Subgroups — C₃×#60571 #10679178

Order 768.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3125	C₂	1	2	yes	maximal, complemented
4	C₃×#3123	C₂	1	2	yes	maximal, complemented
5	C₃×#3120	C₂	1	2	yes	maximal, complemented
6	C₃×#3118	C₂	1	2	yes	maximal, complemented
7	C₃×#3107	C₂	1	2	yes	maximal, complemented
8	C₃×#3105	C₂	1	2	yes	maximal, complemented
9	C₃×#3102	C₂	1	2	yes	maximal, complemented
10	C₃×#3101	C₂	1	2	yes	maximal, complemented
11	C₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#3012	C₂	1	1	yes	maximal, characteristic
18	C₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	#60571	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₃×#135	C₂²	1	1	yes	characteristic
29	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
30	C₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₃×#542	—	2	1	no	—
32	C₃×#542	C₂²	1	2	yes	complemented
33	C₃×#541	—	2	1	no	—
34	C₃×#541	C₂²	1	2	yes	complemented
35	C₃×#539	—	2	2	no	—
36	C₃×#537	C₂²	1	1	yes	characteristic
37	C₃×#536	C₂²	1	1	yes	characteristic
38	C₃×#536	C₂²	1	1	yes	characteristic, complemented
39	C₃×#533	—	2	1	no	—
40	C₃×#533	C₂²	1	2	yes	complemented
41	C₃×#529	—	2	2	no	—
42	C₃×#529	—	2	1	no	—
43	C₃×#529	C₂²	1	2	yes	complemented
44	C₃×#520	—	2	1	no	—
45	C₃×#520	C₂²	1	1	yes	characteristic
46	C₃×#520	C₂²	1	2	yes	—
47	C₃×#520	C₂²	1	1	yes	characteristic
48	C₃×#518	—	2	2	no	—
49	C₃×#518	—	2	1	no	—
50	C₃×#518	C₂²	1	1	yes	characteristic
51	C₃×#518	C₂²	1	2	yes	—
52	C₃×C₄×#41	—	2	1	no	—
53	C₃×C₄×#41	C₂²	1	1	yes	characteristic
54	C₃×C₄×#41	C₂²	1	2	yes	—
55	C₃×C₄×#41	C₂²	1	1	yes	characteristic
56	C₃×C₄×#41	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×C₄×D₄	—	2	1	no	—
59	C₂×C₃×C₄×D₄	—	2	2	no	—
60	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
62	C₃×#485	C₂²	1	2	yes	complemented
63	C₃×#485	C₂²	1	2	yes	complemented
64	C₃×#485	C₂²	1	2	yes	complemented
65	C₃×#484	C₂²	1	2	yes	complemented
66	C₃×#483	C₂²	1	2	yes	complemented
67	C₃×#483	C₂²	1	2	yes	complemented
68	C₃×#482	C₂²	1	2	yes	complemented
69	C₃×#481	C₂²	1	2	yes	complemented
70	C₃×#479	C₂²	1	2	yes	complemented
71	C₃×#478	C₂²	1	2	yes	complemented
72	C₃×#478	C₂²	1	2	yes	complemented
73	C₃×#478	C₂²	1	2	yes	complemented
74	C₃×#476	C₂²	1	2	yes	complemented
75	C₃×#476	C₂²	1	2	yes	complemented
76	C₃×#475	C₂²	1	2	yes	complemented
77	C₃×#474	C₂²	1	2	yes	complemented
78	C₃×#464	C₂²	1	2	yes	complemented
79	C₃×#463	C₂²	1	2	yes	complemented
80	C₃×#463	C₂²	1	2	yes	complemented
81	C₃×#463	C₂²	1	2	yes	complemented
82	C₃×#462	C₂²	1	2	yes	complemented
83	C₃×#461	C₂²	1	2	yes	complemented
84	C₃×#461	C₂²	1	2	yes	complemented
85	C₃×#461	C₂²	1	2	yes	complemented
86	C₃×#452	C₂²	1	2	yes	—
87	C₃×#452	C₂²	1	2	yes	—
88	C₃×#452	C₂²	1	2	yes	—
89	C₃×#450	C₂²	1	2	yes	—
90	C₃×#450	C₂²	1	2	yes	—
91	C₃×#450	C₂²	1	2	yes	—
92	C₃×#449	C₂²	1	2	yes	—
93	C₃×#447	C₂²	1	2	yes	—
94	C₃×#442	C₂²	1	2	yes	complemented
95	C₃×#441	C₂²	1	2	yes	complemented
96	C₃×#440	C₂²	1	2	yes	complemented
97	C₃×#440	C₂²	1	2	yes	complemented
98	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₃×C₄×Q₁₆	C₂²	1	2	yes	complemented
101	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
102	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
103	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
104	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
105	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
107	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
108	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
110	C₃×C₄×SD₁₆	C₂²	1	2	yes	complemented
111	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
112	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
113	C₃×C₄×D₈	C₂²	1	2	yes	complemented
114	C₃×#433	C₂²	1	2	yes	complemented
115	C₃×#433	C₂²	1	2	yes	complemented
116	C₃×#431	C₂²	1	2	yes	complemented
117	C₃×#431	C₂²	1	2	yes	complemented
118	C₃×#428	C₂²	1	1	yes	characteristic, complemented
119	C₃×#428	C₂²	1	1	yes	characteristic, complemented
120	C₃×#427	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₃×#106	C₂²	1	1	yes	characteristic, complemented
122	C₃×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃×#424	C₂²	1	1	yes	characteristic, complemented
124	C₃×#419	C₂²	1	1	yes	characteristic, complemented
125	C₃×#418	C₂²	1	1	yes	characteristic
126	C₃×#417	C₂²	1	1	yes	characteristic
127	C₃×#417	C₂²	1	1	yes	characteristic, complemented
128	C₃×#416	C₂²	1	1	yes	characteristic
129	C₃×#416	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃×#103	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃×#102	C₂²	1	1	yes	characteristic
132	C₃×#408	C₂²	1	1	yes	characteristic
133	C₃×#408	C₂²	1	1	yes	characteristic
134	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
