Subgroups — C₆₇×#60974 #30740225

Order 17152.

1796 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3460	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3263	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3224	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3204	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3199	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3180	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3114	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3109	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
20	#544×C₆₇	C₂²	1	2	yes	complemented
21	#542×C₆₇	—	2	2	no	—
22	#542×C₆₇	C₂²	1	2	yes	—
23	#542×C₆₇	C₂²	1	2	yes	complemented
24	#540×C₆₇	—	2	2	no	—
25	#540×C₆₇	C₂²	1	2	yes	—
26	#540×C₆₇	C₂²	1	2	yes	complemented
27	#538×C₆₇	—	2	2	no	—
28	#538×C₆₇	—	2	2	no	—
29	#537×C₆₇	C₂²	1	2	yes	—
30	#535×C₆₇	C₂²	1	2	yes	—
31	#535×C₆₇	C₂²	1	2	yes	complemented
32	#532×C₆₇	—	2	2	no	—
33	#532×C₆₇	C₂²	1	2	yes	—
34	#532×C₆₇	C₂²	1	2	yes	complemented
35	#529×C₆₇	—	2	2	no	—
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	complemented
38	#525×C₆₇	—	2	2	no	—
39	#525×C₆₇	—	2	2	no	—
40	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
41	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#496×C₆₇	C₂²	1	2	yes	—
47	#495×C₆₇	C₂²	1	1	yes	characteristic
48	#493×C₆₇	C₂²	1	1	yes	characteristic
49	#490×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#488×C₆₇	C₂²	1	2	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	complemented
54	#483×C₆₇	C₂²	1	2	yes	complemented
55	#482×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	2	yes	—
57	#482×C₆₇	C₂²	1	2	yes	complemented
58	#481×C₆₇	C₂²	1	2	yes	—
59	#481×C₆₇	C₂²	1	2	yes	complemented
60	#480×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	2	yes	complemented
62	#478×C₆₇	C₂²	1	2	yes	complemented
63	#478×C₆₇	C₂²	1	2	yes	complemented
64	#478×C₆₇	C₂²	1	2	yes	complemented
65	#476×C₆₇	C₂²	1	2	yes	complemented
66	#476×C₆₇	C₂²	1	2	yes	complemented
67	#475×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#469×C₆₇	C₂²	1	1	yes	characteristic
71	#469×C₆₇	C₂²	1	1	yes	characteristic
72	#469×C₆₇	C₂²	1	2	yes	complemented
73	#469×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#468×C₆₇	C₂²	1	2	yes	complemented
75	#466×C₆₇	C₂²	1	2	yes	—
76	#466×C₆₇	C₂²	1	2	yes	complemented
77	#465×C₆₇	C₂²	1	2	yes	complemented
78	#465×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	—
81	#463×C₆₇	C₂²	1	2	yes	—
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#460×C₆₇	C₂²	1	2	yes	complemented
84	#459×C₆₇	C₂²	1	2	yes	—
85	#459×C₆₇	C₂²	1	2	yes	—
86	#459×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#450×C₆₇	C₂²	1	2	yes	complemented
89	#449×C₆₇	C₂²	1	2	yes	—
90	#449×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	complemented
92	#447×C₆₇	C₂²	1	2	yes	—
93	#447×C₆₇	C₂²	1	2	yes	—
94	#447×C₆₇	C₂²	1	2	yes	complemented
95	#442×C₆₇	C₂²	1	1	yes	characteristic
