Subgroups — C₆₇×#61663 #30740914

Order 17152.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3211	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3202	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3200	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
28	#563×C₆₇	—	2	1	no	—
29	#560×C₆₇	—	2	1	no	—
30	#555×C₆₇	—	2	1	no	—
31	#553×C₆₇	C₂²	1	2	yes	complemented
32	#552×C₆₇	C₂²	1	2	yes	complemented
33	#551×C₆₇	—	2	1	no	—
34	#548×C₆₇	C₂²	1	2	yes	—
35	#548×C₆₇	C₂²	1	2	yes	complemented
36	#548×C₆₇	C₂²	1	2	yes	complemented
37	#546×C₆₇	—	2	2	no	—
38	#546×C₆₇	—	2	2	no	—
39	#546×C₆₇	C₂²	1	2	yes	—
40	#546×C₆₇	C₂²	1	2	yes	complemented
41	#546×C₆₇	C₂²	1	2	yes	complemented
42	#540×C₆₇	—	2	2	no	—
43	#538×C₆₇	—	2	2	no	—
44	#537×C₆₇	C₂²	1	2	yes	complemented
45	#536×C₆₇	—	2	1	no	—
46	#536×C₆₇	C₂²	1	1	yes	characteristic
47	#536×C₆₇	C₂²	1	1	yes	characteristic
48	#535×C₆₇	—	2	1	no	—
49	#535×C₆₇	C₂²	1	1	yes	characteristic
50	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#532×C₆₇	—	2	1	no	—
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#529×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#124×C₆₇	—	2	1	no	—
55	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#495×C₆₇	C₂²	1	2	yes	complemented
58	#495×C₆₇	C₂²	1	2	yes	complemented
59	#488×C₆₇	C₂²	1	2	yes	complemented
60	#488×C₆₇	C₂²	1	2	yes	complemented
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#485×C₆₇	C₂²	1	2	yes	complemented
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#482×C₆₇	C₂²	1	2	yes	complemented
65	#481×C₆₇	C₂²	1	2	yes	complemented
66	#480×C₆₇	C₂²	1	2	yes	complemented
67	#479×C₆₇	C₂²	1	2	yes	complemented
68	#478×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#469×C₆₇	C₂²	1	2	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#467×C₆₇	C₂²	1	2	yes	complemented
74	#466×C₆₇	C₂²	1	2	yes	complemented
75	#465×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#463×C₆₇	C₂²	1	2	yes	complemented
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	—
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#451×C₆₇	C₂²	1	2	yes	complemented
87	#451×C₆₇	C₂²	1	2	yes	complemented
88	#451×C₆₇	C₂²	1	2	yes	complemented
89	#450×C₆₇	C₂²	1	2	yes	—
90	#450×C₆₇	C₂²	1	2	yes	complemented
91	#450×C₆₇	C₂²	1	2	yes	complemented
92	#449×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	complemented
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#448×C₆₇	C₂²	1	2	yes	complemented
98	#448×C₆₇	C₂²	1	2	yes	complemented
99	#447×C₆₇	C₂²	1	2	yes	—
100	#447×C₆₇	C₂²	1	2	yes	—
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
105	#436×C₆₇	C₂²	1	2	yes	complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
109	#431×C₆₇	C₂²	1	2	yes	complemented
110	#418×C₆₇	C₂²	1	1	yes	characteristic
111	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#417×C₆₇	C₂²	1	2	yes	complemented
113	#416×C₆₇	C₂²	1	1	yes	characteristic
114	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	1	yes	characteristic
117	#408×C₆₇	C₂²	1	1	yes	characteristic
118	#408×C₆₇	C₂²	1	2	yes	complemented
119	2₋¹⁺⁴×C₆₇	—	4	2	no	—
120	2₋¹⁺⁴×C₆₇	—	4	2	no	—
121	H(5,𝔽₂)×C₆₇	—	4	2	no	—
122	H(5,𝔽₂)×C₆₇	—	4	2	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	2	1	no	—
125	C₂×#41×C₆₇	—	2	2	no	—
126	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×#41×C₆₇	C₂³	1	2	yes	—