136	#3461	C₂×C₃	1	1	yes	characteristic, complemented
137	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
138	#3125	C₂×C₃	1	2	yes	complemented
139	#3123	C₂×C₃	1	2	yes	complemented
140	#3120	C₂×C₃	1	2	yes	complemented
141	#3118	C₂×C₃	1	2	yes	complemented
142	#3107	C₂×C₃	1	2	yes	complemented
143	#3105	C₂×C₃	1	2	yes	complemented
144	#3102	C₂×C₃	1	2	yes	complemented
145	#3101	C₂×C₃	1	2	yes	complemented
146	#3099	C₂×C₃	1	1	yes	characteristic, complemented
147	#3097	C₂×C₃	1	1	yes	characteristic, complemented
148	#3084	C₂×C₃	1	1	yes	characteristic, complemented
149	#3081	C₂×C₃	1	1	yes	characteristic, complemented
150	#3046	C₂×C₃	1	1	yes	characteristic, complemented
151	#3042	C₂×C₃	1	1	yes	characteristic, complemented
152	#3012	C₂×C₃	1	1	yes	characteristic
153	#3009	C₂×C₃	1	1	yes	characteristic, complemented
154	C₄×#137	C₂×C₃	1	1	yes	characteristic, complemented
155	C₄×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
156	C₄×#135	C₂×C₃	1	1	yes	characteristic, complemented
157	C₂×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
158	#2922	C₂×C₃	1	1	yes	characteristic, complemented
159	C₃×H(5,𝔽₂)	—	2	4	no	—
160	C₃×H(5,𝔽₂)	—	2	4	no	—
161	C₂×C₃×#41	—	2	1	no	—
162	C₂×C₃×#41	C₂³	1	1	yes	characteristic
163	C₂×C₃×#41	C₂³	1	2	yes	—
164	C₂×C₃×#41	C₂³	1	1	yes	characteristic
165	C₂×C₃×#41	C₂³	1	1	yes	characteristic
166	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	—	2	2	no	—
168	C₂²×C₃×D₄	—	2	1	no	—
169	C₂²×C₃×D₄	C₂³	1	2	yes	—
170	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
171	C₂³×C₃×C₄	—	2	1	no	—
172	C₂³×C₃×C₄	—	2	2	no	—
173	C₃×#137	—	2	4	no	—
174	C₃×AGL(1,ℤ/8)	—	2	4	no	—
175	C₃×#135	—	2	4	no	—
176	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
177	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
178	C₂×C₃×SD₁₆	—	2	4	no	—
179	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
180	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
181	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
182	C₂×C₃×SD₁₆	C₂³	1	1	yes	characteristic
183	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
184	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
185	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
186	C₂×C₃×D₈	C₂³	1	2	yes	—
187	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
190	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
191	C₃×C₄⋊Q₈	—	2	1	no	—
192	C₃×C₄⋊Q₈	—	2	1	no	—
193	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
195	C₃×#126	—	2	2	no	—
196	C₃×#126	—	2	2	no	—
197	C₃×#126	—	2	2	no	—
198	C₃×#126	—	2	2	no	—
199	C₃×#125	—	2	2	no	—
200	C₃×#125	—	2	1	no	—
201	C₃×#125	—	2	2	no	—
202	C₃×#125	—	2	2	no	—
203	C₃×#125	C₂³	1	2	yes	—
204	C₃×#124	—	2	1	no	—
205	C₃×#124	—	2	2	no	—
206	C₃×#124	C₂³	1	2	yes	—
207	C₃×#123	—	2	2	no	—
208	C₃×#123	—	2	2	no	—
209	C₃×#123	—	2	2	no	—
210	C₃×#123	—	2	2	no	—
211	C₃×C₂²⋊Q₈	—	2	1	no	—
212	C₃×C₂²⋊Q₈	—	2	2	no	—
213	C₃×C₂²⋊Q₈	—	2	1	no	—
214	C₃×C₂²⋊Q₈	—	2	1	no	—
215	C₃×C₂²⋊Q₈	—	2	2	no	—
216	C₃×C₂²⋊Q₈	—	2	2	no	—
217	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃×#121	—	2	2	no	—
221	C₃×#121	—	2	1	no	—
222	C₃×#121	C₂³	1	2	yes	—
223	C₃×C₄×Q₈	—	2	1	no	—
224	C₃×C₄×Q₈	—	2	1	no	—
225	C₃×C₄×Q₈	—	2	1	no	—
226	C₃×C₄×Q₈	—	2	2	no	—
227	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
228	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
229	C₃×C₄×Q₈	C₂³	1	2	yes	—
230	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₃×C₄×Q₈	C₂³	1	2	yes	—
232	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₃×C₄×Q₈	C₂³	1	2	yes	—
236	C₃×C₄×D₄	—	2	2	no	—
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	—	2	1	no	—
239	C₃×C₄×D₄	—	2	2	no	—
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	—	2	2	no	—
242	C₃×C₄×D₄	—	2	1	no	—
243	C₃×C₄×D₄	—	2	1	no	—
244	C₃×C₄×D₄	—	2	2	no	—
245	C₃×C₄×D₄	—	2	1	no	—
246	C₃×C₄×D₄	—	2	2	no	—
247	C₃×C₄×D₄	—	2	2	no	—
248	C₃×C₄×D₄	—	2	1	no	—
249	C₃×C₄×D₄	—	2	2	no	—
250	C₃×C₄×D₄	—	2	2	no	—
251	C₃×C₄×D₄	—	2	2	no	—
252	C₃×C₄×D₄	—	2	1	no	—
253	C₃×C₄×D₄	—	2	2	no	—
254	C₃×C₄×D₄	—	2	1	no	—
255	C₃×C₄×D₄	—	2	2	no	—
256	C₃×C₄×D₄	D₄	1	1	yes	characteristic
257	C₃×C₄×D₄	D₄	1	2	yes	—
258	C₃×C₄×D₄	D₄	1	2	yes	—
259	C₃×C₄×D₄	D₄	1	1	yes	characteristic
260	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
261	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
262	C₃×C₄×D₄	C₂³	1	2	yes	—
263	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
264	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
265	C₃×C₄×D₄	C₂³	1	2	yes	—
266	C₃×C₄×D₄	C₂³	1	2	yes	—
267	C₃×C₄×D₄	C₂³	1	2	yes	—
268	C₃×C₄×D₄	C₂³	1	2	yes	—
269	C₃×#117	—	2	2	no	—
270	C₃×#117	—	2	2	no	—
271	C₃×#117	—	2	1	no	—
272	C₃×#117	—	2	1	no	—
273	C₃×#117	—	2	2	no	—
274	C₃×#117	—	2	1	no	—
275	C₃×#117	—	2	2	no	—