96	#442×C₆₇	C₂²	1	2	yes	—
97	#442×C₆₇	C₂²	1	1	yes	characteristic
98	#442×C₆₇	C₂²	1	2	yes	complemented
99	#442×C₆₇	C₂²	1	2	yes	complemented
100	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	2	yes	complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	complemented
106	#433×C₆₇	C₂²	1	2	yes	complemented
107	#432×C₆₇	C₂²	1	2	yes	complemented
108	#432×C₆₇	C₂²	1	2	yes	complemented
109	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#408×C₆₇	C₂²	1	1	yes	characteristic
112	#408×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	C₂³	1	2	yes	—
118	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	—	2	2	no	—
121	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×D₈×C₆₇	C₂³	1	2	yes	—
126	C₂×D₈×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₆₇	C₂³	1	2	yes	—
130	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₇	—	2	2	no	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	#127×C₆₇	—	2	2	no	—
139	#127×C₆₇	C₂³	1	2	yes	—
140	#127×C₆₇	C₂³	1	2	yes	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#125×C₆₇	—	2	2	no	—
146	#125×C₆₇	C₂³	1	2	yes	—
147	#125×C₆₇	C₂³	1	2	yes	—
148	#124×C₆₇	—	2	2	no	—
149	#124×C₆₇	—	2	2	no	—
150	#124×C₆₇	—	2	2	no	—
151	#124×C₆₇	—	2	2	no	—
152	#124×C₆₇	—	2	2	no	—
153	#124×C₆₇	C₂³	1	2	yes	—
154	#124×C₆₇	C₂³	1	2	yes	—
155	#123×C₆₇	—	2	2	no	—
156	#123×C₆₇	—	2	2	no	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
169	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	2	no	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	—	2	2	no	—
179	#121×C₆₇	—	2	2	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#121×C₆₇	C₂³	1	2	yes	—
185	#121×C₆₇	C₂³	1	2	yes	—
186	#121×C₆₇	C₂³	1	2	yes	—
187	#120×C₆₇	—	2	2	no	—
188	#120×C₆₇	—	2	2	no	—
189	#120×C₆₇	—	2	2	no	—
190	#120×C₆₇	—	2	2	no	—
191	C₄×Q₈×C₆₇	D₄	1	2	yes	—
192	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	—	2	2	no	—
201	C₄×D₄×C₆₇	—	2	2	no	—
202	C₄×D₄×C₆₇	D₄	1	2	yes	—
203	C₄×D₄×C₆₇	D₄	1	2	yes	—
204	C₄×D₄×C₆₇	D₄	1	2	yes	—
205	C₄×D₄×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	C₂³	1	2	yes	—
207	C₄×D₄×C₆₇	C₂³	1	2	yes	—
208	C₄×D₄×C₆₇	C₂³	1	2	yes	—
209	C₄×D₄×C₆₇	C₂³	1	2	yes	—
210	C₄×D₄×C₆₇	C₂³	1	2	yes	—
211	#117×C₆₇	—	2	2	no	—
212	#117×C₆₇	—	2	2	no	—
213	#117×C₆₇	—	2	2	no	—
214	#117×C₆₇	C₂³	1	2	yes	—
215	#117×C₆₇	C₂³	1	2	yes	—
216	#117×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₄²×C₆₇	—	2	2	no	—
220	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	#107×C₆₇	C₂³	1	2	yes	—
223	#107×C₆₇	C₂³	1	2	yes	—
224	#107×C₆₇	C₂³	1	2	yes	—
225	#106×C₆₇	C₂³	1	2	yes	—
226	#106×C₆₇	C₂³	1	2	yes	—
227	#106×C₆₇	C₂³	1	1	yes	characteristic
228	#106×C₆₇	C₂³	1	1	yes	characteristic
229	#106×C₆₇	C₂³	1	2	yes	—
230	#106×C₆₇	C₂³	1	1	yes	characteristic
231	#106×C₆₇	C₂³	1	1	yes	characteristic
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	#103×C₆₇	C₂³	1	2	yes	—
237	#103×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#102×C₆₇	C₂³	1	2	yes	—
