Subgroups — C₃×#60591 #10679198

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
3	C₃×#3123	C₂	1	4	yes	maximal, complemented
4	C₃×#3120	C₂	1	4	yes	maximal, complemented
5	C₃×#3116	C₂	1	2	yes	maximal, complemented
6	C₃×#3110	C₂	1	2	yes	maximal, complemented
7	C₃×#3107	C₂	1	2	yes	maximal, complemented
8	C₃×#3101	C₂	1	2	yes	maximal, complemented
9	C₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3009	C₂	1	2	yes	maximal
15	C₃×#2949	C₂	1	2	yes	maximal, complemented
16	C₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	#60591	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂×C₃×#137	C₂²	1	2	yes	—
21	C₂²×C₃×SD₁₆	C₂²	1	2	yes	—
22	C₃×#557	—	2	1	no	—
23	C₃×#557	—	2	1	no	—
24	C₃×#556	—	2	1	no	—
25	C₃×#556	—	2	1	no	—
26	C₃×#552	—	2	2	no	—
27	C₃×#552	—	2	2	no	—
28	C₃×#541	C₂²	1	4	yes	complemented
29	C₃×#536	C₂²	1	2	yes	—
30	C₃×#533	C₂²	1	2	yes	complemented
31	C₃×#533	C₂²	1	2	yes	complemented
32	C₃×#533	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#520	—	2	1	no	—
35	C₃×#520	C₂²	1	1	yes	characteristic
36	C₃×#520	C₂²	1	2	yes	—
37	C₃×#520	C₂²	1	1	yes	characteristic
38	C₃×#519	C₂²	1	2	yes	complemented
39	C₃×#518	—	2	2	no	—
40	C₃×#518	—	2	1	no	—
41	C₃×#518	C₂²	1	1	yes	characteristic
42	C₃×#518	C₂²	1	2	yes	—
43	C₃×C₄×#41	—	2	1	no	—
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₃×C₄×#41	C₂²	1	2	yes	—
46	C₃×C₄×#41	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	—	2	2	no	—
48	C₂×C₃×C₄×D₄	—	2	1	no	—
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
51	C₃×#485	C₂²	1	4	yes	complemented
52	C₃×#485	C₂²	1	4	yes	complemented
53	C₃×#484	C₂²	1	4	yes	complemented
54	C₃×#483	C₂²	1	4	yes	complemented
55	C₃×#479	C₂²	1	2	yes	complemented
56	C₃×#478	C₂²	1	2	yes	complemented
57	C₃×#478	C₂²	1	4	yes	complemented
58	C₃×#477	C₂²	1	1	yes	characteristic, complemented
59	C₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₃×#476	C₂²	1	2	yes	complemented
61	C₃×#475	C₂²	1	1	yes	characteristic, complemented
62	C₃×#474	C₂²	1	1	yes	characteristic, complemented
63	C₃×#474	C₂²	1	2	yes	complemented
64	C₃×#462	C₂²	1	2	yes	complemented
65	C₃×#462	C₂²	1	2	yes	complemented
66	C₃×#461	C₂²	1	2	yes	complemented
67	C₃×#461	C₂²	1	2	yes	complemented
68	C₃×#461	C₂²	1	4	yes	complemented
69	C₃×#461	C₂²	1	2	yes	complemented
70	C₃×#461	C₂²	1	2	yes	complemented
71	C₃×#452	C₂²	1	4	yes	—
72	C₃×#452	C₂²	1	4	yes	—
73	C₃×#450	C₂²	1	4	yes	—
74	C₃×#450	C₂²	1	4	yes	—
75	C₃×#441	C₂²	1	4	yes	complemented
76	C₃×#440	C₂²	1	4	yes	complemented
77	C₃×#440	C₂²	1	4	yes	complemented
78	C₃×#440	C₂²	1	4	yes	complemented
79	C₃×C₄×Q₁₆	C₂²	1	4	yes	complemented
80	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
81	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
82	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	complemented
84	C₃×#432	C₂²	1	2	yes	complemented
85	C₃×#431	C₂²	1	2	yes	complemented
86	C₃×#428	C₂²	1	2	yes	complemented
87	C₃×#427	C₂²	1	2	yes	complemented
88	C₃×#423	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
90	C₃×#419	C₂²	1	2	yes	complemented
91	C₃×#418	C₂²	1	2	yes	—
92	C₃×#416	C₂²	1	2	yes	—
93	C₂×C₃×#103	C₂²	1	2	yes	complemented
94	C₃×#408	C₂²	1	2	yes	—
95	C₃×#405	C₂²	1	2	yes	complemented
96	#3509	C₂×C₃	1	1	yes	characteristic, complemented
97	C₄×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