276	C₃×#117	C₂³	1	1	yes	characteristic
277	C₃×#117	C₂³	1	1	yes	characteristic
278	C₃×#117	C₂³	1	2	yes	—
279	C₃×#117	C₂³	1	1	yes	characteristic
280	C₃×#117	C₂³	1	2	yes	—
281	C₂×C₃×C₄⋊C₄	—	2	1	no	—
282	C₂×C₃×C₄⋊C₄	—	2	1	no	—
283	C₂×C₃×C₄⋊C₄	—	2	2	no	—
284	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₃×C₄²	—	2	1	no	—
293	C₂×C₃×C₄²	—	2	1	no	—
294	C₂×C₃×C₄²	—	2	2	no	—
295	C₂×C₃×C₄²	—	2	1	no	—
296	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
297	C₂×C₃×C₄²	C₂³	1	2	yes	—
298	C₃×#107	C₂³	1	1	yes	characteristic
299	C₃×#107	C₂³	1	1	yes	characteristic
300	C₃×#107	C₂³	1	2	yes	—
301	C₃×#107	C₂³	1	2	yes	—
302	C₃×#106	C₂³	1	2	yes	—
303	C₃×#106	C₂³	1	2	yes	—
304	C₃×#106	C₂³	1	1	yes	characteristic
305	C₃×#106	C₂³	1	1	yes	characteristic
306	C₃×#106	C₂³	1	2	yes	—
307	C₃×#106	C₂³	1	2	yes	—
308	C₃×C₄⋊C₈	C₂³	1	2	yes	—
309	C₃×C₄⋊C₈	C₂³	1	2	yes	—
310	C₃×C₄⋊C₈	C₂³	1	2	yes	—
311	C₃×C₄⋊C₈	C₂³	1	2	yes	—
312	C₃×#103	C₂³	1	2	yes	—
313	C₃×#103	C₂³	1	2	yes	—
314	C₃×#103	C₂³	1	1	yes	characteristic
315	C₃×#103	C₂³	1	1	yes	characteristic
316	C₃×#103	C₂³	1	1	yes	characteristic
317	C₃×#103	C₂³	1	1	yes	characteristic
318	C₃×#103	C₂³	1	2	yes	—
319	C₃×#103	C₂³	1	2	yes	—
320	C₃×#103	C₂³	1	2	yes	—
321	C₃×#103	C₂³	1	2	yes	—
322	C₃×#102	C₂³	1	2	yes	—
323	C₃×#102	C₂³	1	2	yes	—
324	C₃×#102	C₂³	1	1	yes	characteristic
325	C₃×#102	C₂³	1	1	yes	characteristic
326	C₃×#102	C₂³	1	1	yes	characteristic
327	C₃×#102	C₂³	1	1	yes	characteristic
328	C₃×#102	C₂³	1	2	yes	—
329	C₃×#102	C₂³	1	2	yes	—
330	C₃×#102	C₂³	1	2	yes	—
331	C₃×#102	C₂³	1	2	yes	—
332	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₃×#97	C₂³	1	2	yes	—
337	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
338	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
339	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₃×C₄×C₈	C₂³	1	2	yes	—
342	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
343	C₂×#137	C₂²×C₃	1	1	yes	characteristic
344	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	1	yes	characteristic
345	C₂×#135	C₂²×C₃	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
347	#544	C₂²×C₃	1	1	yes	characteristic, complemented
348	#542	—	2	1	no	—
349	#542	C₂²×C₃	1	2	yes	complemented
350	#541	—	2	1	no	—
351	#541	C₂²×C₃	1	2	yes	complemented
352	#539	—	2	2	no	—
353	#537	C₂²×C₃	1	1	yes	characteristic
354	#536	C₂²×C₃	1	1	yes	characteristic
355	#536	C₂²×C₃	1	1	yes	characteristic, complemented
356	#533	—	2	1	no	—
357	#533	C₂²×C₃	1	2	yes	complemented
358	#529	—	2	2	no	—
359	#529	—	2	1	no	—
360	#529	C₂²×C₃	1	2	yes	complemented
361	#520	—	2	1	no	—
362	#520	C₂²×C₃	1	1	yes	characteristic
363	#520	C₂²×C₃	1	2	yes	—
364	#520	C₂²×C₃	1	1	yes	characteristic
365	#518	—	2	2	no	—
366	#518	—	2	1	no	—
367	#518	C₂²×C₃	1	1	yes	characteristic
368	#518	C₂²×C₃	1	2	yes	—
369	C₄×#41	—	2	1	no	—
370	C₄×#41	C₂²×C₃	1	2	yes	—
371	C₄×#41	C₂²×C₃	1	1	yes	characteristic
372	C₄×#41	C₂²×C₃	1	1	yes	characteristic
373	C₄×#41	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
375	C₂×C₄×D₄	—	2	1	no	—
376	C₂×C₄×D₄	—	2	2	no	—
377	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
378	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
379	#485	C₂²×C₃	1	2	yes	complemented
380	#485	C₂²×C₃	1	2	yes	complemented
381	#485	C₂²×C₃	1	2	yes	complemented
382	#484	C₂²×C₃	1	2	yes	complemented
383	#483	C₂²×C₃	1	2	yes	complemented
384	#483	C₂²×C₃	1	2	yes	complemented
385	#482	C₂²×C₃	1	2	yes	complemented
386	#481	C₂²×C₃	1	2	yes	complemented
387	#479	C₂²×C₃	1	2	yes	complemented
388	#478	C₂²×C₃	1	2	yes	complemented
389	#478	C₂²×C₃	1	2	yes	complemented
390	#478	C₂²×C₃	1	2	yes	complemented
391	#476	C₂²×C₃	1	2	yes	complemented
392	#476	C₂²×C₃	1	2	yes	complemented
393	#475	C₂²×C₃	1	2	yes	complemented
394	#474	C₂²×C₃	1	2	yes	complemented
395	#464	C₂²×C₃	1	2	yes	complemented
396	#463	C₂²×C₃	1	2	yes	complemented
397	#463	C₂²×C₃	1	2	yes	complemented
398	#463	C₂²×C₃	1	2	yes	complemented
399	#462	C₂²×C₃	1	2	yes	complemented
400	#461	C₂²×C₃	1	2	yes	complemented
401	#461	C₂²×C₃	1	2	yes	complemented
402	#461	C₂²×C₃	1	2	yes	complemented
403	#452	C₂²×C₃	1	2	yes	—
404	#452	C₂²×C₃	1	2	yes	—
405	#452	C₂²×C₃	1	2	yes	—
406	#450	C₂²×C₃	1	2	yes	—
407	#450	C₂²×C₃	1	2	yes	—
408	#450	C₂²×C₃	1	2	yes	—
409	#449	C₂²×C₃	1	2	yes	—
410	#447	C₂²×C₃	1	2	yes	—
411	#442	C₂²×C₃	1	2	yes	complemented
412	#441	C₂²×C₃	1	2	yes	complemented
413	#440	C₂²×C₃	1	2	yes	complemented
414	#440	C₂²×C₃	1	2	yes	complemented
415	C₄×Q₁₆	C₂²×C₃	1	2	yes	complemented
416	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
417	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
418	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
419	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