129	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×#41×C₆₇	C₂³	1	2	yes	—
131	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₆₇	—	2	1	no	—
134	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	—	2	1	no	—
138	C₂²×D₄×C₆₇	—	2	1	no	—
139	C₂²×D₄×C₆₇	—	2	1	no	—
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
144	#137×C₆₇	—	4	4	no	—
145	#137×C₆₇	—	4	2	no	—
146	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
147	#135×C₆₇	—	4	4	no	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	—	4	2	no	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	—	4	2	no	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×D₈×C₆₇	C₂³	1	2	yes	—
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₇	—	2	1	no	—
169	C₄⋊Q₈×C₆₇	—	2	1	no	—
170	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
171	#127×C₆₇	—	2	1	no	—
172	#127×C₆₇	—	2	1	no	—
173	#127×C₆₇	D₄	1	1	yes	characteristic
174	#126×C₆₇	—	2	2	no	—
175	#126×C₆₇	—	2	2	no	—
176	#126×C₆₇	—	2	2	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	C₂³	1	2	yes	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	1	no	—
182	#124×C₆₇	—	2	1	no	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	2	no	—
185	#124×C₆₇	—	2	2	no	—
186	#124×C₆₇	—	2	1	no	—
187	#124×C₆₇	—	2	1	no	—
188	#124×C₆₇	D₄	1	1	yes	characteristic
189	#124×C₆₇	D₄	1	1	yes	characteristic
190	#124×C₆₇	C₂³	1	2	yes	—
191	#124×C₆₇	C₂³	1	2	yes	—
192	#124×C₆₇	C₂³	1	2	yes	—
193	#123×C₆₇	—	2	1	no	—
194	#123×C₆₇	—	2	1	no	—
195	#123×C₆₇	—	2	1	no	—
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	2	no	—
198	#123×C₆₇	—	2	2	no	—
199	#123×C₆₇	—	2	2	no	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	—	2	2	no	—
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	D₄	1	2	yes	—
223	#121×C₆₇	D₄	1	2	yes	—
224	#121×C₆₇	C₂³	1	2	yes	—
225	#121×C₆₇	C₂³	1	2	yes	—
226	#121×C₆₇	C₂³	1	2	yes	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#120×C₆₇	—	2	2	no	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	1	no	—
232	#120×C₆₇	—	2	1	no	—
233	#120×C₆₇	—	2	2	no	—
234	#120×C₆₇	—	2	2	no	—
235	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	2	yes	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	1	no	—
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	C₂³	1	1	yes	characteristic
251	#117×C₆₇	C₂³	1	1	yes	characteristic
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
255	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
256	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
257	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
258	C₂×C₄²×C₆₇	—	2	1	no	—
259	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
260	#107×C₆₇	C₂³	1	2	yes	—
261	#107×C₆₇	C₂³	1	2	yes	—
262	#106×C₆₇	C₂³	1	2	yes	—
263	#106×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#103×C₆₇	C₂³	1	2	yes	—
272	#103×C₆₇	C₂³	1	2	yes	—
273	#103×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	#102×C₆₇	C₂³	1	2	yes	—
277	#102×C₆₇	C₂³	1	2	yes	—
278	#102×C₆₇	C₂³	1	2	yes	—
279	#102×C₆₇	C₂³	1	2	yes	—
280	#102×C₆₇	C₂³	1	2	yes	—
281	#102×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄×C₈×C₆₇	C₂³	1	2	yes	—
289	C₄×C₈×C₆₇	C₂³	1	2	yes	—
290	C₂⁴×C₆₇	—	2	1	no	—
291	C₂⁴×C₆₇	—	2	1	no	—
292	C₂⁴×C₆₇	—	2	1	no	—
293	C₂⁴×C₆₇	—	2	1	no	—
294	#41×C₆₇	—	2	2	no	—
295	#41×C₆₇	—	2	2	no	—
296	#41×C₆₇	—	2	2	no	—
297	#41×C₆₇	—	2	2	no	—
298	#41×C₆₇	—	2	4	no	—
299	#41×C₆₇	—	4	1	no	—