98	#3123	C₂×C₃	1	4	yes	complemented
99	#3120	C₂×C₃	1	4	yes	complemented
100	#3116	C₂×C₃	1	2	yes	complemented
101	#3110	C₂×C₃	1	2	yes	complemented
102	#3107	C₂×C₃	1	2	yes	complemented
103	#3101	C₂×C₃	1	2	yes	complemented
104	#3097	C₂×C₃	1	2	yes	complemented
105	#3077	C₂×C₃	1	1	yes	characteristic, complemented
106	#3076	C₂×C₃	1	1	yes	characteristic, complemented
107	#3039	C₂×C₃	1	1	yes	characteristic, complemented
108	C₂×#461	C₂×C₃	1	1	yes	characteristic, complemented
109	#3009	C₂×C₃	1	2	yes	—
110	#2949	C₂×C₃	1	2	yes	complemented
111	#2947	C₂×C₃	1	2	yes	complemented
112	#2925	C₂×C₃	1	1	yes	characteristic, complemented
113	C₃×H(5,𝔽₂)	—	2	4	no	—
114	C₃×H(5,𝔽₂)	—	2	4	no	—
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	C₂³	1	2	yes	—
117	C₂×C₃×#41	C₂³	1	1	yes	characteristic
118	C₂×C₃×#41	C₂³	1	1	yes	characteristic
119	C₂²×C₃×Q₈	C₂³	1	2	yes	—
120	C₂²×C₃×D₄	—	2	2	no	—
121	C₂²×C₃×D₄	—	2	1	no	—
122	C₂²×C₃×D₄	C₂³	1	2	yes	—
123	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
124	C₂³×C₃×C₄	—	2	1	no	—
125	C₂³×C₃×C₄	—	2	2	no	—
126	C₃×#137	—	2	8	no	—
127	C₂×C₃×Q₁₆	C₂³	1	4	yes	—
128	C₂×C₃×SD₁₆	—	2	8	no	—
129	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₃×M₁₆	C₂³	1	2	yes	—
133	C₂²×C₃×C₈	C₂³	1	2	yes	—
134	C₃×C₄⋊Q₈	—	2	2	no	—
135	C₃×C₄⋊Q₈	—	2	1	no	—
136	C₃×C₄⋊Q₈	—	2	1	no	—
137	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃×#126	—	2	4	no	—
142	C₃×#126	—	2	4	no	—
143	C₃×#125	—	2	4	no	—
144	C₃×#125	—	2	4	no	—
145	C₃×#125	—	2	2	no	—
146	C₃×#125	—	2	2	no	—
147	C₃×#125	C₂³	1	2	yes	—
148	C₃×#124	—	2	2	no	—
149	C₃×#123	—	2	4	no	—
150	C₃×C₂²⋊Q₈	—	2	1	no	—
151	C₃×C₂²⋊Q₈	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	2	2	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₃×C₄×Q₈	—	2	1	no	—
157	C₃×C₄×Q₈	—	2	2	no	—
158	C₃×C₄×Q₈	—	2	2	no	—
159	C₃×C₄×Q₈	—	2	2	no	—
160	C₃×C₄×Q₈	—	2	2	no	—
161	C₃×C₄×Q₈	—	2	1	no	—
162	C₃×C₄×Q₈	—	2	1	no	—
163	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
164	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
165	C₃×C₄×Q₈	C₂³	1	4	yes	—
166	C₃×C₄×Q₈	C₂³	1	4	yes	—
167	C₃×C₄×Q₈	C₂³	1	2	yes	—
168	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
169	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
170	C₃×C₄×D₄	—	2	2	no	—
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	—	2	2	no	—
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	—	2	2	no	—
176	C₃×C₄×D₄	—	2	1	no	—
177	C₃×C₄×D₄	—	2	2	no	—
178	C₃×C₄×D₄	—	2	1	no	—
179	C₃×C₄×D₄	—	2	2	no	—
180	C₃×C₄×D₄	—	2	2	no	—
181	C₃×C₄×D₄	—	2	2	no	—
182	C₃×C₄×D₄	—	2	2	no	—
183	C₃×C₄×D₄	—	2	2	no	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	—	2	2	no	—
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	D₄	1	2	yes	—
188	C₃×C₄×D₄	D₄	1	1	yes	characteristic
189	C₃×C₄×D₄	D₄	1	2	yes	—
190	C₃×C₄×D₄	D₄	1	1	yes	characteristic
191	C₃×C₄×D₄	C₂³	1	2	yes	—
192	C₃×C₄×D₄	C₂³	1	2	yes	—
193	C₃×C₄×D₄	C₂³	1	2	yes	—
194	C₃×C₄×D₄	C₂³	1	2	yes	—
195	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
196	C₃×C₄×D₄	C₂³	1	2	yes	—
197	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
198	C₃×#117	—	2	2	no	—
199	C₃×#117	—	2	2	no	—
200	C₃×#117	—	2	1	no	—
201	C₃×#117	—	2	2	no	—
202	C₃×#117	—	2	4	no	—
203	C₃×#117	—	2	2	no	—
204	C₃×#117	—	2	1	no	—
205	C₃×#117	C₂³	1	2	yes	—
206	C₃×#117	C₂³	1	1	yes	characteristic
207	C₃×#117	C₂³	1	2	yes	—
208	C₃×#117	C₂³	1	1	yes	characteristic