420	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
421	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
422	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
423	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
424	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
425	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
426	C₄×SD₁₆	C₂²×C₃	1	2	yes	complemented
427	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
428	C₄×D₈	C₂²×C₃	1	2	yes	complemented
429	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
430	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
431	#433	C₂²×C₃	1	2	yes	complemented
432	#433	C₂²×C₃	1	2	yes	complemented
433	#431	C₂²×C₃	1	2	yes	complemented
434	#431	C₂²×C₃	1	2	yes	complemented
435	#428	C₂²×C₃	1	1	yes	characteristic, complemented
436	#428	C₂²×C₃	1	1	yes	characteristic, complemented
437	#427	C₂²×C₃	1	1	yes	characteristic, complemented
438	C₂×#106	C₂²×C₃	1	1	yes	characteristic, complemented
439	#424	C₂²×C₃	1	1	yes	characteristic, complemented
440	#424	C₂²×C₃	1	1	yes	characteristic, complemented
441	#419	C₂²×C₃	1	1	yes	characteristic, complemented
442	#418	C₂²×C₃	1	1	yes	characteristic
443	#417	C₂²×C₃	1	1	yes	characteristic
444	#417	C₂²×C₃	1	1	yes	characteristic, complemented
445	#416	C₂²×C₃	1	1	yes	characteristic
446	#416	C₂²×C₃	1	1	yes	characteristic, complemented
447	C₂×#103	C₂²×C₃	1	1	yes	characteristic, complemented
448	C₂×#102	C₂²×C₃	1	1	yes	characteristic
449	#408	C₂²×C₃	1	1	yes	characteristic
450	#408	C₂²×C₃	1	1	yes	characteristic
451	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
452	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
453	C₂⁴×C₃	—	2	2	no	—
454	C₂⁴×C₃	—	2	1	no	—
455	C₃×#41	—	2	8	no	—
456	C₃×#41	—	2	4	no	—
457	C₃×#41	—	2	4	no	—
458	C₃×#41	—	2	2	no	—
459	C₃×#41	—	2	2	no	—
460	C₃×#41	—	2	2	no	—
461	C₃×#41	—	2	2	no	—
462	C₃×#41	—	2	2	no	—
463	C₃×#41	#41	1	4	yes	—
464	C₂×C₃×Q₈	—	2	1	no	—
465	C₂×C₃×Q₈	—	2	2	no	—
466	C₂×C₃×Q₈	—	2	2	no	—
467	C₂×C₃×Q₈	—	2	2	no	—
468	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
469	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
470	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
471	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
472	C₂×C₃×D₄	—	2	16	no	—
473	C₂×C₃×D₄	—	2	8	no	—
474	C₂×C₃×D₄	—	2	2	no	—
475	C₂×C₃×D₄	—	2	1	no	—
476	C₂×C₃×D₄	—	2	4	no	—
477	C₂×C₃×D₄	—	2	4	no	—
478	C₂×C₃×D₄	—	2	1	no	—
479	C₂×C₃×D₄	—	2	2	no	—
480	C₂×C₃×D₄	—	2	2	no	—
481	C₂×C₃×D₄	—	2	1	no	—
482	C₂×C₃×D₄	—	2	2	no	—
483	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
484	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
485	C₂×C₃×D₄	#41	1	4	yes	—
486	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
487	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
488	C₂×C₃×D₄	C₂⁴	1	2	yes	—
489	C₂²×C₃×C₄	—	2	2	no	—
490	C₂²×C₃×C₄	—	2	1	no	—
491	C₂²×C₃×C₄	—	2	1	no	—
492	C₂²×C₃×C₄	—	2	1	no	—
493	C₂²×C₃×C₄	—	2	2	no	—
494	C₂²×C₃×C₄	—	2	1	no	—
495	C₂²×C₃×C₄	—	2	1	no	—
496	C₂²×C₃×C₄	—	2	1	no	—
497	C₂²×C₃×C₄	—	2	1	no	—
498	C₂²×C₃×C₄	—	2	2	no	—
499	C₂²×C₃×C₄	—	2	1	no	—
500	C₂²×C₃×C₄	—	2	2	no	—
501	C₂²×C₃×C₄	—	2	1	no	—
502	C₂²×C₃×C₄	—	2	2	no	—
503	C₂²×C₃×C₄	—	2	2	no	—
504	C₂²×C₃×C₄	—	2	2	no	—
505	C₂²×C₃×C₄	—	8	2	no	—
506	C₂²×C₃×C₄	—	8	4	no	—
507	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
509	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
511	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
512	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
513	C₃×Q₁₆	—	2	2	no	—
514	C₃×Q₁₆	—	2	4	no	—
515	C₃×SD₁₆	—	2	2	no	—
516	C₃×SD₁₆	—	2	4	no	—
517	C₃×SD₁₆	—	2	4	no	—
518	C₃×SD₁₆	—	2	2	no	—
519	C₃×SD₁₆	—	2	4	no	—
520	C₃×SD₁₆	—	2	4	no	—
521	C₃×D₈	—	2	2	no	—
522	C₃×D₈	—	2	4	no	—
523	C₃×M₁₆	—	2	2	no	—
524	C₃×M₁₆	—	2	2	no	—
525	C₂×C₃×C₈	—	2	2	no	—
526	C₂×C₃×C₈	—	2	2	no	—
527	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
528	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
529	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
530	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
531	C₂×C₃×C₈	C₂⁴	1	2	yes	—
532	C₂×C₃×C₈	C₂⁴	1	2	yes	—
533	C₃×C₄⋊C₄	—	2	1	no	—
534	C₃×C₄⋊C₄	—	2	2	no	—
535	C₃×C₄⋊C₄	—	2	2	no	—
536	C₃×C₄⋊C₄	—	2	1	no	—
537	C₃×C₄⋊C₄	—	2	2	no	—
538	C₃×C₄⋊C₄	—	2	2	no	—
539	C₃×C₄⋊C₄	—	2	1	no	—
540	C₃×C₄⋊C₄	—	2	1	no	—
541	C₃×C₄⋊C₄	—	2	1	no	—
542	C₃×C₄⋊C₄	—	2	1	no	—
543	C₃×C₄⋊C₄	—	2	2	no	—
544	C₃×C₄⋊C₄	—	2	2	no	—
545	C₃×C₄⋊C₄	—	2	2	no	—
546	C₃×C₄⋊C₄	—	2	2	no	—
547	C₃×C₄⋊C₄	—	2	2	no	—
548	C₃×C₄⋊C₄	—	2	2	no	—
549	C₃×C₄⋊C₄	—	2	2	no	—
550	C₃×C₄⋊C₄	—	2	2	no	—
551	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
552	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
553	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