300	#41×C₆₇	—	4	1	no	—
301	#41×C₆₇	—	4	1	no	—
302	#41×C₆₇	—	4	1	no	—
303	#41×C₆₇	—	4	1	no	—
304	#41×C₆₇	—	4	1	no	—
305	#41×C₆₇	—	4	2	no	—
306	#41×C₆₇	—	4	4	no	—
307	#41×C₆₇	—	4	4	no	—
308	#41×C₆₇	—	4	2	no	—
309	#41×C₆₇	—	4	2	no	—
310	#41×C₆₇	—	4	8	no	—
311	C₂×Q₈×C₆₇	—	2	2	no	—
312	C₂×Q₈×C₆₇	—	2	1	no	—
313	C₂×Q₈×C₆₇	—	2	1	no	—
314	C₂×Q₈×C₆₇	—	2	4	no	—
315	C₂×Q₈×C₆₇	—	4	2	no	—
316	C₂×Q₈×C₆₇	—	4	1	no	—
317	C₂×Q₈×C₆₇	—	4	1	no	—
318	C₂×Q₈×C₆₇	—	4	4	no	—
319	C₂×Q₈×C₆₇	—	4	1	no	—
320	C₂×Q₈×C₆₇	—	4	1	no	—
321	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₆₇	—	2	1	no	—
327	C₂×D₄×C₆₇	—	2	2	no	—
328	C₂×D₄×C₆₇	—	2	2	no	—
329	C₂×D₄×C₆₇	—	2	2	no	—
330	C₂×D₄×C₆₇	—	2	1	no	—
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	1	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	4	1	no	—
343	C₂×D₄×C₆₇	—	4	1	no	—
344	C₂×D₄×C₆₇	—	4	1	no	—
345	C₂×D₄×C₆₇	—	4	1	no	—
346	C₂×D₄×C₆₇	—	4	1	no	—
347	C₂×D₄×C₆₇	—	4	1	no	—
348	C₂×D₄×C₆₇	—	4	4	no	—
349	C₂×D₄×C₆₇	—	4	4	no	—
350	C₂×D₄×C₆₇	—	4	4	no	—
351	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	1	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₆₇	—	2	4	no	—
379	Q₁₆×C₆₇	—	4	2	no	—
380	Q₁₆×C₆₇	—	4	2	no	—
381	SD₁₆×C₆₇	—	2	4	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	4	2	no	—
384	SD₁₆×C₆₇	—	4	2	no	—
385	SD₁₆×C₆₇	—	4	2	no	—
386	SD₁₆×C₆₇	—	4	2	no	—
387	D₈×C₆₇	—	2	4	no	—
388	D₈×C₆₇	—	4	2	no	—
389	D₈×C₆₇	—	4	2	no	—
390	M₁₆×C₆₇	—	4	1	no	—
391	M₁₆×C₆₇	—	4	2	no	—
392	M₁₆×C₆₇	—	4	1	no	—
393	C₂×C₈×C₆₇	—	4	1	no	—
394	C₂×C₈×C₆₇	—	4	1	no	—
395	C₂×C₈×C₆₇	—	4	2	no	—
396	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
397	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
398	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
399	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	1	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	1	no	—
445	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₂³×C₆₇	—	2	1	no	—
449	C₂³×C₆₇	—	2	2	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	—	4	2	no	—
453	C₂³×C₆₇	—	4	2	no	—
454	C₂³×C₆₇	—	4	2	no	—
455	C₂³×C₆₇	—	8	1	no	—
456	C₂³×C₆₇	—	8	2	no	—
457	C₂³×C₆₇	—	8	2	no	—
458	C₂³×C₆₇	—	8	2	no	—
459	C₂³×C₆₇	—	8	2	no	—
460	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
463	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
464	Q₈×C₆₇	—	2	1	no	—
465	Q₈×C₆₇	—	2	2	no	—
466	Q₈×C₆₇	—	2	2	no	—
467	Q₈×C₆₇	—	2	2	no	—
468	Q₈×C₆₇	—	2	2	no	—
469	Q₈×C₆₇	—	4	1	no	—
470	Q₈×C₆₇	—	4	1	no	—
471	Q₈×C₆₇	—	4	4	no	—
472	Q₈×C₆₇	—	4	2	no	—
473	Q₈×C₆₇	—	8	1	no	—
474	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₆₇	—	2	4	no	—
476	D₄×C₆₇	—	2	1	no	—
477	D₄×C₆₇	—	2	2	no	—
478	D₄×C₆₇	—	2	1	no	—
479	D₄×C₆₇	—	2	1	no	—
480	D₄×C₆₇	—	2	2	no	—
481	D₄×C₆₇	—	2	1	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	4	1	no	—
484	D₄×C₆₇	—	4	1	no	—
485	D₄×C₆₇	—	4	1	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	4	2	no	—
488	D₄×C₆₇	—	4	1	no	—
489	D₄×C₆₇	—	4	2	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	2	no	—
493	D₄×C₆₇	—	4	2	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	4	4	no	—
496	D₄×C₆₇	—	8	1	no	—
497	D₄×C₆₇	—	8	2	no	—
498	D₄×C₆₇	—	8	2	no	—
499	D₄×C₆₇	—	8	2	no	—
500	D₄×C₆₇	—	8	2	no	—
501	D₄×C₆₇	—	8	2	no	—
502	D₄×C₆₇	—	8	2	no	—