241	#102×C₆₇	C₂³	1	2	yes	—
242	#102×C₆₇	C₂³	1	2	yes	—
243	#102×C₆₇	C₂³	1	2	yes	—
244	#102×C₆₇	C₂³	1	2	yes	—
245	#102×C₆₇	C₂³	1	2	yes	—
246	#102×C₆₇	C₂³	1	2	yes	—
247	#102×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	2	yes	—
258	#97×C₆₇	C₂³	1	1	yes	characteristic
259	#97×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₂⁴×C₆₇	—	2	2	no	—
263	#41×C₆₇	—	4	1	no	—
264	#41×C₆₇	—	4	1	no	—
265	#41×C₆₇	—	4	2	no	—
266	#41×C₆₇	—	4	2	no	—
267	#41×C₆₇	—	8	4	no	—
268	#41×C₆₇	—	8	4	no	—
269	C₂×Q₈×C₆₇	—	2	2	no	—
270	C₂×Q₈×C₆₇	—	2	2	no	—
271	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
272	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	2	no	—
298	C₂²×C₄×C₆₇	—	2	2	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	8	4	no	—
301	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	Q₁₆×C₆₇	—	4	1	no	—
307	SD₁₆×C₆₇	—	4	2	no	—
308	SD₁₆×C₆₇	—	4	2	no	—
309	SD₁₆×C₆₇	—	4	2	no	—
310	D₈×C₆₇	—	4	2	no	—
311	D₈×C₆₇	—	4	2	no	—
312	D₈×C₆₇	—	4	2	no	—
313	D₈×C₆₇	—	4	1	no	—
314	D₈×C₆₇	—	4	1	no	—
315	D₈×C₆₇	—	4	1	no	—
316	M₁₆×C₆₇	—	4	1	no	—
317	M₁₆×C₆₇	—	4	1	no	—
318	C₂×C₈×C₆₇	—	4	1	no	—
319	C₂×C₈×C₆₇	—	4	1	no	—
320	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
324	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	C₂×D₄	1	2	yes	—
371	C₄²×C₆₇	C₂×D₄	1	2	yes	—
372	C₄²×C₆₇	C₂×D₄	1	2	yes	—
373	C₄²×C₆₇	C₂⁴	1	2	yes	—
374	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	4	4	no	—
380	C₂³×C₆₇	—	8	2	no	—
381	C₂³×C₆₇	—	8	2	no	—
382	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
383	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₆₇	—	2	2	no	—
385	Q₈×C₆₇	—	2	2	no	—
386	Q₈×C₆₇	—	4	1	no	—
387	Q₈×C₆₇	—	8	2	no	—
388	Q₈×C₆₇	—	8	2	no	—
389	D₄×C₆₇	—	2	2	no	—
390	D₄×C₆₇	—	2	2	no	—
391	D₄×C₆₇	—	2	2	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	2	no	—
394	D₄×C₆₇	—	2	2	no	—
395	D₄×C₆₇	—	4	2	no	—
396	D₄×C₆₇	—	4	1	no	—
397	D₄×C₆₇	—	4	4	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	8	2	no	—
400	D₄×C₆₇	—	8	2	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	—	8	2	no	—
403	D₄×C₆₇	—	8	2	no	—
404	D₄×C₆₇	—	8	2	no	—
405	D₄×C₆₇	—	8	2	no	—
406	D₄×C₆₇	—	8	2	no	—
407	D₄×C₆₇	—	8	2	no	—
408	D₄×C₆₇	—	8	2	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	4	2	no	—
419	C₂×C₄×C₆₇	—	4	2	no	—
420	C₂×C₄×C₆₇	—	4	2	no	—
421	C₂×C₄×C₆₇	—	4	4	no	—
422	C₂×C₄×C₆₇	—	4	4	no	—
423	C₂×C₄×C₆₇	—	4	4	no	—
424	C₂×C₄×C₆₇	—	4	4	no	—
425	C₂×C₄×C₆₇	—	8	2	no	—
426	C₂×C₄×C₆₇	—	8	2	no	—
427	C₂×C₄×C₆₇	—	8	2	no	—
428	C₂×C₄×C₆₇	—	8	2	no	—
429	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
436	C₈×C₆₇	—	2	2	no	—
437	C₈×C₆₇	—	2	2	no	—
438	C₈×C₆₇	—	2	1	no	—
439	C₈×C₆₇	—	2	1	no	—
440	C₈×C₆₇	—	2	1	no	—
441	C₈×C₆₇	—	2	1	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	1	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	2	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	4	2	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	2	no	—
456	C₂²×C₆₇	—	8	8	no	—