554	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
555	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
556	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
557	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
558	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
559	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
560	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
561	C₃×C₂²⋊C₄	—	2	2	no	—
562	C₃×C₂²⋊C₄	—	2	1	no	—
563	C₃×C₂²⋊C₄	—	2	2	no	—
564	C₃×C₂²⋊C₄	—	2	2	no	—
565	C₃×C₂²⋊C₄	—	2	1	no	—
566	C₃×C₂²⋊C₄	—	2	2	no	—
567	C₃×C₂²⋊C₄	—	2	1	no	—
568	C₃×C₂²⋊C₄	—	2	2	no	—
569	C₃×C₂²⋊C₄	—	2	2	no	—
570	C₃×C₂²⋊C₄	—	2	2	no	—
571	C₃×C₂²⋊C₄	—	2	2	no	—
572	C₃×C₂²⋊C₄	—	2	2	no	—
573	C₃×C₂²⋊C₄	—	2	1	no	—
574	C₃×C₂²⋊C₄	—	2	1	no	—
575	C₃×C₂²⋊C₄	—	2	1	no	—
576	C₃×C₂²⋊C₄	—	2	2	no	—
577	C₃×C₂²⋊C₄	—	2	2	no	—
578	C₃×C₂²⋊C₄	—	2	2	no	—
579	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
580	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
581	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
582	C₃×C₄²	—	2	1	no	—
583	C₃×C₄²	—	2	2	no	—
584	C₃×C₄²	—	2	2	no	—
585	C₃×C₄²	—	2	1	no	—
586	C₃×C₄²	—	2	1	no	—
587	C₃×C₄²	—	2	1	no	—
588	C₃×C₄²	—	2	2	no	—
589	C₃×C₄²	—	2	1	no	—
590	C₃×C₄²	—	2	2	no	—
591	C₃×C₄²	—	2	1	no	—
592	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
593	C₃×C₄²	C₂×D₄	1	2	yes	—
594	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
595	C₃×C₄²	C₂×D₄	1	2	yes	—
596	C₃×C₄²	C₂⁴	1	1	yes	characteristic
597	C₃×C₄²	C₂⁴	1	2	yes	—
598	C₃×C₄²	C₂⁴	1	1	yes	characteristic
599	H(5,𝔽₂)	—	2	4	no	—
600	H(5,𝔽₂)	—	2	4	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	C₂³×C₃	1	2	yes	—
603	C₂×#41	C₂³×C₃	1	1	yes	characteristic
604	C₂×#41	C₂³×C₃	1	1	yes	characteristic
605	C₂×#41	C₂³×C₃	1	1	yes	characteristic
606	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
607	C₂²×D₄	—	2	2	no	—
608	C₂²×D₄	—	2	1	no	—
609	C₂²×D₄	C₂³×C₃	1	2	yes	—
610	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
611	C₂³×C₄	—	2	1	no	—
612	C₂³×C₄	—	2	2	no	—
613	#137	—	2	4	no	—
614	AGL(1,ℤ/8)	—	2	4	no	—
615	#135	—	2	4	no	—
616	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
617	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
618	C₂×SD₁₆	—	2	4	no	—
619	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
622	C₂×SD₁₆	C₂³×C₃	1	1	yes	characteristic
623	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
624	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
625	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
626	C₂×D₈	C₂³×C₃	1	2	yes	—
627	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
628	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
629	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
630	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
631	C₄⋊Q₈	—	2	1	no	—
632	C₄⋊Q₈	—	2	1	no	—
633	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	1	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	C₂³×C₃	1	2	yes	—
644	#124	—	2	1	no	—
645	#124	—	2	2	no	—
646	#124	C₂³×C₃	1	2	yes	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
659	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
660	#121	—	2	2	no	—
661	#121	—	2	1	no	—
662	#121	C₂³×C₃	1	2	yes	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
668	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
669	C₄×Q₈	C₂³×C₃	1	2	yes	—
670	C₄×Q₈	C₂³×C₃	1	2	yes	—
671	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
672	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
673	C₄×Q₈	C₂³×C₃	1	2	yes	—
674	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
675	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	C₃×D₄	1	1	yes	characteristic
697	C₄×D₄	C₃×D₄	1	2	yes	—
698	C₄×D₄	C₃×D₄	1	2	yes	—
699	C₄×D₄	C₃×D₄	1	1	yes	characteristic
700	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
701	C₄×D₄	C₂³×C₃	1	2	yes	—
702	C₄×D₄	C₂³×C₃	1	2	yes	—
703	C₄×D₄	C₂³×C₃	1	2	yes	—
704	C₄×D₄	C₂³×C₃	1	2	yes	—
705	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
706	C₄×D₄	C₂³×C₃	1	2	yes	—
707	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
708	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	—	2	1	no	—
712	#117	—	2	1	no	—
713	#117	—	2	2	no	—
714	#117	—	2	1	no	—
715	#117	—	2	2	no	—
716	#117	C₂³×C₃	1	1	yes	characteristic
717	#117	C₂³×C₃	1	2	yes	—
718	#117	C₂³×C₃	1	1	yes	characteristic
719	#117	C₂³×C₃	1	1	yes	characteristic
720	#117	C₂³×C₃	1	2	yes	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	2	no	—
724	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	—	2	1	no	—
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	C₂×C₂²⋊C₄	—	2	2	no	—
730	C₂×C₂²⋊C₄	—	2	2	no	—
731	C₂×C₂²⋊C₄	—	2	2	no	—
732	C₂×C₄²	—	2	1	no	—
733	C₂×C₄²	—	2	1	no	—
734	C₂×C₄²	—	2	2	no	—