503	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₆₇	—	2	4	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	2	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	2	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	2	no	—
518	C₂×C₄×C₆₇	—	2	2	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	4	4	no	—
523	C₂×C₄×C₆₇	—	4	4	no	—
524	C₂×C₄×C₆₇	—	4	2	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	2	no	—
527	C₂×C₄×C₆₇	—	8	2	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	—	8	1	no	—
530	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
537	C₈×C₆₇	—	2	2	no	—
538	C₈×C₆₇	—	2	2	no	—
539	C₈×C₆₇	—	2	2	no	—
540	C₈×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	2	no	—
543	C₂²×C₆₇	—	2	2	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	2	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	4	2	no	—
552	C₂²×C₆₇	—	4	2	no	—
553	C₂²×C₆₇	—	4	2	no	—
554	C₂²×C₆₇	—	4	2	no	—
555	C₂²×C₆₇	—	4	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	2	no	—
559	C₂²×C₆₇	—	16	2	no	—
560	C₂²×C₆₇	—	16	2	no	—
561	C₂²×C₆₇	—	16	2	no	—
562	C₂²×C₆₇	—	16	2	no	—
563	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	1	no	—
567	C₄×C₆₇	—	2	2	no	—
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	1	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	4	2	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	—	4	2	no	—
574	C₄×C₆₇	—	4	2	no	—
575	C₄×C₆₇	—	4	2	no	—
576	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	#61663	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
579	C₂×C₆₇	—	4	2	no	—
580	C₂×C₆₇	—	4	1	no	—
581	C₂×C₆₇	—	4	1	no	—
582	C₂×C₆₇	—	4	1	no	—
583	C₂×C₆₇	—	4	2	no	—
584	C₂×C₆₇	—	8	2	no	—
585	C₂×C₆₇	—	8	1	no	—
586	C₂×C₆₇	—	8	1	no	—
587	C₂×C₆₇	#3484	1	1	yes	characteristic
588	C₂×C₆₇	#3584	1	2	yes	—
589	#3551	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3323	C₂×C₆₇	1	2	yes	complemented
592	#3322	C₂×C₆₇	1	2	yes	complemented
593	#3301	C₂×C₆₇	1	2	yes	complemented
594	#3300	C₂×C₆₇	1	2	yes	complemented
595	#3282	C₂×C₆₇	1	2	yes	complemented
596	#3280	C₂×C₆₇	1	2	yes	complemented
597	#3277	C₂×C₆₇	1	2	yes	complemented
598	#3275	C₂×C₆₇	1	2	yes	complemented
599	#3211	C₂×C₆₇	1	2	yes	complemented
600	#3202	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3200	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3198	C₂×C₆₇	1	2	yes	complemented
603	#3102	C₂×C₆₇	1	2	yes	complemented
604	#3013	C₂×C₆₇	1	2	yes	complemented
605	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2979	C₂×C₆₇	1	1	yes	characteristic, complemented
608	C₆₇	#61663	1	1	yes	characteristic, direct product factor, Sylow
609	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
612	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
613	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
614	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
615	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
617	#563	—	2	1	no	—
618	#560	—	2	1	no	—
619	#555	—	2	1	no	—
620	#553	C₂²×C₆₇	1	2	yes	complemented
621	#552	C₂²×C₆₇	1	2	yes	complemented
622	#551	—	2	1	no	—
623	#548	C₂²×C₆₇	1	2	yes	—
624	#548	C₂²×C₆₇	1	2	yes	complemented
625	#548	C₂²×C₆₇	1	2	yes	complemented
626	#546	—	2	2	no	—
627	#546	—	2	2	no	—
628	#546	C₂²×C₆₇	1	2	yes	—
629	#546	C₂²×C₆₇	1	2	yes	complemented
630	#546	C₂²×C₆₇	1	2	yes	complemented
631	#540	—	2	2	no	—
632	#538	—	2	2	no	—
633	#537	C₂²×C₆₇	1	2	yes	complemented
634	#536	—	2	1	no	—
635	#536	C₂²×C₆₇	1	1	yes	characteristic