457	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	—	2	1	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	—	4	2	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	—	4	2	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	#585	1	1	yes	characteristic
470	C₄×C₆₇	#585	1	1	yes	characteristic
471	#60974	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂×C₆₇	—	4	1	no	—
473	C₂×C₆₇	—	4	2	no	—
474	C₂×C₆₇	—	8	2	no	—
475	C₂×C₆₇	—	8	2	no	—
476	C₂×C₆₇	—	8	2	no	—
477	C₂×C₆₇	#3449	1	1	yes	characteristic
478	C₂×C₆₇	#3585	1	2	yes	—
479	#3460	C₂×C₆₇	1	2	yes	complemented
480	#3263	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3259	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#3257	C₂×C₆₇	1	2	yes	complemented
483	#3244	C₂×C₆₇	1	2	yes	complemented
484	#3241	C₂×C₆₇	1	2	yes	complemented
485	#3224	C₂×C₆₇	1	2	yes	complemented
486	#3220	C₂×C₆₇	1	2	yes	complemented
487	#3204	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#3199	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#3198	C₂×C₆₇	1	2	yes	complemented
490	#3184	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#3183	C₂×C₆₇	1	1	yes	characteristic, complemented
492	#3180	C₂×C₆₇	1	2	yes	complemented
493	#3115	C₂×C₆₇	1	2	yes	complemented
494	#3114	C₂×C₆₇	1	2	yes	complemented
495	#3111	C₂×C₆₇	1	2	yes	complemented
496	#3109	C₂×C₆₇	1	2	yes	complemented
497	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
498	C₆₇	#60974	1	1	yes	characteristic, direct product factor, Sylow
499	#544	C₂²×C₆₇	1	2	yes	complemented
500	#542	—	2	2	no	—
501	#542	C₂²×C₆₇	1	2	yes	—
502	#542	C₂²×C₆₇	1	2	yes	complemented
503	#540	—	2	2	no	—
504	#540	C₂²×C₆₇	1	2	yes	—
505	#540	C₂²×C₆₇	1	2	yes	complemented
506	#538	—	2	2	no	—
507	#538	—	2	2	no	—
508	#537	C₂²×C₆₇	1	2	yes	—
509	#535	C₂²×C₆₇	1	2	yes	—
510	#535	C₂²×C₆₇	1	2	yes	complemented
511	#532	—	2	2	no	—
512	#532	C₂²×C₆₇	1	2	yes	—
513	#532	C₂²×C₆₇	1	2	yes	complemented
514	#529	—	2	2	no	—
515	#529	C₂²×C₆₇	1	2	yes	—
516	#529	C₂²×C₆₇	1	2	yes	complemented
517	#525	—	2	2	no	—
518	#525	—	2	2	no	—
519	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
520	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
521	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
522	#501	C₂²×C₆₇	1	2	yes	complemented
523	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	#496	C₂²×C₆₇	1	2	yes	—
526	#495	C₂²×C₆₇	1	1	yes	characteristic
527	#493	C₂²×C₆₇	1	1	yes	characteristic
528	#490	C₂²×C₆₇	1	2	yes	complemented
529	#489	C₂²×C₆₇	1	2	yes	complemented
530	#488	C₂²×C₆₇	1	2	yes	complemented
531	#486	C₂²×C₆₇	1	2	yes	complemented
532	#485	C₂²×C₆₇	1	2	yes	complemented
533	#483	C₂²×C₆₇	1	2	yes	complemented
534	#482	C₂²×C₆₇	1	2	yes	—
535	#482	C₂²×C₆₇	1	2	yes	—
536	#482	C₂²×C₆₇	1	2	yes	complemented
537	#481	C₂²×C₆₇	1	2	yes	—
538	#481	C₂²×C₆₇	1	2	yes	complemented
539	#480	C₂²×C₆₇	1	2	yes	—
540	#479	C₂²×C₆₇	1	2	yes	complemented
541	#478	C₂²×C₆₇	1	2	yes	complemented