209	C₃×#117	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	—	2	1	no	—
211	C₂×C₃×C₄⋊C₄	—	2	1	no	—
212	C₂×C₃×C₄⋊C₄	—	2	1	no	—
213	C₂×C₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₃×C₄²	—	2	2	no	—
222	C₂×C₃×C₄²	—	2	1	no	—
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₃×#107	C₂³	1	2	yes	—
226	C₃×#107	C₂³	1	2	yes	—
227	C₃×#107	C₂³	1	4	yes	—
228	C₃×#106	C₂³	1	2	yes	—
229	C₃×#106	C₂³	1	2	yes	—
230	C₃×#106	C₂³	1	4	yes	—
231	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
233	C₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃×#103	C₂³	1	4	yes	—
237	C₃×#103	C₂³	1	4	yes	—
238	C₃×#103	C₂³	1	2	yes	—
239	C₃×#103	C₂³	1	2	yes	—
240	C₃×#103	C₂³	1	4	yes	—
241	C₃×#103	C₂³	1	4	yes	—
242	C₃×#102	C₂³	1	2	yes	—
243	C₃×#102	C₂³	1	2	yes	—
244	C₃×#102	C₂³	1	4	yes	—
245	C₃×#102	C₂³	1	4	yes	—
246	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
248	C₃×#97	C₂³	1	4	yes	—
249	C₃×C₄×C₈	C₂³	1	4	yes	—
250	C₂×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
251	C₂×#137	C₂²×C₃	1	2	yes	—
252	C₂²×SD₁₆	C₂²×C₃	1	2	yes	—
253	#557	—	2	1	no	—
254	#557	—	2	1	no	—
255	#556	—	2	1	no	—
256	#556	—	2	1	no	—
257	#552	—	2	2	no	—
258	#552	—	2	2	no	—
259	#541	C₂²×C₃	1	4	yes	complemented
260	#536	C₂²×C₃	1	2	yes	—
261	#533	C₂²×C₃	1	2	yes	complemented
262	#533	C₂²×C₃	1	2	yes	complemented
263	#533	C₂²×C₃	1	1	yes	characteristic, complemented
264	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
265	#520	—	2	1	no	—
266	#520	C₂²×C₃	1	2	yes	—
267	#520	C₂²×C₃	1	1	yes	characteristic
268	#520	C₂²×C₃	1	1	yes	characteristic
269	#519	C₂²×C₃	1	2	yes	complemented
270	#518	—	2	2	no	—
271	#518	—	2	1	no	—
272	#518	C₂²×C₃	1	2	yes	—
273	#518	C₂²×C₃	1	1	yes	characteristic
274	C₄×#41	—	2	1	no	—
275	C₄×#41	C₂²×C₃	1	1	yes	characteristic
276	C₄×#41	C₂²×C₃	1	2	yes	—
277	C₄×#41	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄×D₄	—	2	2	no	—
279	C₂×C₄×D₄	—	2	1	no	—
280	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
282	#485	C₂²×C₃	1	4	yes	complemented
283	#485	C₂²×C₃	1	4	yes	complemented
284	#484	C₂²×C₃	1	4	yes	complemented
285	#483	C₂²×C₃	1	4	yes	complemented
286	#479	C₂²×C₃	1	2	yes	complemented
287	#478	C₂²×C₃	1	2	yes	complemented
288	#478	C₂²×C₃	1	4	yes	complemented
289	#477	C₂²×C₃	1	1	yes	characteristic, complemented
290	#476	C₂²×C₃	1	1	yes	characteristic, complemented
291	#476	C₂²×C₃	1	2	yes	complemented
292	#475	C₂²×C₃	1	1	yes	characteristic, complemented
293	#474	C₂²×C₃	1	1	yes	characteristic, complemented
294	#474	C₂²×C₃	1	2	yes	complemented
295	#462	C₂²×C₃	1	2	yes	complemented
296	#462	C₂²×C₃	1	2	yes	complemented
297	#461	C₂²×C₃	1	2	yes	complemented
298	#461	C₂²×C₃	1	2	yes	complemented
299	#461	C₂²×C₃	1	2	yes	complemented
300	#461	C₂²×C₃	1	4	yes	complemented
301	#461	C₂²×C₃	1	2	yes	complemented
302	#452	C₂²×C₃	1	4	yes	—
303	#452	C₂²×C₃	1	4	yes	—
304	#450	C₂²×C₃	1	4	yes	—
305	#450	C₂²×C₃	1	4	yes	—
306	#441	C₂²×C₃	1	4	yes	complemented
307	#440	C₂²×C₃	1	4	yes	complemented
308	#440	C₂²×C₃	1	4	yes	complemented
309	#440	C₂²×C₃	1	4	yes	complemented
310	C₄×Q₁₆	C₂²×C₃	1	4	yes	complemented
311	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
312	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
313	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
314	#433	C₂²×C₃	1	4	yes	complemented