735	C₂×C₄²	—	2	1	no	—
736	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₃	1	2	yes	—
738	#107	C₂³×C₃	1	1	yes	characteristic
739	#107	C₂³×C₃	1	1	yes	characteristic
740	#107	C₂³×C₃	1	2	yes	—
741	#107	C₂³×C₃	1	2	yes	—
742	#106	C₂³×C₃	1	2	yes	—
743	#106	C₂³×C₃	1	2	yes	—
744	#106	C₂³×C₃	1	1	yes	characteristic
745	#106	C₂³×C₃	1	1	yes	characteristic
746	#106	C₂³×C₃	1	2	yes	—
747	#106	C₂³×C₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃	1	2	yes	—
752	#103	C₂³×C₃	1	2	yes	—
753	#103	C₂³×C₃	1	2	yes	—
754	#103	C₂³×C₃	1	1	yes	characteristic
755	#103	C₂³×C₃	1	1	yes	characteristic
756	#103	C₂³×C₃	1	1	yes	characteristic
757	#103	C₂³×C₃	1	1	yes	characteristic
758	#103	C₂³×C₃	1	2	yes	—
759	#103	C₂³×C₃	1	2	yes	—
760	#103	C₂³×C₃	1	2	yes	—
761	#103	C₂³×C₃	1	2	yes	—
762	#102	C₂³×C₃	1	2	yes	—
763	#102	C₂³×C₃	1	2	yes	—
764	#102	C₂³×C₃	1	1	yes	characteristic
765	#102	C₂³×C₃	1	1	yes	characteristic
766	#102	C₂³×C₃	1	1	yes	characteristic
767	#102	C₂³×C₃	1	1	yes	characteristic
768	#102	C₂³×C₃	1	2	yes	—
769	#102	C₂³×C₃	1	2	yes	—
770	#102	C₂³×C₃	1	2	yes	—
771	#102	C₂³×C₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
776	#97	C₂³×C₃	1	2	yes	—
777	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
780	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
781	C₄×C₈	C₂³×C₃	1	2	yes	—
782	C₂³×C₃	—	2	8	no	—
783	C₂³×C₃	—	2	2	no	—
784	C₂³×C₃	—	2	1	no	—
785	C₂³×C₃	—	2	4	no	—
786	C₂³×C₃	—	2	1	no	—
787	C₂³×C₃	—	8	1	no	—
788	C₂³×C₃	—	8	2	no	—
789	C₂³×C₃	—	8	1	no	—
790	C₂³×C₃	—	8	2	no	—
791	C₂³×C₃	C₂²×D₄	1	2	yes	—
792	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
793	C₃×Q₈	—	2	2	no	—
794	C₃×Q₈	—	2	1	no	—
795	C₃×Q₈	—	2	2	no	—
796	C₃×Q₈	—	2	1	no	—
797	C₃×Q₈	—	2	2	no	—
798	C₃×Q₈	—	2	1	no	—
799	C₃×Q₈	—	4	2	no	—
800	C₃×Q₈	—	8	2	no	—
801	C₃×Q₈	C₂×#41	1	2	yes	—
802	C₃×D₄	—	2	8	no	—
803	C₃×D₄	—	2	8	no	—
804	C₃×D₄	—	2	4	no	—
805	C₃×D₄	—	2	4	no	—
806	C₃×D₄	—	2	2	no	—
807	C₃×D₄	—	2	4	no	—
808	C₃×D₄	—	2	2	no	—
809	C₃×D₄	—	2	1	no	—
810	C₃×D₄	—	2	1	no	—
811	C₃×D₄	—	2	1	no	—
812	C₃×D₄	—	4	2	no	—
813	C₃×D₄	—	8	2	no	—
814	C₃×D₄	C₂×#41	1	2	yes	—
815	C₃×D₄	C₂×#41	1	4	yes	—
816	C₂×C₃×C₄	—	2	8	no	—
817	C₂×C₃×C₄	—	2	1	no	—
818	C₂×C₃×C₄	—	2	4	no	—
819	C₂×C₃×C₄	—	2	2	no	—
820	C₂×C₃×C₄	—	2	4	no	—
821	C₂×C₃×C₄	—	2	2	no	—
822	C₂×C₃×C₄	—	2	2	no	—
823	C₂×C₃×C₄	—	2	1	no	—
824	C₂×C₃×C₄	—	2	1	no	—
825	C₂×C₃×C₄	—	2	2	no	—
826	C₂×C₃×C₄	—	2	1	no	—
827	C₂×C₃×C₄	—	2	1	no	—
828	C₂×C₃×C₄	—	2	2	no	—
829	C₂×C₃×C₄	—	2	1	no	—
830	C₂×C₃×C₄	—	2	2	no	—
831	C₂×C₃×C₄	—	4	1	no	—
832	C₂×C₃×C₄	—	4	2	no	—
833	C₂×C₃×C₄	—	4	2	no	—
834	C₂×C₃×C₄	—	4	2	no	—
835	C₂×C₃×C₄	—	4	2	no	—
836	C₂×C₃×C₄	—	4	4	no	—
837	C₂×C₃×C₄	—	4	2	no	—
838	C₂×C₃×C₄	—	8	1	no	—
839	C₂×C₃×C₄	—	8	1	no	—
840	C₂×C₃×C₄	—	8	2	no	—
841	C₂×C₃×C₄	—	8	2	no	—
842	C₂×C₃×C₄	—	8	2	no	—
843	C₂×C₃×C₄	—	8	2	no	—
844	C₂×C₃×C₄	—	8	1	no	—
845	C₂×C₃×C₄	—	8	1	no	—
846	C₂×C₃×C₄	—	8	2	no	—
847	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
850	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
851	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
853	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂×C₃×C₄	C₂×#41	1	2	yes	—
856	C₂×C₃×C₄	C₂×#41	1	2	yes	—
857	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
858	C₃×C₈	—	2	1	no	—
859	C₃×C₈	—	2	1	no	—
860	C₃×C₈	—	2	1	no	—
861	C₃×C₈	—	2	1	no	—
862	C₃×C₈	—	2	2	no	—
863	C₃×C₈	—	2	2	no	—
864	C₂⁴	—	2	2	no	—
865	C₂⁴	—	2	1	no	—
866	#41	—	2	8	no	—
867	#41	—	2	4	no	—
868	#41	—	2	4	no	—
869	#41	—	2	2	no	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	2	2	no	—
874	#41	C₃×#41	1	4	yes	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
881	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
883	C₂×D₄	—	2	16	no	—
884	C₂×D₄	—	2	8	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
895	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
896	C₂×D₄	C₃×#41	1	4	yes	—
897	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₃	1	2	yes	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	8	2	no	—
917	C₂²×C₄	—	8	4	no	—
918	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
919	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
920	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
921	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
924	Q₁₆	—	2	2	no	—
925	Q₁₆	—	2	4	no	—
926	SD₁₆	—	2	2	no	—
927	SD₁₆	—	2	4	no	—
928	SD₁₆	—	2	4	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	4	no	—
932	D₈	—	2	2	no	—
933	D₈	—	2	4	no	—
934	M₁₆	—	2	2	no	—
935	M₁₆	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₃	1	2	yes	—
943	C₂×C₈	C₂⁴×C₃	1	2	yes	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
963	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
964	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