542	#478	C₂²×C₆₇	1	2	yes	complemented
543	#478	C₂²×C₆₇	1	2	yes	complemented
544	#476	C₂²×C₆₇	1	2	yes	complemented
545	#476	C₂²×C₆₇	1	2	yes	complemented
546	#475	C₂²×C₆₇	1	2	yes	complemented
547	#474	C₂²×C₆₇	1	2	yes	complemented
548	#470	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	#469	C₂²×C₆₇	1	1	yes	characteristic
550	#469	C₂²×C₆₇	1	1	yes	characteristic
551	#469	C₂²×C₆₇	1	2	yes	complemented
552	#469	C₂²×C₆₇	1	1	yes	characteristic, complemented
553	#468	C₂²×C₆₇	1	2	yes	complemented
554	#466	C₂²×C₆₇	1	2	yes	—
555	#466	C₂²×C₆₇	1	2	yes	complemented
556	#465	C₂²×C₆₇	1	2	yes	complemented
557	#465	C₂²×C₆₇	1	2	yes	complemented
558	#464	C₂²×C₆₇	1	2	yes	complemented
559	#463	C₂²×C₆₇	1	2	yes	—
560	#463	C₂²×C₆₇	1	2	yes	—
561	#463	C₂²×C₆₇	1	2	yes	complemented
562	#460	C₂²×C₆₇	1	2	yes	complemented
563	#459	C₂²×C₆₇	1	2	yes	—
564	#459	C₂²×C₆₇	1	2	yes	—
565	#459	C₂²×C₆₇	1	2	yes	complemented
566	#452	C₂²×C₆₇	1	2	yes	complemented
567	#450	C₂²×C₆₇	1	2	yes	complemented
568	#449	C₂²×C₆₇	1	2	yes	—
569	#449	C₂²×C₆₇	1	2	yes	—
570	#449	C₂²×C₆₇	1	2	yes	complemented
571	#447	C₂²×C₆₇	1	2	yes	—
572	#447	C₂²×C₆₇	1	2	yes	—
573	#447	C₂²×C₆₇	1	2	yes	complemented
574	#442	C₂²×C₆₇	1	1	yes	characteristic
575	#442	C₂²×C₆₇	1	2	yes	—
576	#442	C₂²×C₆₇	1	1	yes	characteristic
577	#442	C₂²×C₆₇	1	2	yes	complemented
578	#442	C₂²×C₆₇	1	2	yes	complemented
579	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
581	#440	C₂²×C₆₇	1	2	yes	complemented
582	#440	C₂²×C₆₇	1	2	yes	complemented
583	#440	C₂²×C₆₇	1	2	yes	complemented
584	#433	C₂²×C₆₇	1	2	yes	complemented
585	#433	C₂²×C₆₇	1	2	yes	complemented
586	#432	C₂²×C₆₇	1	2	yes	complemented
587	#432	C₂²×C₆₇	1	2	yes	complemented
588	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
590	#408	C₂²×C₆₇	1	1	yes	characteristic
591	#408	C₂²×C₆₇	1	1	yes	characteristic
592	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₂×#41	—	2	2	no	—
595	C₂×#41	—	2	2	no	—
596	C₂×#41	C₂³×C₆₇	1	2	yes	—
597	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
599	C₂³×C₄	—	2	2	no	—
600	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
601	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
604	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×D₈	C₂³×C₆₇	1	2	yes	—
606	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×D₈	C₂³×C₆₇	1	2	yes	—
608	C₂×D₈	C₂³×C₆₇	1	2	yes	—
609	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
612	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
616	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
617	#127	—	2	2	no	—
618	#127	C₂³×C₆₇	1	2	yes	—
619	#127	C₂³×C₆₇	1	2	yes	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	C₂³×C₆₇	1	2	yes	—
626	#125	C₂³×C₆₇	1	2	yes	—
627	#124	—	2	2	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	C₂³×C₆₇	1	2	yes	—
633	#124	C₂³×C₆₇	1	2	yes	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₆₇	1	2	yes	—
661	#121	C₂³×C₆₇	1	2	yes	—
662	#121	C₂³×C₆₇	1	2	yes	—
663	#121	C₂³×C₆₇	1	2	yes	—
