₂×C₃×D₈	C₂³	1	4	yes	—
132	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
133	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
134	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
135	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
136	C₃×C₄⋊Q₈	—	2	2	no	—
137	C₃×C₄⋊Q₈	—	2	2	no	—
138	C₃×C₄⋊Q₈	—	2	2	no	—
139	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
140	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
141	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
142	C₃×#126	—	2	8	no	—
143	C₃×#124	—	2	8	no	—
144	C₃×#124	—	2	2	no	—
145	C₃×#124	—	2	2	no	—
146	C₃×#124	—	2	2	no	—
147	C₃×#124	C₂³	1	4	yes	—
148	C₃×#124	C₂³	1	4	yes	—
149	C₃×#124	C₂³	1	4	yes	—
150	C₃×#123	—	2	8	no	—
151	C₃×#123	—	2	8	no	—
152	C₃×#123	—	2	8	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	8	no	—
155	C₃×C₂²⋊Q₈	—	2	8	no	—
156	C₃×C₂²⋊Q₈	—	2	8	no	—
157	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	C₂³	1	4	yes	—
160	C₃×C₄×Q₈	—	2	2	no	—
161	C₃×C₄×Q₈	C₂³	1	4	yes	—
162	C₃×C₄×D₄	—	2	2	no	—
163	C₃×C₄×D₄	C₂³	1	4	yes	—
164	C₃×#117	D₄	1	4	yes	—
165	C₃×#117	C₂³	1	4	yes	—
166	C₂×C₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₃×C₄²	—	2	1	no	—
189	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊C₈	C₂³	1	4	yes	—
192	C₃×C₄⋊C₈	C₂³	1	4	yes	—
193	C₃×#103	C₂³	1	4	yes	—
194	C₃×#103	C₂³	1	4	yes	—
195	C₃×#103	C₂³	1	4	yes	—
196	C₃×#103	C₂³	1	4	yes	—
197	C₃×#103	C₂³	1	4	yes	—
198	C₃×#103	C₂³	1	4	yes	—
199	C₃×#102	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	4	yes	—
201	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
202	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
203	C₃×#97	C₂³	1	4	yes	—
204	C₃×C₄×C₈	C₂³	1	4	yes	—
205	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
206	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
207	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
212	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
213	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
214	C₂²×D₈	C₂²×C₃	1	1	yes	characteristic
215	#542	—	2	4	no	—
216	#542	C₂²×C₃	1	8	yes	complemented
217	#536	—	2	4	no	—
218	#536	C₂²×C₃	1	8	yes	complemented
219	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
222	C₂×#126	—	2	1	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×#124	C₂²×C₃	1	1	yes	characteristic
225	C₂×#124	C₂²×C₃	1	1	yes	characteristic
226	C₂×#124	C₂²×C₃	1	1	yes	characteristic
227	C₂×#123	—	2	1	no	—
228	C₂×#123	—	2	1	no	—
229	C₂×#123	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	—	2	1	no	—
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
234	C₂×#121	C₂²×C₃	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
237	C₂×#117	C₂²×C₃	1	1	yes	characteristic
238	#497	C₂²×C₃	1	8	yes	complemented
239	#495	C₂²×C₃	1	8	yes	complemented
240	#489	C₂²×C₃	1	8	yes	complemented
241	#487	C₂²×C₃	1	8	yes	complemented
242	#464	C₂²×C₃	1	8	yes	complemented