965	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
991	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
992	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1004	C₄²	C₂×C₃×D₄	1	2	yes	—
1005	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
1006	C₄²	C₂×C₃×D₄	1	2	yes	—
1007	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₃	1	2	yes	—
1010	C₂²×C₃	—	2	1	no	—
1011	C₂²×C₃	—	2	1	no	—
1012	C₂²×C₃	—	2	2	no	—
1013	C₂²×C₃	—	2	2	no	—
1014	C₂²×C₃	—	2	4	no	—
1015	C₂²×C₃	—	2	2	no	—
1016	C₂²×C₃	—	2	2	no	—
1017	C₂²×C₃	—	4	2	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	2	no	—
1020	C₂²×C₃	—	4	1	no	—
1021	C₂²×C₃	—	4	1	no	—
1022	C₂²×C₃	—	4	1	no	—
1023	C₂²×C₃	—	4	1	no	—
1024	C₂²×C₃	—	8	4	no	—
1025	C₂²×C₃	—	8	8	no	—
1026	C₂²×C₃	#525	1	2	yes	—
1027	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1028	C₃×C₄	—	2	1	no	—
1029	C₃×C₄	—	2	1	no	—
1030	C₃×C₄	—	2	2	no	—
1031	C₃×C₄	—	2	2	no	—
1032	C₃×C₄	—	2	2	no	—
1033	C₃×C₄	—	2	1	no	—
1034	C₃×C₄	—	2	2	no	—
1035	C₃×C₄	—	4	1	no	—
1036	C₃×C₄	—	4	2	no	—
1037	C₃×C₄	—	4	1	no	—
1038	C₃×C₄	—	4	1	no	—
1039	C₃×C₄	—	4	2	no	—
1040	C₃×C₄	—	4	1	no	—
1041	C₃×C₄	—	4	2	no	—
1042	C₃×C₄	—	4	1	no	—
1043	C₃×C₄	#525	1	2	yes	—
1044	C₃×C₄	#577	1	2	yes	—
1045	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1046	C₃×C₄	C₂²×#41	1	1	yes	characteristic
1047	C₂³	—	2	8	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	4	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	1	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	C₂²×C₃×D₄	1	2	yes	—
1057	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	4	2	no	—
1065	Q₈	—	8	2	no	—
1066	Q₈	C₂×C₃×#41	1	2	yes	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	8	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	4	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	4	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	C₂×C₃×#41	1	2	yes	—
1080	D₄	C₂×C₃×#41	1	4	yes	—
1081	C₂×C₄	—	2	8	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	4	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	4	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	1	no	—
1112	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1113	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1114	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1115	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1116	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1117	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1118	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1119	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
1120	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1121	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1122	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₂×C₃	—	2	2	no	—
1130	C₂×C₃	—	4	2	no	—
1131	C₂×C₃	—	4	4	no	—
1132	C₂×C₃	—	4	2	no	—
1133	C₂×C₃	—	8	1	no	—
1134	C₂×C₃	C₂×#525	1	1	yes	characteristic
1135	C₂×C₃	C₂×#577	1	1	yes	characteristic
1136	C₂×C₃	#3584	1	1	yes	characteristic
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	8	4	no	—
1152	C₂²	—	8	8	no	—
1153	C₂²	C₃×#525	1	2	yes	—
1154	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	C₃×#525	1	2	yes	—
1171	C₄	C₃×#577	1	2	yes	—
1172	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1173	C₄	C₂²×C₃×#41	1	1	yes	characteristic
1174	C₃	#60571	1	1	yes	characteristic, direct product factor, Sylow
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	C₂×C₃×#525	1	1	yes	characteristic
1181	C₂	C₂×C₃×#577	1	1	yes	characteristic
1182	C₂	C₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂²×C₃	C₂³×D₄
prime radical	C₃×#3012	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3461	C₂	semidirect
2. C₃×C₄×H(5,𝔽₂)	C₂	semidirect
3. C₃×#3125	C₂	semidirect
4. C₃×#3123	C₂	semidirect
5. C₃×#3120	C₂	semidirect
6. C₃×#3118	C₂	semidirect
7. C₃×#3107	C₂	semidirect
8. C₃×#3105	C₂	semidirect
9. C₃×#3102	C₂	semidirect
10. C₃×#3101	C₂	semidirect
11. C₃×#3099	C₂	semidirect
12. C₃×#3097	C₂	semidirect
13. C₃×#3084	C₂	semidirect
14. C₃×#3081	C₂	semidirect
15. C₃×#3046	C₂	semidirect
16. C₃×#3042	C₂	semidirect
18. C₃×#3009	C₂	semidirect
19. C₃×C₄×#137	C₂	semidirect
20. C₃×C₄×AGL(1,ℤ/8)	C₂	semidirect
21. C₃×C₄×#135	C₂	semidirect
22. C₂×C₃×C₄×SD₁₆	C₂	semidirect
23. C₃×#2922	C₂	semidirect
24. #60571	C₃	direct (N × H)
30. C₃×#544	C₂²	semidirect
32. C₃×#542	C₂²	semidirect
34. C₃×#541	C₂²	semidirect
38. C₃×#536	C₂²	semidirect
40. C₃×#533	C₂²	semidirect
43. C₃×#529	C₂²	semidirect
56. C₃×C₄×#41	C₂²	semidirect
57. C₂×C₃×C₄×Q₈	C₂²	semidirect
62. C₃×#485	C₂²	semidirect
63. C₃×#485	C₂²	semidirect
64. C₃×#485	C₂²	semidirect
65. C₃×#484	C₂²	semidirect
66. C₃×#483	C₂²	semidirect
67. C₃×#483	C₂²	semidirect