636	#536	C₂²×C₆₇	1	1	yes	characteristic
637	#535	—	2	1	no	—
638	#535	C₂²×C₆₇	1	1	yes	characteristic
639	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#532	—	2	1	no	—
641	#532	C₂²×C₆₇	1	1	yes	characteristic
642	#529	C₂²×C₆₇	1	2	yes	complemented
643	C₂×#124	—	2	1	no	—
644	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#495	C₂²×C₆₇	1	2	yes	complemented
647	#495	C₂²×C₆₇	1	2	yes	complemented
648	#488	C₂²×C₆₇	1	2	yes	complemented
649	#488	C₂²×C₆₇	1	2	yes	complemented
650	#485	C₂²×C₆₇	1	2	yes	complemented
651	#485	C₂²×C₆₇	1	2	yes	complemented
652	#485	C₂²×C₆₇	1	2	yes	complemented
653	#482	C₂²×C₆₇	1	2	yes	complemented
654	#481	C₂²×C₆₇	1	2	yes	complemented
655	#480	C₂²×C₆₇	1	2	yes	complemented
656	#479	C₂²×C₆₇	1	2	yes	complemented
657	#478	C₂²×C₆₇	1	2	yes	complemented
658	#470	C₂²×C₆₇	1	2	yes	complemented
659	#469	C₂²×C₆₇	1	2	yes	complemented
660	#468	C₂²×C₆₇	1	2	yes	complemented
661	#468	C₂²×C₆₇	1	2	yes	complemented
662	#467	C₂²×C₆₇	1	2	yes	complemented
663	#466	C₂²×C₆₇	1	2	yes	complemented
664	#465	C₂²×C₆₇	1	2	yes	complemented
665	#465	C₂²×C₆₇	1	2	yes	complemented
666	#464	C₂²×C₆₇	1	2	yes	complemented
667	#464	C₂²×C₆₇	1	2	yes	complemented
668	#464	C₂²×C₆₇	1	2	yes	complemented
669	#463	C₂²×C₆₇	1	2	yes	complemented
670	#463	C₂²×C₆₇	1	2	yes	complemented
671	#463	C₂²×C₆₇	1	2	yes	complemented
672	#452	C₂²×C₆₇	1	2	yes	—
673	#452	C₂²×C₆₇	1	2	yes	complemented
674	#452	C₂²×C₆₇	1	2	yes	complemented
675	#451	C₂²×C₆₇	1	2	yes	complemented
676	#451	C₂²×C₆₇	1	2	yes	complemented
677	#451	C₂²×C₆₇	1	2	yes	complemented
678	#450	C₂²×C₆₇	1	2	yes	—
679	#450	C₂²×C₆₇	1	2	yes	complemented
680	#450	C₂²×C₆₇	1	2	yes	complemented
681	#449	C₂²×C₆₇	1	2	yes	—
682	#449	C₂²×C₆₇	1	2	yes	—
683	#449	C₂²×C₆₇	1	2	yes	complemented
684	#449	C₂²×C₆₇	1	2	yes	complemented
685	#449	C₂²×C₆₇	1	2	yes	complemented
686	#448	C₂²×C₆₇	1	2	yes	complemented
687	#448	C₂²×C₆₇	1	2	yes	complemented
688	#447	C₂²×C₆₇	1	2	yes	—
689	#447	C₂²×C₆₇	1	2	yes	—
690	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
691	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
693	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
694	#436	C₂²×C₆₇	1	2	yes	complemented
695	#436	C₂²×C₆₇	1	2	yes	complemented
696	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
697	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
698	#431	C₂²×C₆₇	1	2	yes	complemented
699	#418	C₂²×C₆₇	1	1	yes	characteristic
700	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	#417	C₂²×C₆₇	1	2	yes	complemented
702	#416	C₂²×C₆₇	1	1	yes	characteristic
703	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
705	#408	C₂²×C₆₇	1	1	yes	characteristic
706	#408	C₂²×C₆₇	1	1	yes	characteristic
707	#408	C₂²×C₆₇	1	2	yes	complemented
708	2₋¹⁺⁴	—	4	2	no	—
709	2₋¹⁺⁴	—	4	2	no	—
710	H(5,𝔽₂)	—	4	2	no	—
711	H(5,𝔽₂)	—	4	2	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	—	2	2	no	—
715	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×#41	C₂³×C₆₇	1	2	yes	—
717	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×#41	C₂³×C₆₇	1	2	yes	—
720	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
721	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
722	C₂²×Q₈	—	2	1	no	—
723	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
724	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
733	#137	—	4	4	no	—