243	#463	C₂²×C₃	1	8	yes	complemented
244	#462	C₂²×C₃	1	8	yes	complemented
245	#461	C₂²×C₃	1	8	yes	complemented
246	#452	C₂²×C₃	1	8	yes	complemented
247	#451	C₂²×C₃	1	8	yes	complemented
248	#449	C₂²×C₃	1	8	yes	—
249	#448	C₂²×C₃	1	8	yes	complemented
250	#433	C₂²×C₃	1	8	yes	complemented
251	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
253	C₂×#103	C₂²×C₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₃	1	1	yes	characteristic
256	C₂×#103	C₂²×C₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₃	1	1	yes	characteristic
258	C₂×#103	C₂²×C₃	1	1	yes	characteristic
259	C₂×#102	C₂²×C₃	1	1	yes	characteristic
260	C₂×#102	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
263	C₂×#97	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
265	C₂⁴×C₃	—	2	1	no	—
266	C₂⁴×C₃	—	2	1	no	—
267	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
268	C₃×#41	—	4	4	no	—
269	C₃×#41	—	4	4	no	—
270	C₃×#41	—	4	8	no	—
271	C₂×C₃×Q₈	—	2	1	no	—
272	C₂×C₃×Q₈	—	2	4	no	—
273	C₂×C₃×Q₈	—	2	1	no	—
274	C₂×C₃×Q₈	—	2	1	no	—
275	C₂×C₃×Q₈	—	2	1	no	—
276	C₂×C₃×Q₈	—	2	4	no	—
277	C₂×C₃×Q₈	—	2	2	no	—
278	C₂×C₃×Q₈	—	2	2	no	—
279	C₂×C₃×Q₈	—	2	2	no	—
280	C₂×C₃×Q₈	—	2	2	no	—
281	C₂×C₃×Q₈	—	2	2	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	—	2	2	no	—
284	C₂×C₃×Q₈	—	2	2	no	—
285	C₂×C₃×Q₈	—	4	4	no	—
286	C₂×C₃×Q₈	—	4	4	no	—
287	C₂×C₃×Q₈	—	4	4	no	—
288	C₂×C₃×Q₈	—	4	8	no	—
289	C₂×C₃×Q₈	—	8	2	no	—
290	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
291	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
292	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
293	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
294	C₂×C₃×D₄	—	2	4	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	2	no	—
302	C₂×C₃×D₄	—	4	4	no	—
303	C₂×C₃×D₄	—	8	2	no	—
304	C₂×C₃×D₄	C₂⁴	1	2	yes	—
305	C₂×C₃×D₄	C₂⁴	1	2	yes	—
306	C₂²×C₃×C₄	—	2	2	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	1	no	—
310	C₂²×C₃×C₄	—	2	1	no	—
311	C₂²×C₃×C₄	—	2	1	no	—
312	C₂²×C₃×C₄	—	2	1	no	—
313	C₂²×C₃×C₄	—	2	1	no	—
314	C₂²×C₃×C₄	—	2	1	no	—
315	C₂²×C₃×C₄	—	2	4	no	—
316	C₂²×C₃×C₄	—	2	4	no	—
317	C₂²×C₃×C₄	—	4	4	no	—
318	C₂²×C₃×C₄	—	4	4	no	—
319	C₂²×C₃×C₄	—	8	2	no	—
320	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
321	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
327	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
328	C₃×Q₁₆	—	4	4	no	—
329	C₃×Q₁₆	—	4	4	no	—
330	C₃×Q₁₆	—	4	4	no	—
331	C₃×SD₁₆	—	4	4	no	—
332	C₃×SD₁₆	—	4	4	no	—
333	C₃×SD₁₆	—	4	4	no	—
334	C₃×SD₁₆	—	4	4	no	—
335	C₃×D₈	—	4	4	no	—
336	C₂×C₃×C₈	—	2	2	no	—
337	C₂×C₃×C₈	—	2	2	no	—
338	C₂×C₃×C₈	—	2	2	no	—
339	C₂×C₃×C₈	—	2	2	no	—
340	C₂×C₃×C₈	C₂⁴	1	2	yes	—
341	C₂×C₃×C₈	C₂⁴	1	2	yes	—
342	C₂×C₃×C₈	C₂⁴	1	2	yes	—
343	C₂×C₃×C₈	C₂⁴	1	2	yes	—
344	C₃×C₄⋊C₄	—	2	4	no	—
345	C₃×C₄⋊C₄	—	2	4	no	—
346	C₃×C₄⋊C₄	—	2	4	no	—
347	C₃×C₄⋊C₄	—	2	4	no	—
348	C₃×C₄⋊C₄	—	2	4	no	—