664	#121	C₂³×C₆₇	1	2	yes	—
665	#121	C₂³×C₆₇	1	2	yes	—
666	#120	—	2	2	no	—
667	#120	—	2	2	no	—
668	#120	—	2	2	no	—
669	#120	—	2	2	no	—
670	C₄×Q₈	D₄×C₆₇	1	2	yes	—
671	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
672	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	D₄×C₆₇	1	2	yes	—
682	C₄×D₄	D₄×C₆₇	1	2	yes	—
683	C₄×D₄	D₄×C₆₇	1	2	yes	—
684	C₄×D₄	C₂³×C₆₇	1	2	yes	—
685	C₄×D₄	C₂³×C₆₇	1	2	yes	—
686	C₄×D₄	C₂³×C₆₇	1	2	yes	—
687	C₄×D₄	C₂³×C₆₇	1	2	yes	—
688	C₄×D₄	C₂³×C₆₇	1	2	yes	—
689	C₄×D₄	C₂³×C₆₇	1	2	yes	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	C₂³×C₆₇	1	2	yes	—
694	#117	C₂³×C₆₇	1	2	yes	—
695	#117	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₄²	—	2	2	no	—
699	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
701	#107	C₂³×C₆₇	1	2	yes	—
702	#107	C₂³×C₆₇	1	2	yes	—
703	#107	C₂³×C₆₇	1	2	yes	—
704	#106	C₂³×C₆₇	1	1	yes	characteristic
705	#106	C₂³×C₆₇	1	2	yes	—
706	#106	C₂³×C₆₇	1	1	yes	characteristic
707	#106	C₂³×C₆₇	1	1	yes	characteristic
708	#106	C₂³×C₆₇	1	2	yes	—
709	#106	C₂³×C₆₇	1	1	yes	characteristic
710	#106	C₂³×C₆₇	1	2	yes	—
711	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
712	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
714	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
715	#103	C₂³×C₆₇	1	2	yes	—
716	#103	C₂³×C₆₇	1	2	yes	—
717	#103	C₂³×C₆₇	1	2	yes	—
718	#103	C₂³×C₆₇	1	2	yes	—
719	#102	C₂³×C₆₇	1	2	yes	—
720	#102	C₂³×C₆₇	1	2	yes	—
721	#102	C₂³×C₆₇	1	2	yes	—
722	#102	C₂³×C₆₇	1	2	yes	—
723	#102	C₂³×C₆₇	1	2	yes	—
724	#102	C₂³×C₆₇	1	2	yes	—
725	#102	C₂³×C₆₇	1	2	yes	—
726	#102	C₂³×C₆₇	1	2	yes	—
727	#102	C₂³×C₆₇	1	2	yes	—
728	#102	C₂³×C₆₇	1	2	yes	—
729	#102	C₂³×C₆₇	1	2	yes	—
730	#102	C₂³×C₆₇	1	2	yes	—
731	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
732	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
735	#97	C₂³×C₆₇	1	2	yes	—
736	#97	C₂³×C₆₇	1	2	yes	—
737	#97	C₂³×C₆₇	1	1	yes	characteristic
738	#97	C₂³×C₆₇	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₂⁴	—	2	2	no	—
742	#41	—	4	1	no	—
743	#41	—	4	1	no	—
744	#41	—	4	2	no	—
745	#41	—	4	2	no	—
746	#41	—	8	4	no	—
747	#41	—	8	4	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
751	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
768	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
769	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	8	4	no	—
780	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	Q₁₆	—	4	1	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	2	no	—
788	SD₁₆	—	4	2	no	—
789	D₈	—	4	2	no	—
790	D₈	—	4	2	no	—
791	D₈	—	4	2	no	—
792	D₈	—	4	1	no	—
793	D₈	—	4	1	no	—
794	D₈	—	4	1	no	—
795	M₁₆	—	4	1	no	—
796	M₁₆	—	4	1	no	—
797	C₂×C₈	—	4	1	no	—
798	C₂×C₈	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
804	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
817	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
845	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	C₂×D₄×C₆₇	1	2	yes	—