315	#432	C₂²×C₃	1	2	yes	complemented
316	#431	C₂²×C₃	1	2	yes	complemented
317	#428	C₂²×C₃	1	2	yes	complemented
318	#427	C₂²×C₃	1	2	yes	complemented
319	#423	C₂²×C₃	1	1	yes	characteristic, complemented
320	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
321	#419	C₂²×C₃	1	2	yes	complemented
322	#418	C₂²×C₃	1	2	yes	—
323	#416	C₂²×C₃	1	2	yes	—
324	C₂×#103	C₂²×C₃	1	2	yes	complemented
325	#408	C₂²×C₃	1	2	yes	—
326	#405	C₂²×C₃	1	2	yes	complemented
327	C₂⁴×C₃	—	2	2	no	—
328	C₂⁴×C₃	—	2	1	no	—
329	C₃×#41	—	2	8	no	—
330	C₃×#41	—	2	4	no	—
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	2	no	—
333	C₃×#41	—	2	2	no	—
334	C₃×#41	—	2	2	no	—
335	C₃×#41	#41	1	4	yes	—
336	C₂×C₃×Q₈	—	2	1	no	—
337	C₂×C₃×Q₈	—	2	1	no	—
338	C₂×C₃×Q₈	—	2	2	no	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	—	2	4	no	—
341	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
342	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
343	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₃×D₄	—	2	16	no	—
345	C₂×C₃×D₄	—	2	8	no	—
346	C₂×C₃×D₄	—	2	2	no	—
347	C₂×C₃×D₄	—	2	1	no	—
348	C₂×C₃×D₄	—	2	4	no	—
349	C₂×C₃×D₄	—	2	4	no	—
350	C₂×C₃×D₄	—	2	2	no	—
351	C₂×C₃×D₄	—	2	1	no	—
352	C₂×C₃×D₄	—	2	2	no	—
353	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
354	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
355	C₂×C₃×D₄	#41	1	4	yes	—
356	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
357	C₂×C₃×D₄	C₂⁴	1	2	yes	—
358	C₂²×C₃×C₄	—	2	2	no	—
359	C₂²×C₃×C₄	—	2	1	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	2	2	no	—
362	C₂²×C₃×C₄	—	2	1	no	—
363	C₂²×C₃×C₄	—	2	2	no	—
364	C₂²×C₃×C₄	—	2	1	no	—
365	C₂²×C₃×C₄	—	2	2	no	—
366	C₂²×C₃×C₄	—	2	1	no	—
367	C₂²×C₃×C₄	—	2	2	no	—
368	C₂²×C₃×C₄	—	2	2	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	8	2	no	—
371	C₂²×C₃×C₄	—	8	4	no	—
372	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
374	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₃×Q₁₆	—	2	8	no	—
379	C₃×SD₁₆	—	2	8	no	—
380	C₃×SD₁₆	—	2	8	no	—
381	C₃×SD₁₆	—	2	8	no	—
382	C₃×M₁₆	—	2	4	no	—
383	C₂×C₃×C₈	—	2	4	no	—
384	C₂×C₃×C₈	C₂⁴	1	2	yes	—
385	C₂×C₃×C₈	C₂⁴	1	4	yes	—
386	C₂×C₃×C₈	C₂⁴	1	2	yes	—
387	C₃×C₄⋊C₄	—	2	2	no	—
388	C₃×C₄⋊C₄	—	2	1	no	—
389	C₃×C₄⋊C₄	—	2	2	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	2	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	2	1	no	—
396	C₃×C₄⋊C₄	—	2	1	no	—
397	C₃×C₄⋊C₄	—	2	1	no	—
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	4	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	4	no	—
403	C₃×C₄⋊C₄	—	2	4	no	—
404	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₃×C₂²⋊C₄	—	2	2	no	—
414	C₃×C₂²⋊C₄	—	2	1	no	—
415	C₃×C₂²⋊C₄	—	2	2	no	—
416	C₃×C₂²⋊C₄	—	2	4	no	—
417	C₃×C₂²⋊C₄	—	2	4	no	—
418	C₃×C₂²⋊C₄	—	2	2	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	2	no	—
421	C₃×C₂²⋊C₄	—	2	2	no	—
422	C₃×C₂²⋊C₄	—	2	2	no	—
423	C₃×C₂²⋊C₄	—	2	2	no	—
424	C₃×C₂²⋊C₄	—	2	1	no	—
425	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₃×C₄²	—	2	1	no	—
429	C₃×C₄²	—	2	2	no	—
430	C₃×C₄²	—	2	1	no	—
431	C₃×C₄²	—	2	2	no	—
432	C₃×C₄²	—	2	1	no	—
433	C₃×C₄²	—	2	4	no	—
434	C₃×C₄²	—	2	4	no	—
435	C₃×C₄²	—	2	2	no	—
436	C₃×C₄²	C₂×D₄	1	2	yes	—
437	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
438	C₃×C₄²	C₂×D₄	1	2	yes	—
439	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
440	C₃×C₄²	C₂⁴	1	2	yes	—
441	C₃×C₄²	C₂⁴	1	1	yes	characteristic