349	C₃×C₄⋊C₄	—	2	4	no	—
350	C₃×C₄⋊C₄	—	2	4	no	—
351	C₃×C₄⋊C₄	—	2	1	no	—
352	C₃×C₄⋊C₄	—	2	1	no	—
353	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
354	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
355	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
356	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	4	no	—
360	C₃×C₂²⋊C₄	—	2	4	no	—
361	C₃×C₂²⋊C₄	—	2	4	no	—
362	C₃×C₂²⋊C₄	—	2	4	no	—
363	C₃×C₂²⋊C₄	—	2	4	no	—
364	C₃×C₂²⋊C₄	—	2	4	no	—
365	C₃×C₂²⋊C₄	—	2	4	no	—
366	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
367	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
368	C₃×C₄²	—	2	4	no	—
369	C₃×C₄²	C₂×D₄	1	2	yes	—
370	C₃×C₄²	C₂×D₄	1	2	yes	—
371	C₃×C₄²	C₂⁴	1	2	yes	—
372	C₃×C₄²	C₂⁴	1	2	yes	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	4	2	no	—
375	C₂×#41	—	4	2	no	—
376	C₂×#41	C₂³×C₃	1	4	yes	—
377	C₂²×Q₈	—	2	1	no	—
378	C₂²×Q₈	—	2	2	no	—
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×Q₈	—	4	2	no	—
381	C₂²×Q₈	—	4	2	no	—
382	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₃	1	4	yes	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
395	C₂×Q₁₆	—	4	2	no	—
396	C₂×Q₁₆	—	4	2	no	—
397	C₂×Q₁₆	—	4	2	no	—
398	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
399	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
400	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
401	C₂×SD₁₆	—	4	2	no	—
402	C₂×SD₁₆	—	4	2	no	—
403	C₂×SD₁₆	—	4	2	no	—
404	C₂×SD₁₆	—	4	2	no	—
405	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
406	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
407	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
408	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
409	C₂×D₈	—	4	2	no	—
410	C₂×D₈	C₂³×C₃	1	4	yes	—
411	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
415	C₄⋊Q₈	—	2	2	no	—
416	C₄⋊Q₈	—	2	2	no	—
417	C₄⋊Q₈	—	2	2	no	—
418	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
419	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
420	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
421	#126	—	2	8	no	—
422	#124	—	2	8	no	—
423	#124	—	2	2	no	—
424	#124	—	2	2	no	—
425	#124	—	2	2	no	—
426	#124	C₂³×C₃	1	4	yes	—
427	#124	C₂³×C₃	1	4	yes	—
428	#124	C₂³×C₃	1	4	yes	—
429	#123	—	2	8	no	—
430	#123	—	2	8	no	—
431	#123	—	2	8	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	8	no	—
434	C₂²⋊Q₈	—	2	8	no	—
435	C₂²⋊Q₈	—	2	8	no	—
436	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
437	#121	—	2	2	no	—
438	#121	C₂³×C₃	1	4	yes	—
439	C₄×Q₈	—	2	2	no	—
440	C₄×Q₈	C₂³×C₃	1	4	yes	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	C₂³×C₃	1	4	yes	—
443	#117	C₃×D₄	1	4	yes	—
444	#117	C₂³×C₃	1	4	yes	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
470	C₄⋊C₈	C₂³×C₃	1	4	yes	—
471	C₄⋊C₈	C₂³×C₃	1	4	yes	—
472	#103	C₂³×C₃	1	4	yes	—
473	#103	C₂³×C₃	1	4	yes	—
474	#103	C₂³×C₃	1	4	yes	—
475	#103	C₂³×C₃	1	4	yes	—