734	#137	—	4	2	no	—
735	AGL(1,ℤ/8)	—	4	2	no	—
736	#135	—	4	4	no	—
737	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
740	C₂×SD₁₆	—	4	2	no	—
741	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
747	C₂×D₈	—	4	2	no	—
748	C₂×D₈	C₂³×C₆₇	1	2	yes	—
749	C₂×D₈	C₂³×C₆₇	1	2	yes	—
750	C₂×D₈	C₂³×C₆₇	1	2	yes	—
751	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
754	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
760	#127	—	2	1	no	—
761	#127	—	2	1	no	—
762	#127	D₄×C₆₇	1	1	yes	characteristic
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	C₂³×C₆₇	1	2	yes	—
768	#124	—	2	1	no	—
769	#124	—	2	1	no	—
770	#124	—	2	1	no	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	D₄×C₆₇	1	1	yes	characteristic
778	#124	D₄×C₆₇	1	1	yes	characteristic
779	#124	C₂³×C₆₇	1	2	yes	—
780	#124	C₂³×C₆₇	1	2	yes	—
781	#124	C₂³×C₆₇	1	2	yes	—
782	#123	—	2	1	no	—
783	#123	—	2	1	no	—
784	#123	—	2	1	no	—
785	#123	—	2	1	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	D₄×C₆₇	1	2	yes	—
812	#121	D₄×C₆₇	1	2	yes	—
813	#121	C₂³×C₆₇	1	2	yes	—
814	#121	C₂³×C₆₇	1	2	yes	—
815	#121	C₂³×C₆₇	1	2	yes	—
816	#121	C₂³×C₆₇	1	2	yes	—
817	#121	C₂³×C₆₇	1	2	yes	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	1	no	—
821	#120	—	2	1	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
825	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	C₂³×C₆₇	1	2	yes	—
833	C₄×D₄	C₂³×C₆₇	1	2	yes	—
834	C₄×D₄	C₂³×C₆₇	1	2	yes	—
835	C₄×D₄	C₂³×C₆₇	1	2	yes	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	C₂³×C₆₇	1	1	yes	characteristic
840	#117	C₂³×C₆₇	1	1	yes	characteristic
841	#117	C₂³×C₆₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₄²	—	2	1	no	—
848	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
849	#107	C₂³×C₆₇	1	2	yes	—
850	#107	C₂³×C₆₇	1	2	yes	—
851	#106	C₂³×C₆₇	1	2	yes	—
852	#106	C₂³×C₆₇	1	2	yes	—
853	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
854	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
855	#103	C₂³×C₆₇	1	2	yes	—
856	#103	C₂³×C₆₇	1	2	yes	—
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#103	C₂³×C₆₇	1	2	yes	—
862	#103	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	2	yes	—
866	#102	C₂³×C₆₇	1	2	yes	—
867	#102	C₂³×C₆₇	1	2	yes	—
868	#102	C₂³×C₆₇	1	2	yes	—
869	#102	C₂³×C₆₇	1	2	yes	—
870	#102	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₄×C₈	C₂³×C₆₇	1	2	yes	—
878	C₄×C₈	C₂³×C₆₇	1	2	yes	—
879	C₂⁴	—	2	1	no	—
880	C₂⁴	—	2	1	no	—
881	C₂⁴	—	2	1	no	—
882	C₂⁴	—	2	1	no	—
883	#41	—	2	2	no	—
884	#41	—	2	2	no	—
885	#41	—	2	2	no	—
886	#41	—	2	2	no	—
887	#41	—	2	4	no	—
888	#41	—	4	1	no	—
889	#41	—	4	1	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	4	1	no	—
893	#41	—	4	1	no	—
894	#41	—	4	2	no	—
895	#41	—	4	4	no	—
896	#41	—	4	4	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	8	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	4	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	—	4	1	no	—
907	C₂×Q₈	—	4	4	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	4	1	no	—
932	C₂×D₄	—	4	1	no	—
933	C₂×D₄	—	4	1	no	—
934	C₂×D₄	—	4	1	no	—
935	C₂×D₄	—	4	1	no	—
936	C₂×D₄	—	4	1	no	—
937	C₂×D₄	—	4	4	no	—
938	C₂×D₄	—	4	4	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
944	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
945	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