68. C₃×#482	C₂²	semidirect
69. C₃×#481	C₂²	semidirect
70. C₃×#479	C₂²	semidirect
71. C₃×#478	C₂²	semidirect
72. C₃×#478	C₂²	semidirect
73. C₃×#478	C₂²	semidirect
74. C₃×#476	C₂²	semidirect
75. C₃×#476	C₂²	semidirect
76. C₃×#475	C₂²	semidirect
77. C₃×#474	C₂²	semidirect
78. C₃×#464	C₂²	semidirect
79. C₃×#463	C₂²	semidirect
80. C₃×#463	C₂²	semidirect
81. C₃×#463	C₂²	semidirect
82. C₃×#462	C₂²	semidirect
83. C₃×#461	C₂²	semidirect
84. C₃×#461	C₂²	semidirect
85. C₃×#461	C₂²	semidirect
94. C₃×#442	C₂²	semidirect
95. C₃×#441	C₂²	semidirect
96. C₃×#440	C₂²	semidirect
97. C₃×#440	C₂²	semidirect
98. C₃×C₄×Q₁₆	C₂²	semidirect
99. C₃×C₄×Q₁₆	C₂²	semidirect
100. C₃×C₄×Q₁₆	C₂²	semidirect
101. C₃×C₄×SD₁₆	C₂²	semidirect
102. C₃×C₄×SD₁₆	C₂²	semidirect
103. C₃×C₄×SD₁₆	C₂²	semidirect
104. C₃×C₄×SD₁₆	C₂²	semidirect
105. C₃×C₄×SD₁₆	C₂²	semidirect
106. C₃×C₄×SD₁₆	C₂²	semidirect
107. C₃×C₄×SD₁₆	C₂²	semidirect
108. C₃×C₄×SD₁₆	C₂²	semidirect
109. C₃×C₄×SD₁₆	C₂²	semidirect
110. C₃×C₄×SD₁₆	C₂²	semidirect
111. C₃×C₄×D₈	C₂²	semidirect
112. C₃×C₄×D₈	C₂²	semidirect
113. C₃×C₄×D₈	C₂²	semidirect
114. C₃×#433	C₂²	semidirect
115. C₃×#433	C₂²	semidirect
116. C₃×#431	C₂²	semidirect
117. C₃×#431	C₂²	semidirect
118. C₃×#428	C₂²	semidirect
119. C₃×#428	C₂²	semidirect
120. C₃×#427	C₂²	semidirect
121. C₂×C₃×#106	C₂²	semidirect
122. C₃×#424	C₂²	semidirect
123. C₃×#424	C₂²	semidirect
124. C₃×#419	C₂²	semidirect
127. C₃×#417	C₂²	semidirect
129. C₃×#416	C₂²	semidirect
130. C₂×C₃×#103	C₂²	semidirect
134. C₃×C₄×M₁₆	C₂²	semidirect
135. C₂×C₃×C₄×C₈	C₂²	semidirect
136. #3461	C₂×C₃	semidirect
137. C₄×H(5,𝔽₂)	C₂×C₃	semidirect
138. #3125	C₂×C₃	semidirect
139. #3123	C₂×C₃	semidirect
140. #3120	C₂×C₃	semidirect
141. #3118	C₂×C₃	semidirect
142. #3107	C₂×C₃	semidirect
143. #3105	C₂×C₃	semidirect
144. #3102	C₂×C₃	semidirect
145. #3101	C₂×C₃	semidirect
146. #3099	C₂×C₃	semidirect
147. #3097	C₂×C₃	semidirect
148. #3084	C₂×C₃	semidirect
149. #3081	C₂×C₃	semidirect
150. #3046	C₂×C₃	semidirect
151. #3042	C₂×C₃	semidirect
153. #3009	C₂×C₃	semidirect
154. C₄×#137	C₂×C₃	semidirect
155. C₄×AGL(1,ℤ/8)	C₂×C₃	semidirect
156. C₄×#135	C₂×C₃	semidirect
157. C₂×C₄×SD₁₆	C₂×C₃	semidirect
158. #2922	C₂×C₃	semidirect
347. #544	C₂²×C₃	semidirect
349. #542	C₂²×C₃	semidirect
351. #541	C₂²×C₃	semidirect
355. #536	C₂²×C₃	semidirect
357. #533	C₂²×C₃	semidirect
360. #529	C₂²×C₃	semidirect
373. C₄×#41	C₂²×C₃	semidirect
374. C₂×C₄×Q₈	C₂²×C₃	semidirect
379. #485	C₂²×C₃	semidirect
380. #485	C₂²×C₃	semidirect
381. #485	C₂²×C₃	semidirect
382. #484	C₂²×C₃	semidirect
383. #483	C₂²×C₃	semidirect
384. #483	C₂²×C₃	semidirect
385. #482	C₂²×C₃	semidirect
386. #481	C₂²×C₃	semidirect
387. #479	C₂²×C₃	semidirect
388. #478	C₂²×C₃	semidirect
389. #478	C₂²×C₃	semidirect
390. #478	C₂²×C₃	semidirect
391. #476	C₂²×C₃	semidirect
392. #476	C₂²×C₃	semidirect
393. #475	C₂²×C₃	semidirect
394. #474	C₂²×C₃	semidirect
395. #464	C₂²×C₃	semidirect
396. #463	C₂²×C₃	semidirect
397. #463	C₂²×C₃	semidirect
398. #463	C₂²×C₃	semidirect
399. #462	C₂²×C₃	semidirect
400. #461	C₂²×C₃	semidirect
401. #461	C₂²×C₃	semidirect
402. #461	C₂²×C₃	semidirect
411. #442	C₂²×C₃	semidirect
412. #441	C₂²×C₃	semidirect
413. #440	C₂²×C₃	semidirect
414. #440	C₂²×C₃	semidirect
415. C₄×Q₁₆	C₂²×C₃	semidirect
416. C₄×Q₁₆	C₂²×C₃	semidirect
417. C₄×Q₁₆	C₂²×C₃	semidirect
418. C₄×SD₁₆	C₂²×C₃	semidirect
419. C₄×SD₁₆	C₂²×C₃	semidirect
420. C₄×SD₁₆	C₂²×C₃	semidirect
421. C₄×SD₁₆	C₂²×C₃	semidirect
422. C₄×SD₁₆	C₂²×C₃	semidirect
423. C₄×SD₁₆	C₂²×C₃	semidirect
424. C₄×SD₁₆	C₂²×C₃	semidirect
425. C₄×SD₁₆	C₂²×C₃	semidirect
426. C₄×SD₁₆	C₂²×C₃	semidirect
427. C₄×SD₁₆	C₂²×C₃	semidirect
428. C₄×D₈	C₂²×C₃	semidirect
429. C₄×D₈	C₂²×C₃	semidirect
430. C₄×D₈	C₂²×C₃	semidirect
431. #433	C₂²×C₃	semidirect
432. #433	C₂²×C₃	semidirect
433. #431	C₂²×C₃	semidirect
434. #431	C₂²×C₃	semidirect
435. #428	C₂²×C₃	semidirect
436. #428	C₂²×C₃	semidirect
437. #427	C₂²×C₃	semidirect
438. C₂×#106	C₂²×C₃	semidirect
439. #424	C₂²×C₃	semidirect
440. #424	C₂²×C₃	semidirect
441. #419	C₂²×C₃	semidirect
444. #417	C₂²×C₃	semidirect
446. #416	C₂²×C₃	semidirect
447. C₂×#103	C₂²×C₃	semidirect
451. C₄×M₁₆	C₂²×C₃	semidirect
452. C₂×C₄×C₈	C₂²×C₃	semidirect
1174. C₃	#60571	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3461	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3125	2
C₃×#3123	2
C₃×#3120	2
C₃×#3118	2
C₃×#3107	2
C₃×#3105	2
C₃×#3102	2
C₃×#3101	2
C₃×#3099	2
C₃×#3097	2
C₃×#3084	2
C₃×#3081	2
C₃×#3046	2
C₃×#3042	2
C₃×#3012	2
C₃×#3009	2
C₃×C₄×#137	2
C₃×C₄×AGL(1,ℤ/8)	2
C₃×C₄×#135	2
C₂×C₃×C₄×SD₁₆	2
C₃×#2922	2
#60571	3

Subgroups — C3×#60571 #10679178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60571 #10679178