476	#103	C₂³×C₃	1	4	yes	—
477	#103	C₂³×C₃	1	4	yes	—
478	#102	C₂³×C₃	1	4	yes	—
479	#102	C₂³×C₃	1	4	yes	—
480	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
481	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
482	#97	C₂³×C₃	1	4	yes	—
483	C₄×C₈	C₂³×C₃	1	4	yes	—
484	C₂³×C₃	—	2	2	no	—
485	C₂³×C₃	—	2	2	no	—
486	C₂³×C₃	—	2	2	no	—
487	C₂³×C₃	—	2	2	no	—
488	C₂³×C₃	—	2	2	no	—
489	C₂³×C₃	—	4	2	no	—
490	C₂³×C₃	—	4	2	no	—
491	C₂³×C₃	—	4	2	no	—
492	C₂³×C₃	—	4	2	no	—
493	C₂³×C₃	—	4	2	no	—
494	C₂³×C₃	—	4	2	no	—
495	C₂³×C₃	C₂²×D₄	1	2	yes	—
496	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
497	C₃×Q₈	—	2	2	no	—
498	C₃×Q₈	—	2	2	no	—
499	C₃×Q₈	—	2	2	no	—
500	C₃×Q₈	—	2	2	no	—
501	C₃×Q₈	—	2	2	no	—
502	C₃×Q₈	—	2	2	no	—
503	C₃×Q₈	—	2	2	no	—
504	C₃×Q₈	—	2	2	no	—
505	C₃×Q₈	—	4	8	no	—
506	C₃×Q₈	—	4	2	no	—
507	C₃×Q₈	—	4	2	no	—
508	C₃×Q₈	—	4	2	no	—
509	C₃×Q₈	—	4	2	no	—
510	C₃×Q₈	—	8	4	no	—
511	C₃×D₄	—	2	2	no	—
512	C₃×D₄	—	2	2	no	—
513	C₃×D₄	—	2	2	no	—
514	C₃×D₄	—	2	2	no	—
515	C₃×D₄	—	4	8	no	—
516	C₃×D₄	—	4	2	no	—
517	C₃×D₄	—	4	2	no	—
518	C₃×D₄	—	8	4	no	—
519	C₂×C₃×C₄	—	2	2	no	—
520	C₂×C₃×C₄	—	2	2	no	—
521	C₂×C₃×C₄	—	2	2	no	—
522	C₂×C₃×C₄	—	2	2	no	—
523	C₂×C₃×C₄	—	2	2	no	—
524	C₂×C₃×C₄	—	2	4	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	2	no	—
527	C₂×C₃×C₄	—	2	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	2	2	no	—
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	4	8	no	—
534	C₂×C₃×C₄	—	4	8	no	—
535	C₂×C₃×C₄	—	4	2	no	—
536	C₂×C₃×C₄	—	4	2	no	—
537	C₂×C₃×C₄	—	4	2	no	—
538	C₂×C₃×C₄	—	4	2	no	—
539	C₂×C₃×C₄	—	4	2	no	—
540	C₂×C₃×C₄	—	4	2	no	—
541	C₂×C₃×C₄	—	8	4	no	—
542	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
543	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
544	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
545	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
546	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
547	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
549	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
550	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
551	C₃×C₈	—	2	2	no	—
552	C₃×C₈	—	2	2	no	—
553	C₃×C₈	—	2	2	no	—
554	C₃×C₈	—	2	2	no	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	2	1	no	—
557	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
558	#41	—	4	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	8	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	4	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×Q₈	—	4	8	no	—
579	C₂×Q₈	—	8	2	no	—
580	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
581	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
583	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	8	2	no	—
594	C₂×D₄	C₂⁴×C₃	1	2	yes	—
595	C₂×D₄	C₂⁴×C₃	1	2	yes	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
612	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