850	C₄²	C₂×D₄×C₆₇	1	2	yes	—
851	C₄²	C₂×D₄×C₆₇	1	2	yes	—
852	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
853	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₄²	C₂⁴×C₆₇	1	2	yes	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	8	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
862	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
863	Q₈	—	2	2	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	4	1	no	—
866	Q₈	—	8	2	no	—
867	Q₈	—	8	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	4	2	no	—
875	D₄	—	4	1	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	8	2	no	—
879	D₄	—	8	2	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
909	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
914	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
915	C₈	—	2	2	no	—
916	C₈	—	2	2	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	1	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	8	8	no	—
936	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	#585×C₆₇	1	1	yes	characteristic
949	C₄	#585×C₆₇	1	1	yes	characteristic
950	C₂	—	4	2	no	—
951	C₂	—	4	1	no	—
952	C₂	—	8	2	no	—
953	C₂	—	8	2	no	—
954	C₂	—	8	2	no	—
955	C₂	C₆₇×#3449	1	1	yes	characteristic
956	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3460	C₂	semidirect
2. C₆₇×#3263	C₂	semidirect
3. C₆₇×#3259	C₂	semidirect
4. C₆₇×#3257	C₂	semidirect
5. C₆₇×#3244	C₂	semidirect
6. C₆₇×#3241	C₂	semidirect
7. C₆₇×#3224	C₂	semidirect
8. C₆₇×#3220	C₂	semidirect
9. C₆₇×#3204	C₂	semidirect
10. C₆₇×#3199	C₂	semidirect
11. C₆₇×#3198	C₂	semidirect
12. C₆₇×#3184	C₂	semidirect
13. C₆₇×#3183	C₂	semidirect
14. C₆₇×#3180	C₂	semidirect
15. C₆₇×#3115	C₂	semidirect
16. C₆₇×#3114	C₂	semidirect
17. C₆₇×#3111	C₂	semidirect
18. C₆₇×#3109	C₂	semidirect
19. C₆₇×#2923	C₂	semidirect
20. #544×C₆₇	C₂²	semidirect
23. #542×C₆₇	C₂²	semidirect
26. #540×C₆₇	C₂²	semidirect
31. #535×C₆₇	C₂²	semidirect
34. #532×C₆₇	C₂²	semidirect
37. #529×C₆₇	C₂²	semidirect
41. C₄×#41×C₆₇	C₂²	semidirect
42. C₂×C₄×D₄×C₆₇	C₂²	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #499×C₆₇	C₂²	semidirect
45. #498×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
57. #482×C₆₇	C₂²	semidirect
59. #481×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #478×C₆₇	C₂²	semidirect
63. #478×C₆₇	C₂²	semidirect
64. #478×C₆₇	C₂²	semidirect
65. #476×C₆₇	C₂²	semidirect
66. #476×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
72. #469×C₆₇	C₂²	semidirect
73. #469×C₆₇	C₂²	semidirect
74. #468×C₆₇	C₂²	semidirect
76. #466×C₆₇	C₂²	semidirect
77. #465×C₆₇	C₂²	semidirect
78. #465×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
83. #460×C₆₇	C₂²	semidirect
86. #459×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #450×C₆₇	C₂²	semidirect
91. #449×C₆₇	C₂²	semidirect
94. #447×C₆₇	C₂²	semidirect
98. #442×C₆₇	C₂²	semidirect
99. #442×C₆₇	C₂²	semidirect
100. #442×C₆₇	C₂²	semidirect
101. #441×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. #433×C₆₇	C₂²	semidirect