950	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
967	Q₁₆	—	2	4	no	—
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	4	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	D₈	—	2	4	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	4	1	no	—
980	M₁₆	—	4	2	no	—
981	M₁₆	—	4	1	no	—
982	C₂×C₈	—	4	1	no	—
983	C₂×C₈	—	4	1	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
986	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
987	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
988	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₆₇	1	2	yes	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1051	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1052	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	4	no	—
1061	Q₈	—	4	2	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1064	D₄	—	2	4	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1093	C₂×C₄	—	2	4	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1125	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1126	C₈	—	2	2	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	16	2	no	—
1149	C₂²	—	16	2	no	—
1150	C₂²	—	16	2	no	—
1151	C₂²	—	16	2	no	—
1152	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1166	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1167	C₂	—	4	1	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	2	no	—
1171	C₂	—	4	2	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	1	no	—
1174	C₂	—	8	2	no	—
1175	C₂	C₆₇×#3484	1	1	yes	characteristic
1176	C₂	C₆₇×#3584	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3551	C₂	semidirect
2. C₆₇×#3500	C₂	semidirect
3. C₆₇×#3323	C₂	semidirect
4. C₆₇×#3322	C₂	semidirect
5. C₆₇×#3301	C₂	semidirect
6. C₆₇×#3300	C₂	semidirect
7. C₆₇×#3282	C₂	semidirect
8. C₆₇×#3280	C₂	semidirect
9. C₆₇×#3277	C₂	semidirect
10. C₆₇×#3275	C₂	semidirect
11. C₆₇×#3211	C₂	semidirect
12. C₆₇×#3202	C₂	semidirect
13. C₆₇×#3200	C₂	semidirect
14. C₆₇×#3198	C₂	semidirect
15. C₆₇×#3102	C₂	semidirect
16. C₆₇×#3013	C₂	semidirect
17. C₆₇×#3009	C₂	semidirect
18. C₆₇×#3008	C₂	semidirect
19. C₆₇×#2979	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
26. C₂²×SD₁₆×C₆₇	C₂²	semidirect
31. #553×C₆₇	C₂²	semidirect
32. #552×C₆₇	C₂²	semidirect
35. #548×C₆₇	C₂²	semidirect
36. #548×C₆₇	C₂²	semidirect
40. #546×C₆₇	C₂²	semidirect
41. #546×C₆₇	C₂²	semidirect
44. #537×C₆₇	C₂²	semidirect
50. #535×C₆₇	C₂²	semidirect
53. #529×C₆₇	C₂²	semidirect
55. C₂×#124×C₆₇	C₂²	semidirect
56. C₄×#41×C₆₇	C₂²	semidirect
57. #495×C₆₇	C₂²	semidirect
58. #495×C₆₇	C₂²	semidirect
59. #488×C₆₇	C₂²	semidirect
60. #488×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #485×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #482×C₆₇	C₂²	semidirect
65. #481×C₆₇	C₂²	semidirect
66. #480×C₆₇	C₂²	semidirect
67. #479×C₆₇	C₂²	semidirect
68. #478×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #467×C₆₇	C₂²	semidirect
74. #466×C₆₇	C₂²	semidirect
75. #465×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #463×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #451×C₆₇	C₂²	semidirect
87. #451×C₆₇	C₂²	semidirect
88. #451×C₆₇	C₂²	semidirect
90. #450×C₆₇	C₂²	semidirect
91. #450×C₆₇	C₂²	semidirect
94. #449×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #448×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
105. #436×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. C₈×D₄×C₆₇	C₂²	semidirect