613	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
614	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
615	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
618	Q₁₆	—	4	4	no	—
619	Q₁₆	—	4	4	no	—
620	Q₁₆	—	4	4	no	—
621	SD₁₆	—	4	4	no	—
622	SD₁₆	—	4	4	no	—
623	SD₁₆	—	4	4	no	—
624	SD₁₆	—	4	4	no	—
625	D₈	—	4	4	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	2	2	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	C₂⁴×C₃	1	2	yes	—
631	C₂×C₈	C₂⁴×C₃	1	2	yes	—
632	C₂×C₈	C₂⁴×C₃	1	2	yes	—
633	C₂×C₈	C₂⁴×C₃	1	2	yes	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
644	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
645	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
657	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
658	C₄²	—	2	4	no	—
659	C₄²	C₂×C₃×D₄	1	2	yes	—
660	C₄²	C₂×C₃×D₄	1	2	yes	—
661	C₄²	C₂⁴×C₃	1	2	yes	—
662	C₄²	C₂⁴×C₃	1	2	yes	—
663	C₂²×C₃	—	2	2	no	—
664	C₂²×C₃	—	2	2	no	—
665	C₂²×C₃	—	2	2	no	—
666	C₂²×C₃	—	4	4	no	—
667	C₂²×C₃	—	4	2	no	—
668	C₂²×C₃	—	4	2	no	—
669	C₂²×C₃	—	4	2	no	—
670	C₂²×C₃	—	4	2	no	—
671	C₂²×C₃	—	4	2	no	—
672	C₂²×C₃	—	4	2	no	—
673	C₂²×C₃	—	8	4	no	—
674	C₂²×C₃	—	8	4	no	—
675	C₂²×C₃	#535	1	2	yes	—
676	C₂²×C₃	#577	1	2	yes	—
677	C₂²×C₃	#578	1	2	yes	—
678	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
679	C₃×C₄	—	2	2	no	—
680	C₃×C₄	—	2	2	no	—
681	C₃×C₄	—	2	2	no	—
682	C₃×C₄	—	2	2	no	—
683	C₃×C₄	—	2	2	no	—
684	C₃×C₄	—	4	2	no	—
685	C₃×C₄	—	4	2	no	—
686	C₃×C₄	—	4	2	no	—
687	C₃×C₄	—	4	2	no	—
688	C₃×C₄	—	4	2	no	—
689	C₃×C₄	—	4	2	no	—
690	C₃×C₄	#535	1	2	yes	—
691	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
692	C₃×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	2	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	4	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	4	2	no	—
703	C₂³	—	4	2	no	—
704	C₂³	C₂²×C₃×D₄	1	2	yes	—
705	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	4	8	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	8	4	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	8	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	8	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	4	8	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
752	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
753	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
754	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
755	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
756	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
757	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
758	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
759	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	2	2	no	—
763	C₈	—	2	2	no	—
764	C₂×C₃	—	4	2	no	—
765	C₂×C₃	—	8	2	no	—
766	C₂×C₃	—	8	2	no	—
767	C₂×C₃	#3225	1	4	yes	direct product factor
768	C₂×C₃	C₂×#535	1	1	yes	characteristic