442	C₃×C₄²	C₂⁴	1	1	yes	characteristic
443	H(5,𝔽₂)	—	2	4	no	—
444	H(5,𝔽₂)	—	2	4	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	C₂³×C₃	1	2	yes	—
447	C₂×#41	C₂³×C₃	1	1	yes	characteristic
448	C₂×#41	C₂³×C₃	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₃	1	2	yes	—
450	C₂²×D₄	—	2	2	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	C₂³×C₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	—	2	2	no	—
456	#137	—	2	8	no	—
457	C₂×Q₁₆	C₂³×C₃	1	4	yes	—
458	C₂×SD₁₆	—	2	8	no	—
459	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
460	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
461	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
462	C₂×M₁₆	C₂³×C₃	1	2	yes	—
463	C₂²×C₈	C₂³×C₃	1	2	yes	—
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
469	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#125	—	2	4	no	—
474	#125	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	—	2	2	no	—
477	#125	C₂³×C₃	1	2	yes	—
478	#124	—	2	2	no	—
479	#123	—	2	4	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
485	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
494	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
495	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
496	C₄×Q₈	C₂³×C₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
498	C₄×Q₈	C₂³×C₃	1	4	yes	—
499	C₄×Q₈	C₂³×C₃	1	4	yes	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	C₃×D₄	1	2	yes	—
518	C₄×D₄	C₃×D₄	1	1	yes	characteristic
519	C₄×D₄	C₃×D₄	1	2	yes	—
520	C₄×D₄	C₃×D₄	1	1	yes	characteristic
521	C₄×D₄	C₂³×C₃	1	2	yes	—
522	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
523	C₄×D₄	C₂³×C₃	1	2	yes	—
524	C₄×D₄	C₂³×C₃	1	2	yes	—
525	C₄×D₄	C₂³×C₃	1	2	yes	—
526	C₄×D₄	C₂³×C₃	1	2	yes	—
527	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
528	#117	—	2	2	no	—
529	#117	—	2	2	no	—
530	#117	—	2	1	no	—
531	#117	—	2	2	no	—
532	#117	—	2	4	no	—
533	#117	—	2	2	no	—
534	#117	—	2	1	no	—
535	#117	C₂³×C₃	1	1	yes	characteristic
536	#117	C₂³×C₃	1	2	yes	—
537	#117	C₂³×C₃	1	2	yes	—
538	#117	C₂³×C₃	1	1	yes	characteristic
539	#117	C₂³×C₃	1	2	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	2	no	—
548	C₂×C₂²⋊C₄	—	2	2	no	—
549	C₂×C₂²⋊C₄	—	2	2	no	—
550	C₂×C₂²⋊C₄	—	2	2	no	—
551	C₂×C₄²	—	2	2	no	—
552	C₂×C₄²	—	2	1	no	—
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	2	yes	—
555	#107	C₂³×C₃	1	2	yes	—
556	#107	C₂³×C₃	1	2	yes	—
557	#107	C₂³×C₃	1	4	yes	—
558	#106	C₂³×C₃	1	2	yes	—
559	#106	C₂³×C₃	1	2	yes	—
560	#106	C₂³×C₃	1	4	yes	—
561	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
563	C₄⋊C₈	C₂³×C₃	1	2	yes	—
564	C₄⋊C₈	C₂³×C₃	1	2	yes	—
565	C₄⋊C₈	C₂³×C₃	1	2	yes	—
566	#103	C₂³×C₃	1	4	yes	—
567	#103	C₂³×C₃	1	4	yes	—
568	#103	C₂³×C₃	1	2	yes	—
569	#103	C₂³×C₃	1	2	yes	—
570	#103	C₂³×C₃	1	4	yes	—
571	#103	C₂³×C₃	1	4	yes	—
572	#102	C₂³×C₃	1	2	yes	—
573	#102	C₂³×C₃	1	2	yes	—
574	#102	C₂³×C₃	1	4	yes	—
575	#102	C₂³×C₃	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
578	#97	C₂³×C₃	1	4	yes	—
579	C₄×C₈	C₂³×C₃	1	4	yes	—
580	C₂³×C₃	—	2	8	no	—
581	C₂³×C₃	—	2	2	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	2	4	no	—
584	C₂³×C₃	—	8	1	no	—
585	C₂³×C₃	—	8	2	no	—
586	C₂³×C₃	—	8	1	no	—
587	C₂³×C₃	—	8	2	no	—
588	C₂³×C₃	C₂²×D₄	1	2	yes	—
589	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
590	C₃×Q₈	—	2	2	no	—
591	C₃×Q₈	—	2	1	no	—