106. #433×C₆₇	C₂²	semidirect
107. #432×C₆₇	C₂²	semidirect
108. #432×C₆₇	C₂²	semidirect
109. #424×C₆₇	C₂²	semidirect
110. #424×C₆₇	C₂²	semidirect
113. C₄×M₁₆×C₆₇	C₂²	semidirect
114. C₂×#97×C₆₇	C₂²	semidirect
471. #60974	C₆₇	direct (N × H)
479. #3460	C₂×C₆₇	semidirect
480. #3263	C₂×C₆₇	semidirect
481. #3259	C₂×C₆₇	semidirect
482. #3257	C₂×C₆₇	semidirect
483. #3244	C₂×C₆₇	semidirect
484. #3241	C₂×C₆₇	semidirect
485. #3224	C₂×C₆₇	semidirect
486. #3220	C₂×C₆₇	semidirect
487. #3204	C₂×C₆₇	semidirect
488. #3199	C₂×C₆₇	semidirect
489. #3198	C₂×C₆₇	semidirect
490. #3184	C₂×C₆₇	semidirect
491. #3183	C₂×C₆₇	semidirect
492. #3180	C₂×C₆₇	semidirect
493. #3115	C₂×C₆₇	semidirect
494. #3114	C₂×C₆₇	semidirect
495. #3111	C₂×C₆₇	semidirect
496. #3109	C₂×C₆₇	semidirect
497. #2923	C₂×C₆₇	semidirect
498. C₆₇	#60974	direct (N × H)
499. #544	C₂²×C₆₇	semidirect
502. #542	C₂²×C₆₇	semidirect
505. #540	C₂²×C₆₇	semidirect
510. #535	C₂²×C₆₇	semidirect
513. #532	C₂²×C₆₇	semidirect
516. #529	C₂²×C₆₇	semidirect
520. C₄×#41	C₂²×C₆₇	semidirect
521. C₂×C₄×D₄	C₂²×C₆₇	semidirect
522. #501	C₂²×C₆₇	semidirect
523. #499	C₂²×C₆₇	semidirect
524. #498	C₂²×C₆₇	semidirect
528. #490	C₂²×C₆₇	semidirect
529. #489	C₂²×C₆₇	semidirect
530. #488	C₂²×C₆₇	semidirect
531. #486	C₂²×C₆₇	semidirect
532. #485	C₂²×C₆₇	semidirect
533. #483	C₂²×C₆₇	semidirect
536. #482	C₂²×C₆₇	semidirect
538. #481	C₂²×C₆₇	semidirect
540. #479	C₂²×C₆₇	semidirect
541. #478	C₂²×C₆₇	semidirect
542. #478	C₂²×C₆₇	semidirect
543. #478	C₂²×C₆₇	semidirect
544. #476	C₂²×C₆₇	semidirect
545. #476	C₂²×C₆₇	semidirect
546. #475	C₂²×C₆₇	semidirect
547. #474	C₂²×C₆₇	semidirect
548. #470	C₂²×C₆₇	semidirect
551. #469	C₂²×C₆₇	semidirect
552. #469	C₂²×C₆₇	semidirect
553. #468	C₂²×C₆₇	semidirect
555. #466	C₂²×C₆₇	semidirect
556. #465	C₂²×C₆₇	semidirect
557. #465	C₂²×C₆₇	semidirect
558. #464	C₂²×C₆₇	semidirect
561. #463	C₂²×C₆₇	semidirect
562. #460	C₂²×C₆₇	semidirect
565. #459	C₂²×C₆₇	semidirect
566. #452	C₂²×C₆₇	semidirect
567. #450	C₂²×C₆₇	semidirect
570. #449	C₂²×C₆₇	semidirect
573. #447	C₂²×C₆₇	semidirect
577. #442	C₂²×C₆₇	semidirect
578. #442	C₂²×C₆₇	semidirect
579. #442	C₂²×C₆₇	semidirect
580. #441	C₂²×C₆₇	semidirect
581. #440	C₂²×C₆₇	semidirect
582. #440	C₂²×C₆₇	semidirect
583. #440	C₂²×C₆₇	semidirect
584. #433	C₂²×C₆₇	semidirect
585. #433	C₂²×C₆₇	semidirect
586. #432	C₂²×C₆₇	semidirect
587. #432	C₂²×C₆₇	semidirect
588. #424	C₂²×C₆₇	semidirect
589. #424	C₂²×C₆₇	semidirect
592. C₄×M₁₆	C₂²×C₆₇	semidirect
593. C₂×#97	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3460	2
C₆₇×#3263	2
C₆₇×#3259	2
C₆₇×#3257	2
C₆₇×#3244	2
C₆₇×#3241	2
C₆₇×#3224	2
C₆₇×#3220	2
C₆₇×#3204	2
C₆₇×#3199	2
C₆₇×#3198	2
C₆₇×#3184	2
C₆₇×#3183	2
C₆₇×#3180	2
C₆₇×#3115	2
C₆₇×#3114	2
C₆₇×#3111	2
C₆₇×#3109	2
C₆₇×#2923	2
#60974	67

Subgroups — C67×#60974 #30740225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60974 #30740225