108. C₈×D₄×C₆₇	C₂²	semidirect
109. #431×C₆₇	C₂²	semidirect
111. #418×C₆₇	C₂²	semidirect
112. #417×C₆₇	C₂²	semidirect
114. #416×C₆₇	C₂²	semidirect
115. C₂×#103×C₆₇	C₂²	semidirect
118. #408×C₆₇	C₂²	semidirect
578. #61663	C₆₇	direct (N × H)
589. #3551	C₂×C₆₇	semidirect
590. #3500	C₂×C₆₇	semidirect
591. #3323	C₂×C₆₇	semidirect
592. #3322	C₂×C₆₇	semidirect
593. #3301	C₂×C₆₇	semidirect
594. #3300	C₂×C₆₇	semidirect
595. #3282	C₂×C₆₇	semidirect
596. #3280	C₂×C₆₇	semidirect
597. #3277	C₂×C₆₇	semidirect
598. #3275	C₂×C₆₇	semidirect
599. #3211	C₂×C₆₇	semidirect
600. #3202	C₂×C₆₇	semidirect
601. #3200	C₂×C₆₇	semidirect
602. #3198	C₂×C₆₇	semidirect
603. #3102	C₂×C₆₇	semidirect
604. #3013	C₂×C₆₇	semidirect
605. #3009	C₂×C₆₇	semidirect
606. #3008	C₂×C₆₇	semidirect
607. #2979	C₂×C₆₇	semidirect
608. C₆₇	#61663	direct (N × H)
609. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
611. C₂×#137	C₂²×C₆₇	semidirect
612. C₂×#137	C₂²×C₆₇	semidirect
614. C₂×#135	C₂²×C₆₇	semidirect
615. C₂²×SD₁₆	C₂²×C₆₇	semidirect
620. #553	C₂²×C₆₇	semidirect
621. #552	C₂²×C₆₇	semidirect
624. #548	C₂²×C₆₇	semidirect
625. #548	C₂²×C₆₇	semidirect
629. #546	C₂²×C₆₇	semidirect
630. #546	C₂²×C₆₇	semidirect
633. #537	C₂²×C₆₇	semidirect
639. #535	C₂²×C₆₇	semidirect
642. #529	C₂²×C₆₇	semidirect
644. C₂×#124	C₂²×C₆₇	semidirect
645. C₄×#41	C₂²×C₆₇	semidirect
646. #495	C₂²×C₆₇	semidirect
647. #495	C₂²×C₆₇	semidirect
648. #488	C₂²×C₆₇	semidirect
649. #488	C₂²×C₆₇	semidirect
650. #485	C₂²×C₆₇	semidirect
651. #485	C₂²×C₆₇	semidirect
652. #485	C₂²×C₆₇	semidirect
653. #482	C₂²×C₆₇	semidirect
654. #481	C₂²×C₆₇	semidirect
655. #480	C₂²×C₆₇	semidirect
656. #479	C₂²×C₆₇	semidirect
657. #478	C₂²×C₆₇	semidirect
658. #470	C₂²×C₆₇	semidirect
659. #469	C₂²×C₆₇	semidirect
660. #468	C₂²×C₆₇	semidirect
661. #468	C₂²×C₆₇	semidirect
662. #467	C₂²×C₆₇	semidirect
663. #466	C₂²×C₆₇	semidirect
664. #465	C₂²×C₆₇	semidirect
665. #465	C₂²×C₆₇	semidirect
666. #464	C₂²×C₆₇	semidirect
667. #464	C₂²×C₆₇	semidirect
668. #464	C₂²×C₆₇	semidirect
669. #463	C₂²×C₆₇	semidirect
670. #463	C₂²×C₆₇	semidirect
671. #463	C₂²×C₆₇	semidirect
673. #452	C₂²×C₆₇	semidirect
674. #452	C₂²×C₆₇	semidirect
675. #451	C₂²×C₆₇	semidirect
676. #451	C₂²×C₆₇	semidirect
677. #451	C₂²×C₆₇	semidirect
679. #450	C₂²×C₆₇	semidirect
680. #450	C₂²×C₆₇	semidirect
683. #449	C₂²×C₆₇	semidirect
684. #449	C₂²×C₆₇	semidirect
685. #449	C₂²×C₆₇	semidirect
686. #448	C₂²×C₆₇	semidirect
687. #448	C₂²×C₆₇	semidirect
690. C₄×Q₁₆	C₂²×C₆₇	semidirect
691. C₄×SD₁₆	C₂²×C₆₇	semidirect
692. C₄×SD₁₆	C₂²×C₆₇	semidirect
693. C₄×D₈	C₂²×C₆₇	semidirect
694. #436	C₂²×C₆₇	semidirect
695. #436	C₂²×C₆₇	semidirect
696. C₈×D₄	C₂²×C₆₇	semidirect
697. C₈×D₄	C₂²×C₆₇	semidirect
698. #431	C₂²×C₆₇	semidirect
700. #418	C₂²×C₆₇	semidirect
701. #417	C₂²×C₆₇	semidirect
703. #416	C₂²×C₆₇	semidirect
704. C₂×#103	C₂²×C₆₇	semidirect
707. #408	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×#3551	2
C₆₇×#3500	2
C₆₇×#3323	2
C₆₇×#3322	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3282	2
C₆₇×#3280	2
C₆₇×#3277	2
C₆₇×#3275	2
C₆₇×#3211	2
C₆₇×#3202	2
C₆₇×#3200	2
C₆₇×#3198	2
C₆₇×#3102	2
C₆₇×#3013	2
C₆₇×#3009	2
C₆₇×#3008	2
C₆₇×#2979	2
#61663	67

Subgroups — C67×#61663 #30740914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61663 #30740914