592	C₃×Q₈	—	2	4	no	—
593	C₃×Q₈	—	2	4	no	—
594	C₃×Q₈	—	4	2	no	—
595	C₃×Q₈	—	4	4	no	—
596	C₃×Q₈	—	4	2	no	—
597	C₃×Q₈	C₂×#41	1	2	yes	—
598	C₃×D₄	—	2	8	no	—
599	C₃×D₄	—	2	8	no	—
600	C₃×D₄	—	2	4	no	—
601	C₃×D₄	—	2	4	no	—
602	C₃×D₄	—	2	2	no	—
603	C₃×D₄	—	2	4	no	—
604	C₃×D₄	—	2	2	no	—
605	C₃×D₄	—	2	1	no	—
606	C₃×D₄	C₂×#41	1	2	yes	—
607	C₃×D₄	C₂×#41	1	4	yes	—
608	C₂×C₃×C₄	—	2	8	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	4	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	4	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	2	2	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	4	no	—
621	C₂×C₃×C₄	—	4	1	no	—
622	C₂×C₃×C₄	—	4	2	no	—
623	C₂×C₃×C₄	—	4	4	no	—
624	C₂×C₃×C₄	—	4	4	no	—
625	C₂×C₃×C₄	—	4	2	no	—
626	C₂×C₃×C₄	—	8	2	no	—
627	C₂×C₃×C₄	—	8	1	no	—
628	C₂×C₃×C₄	—	8	2	no	—
629	C₂×C₃×C₄	—	8	2	no	—
630	C₂×C₃×C₄	—	8	2	no	—
631	C₂×C₃×C₄	—	8	1	no	—
632	C₂×C₃×C₄	—	8	2	no	—
633	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
634	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
635	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
636	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
639	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₃×C₄	C₂×#41	1	2	yes	—
642	C₂×C₃×C₄	C₂×#41	1	2	yes	—
643	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
644	C₃×C₈	—	2	2	no	—
645	C₃×C₈	—	2	2	no	—
646	C₃×C₈	—	2	4	no	—
647	C₂⁴	—	2	2	no	—
648	C₂⁴	—	2	1	no	—
649	#41	—	2	8	no	—
650	#41	—	2	4	no	—
651	#41	—	2	4	no	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	#41	—	2	2	no	—
655	#41	C₃×#41	1	4	yes	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
662	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
663	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
664	C₂×D₄	—	2	16	no	—
665	C₂×D₄	—	2	8	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
674	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
675	C₂×D₄	C₃×#41	1	4	yes	—
676	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
677	C₂×D₄	C₂⁴×C₃	1	2	yes	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	8	2	no	—
691	C₂²×C₄	—	8	4	no	—
692	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
694	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
698	Q₁₆	—	2	8	no	—
699	SD₁₆	—	2	8	no	—
700	SD₁₆	—	2	8	no	—
701	SD₁₆	—	2	8	no	—
702	M₁₆	—	2	4	no	—
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₃	1	4	yes	—
706	C₂×C₈	C₂⁴×C₃	1	2	yes	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
725	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
726	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
727	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
746	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
747	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
748	C₄²	—	2	1	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	2	no	—
756	C₄²	C₂×C₃×D₄	1	2	yes	—
757	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
758	C₄²	C₂×C₃×D₄	1	2	yes	—
759	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
760	C₄²	C₂⁴×C₃	1	2	yes	—
761	C₄²	C₂⁴×C₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₃	1	1	yes	characteristic
763	C₂²×C₃	—	2	1	no	—
764	C₂²×C₃	—	2	1	no	—
765	C₂²×C₃	—	2	2	no	—
766	C₂²×C₃	—	2	2	no	—
767	C₂²×C₃	—	2	4	no	—
768	C₂²×C₃	—	2	2	no	—
769	C₂²×C₃	—	2	2	no	—
770	C₂²×C₃	—	4	2	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	—	4	2	no	—