769	C₂×C₃	C₂×#577	1	1	yes	characteristic
770	C₂×C₃	C₂×#578	1	1	yes	characteristic
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	8	4	no	—
782	C₂²	—	8	4	no	—
783	C₂²	C₃×#535	1	2	yes	—
784	C₂²	C₃×#577	1	2	yes	—
785	C₂²	C₃×#578	1	2	yes	—
786	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	C₃×#535	1	2	yes	—
799	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₄	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₃	C₂×#3225	1	1	yes	characteristic, direct product factor, Sylow
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	2	no	—
805	C₂	C₃×#3225	1	4	yes	direct product factor
806	C₂	C₂×C₃×#535	1	1	yes	characteristic
807	C₂	C₂×C₃×#577	1	1	yes	characteristic
808	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#542	C₂	semidirect
2. C₂×C₃×#536	C₂	semidirect
3. C₃×#3225	C₂	direct (N × H)
4. C₂×C₃×#497	C₂	semidirect
5. C₂×C₃×#495	C₂	semidirect
6. C₂×C₃×#489	C₂	semidirect
7. C₂×C₃×#487	C₂	semidirect
8. C₂×C₃×#464	C₂	semidirect
9. C₂×C₃×#462	C₂	semidirect
10. C₂×C₃×#463	C₂	semidirect
11. C₂×C₃×#461	C₂	semidirect
12. C₂×C₃×#452	C₂	semidirect
14. C₂×C₃×#451	C₂	semidirect
15. C₂×C₃×#448	C₂	semidirect
16. C₂×C₃×#433	C₂	semidirect
17. C₂×#3225	C₃	direct (N × H)
29. C₃×#542	C₂²	semidirect
31. C₃×#536	C₂²	semidirect
51. C₃×#497	C₂²	semidirect
52. C₃×#495	C₂²	semidirect
53. C₃×#489	C₂²	semidirect
54. C₃×#487	C₂²	semidirect
55. C₃×#464	C₂²	semidirect
56. C₃×#463	C₂²	semidirect
57. C₃×#462	C₂²	semidirect
58. C₃×#461	C₂²	semidirect
59. C₃×#452	C₂²	semidirect
60. C₃×#451	C₂²	semidirect
62. C₃×#448	C₂²	semidirect
63. C₃×#433	C₂²	semidirect
78. C₂×#542	C₂×C₃	semidirect
79. C₂×#536	C₂×C₃	semidirect
80. #3225	C₂×C₃	direct (N × H)
81. C₂×#497	C₂×C₃	semidirect
82. C₂×#495	C₂×C₃	semidirect
83. C₂×#489	C₂×C₃	semidirect
84. C₂×#487	C₂×C₃	semidirect
85. C₂×#464	C₂×C₃	semidirect
86. C₂×#462	C₂×C₃	semidirect
87. C₂×#463	C₂×C₃	semidirect
88. C₂×#461	C₂×C₃	semidirect
89. C₂×#452	C₂×C₃	semidirect
91. C₂×#451	C₂×C₃	semidirect
92. C₂×#448	C₂×C₃	semidirect
93. C₂×#433	C₂×C₃	semidirect
216. #542	C₂²×C₃	semidirect
218. #536	C₂²×C₃	semidirect
238. #497	C₂²×C₃	semidirect
239. #495	C₂²×C₃	semidirect
240. #489	C₂²×C₃	semidirect
241. #487	C₂²×C₃	semidirect
242. #464	C₂²×C₃	semidirect
243. #463	C₂²×C₃	semidirect
244. #462	C₂²×C₃	semidirect
245. #461	C₂²×C₃	semidirect
246. #452	C₂²×C₃	semidirect
247. #451	C₂²×C₃	semidirect
249. #448	C₂²×C₃	semidirect
250. #433	C₂²×C₃	semidirect
767. C₂×C₃	#3225	direct (N × H)
801. C₃	C₂×#3225	direct (N × H)
805. C₂	C₃×#3225	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#542	2
C₂×C₃×#536	2
C₃×#3225	2
C₂×C₃×#497	2
C₂×C₃×#495	2
C₂×C₃×#489	2
C₂×C₃×#487	2
C₂×C₃×#464	2
C₂×C₃×#462	2
C₂×C₃×#463	2
C₂×C₃×#461	2
C₂×C₃×#452	2
C₂×C₃×#449	2
C₂×C₃×#451	2
C₂×C₃×#448	2
C₂×C₃×#433	2
C₂×#3225	3

Subgroups — C2×C3×#3225 #10679403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3225 #10679403