773	C₂²×C₃	—	4	1	no	—
774	C₂²×C₃	—	8	4	no	—
775	C₂²×C₃	—	8	8	no	—
776	C₂²×C₃	#525	1	2	yes	—
777	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
778	C₃×C₄	—	2	1	no	—
779	C₃×C₄	—	2	2	no	—
780	C₃×C₄	—	2	1	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	2	1	no	—
785	C₃×C₄	—	4	1	no	—
786	C₃×C₄	—	4	2	no	—
787	C₃×C₄	—	4	4	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	1	no	—
790	C₃×C₄	—	4	2	no	—
791	C₃×C₄	#525	1	2	yes	—
792	C₃×C₄	#577	1	2	yes	—
793	C₃×C₄	C₂²×#41	1	1	yes	characteristic
794	C₃×C₄	C₂²×#41	1	1	yes	characteristic
795	C₂³	—	2	8	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	8	1	no	—
800	C₂³	—	8	2	no	—
801	C₂³	—	8	1	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×C₃×D₄	1	2	yes	—
804	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
805	Q₈	—	2	1	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	2	4	no	—
809	Q₈	—	4	2	no	—
810	Q₈	—	4	2	no	—
811	Q₈	—	4	4	no	—
812	Q₈	C₂×C₃×#41	1	2	yes	—
813	D₄	—	2	8	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	4	no	—
816	D₄	—	2	4	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	1	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	4	no	—
821	D₄	C₂×C₃×#41	1	2	yes	—
822	D₄	C₂×C₃×#41	1	4	yes	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	2	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	—	8	1	no	—
846	C₂×C₄	—	8	1	no	—
847	C₂×C₄	—	8	2	no	—
848	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
849	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
850	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
851	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
853	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
854	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
855	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
856	C₂×C₄	C₂×C₃×#41	1	2	yes	—
857	C₂×C₄	C₂×C₃×#41	1	2	yes	—
858	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
859	C₈	—	2	2	no	—
860	C₈	—	2	2	no	—
861	C₈	—	2	4	no	—
862	C₂×C₃	—	2	2	no	—
863	C₂×C₃	—	4	2	no	—
864	C₂×C₃	—	4	4	no	—
865	C₂×C₃	—	4	2	no	—
866	C₂×C₃	C₂×#525	1	1	yes	characteristic
867	C₂×C₃	C₂×#577	1	1	yes	characteristic
868	C₂×C₃	#3586	1	1	yes	characteristic
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	8	4	no	—
881	C₂²	—	8	8	no	—
882	C₂²	C₃×#525	1	2	yes	—
883	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	4	4	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	C₃×#525	1	2	yes	—
898	C₄	C₃×#577	1	2	yes	—
899	C₄	C₂²×C₃×#41	1	1	yes	characteristic
900	C₄	C₂²×C₃×#41	1	1	yes	characteristic
901	C₃	#60591	1	1	yes	characteristic, direct product factor, Sylow
902	C₂	—	2	2	no	—
903	C₂	—	4	2	no	—
904	C₂	—	4	4	no	—
905	C₂	—	4	2	no	—
906	C₂	C₂×C₃×#525	1	1	yes	characteristic
907	C₂	C₂×C₃×#577	1	1	yes	characteristic
908	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3509	C₂	semidirect
3. C₃×#3123	C₂	semidirect
4. C₃×#3120	C₂	semidirect
5. C₃×#3116	C₂	semidirect
6. C₃×#3110	C₂	semidirect
7. C₃×#3107	C₂	semidirect
8. C₃×#3101	C₂	semidirect
9. C₃×#3097	C₂	semidirect
10. C₃×#3077	C₂	semidirect
11. C₃×#3076	C₂	semidirect
12. C₃×#3039	C₂	semidirect
13. C₂×C₃×#461	C₂	semidirect
15. C₃×#2949	C₂	semidirect
16. C₃×#2947	C₂	semidirect
17. C₃×#2925	C₂	semidirect
18. #60591	C₃	direct (N × H)
28. C₃×#541	C₂²	semidirect
30. C₃×#533	C₂²	semidirect
31. C₃×#533	C₂²	semidirect
32. C₃×#533	C₂²	semidirect
33. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
38. C₃×#519	C₂²	semidirect
51. C₃×#485	C₂²	semidirect
52. C₃×#485	C₂²	semidirect
53. C₃×#484	C₂²	semidirect
54. C₃×#483	C₂²	semidirect
55. C₃×#479	C₂²	semidirect
56. C₃×#478	C₂²	semidirect
57. C₃×#478	C₂²	semidirect
58. C₃×#477	C₂²	semidirect
59. C₃×#476	C₂²	semidirect
60. C₃×#476	C₂²	semidirect
61. C₃×#475	C₂²	semidirect
62. C₃×#474	C₂²	semidirect
63. C₃×#474	C₂²	semidirect
64. C₃×#462	C₂²	semidirect
65. C₃×#462	C₂²	semidirect
66. C₃×#461	C₂²	semidirect
67. C₃×#461	C₂²	semidirect
68. C₃×#461	C₂²	semidirect
69. C₃×#461	C₂²	semidirect
70. C₃×#461	C₂²	semidirect
75. C₃×#441	C₂²	semidirect
76. C₃×#440	C₂²	semidirect
77. C₃×#440	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×Q₁₆	C₂²	semidirect
80. C₃×C₄×SD₁₆	C₂²	semidirect
81. C₃×C₄×SD₁₆	C₂²	semidirect
82. C₃×C₄×SD₁₆	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
84. C₃×#432	C₂²	semidirect
85. C₃×#431	C₂²	semidirect
86. C₃×#428	C₂²	semidirect
87. C₃×#427	C₂²	semidirect
88. C₃×#423	C₂²	semidirect
89. C₂×C₃×C₄⋊C₈	C₂²	semidirect
90. C₃×#419	C₂²	semidirect
93. C₂×C₃×#103	C₂²	semidirect
95. C₃×#405	C₂²	semidirect
96. #3509	C₂×C₃	semidirect
98. #3123	C₂×C₃	semidirect
99. #3120	C₂×C₃	semidirect
100. #3116	C₂×C₃	semidirect
101. #3110	C₂×C₃	semidirect
102. #3107	C₂×C₃	semidirect
103. #3101	C₂×C₃	semidirect
104. #3097	C₂×C₃	semidirect
105. #3077	C₂×C₃	semidirect
106. #3076	C₂×C₃	semidirect
107. #3039	C₂×C₃	semidirect
108. C₂×#461	C₂×C₃	semidirect
110. #2949	C₂×C₃	semidirect
111. #2947	C₂×C₃	semidirect
112. #2925	C₂×C₃	semidirect
259. #541	C₂²×C₃	semidirect
261. #533	C₂²×C₃	semidirect
262. #533	C₂²×C₃	semidirect
263. #533	C₂²×C₃	semidirect
264. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
269. #519	C₂²×C₃	semidirect
282. #485	C₂²×C₃	semidirect
283. #485	C₂²×C₃	semidirect
284. #484	C₂²×C₃	semidirect
285. #483	C₂²×C₃	semidirect
286. #479	C₂²×C₃	semidirect
287. #478	C₂²×C₃	semidirect
288. #478	C₂²×C₃	semidirect
289. #477	C₂²×C₃	semidirect
290. #476	C₂²×C₃	semidirect
291. #476	C₂²×C₃	semidirect
292. #475	C₂²×C₃	semidirect
293. #474	C₂²×C₃	semidirect
294. #474	C₂²×C₃	semidirect
295. #462	C₂²×C₃	semidirect
296. #462	C₂²×C₃	semidirect
297. #461	C₂²×C₃	semidirect
298. #461	C₂²×C₃	semidirect
299. #461	C₂²×C₃	semidirect
300. #461	C₂²×C₃	semidirect
301. #461	C₂²×C₃	semidirect
306. #441	C₂²×C₃	semidirect
307. #440	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. #440	C₂²×C₃	semidirect
310. C₄×Q₁₆	C₂²×C₃	semidirect
311. C₄×SD₁₆	C₂²×C₃	semidirect
312. C₄×SD₁₆	C₂²×C₃	semidirect
313. C₄×SD₁₆	C₂²×C₃	semidirect
314. #433	C₂²×C₃	semidirect
315. #432	C₂²×C₃	semidirect
316. #431	C₂²×C₃	semidirect
317. #428	C₂²×C₃	semidirect
318. #427	C₂²×C₃	semidirect
319. #423	C₂²×C₃	semidirect
320. C₂×C₄⋊C₈	C₂²×C₃	semidirect
321. #419	C₂²×C₃	semidirect
324. C₂×#103	C₂²×C₃	semidirect
326. #405	C₂²×C₃	semidirect
901. C₃	#60591	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×#3509	2
C₃×C₄×H(5,𝔽₂)	2
C₃×#3123	2
C₃×#3120	2
C₃×#3116	2
C₃×#3110	2
C₃×#3107	2
C₃×#3101	2
C₃×#3097	2
C₃×#3077	2
C₃×#3076	2
C₃×#3039	2
C₂×C₃×#461	2
C₃×#3009	2
C₃×#2949	2
C₃×#2947	2
C₃×#2925	2
#60591	3

Subgroups — C3×#60591 #10679198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60591 #10679198